Book of Abstracts Wascom19 - Wascom 2019 – XX International … · WASCOM 2019 Monday, June 10th 08.30 - 09.00 REGISTRATION 09.00 - 09.30 Opening CHAIRMAN: TOMMASO RUGGERI 09.30

WASCOM 2019JUNE 10-14, 2019 - MAIORI (SA) ITALY

XX International Conference on Waves and Stability in Continuous MediaBook of Abstracts

CONFERENCE INFORMATION

Overview

Linear and nonlinear stability in fluid dynamics and solid mechanics

Non-linear wave propagation, discontinuity and shock waves

Rational extended thermodynamics and symmetric hyperbolic systems

Kinetic theories and comparison with continuum model

Numerical applications

The International Conference on Waves and Stability in Continuous Media (WASCOM), now in its XX edition, is a biennial international conference on Mathematical Physics.Since its first edition organized in 1981, this meeting turns out to be an opportunity for interaction of Italian and foreign researchers interested in stability and wave propagation problems in continuous media.The conference includes different research fields concerning wave propagation, stability problems and modelling problems such as shock waves, diffusion processes in biology and in continuum mechanics, kinetics models, non-equilibrium thermodynamics, stochastic processes, group methods, numerical techniques.

Main Topics of the Conference

The previous conferences were organized in Catania (1981), Cosenza (1983), Bari (1985), Taormina (1987), Sorrento (1989), Acireale (1991), Bologna (1993), Palermo (1995), Bari (1997), Vulcano (1999), Porto Ercole (2001), Villasimius (2003), Acireale (2005), Scicli (2007), Mondello (2009), Brindisi (2011), Levico (2013), Cetraro (2015), Bologna (2017).

BARI

BRINDISI

COSENZACETRARO (CS)

LEVICO (TN)

BOLOGNA

MONDELLO (PA)PALERMO

SCICLI (RG)

VILLASIMIUS (CA)

PORTO ERCOLE (GR)

VULCANO (ME)

ACIREALE (CT)

SORRENTO (NA)

TAORMINA (ME)

CATANIA

MAIORI (SA)

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Dipartimento di Matematica e Informatica

ChairmenFlorinda Capone

(Naples, Italy)

Scientific CommitteeConstantine M. Dafermos

(USA)

Organizing CommitteeSalvatore Rionero

(Naples, Italy)

ORGANIZERS

Salvatore Rionero (Naples, Italy)

Tommaso Ruggeri (Bologna, Italy)

Laurent Desvillettes (France)

Henri Gouin (France)

Giuseppe Mulone(Italy)

Seung-Yeal Ha (Korea)

Tai-Ping Liu (USA and Taiwan)

Masaru Sugiyama (Japan)

Marco Sammartino (Italy)

Giuseppe Saccomandi (Italy)

Luigi Frunzo (Naples, Italy)

Roberta De Luca (Naples, Italy)

Florinda Capone (Naples, Italy)

GNFM

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WASCOM 2019 JUNE 10-14, 2019

CONFERENCE PROGRAM

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WASCOM 2019

Monday, June 10th08.30 - 09.00 REGISTRATION

09.00 - 09.30 Opening

CHAIRMAN: TOMMASO RUGGERI09.30 - 09.55 Constantine M. Dafermos: Uniqueness of Zero Relaxation Limit10.00 - 10.25 Salvatore Rionero: Hopf Bifurcations in Thermal MHD and Spectrum Instability Driven by Perturbations

to Principal Entries10.30 - 10.55 Henri Gouin: Membranes and Vesicles11.00 - 11.25 COFFEE BREAK

CHAIRMAN: TAI-PING LIU11.25 - 11.50 Florinda Capone: Recent Results on the Onset of MHD Convection in Porous Media11.55 - 12.20 Stéphane Brull: Local Discrete Velocity Grids for Multi-Species Rarefied Flow Simulations12.25 - 12.50 Maurizio Gentile: Thermal Convection in a Rotating Horizontally Isotropic Porous Medium with LTNE12.55 - 13.10 Roberta De Luca: Onset of Double-Diffusive Convection in Porous Media with Soret Effect

13.30 Lunch (Reginna Palace Hotel, Via Cristoforo Colombo 1)

CHAIRMAN: MASARU SUGIYAMA15.30 - 15.55 Seung-Yeal Ha: On the Second-Order Extensions of First-Order Collective Models16.00 - 16.25 Giuseppe Mulone: New Nonlinear Stability Results for Plane Couette and Poiseuille Flows16.30 - 16.55 Andrea Giacobbe: Inclined Convection in a Porous Brinkman Layer: Linear Instability and Nonlinear

Stability17.00 - 17.25 COFFEE BREAK

CHAIRMAN: HENRI GOUIN17.25 - 17.50 Giancarlo Consolo: Propagation of Magnetic Domain Walls in Magnetostrictive Materials with Different

Crystal Symmetry17.55 - 18.10 Paolo Falsaperla: New Stability Results for Hydromagnetic Plane Couette Flows18.15 - 18.30 Monica De Angelis: On Solutions Related to FitzHugh-Rinzel Model

20.00 Dinner (Hotel Pietra di Luna, Via Gaetano Capone 27)

Sunday, June 9th18.00 - 20.00 REGISTRATION (Reginna Palace Hotel, Via Cristoforo Colombo 1)


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CHAIRMAN: SEUNG-YEAL HA09.00 - 09.25 Tai-Ping Liu: On Well-Posedness of Weak Solutions09.30 - 09.55 Marco Sammartino: Viscous MHD Vorticity-Current Equations with Data in L 1 (R 2 )10.00 - 10.25 Peter Vadasz: Instability, Weak Turbulence and Chaos in Porous Media10.30 - 10.55 COFFEE BREAK

CHAIRMAN: PETER VADASZ10.55 - 11.20 Maria Carmela Lombardo: Coherent Structures in a Chemotaxis Model of Acute Inflammation11.25 - 11.40 Valeria Giunta: Aggregation Phenomena and Well-Posedness for a Multiple Sclerosis Model11.45 - 12.10 Vincenzo Sciacca: Up-Wind Difference Approximation and Singularity Formation for a Slow Erosion Model12.15 - 12.40 Gaetano Fiore: On the Impact of Short Laser Pulses on Cold Diluted Plasmas

13.30 Lunch (Hotel Pietra di Luna, Via Gaetano Capone 27)

CHAIRMAN: MARCO SAMMARTINO15.30 - 15.55 Berardino D'Acunto: Mathematical Modelling of Multispecies Biofilms16.00 - 16.25 Sebastiano Pennisi: A 16 Moments Model in Relativistic Extended Thermodynamics of Rarefied

Polyatomic Gas16.30 - 16.55 Francesco Demontis: Reflectionless Solutions for Square Matrix Nonlinear Schroedinger Equation with

Vanishing Boundary Conditions17.00 - 17.25 COFFEE BREAK

CHAIRMAN: GIUSEPPE MULONE17.25 - 17.50 Massimo Trovato: The Extended Thermodynamics for A.C and D.C. Dynamic High-Field Transport in

Graphene17.55 - 18.10 Luigi Frunzo: Mathematical Modeling of Dispersal Phenomenon in Biofilms18.15 - 18.30 Andrea Trucchia: Uncertainty and Sensitivity Analysis for Bacterial Invasion in Multi-Species Biofilms


WASCOM 2019

Tuesday, June 11th

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WASCOM 2019

Wednesday, June 12th

CHAIRMAN: SALVATORE RIONERO09.00 - 09.25 Tommaso Ruggeri: From the Relativistic Mixture of Gases to the Relativistic Cucker-Smale Flocking09.30 - 09.45 Jeongho Kim: From the Relativistic Mixture of Gases to the Relativistic Cucker-Smale Flocking:

Mathematical Analysis09.50 - 10.15 Francesca Brini: On the Hyperbolicity Property of Extended Thermodynamics Models for Rarefied Gases10.20 - 10.45 Elvira Barbera: Stationary Flow and Heat Transfer in Extended Thermodynamics10.50 - 11.15 COFFEE BREAK

CHAIRMAN: GIUSEPPE TOSCANI11.15 - 11.40 Vittorio Romano: Mathematical Modeling of Charge Transport in Graphene11.45 - 12.10 Andrea Mentrelli: Comparison of Shock Structure Behaviours for Increasing Order of Closures12.15 - 12.40 Bruno Buonomo: Optimal Public Health Systems Intervention to Favor Vaccine Propensity for Childhood

Diseases12.45 - 13.00 Giovanni Nastasi: Numerical Solutions of the Semiclassical Boltzmann Equation for Bipolar Charge

Transport in Graphene13.05 - 13.20 Giorgio Martalò: Analysis of Evaporation-Condensation Problems for a Binary Gas Mixture

13.30 Lunch (Hotel Pietra di Luna, Via Gaetano Capone 27)

CHAIRMEN: SALVATORE RIONERO - TOMMASO RUGGERI15.30 - 15.45 Session in honour of Masaru Sugiyama15.45 - 16.10 Masaru Sugiyama: Rational Extended Thermodynamics of a Rarefied Polyatomic Gas with Relaxation

Processes of Molecular Rotation and Vibration16.15 - 16.40 Takashi Arima: Dispersion Relation of a Rarefied Polyatomic Gas with Molecular Relaxation Processes

Based on Rational Extended Thermodynamics with 15 Fields16.45 - 17.10 COFFEE BREAK 17.10 - 17.25 Session in honour of Giuseppe Toscani17.25 - 17.50 Giuseppe Toscani: Kinetic Modeling of Alcohol Consumption17.55 - 18.20 Laurent Desvillettes: About a Class of Cross Diffusion Systems Arising in Chemotaxis

20.00 SOCIAL DINNER (Reginna Palace Hotel, Via Cristoforo Colombo 1)

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WASCOM 2019

Thursday, June 13th

Friday, June 14th

CHAIRMAN: VITTORIO ROMANO09.00 - 09.25 Giuseppe Saccomandi: Helmholtz-Type Solitary Solutions in Non-Linear Elastodynamics09.30 - 09.55 Wendi Wang: Global Analysis of Mathematical Models for Nonlocal Epidemic Diseases10.00 - 10.25 Natale Manganaro: Generalized Simple Waves for Hyperbolic Systems10.30 - 10.55 COFFEE BREAK

CHAIRMAN: GIUSEPPE SACCOMANDI10.55 - 11.20 Maria Groppi: Consistent BGK Models for Gas Mixtures and Hydrodynamic Equations11.25 - 11.50 Marzia Bisi: Maxwell-Stefan Equations for a Reactive Mixture of Polyatomic Gases11.55 - 12.20 Francesco Mainardi: On the Evolution of Fractional Diffusive Waves12.25 - 12.50 Gaetana Gambino: Spatial Patterns and Bistability in a Cross-Diffusive FitzHugh-Nagumo System12.55 - 13.10 Gianfranco Rubino: Resonant Turing Patterns in the FitzHugh-Nagumo Model with Cross Diffusion13.15 - 13.30 Francesco Gargano: Transition to Turbulence in the Weakly Stratified Kolmogorov Flow



CHAIRMAN: LAURENT DESVILLETTES09.00 - 09.25 Shigeru Taniguchi: On the Similarity Solution of Strong Spherical Shock Waves Based on Extended

Thermodynamics09.30 - 09.55 Paolo Maremonti: Weak Solutions To The Navier-Stokes Equations With Non Decaying Data10.00 - 10.25 Raffaele Vitolo: Linearly Degenerate Systems of PDEs and Interacting Waves10.30 - 10.55 COFFEE BREAK

CHAIRMAN: FLORINDA CAPONE10.55 - 11.20 Michele Sciacca: Extension of the Auxiliary Equation Method by Means of Hyperelliptic Functions11.25 - 11.40 Qinghua Xiao: The Riemann Problem of Relativistic Euler Equations11.45 - 12.00 Maria Rosaria Mattei: Modeling Cell Motility in Biofilms12.05 - 12.20 Vincenzo Luongo: Biosorption of Heavy Metals in a Nitrifying Biofilm12.25 - 12.40 Vittorio De Falco: The General Relativistic Poynting-Robertson Effect: Non-Linear Dissipative System in

General Relativity12.45 - 13.00 Alberto Tenore: Modelling of Ecology in a Phototrophic-Heterotrophic Biofilm13.05 - 13.20 Daniele Bernardo Panaro: Anaerobic Digestion in Plug-Flow Reactors: a Mathematical Model13.25 - 13.30 CLOSING


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WASCOM 2019 JUNE 10-14, 2019

ABSTRACTS

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DISPERSION RELATION OF A RAREfiED POLYATOMIC GAS WITH MOLECULAR RELAXATION PROCESSES BASED ON RATIONAL EXTENDED THERMODYNAMICS WITH

15 FIELDS

Takashi Arima

National Institute of Technology, Tomakomai College (Japan)

[email protected]

Rational extended thermodynamics (ET) [1, 2] has been developed as a thermodynamic theory being applicable to nonequilibrium phenomena with steep gradients and rapid changes in space-time, which are out of local equilibrium. Recently, a refined version of ET of rarefied polyatomic gases with 15 fields which generalizes the Navier-Stokes and Fourier theory has been proposed [3]. The theory describes the relaxation processes of molecular rotational and vibrational relaxation processes individually. In this talk, I present the theoretical study of the dispersion relation of a rarefied polyatomic gas basing on the theory [4]. Its temperature dependence is discussed in the cases where the rotational and vibrational modes may or may not be excited. The experimental data obtained in the low-frequency region show the validity of the theory [5]. It is also shown that the curve of the attenuation per wavelength with respect to the frequency has up to three peaks depending on the temperature and on the relaxation times. This is the joint work with M. Sugiyama and T. Ruggeri.

Fig.1: Dependence of the attenuation per wave length on the dimensionless frequency for various

temperatures. The left and right figures show the case that the rotational relaxation time is large and small respectively. , are the dimensionless rotational and vibrational specific heats.

References [1] I. Müller, T. Ruggeri: Rational Extended Thermodynamics, Springer Tracts in Natural Philosophy 37 (II

edition), Springer-Verlag, New York (1998). [2] T. Ruggeri, M. Sugiyama: Rational Extended Thermodynamics beyond the Monatomic Gas, Springer,

Cham, Heidelberg, New York, Dordrecht, London (2015). [3] T. Arima, T. Ruggeri and M. Sugiyama: Entropy 20, 301 (2018). [4] T. Arima and M. Sugiyama: AIP Conf. Proc. To be published. [5] T. Arima, T. Ruggeri and M. Sugiyama: Phys. Rev. E, 96, 042143 (2017).

9

STATIONARY FLOW AND HEAT TRANSFER IN EXTENDED THERMODYNAMICS

Elvira Barbera, Francesca Brini

Department of Mathematical, Computer, Physical and Earth Sciences,

University of Messina (Italy)

[email protected]

In the last 10 years, a particular attention was devoted to the stationary heat transfer in bounded domains within the context of extended thermodynamics. It was shown that 13-moments extended thermodynamics is already able to predict differences from the classical Navier-Stokes thermodynamics and it implies solutions which are in agreement with the kinetic theory. The differences are more visible when different geometries are considered and/or a velocity field is present. The aim of the talk is the presentation of the different results obtained in the context together with some general considerations and future prospectives.

10

MAXWELL-STEFAN EQUATIONS FOR A REACTIVE MIXTURE OF POLYATOMIC GASES

Benjamin Anwasia, Marzia Bisi, Francesco Salvarani, Ana Jacinta Soares

Department of Mathematics and Computer Science,

University of Parma (Italy)

[email protected]

We present the derivation of a hydrodynamic description of Maxwell-Stefan type for a reactive mixture of polyatomic gases with a continuous structure of internal energy. The macroscopic equations are derived in the diffusive limit of a kinetic system of Boltzmann equations for the considered mixture, in the general non-isothermal setting. More precisely, the Maxwell-Stefan system is deduced as a proper asymptotic limit of the kinetic system proposed in [1], based on the Borgnakke- Larsen procedure, that describes a mixture of reactive polyatomic gases by adding to the usual independent variables of the phase-space of the system (time , position and velocity ) a continuous positive internal energy variable which governs, together with the kinetic energy, the binary encounters both of reactive and of non-reactive type. For simplicity we consider a mixture of four constituents, subject to a bimolecular and reversible chemical reaction. The asymptotic analysis of the kinetic system is performed under a reactive-diffusive scaling in which mechanical collisions are dominant with respect to chemical reactions. The resulting system couples the Maxwell-Stefan equations for the species diffusive fluxes with the evolution equations for the species number densities and for the temperature of the mixture. With respect to the standard isothermal non-reactive Maxwell-Stefan system [2], here the continuity equations for the various species are balance equations including effects of the chemical reactions on the number densities, and we have also a proper energy balance equation due to transfer of kinetic energy into internal energy and vice versa. The production terms due to the chemical reaction and the Maxwell-Stefan diffusion coefficients are explicitly obtained in terms of the collisional kernels and of the parameters of the kinetic model, including the internal energy of polyatomic particles [3]. References [1] L. Desvillettes, R. Monaco, F. Salvarani, A kinetic model allowing to obtain the energy law of polytropic

gases in the presence of chemical reactions, Europ. J. Mech. B/Fluids, 24 (2005), 219-236. [2] H. Hutridurga, F. Salvarani, On the Maxwell-Stefan diffusion limit for a mixture of monatomic gases,

Math. Meth. Appl. Sci., 40 (2017), 803-813. [3] B. Anwasia, M. Bisi, F. Salvarani, A.J. Soares, On the Maxwell-Stefan diffusion limit for a reactive

mixture of polyatomic gases in non-isothermal setting, submitted.

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ON THE HYPERBOLICITY PROPERTY OF EXTENDED THERMODYNAMICS MODELS FOR RAREFIED GASES

Francesca Brini, Tommaso Ruggeri

Department of Mathematics and Alma Mater Research Center on Applied Mathematics AM2,

University of Bologna (Italy)

[email protected]

Rational Extended Thermodynamics (RET) is a well-known phenomenological field theory able to describe non-equilibrium phenomena and rapid changes in space-time out of local equilibrium. The theory is constructed starting from the validity requirement of universal principles, such as the objectivity principle and the entropy principle. This gives the theory a particularly elegant and robust structure both from the mathematical and the physical points of view. In fact, the RET models are expected to be hyperbolic PDE systems with a convex extension, so that the well-posedness of the Cauchy problem is guaranteed. The hyperbolicity property is also very important for a realistic physical description, since it is associated to finite speeds of disturbances, in contrast to the infinite speed predicted by the parabolic models of Classical Thermodynamics. Usually, the RET systems are linearized in the neighborhood of an equilibrium state, thereby providing systems of Grad's type and confining the validity of the convexity requirement only to a neighborhood of the equilibrium. Consequently, also the hyperbolicity condition remains valid only in some domain of the state variables (called hyperbolicity region). The analysis about the determination of such region started more than 25 years ago by Mueller and Ruggeri. In this talk we present some very promising results in the case of rarefied monatomic or polyatomic gases and compare them with what is already known in the literature.

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LOCAL DISCRETE VELOCITY GRIDS FOR MULTI-SPECIES RAREFIED FLOW SIMULATIONS

Stéphane Brull

CNRS, Bordeaux INP, IMB,

University of Bordeaux (France)

[email protected]

The aim of this method is to develop a deterministic numerical method for kinetic equations that is adaptative w.r.t the velocity variable. In the classical methods, the velocity grids are chosen identical for each space point and constant in time. Moreover, the construction of such a global grid is based only on the initial conditions. However, in the context of rarefied gas flows, such as the airflow around the walls of a shuttle, important gradients of velocity and temperature can appear. The idea of this work is to define dynamic sets of discrete velocities independently for every species and every space discretization point. These sets are then defined according to the local value of the partial moments of each distribution function, by assuming them to be Maxwellian distributions. To adapt dynamically to the gradients of macroscopic quantities, partial moments are computed by the use of conservation laws obtained by taking the moments of the discrete kinetic equations. This formulation allows an implicit treatment of the relaxation operator leading to an Asymptotic-Preserving scheme for the Euler regime. The method is then implemented and tested on the BGK model for gas mixtures that has been proposed by Andries, Aoki and Perthame.

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OPTIMAL PUBLIC HEALTH SYSTEMS INTERVENTION TO FAVOR VACCINE PROPENSITY FOR CHILDHOOD DISEASES

Bruno Buonomo

Department of Mathematics and Applications “Renato Caccioppoli”,

University of Naples “Federico II” (Italy)

[email protected]

In this talk we present a recent analysis of optimal time-profiles of public health systems (PHS) Intervention to favor vaccine propensity [1]. We apply optimal control (OC) to a SIR model with voluntary vaccination and PHS intervention. We focus on short-term horizons, and on both continuous control strategies resulting from the forwardbackward sweep deterministic algorithm, and piecewise-constant strategies (which are closer to the PHS way of working) investigated by the simulated annealing (SA) stochastic algorithm. For childhood diseases, where disease costs are much larger than vaccination costs, the OC solution sets at its maximum for most of the policy horizon, meaning that the PHS cannot further improve perceptions about the net benefit of immunization. Thus, the subsequent dynamics of vaccine uptake stems entirely from the declining perceived risk of infection (due to declining prevalence) which is communicated by direct contacts among parents, and unavoidably yields a future decline in vaccine uptake. We find that for relatively low communication costs, the piecewise control is close to the continuous control. For large communication costs the SA algorithm converges towards a non- monotone OC that can have oscillations. References [1] B. Buonomo, A. d’Onofrio, P. Manfredi: Optimal time–profiles of Public Health Intervention to shape

voluntary vaccination for childhood diseases. J. Math. Biol., 78, n. 4, 1089–1113 (2019).

14

RECENT RESULTS ON THE ONSET OF MHD CONVECTION IN POROUS MEDIA

Florinda Capone, Roberta De Luca, Salvatore Rionero



[email protected]

Magneto-hydrodynamic (MHD) convection in horizontal porous layers, filled by electrically conducting fluids, uniformly heated from below and embedded in an external transverse constant magnetic field, is analysed [1, 2, 3]. Long-time behaviour of solutions is characterized via the existence of -absorbing sets. A new methodology [7, 8] to obtain necessary and sufficient conditions guaranteeing the onset of steady/unsteady convection, is applied. By mean of the Energy Linearization Principle [5, 6, 7], the absence of subcritical instabilities without any restrictions on the initial data, is proved. Applications to unsalted and salted porous fluid layers with the Vadasz inertia term [4, 9, 10], are provided. References [1] F. Capone, S. Rionero, Porous MHD convection: stabilizing effect of magnetic field and bifurcation

analysis. Ric. Mat. 65, (2016), pp. 163186 [2] F. Capone, R. De Luca, Porous MHD convection: effect of Vadasz inertia term. Transp. Porous Media,

(3), (2017), pp. 519-536 [3] F. Capone, R. De Luca, Double diffusive convection in porous media under the action of a magnetic

field. Ric. Mat. DOI: https://doi.org/10.1007/s11587-018-0417-5 [4] D. A. Nield, A. Bejan, Convection in Porous Media, 5th ed., Springer, Berlin, (2017) [5] S. Rionero, Heat and mass transfer by convection in multicomponent Navier-Stokes mixture: absence

of subcritical instabilities and global nonlinear stability via the Auxiliary System Method. Rend. Lincei Mat. Appl. 25, 368 (2014)

[6] S. Rionero, Dynamic of thermo-MHD flows via a new approach. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei, 28, 21-47, (2017)

[7] S. Rionero, Hopf bifurcations and global nonlinear L2 energy stability in thermal MHD. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (To appear)

[8] S. Rionero, Hopf bifurcations in dynamical systems. Ric. Mat. (To appear) [9] P. Vadasz, Coriolis effect on gravity-driven convection in a rotating porous layer heated from below. J.

Fluid Mech. 376, 351375 (1998) [10] P. Vadasz, Fluid flow and heat transfer in rotating porous media. SpringerBriefs in Applied Sciences

and Technology, Springer, Minneapolis (USA), (2016)

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PROPAGATION OF MAGNETIC DOMAIN WALLS IN MAGNETOSTRICTIVE MATERIALS WITH DIFFERENT CRYSTAL SYMMETRY

Giancarlo Consolo, Salvatore Federico, Giovanna Valenti

Department of Mathematical, Computer, Physical and Earth Sciences,


[email protected]

The possibility to control the magnetization state of nanostructures via electric fields has enabled new research frontiers that involve multiferroic materials. The coupling between magnetic and mechanical energies provides these devices with great potential in a wide variety of applications, even though the weak ferromagnetism at room temperature of natural multiferroics limits their applications. To overcome such a problem, a valid alternative consists in depositing a thin magnetostrictive layer onto a thick piezoelectric actuator. In such bilayer structures, the planar strains undergone by the piezoelectric material under the application of an electric voltage are transferred to the magnetostrictive layer. The resulting piezo-induced strains may be used to control the propagation of magnetic domain-walls into the magnetostrictive material. Here, this phenomenon is theoretically investigated in the framework of the extended Landau- Lifshitz-Gilbert equation [1]. In particular, the present study focuses on elucidating how the crystal symmetry of the magnetostrictive material may affect the key features exhibited by the propagating walls in both steady and precessional dynamical regime. To this aim, the most common symmetries of isotropic, cubic and hexagonal systems are taken into account. A brief review of the literature is first presented in order to address a comparison with some classical published results [2]. Special focuses are given to the determination of those physical quantities involved in the characterization of domain-wall dynamics, such as the second-order stress-free magnetostrictive strain tensor and the magnetoelastic anisotropy field, starting from the knowledge of more primitive objects, i.e. the fourth-order magnetostriction tensor [3] and the magnetoelastic energy density, respectively. Then, results of the analytical solution of the extended Landau-Lifshitz-Gilbert equation calculations are presented. These reveal that the crystal symmetry affects the travelling-wave profile, the domain wall mobility, the propagation threshold and the breakdown of the steady solution. Moreover, our analysis suggests a possible strategy to determine the fourth-order magnetostrictive coefficients. Finally, the results obtained here are in good qualitative agreement with recent experimental observations and might be also used to improve the performance of these devices. References [1] G. Consolo and G. Valenti, Journal of Applied Physics 121, 043903 (2017). [2] W.P. Mason, Physical Review 96, 302 (1954). [3] S. Federico, G. Consolo and G. Valenti, Mathematics and Mechanics of Solids (2018), DOI:

10.1177/1081286518810741.

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MATHEMATICAL MODELLING OF MULTISPECIES BIOFILMS

Berardino D’Acunto



[email protected]

A continuum approach to mathematical modelling of multispecies biofilm formation and growth is presented. The general situation of a biofilm constituted by bacterial species and substrates, nutrients, is considered. The biological process is governed by nonlinear hyperbolic partial differential equations, semilinear parabolic partial differential equations for substrate diffusion and an ordinary differential equation for the biofilm thickness. All equations are mutually connected and lead to free boundary value problems that are essentially hyperbolic. Theorems that prove uniqueness, existence, positiveness of solutions are discussed. Some new processes are also considered, such as the invasion of new bacterial species and colonization into an already constituted biofilm. As engineering and industrial application, a model of biofilm-reactor for the wastewater treatment plants is presented.

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UNIQUENESS OF ZERO RELAXATION LIMIT

Constantine M. Dafermos

Division of Applied Mathematics,

Brown University (USA)

[email protected]

In the setting of a simple hyperbolic system, I will discuss the process by which the vanishing of the relaxation time yields as zero relaxation limit the unique admissible solution of the associated "equilibrium" hyperbolic conservation law.

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ON SOLUTIONS RELATED TO FITZHUGH-RINZEL MODEL

Monica De Angelis, Fabio De Angelis



[email protected]

The FitzHugh-Rinzel (FHR) system is derived from the FitzHugh-Nagumo model [1–3] to incorporate bursting phenomenon of nerve cells. Bursting oscillation is an important phenomenon and it is becoming increasingly important as it is being detected in many different scientific fields. Indeed, phenomena of bursting have been observed as electrical behaviours in many nerve and endocrine cells such as hippocampal and thalamic neurons, mammalian midbrain, and pancreatic in −cells. (see, f.i. [4] and references therein). In the cardiovascular system, bursting oscillations are generated by the electrical activity of cardiac cells that excite the heart membrane to produce the contraction of ventricles and auricles [5]. In addition, bursting phenomena can be observed in several fields of electromechanical engineering such as devices [6] and computational simulations of nonlinear structural problems [7]. In this study the following (FHR) system:

is reduced to a nonlinear integro differential equation and the fundamental solution is explicitly determined. The initial value problem in the whole space is analyzed and, when the source term is linear, by means of the explicit solution is obtained. Otherwise, when the source term is a non linear function, an integral equation is deduced. Moreover, particular solutions of the FitzHugh-Rinzel system have been explicitly determined. References [1] Izhikevich E.M.: Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting. The

MIT press. England (2007). [2] Rinzel J. A Formal Classification of Bursting Mechanisms in Excitable Systems, in Math. Topics in

Population Biology, Lecture Notes in Biomathematics, Springer, NY, 71, 1987. [3] De Angelis, M. Renno, P Existence, uniqueness and a priori estimates for a non linear integro-differential

equation Ricerche di Mat. 57 (2008). [4] R. Bertram, M. J. Butte, T. Kiemel and A. Sherman. Topological and phenomelogical classification of

bursting oscillations, Bulletin of Mathematical Biology, Vol. 57, No. 3, pp. 413 .39, 1995. [5] A. Quarteroni, A. Manzoni and C. Vergara The cardiovascular system: Mathematical modelling,

numerical algorithms and clinical applications Acta Numerica (2017), pp. 365-590. [6] H. Simo, P. Woafo, Bursting oscillations in electromechanical systems, Mechanics Research

Communications 38 (2011) 537 541. [7] F. De Angelis, D. Cancellara, L. Grassia, A. D’Amore, The influence of loading rates on hardening effects

in elasto/viscoplastic strain-hardening materials Mechanics of Time-Dependent Materials, 22 (4) (2018) 533-551.

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THE GENERAL RELATIVISTIC POYNTING-ROBERTSON EFFECT: NON-LINEAR DISSIPATIVE SYSTEM IN GENERAL RELATIVITY

Vittorio De Falco

Research Centre for Computational Physics and Data Processing, Faculty of Philosophy & Science,

Silesian University in Opava (Czech Republic)

[email protected]

In several radiation processes occurring in high-energy astrophysics between an emitting massive source (represented by structures around a black hole or a neutron star) and a relatively small-sized body, the electromagnetic radiation field beside exerting an external radial force, plays also a fundamental role in removing angular momentum and energy from the affected body through a radiation drag force in a relatively short time. This is known in the literature as Poynting-Robertson (PR) effect, which is a pure general relativistic effect, configuring as a viscous force, that induces the matter to spiral in or out towards the compact object depending on the radiation field strength. Having such a model is extremely important to describe the matter behavior in strong gravitational fields. Such configurations represent unique and natural laboratories, which allow us both to test Einstein’s theory in strong field regimes and to infer several critical information on black holes’ structure and neutron stars’ equations of state. In my talk, I introduce the fundamental concepts underpinning the general relativistic model of the PR effect in 2 [2, 3] and 3 [5] dimensions. The governing equations of motion can be obtained as a set of coupled non-linear first order ODEs through the relativity of observer splitting formalism [1], powerful mathematical technique in General Relativity (GR) for considerably reducing the complexity of the equations under study. Due to its non-linear structure, numerical treatments are needed to have insight into the geometrical structure and to understand the main features of this phenomenon. Selected test particle orbits are displayed, and their properties are described. This dynamical system admits the existence of a critical hypersurface, region where gravitational attraction, radiation pressure, and PR drag force are in equilibrium. I show how to prove its asymptotical stability through classical techniques in linear stability theory or alternatively by employing a Lyapunov function (having a more deep physical meaning). To better understand the radiation processes in GR, an analytical treatment of such effect is performed within the Lagrangian formalism. I explain how to prove that such a dissipative system in GR admits a Lagrangian formulation [4], which is a very challenging task in GR, never accomplished before in the literature. Then, I analytically determine the radiation potential by using a new and innovative method termed energy formalism [6], which I stress its broad applicability in different physical and mathematical contexts. References [1] Bini, D. et al. (1997). IJMP D, 6:1 – 38. [2] Bini, D. et al. (2009). CQtt, 26:055009. [3] Bini, D. et al. (2011). CQtt, 28:035008. [4] De Falco, V. et al. (2018). PRD, 97:084048. [5] De Falco, V. et al. (2019a). Physical Review D, 99:023014. [6] De Falco, V. et al. (2019b). Physical Review D.

20

ONSET OF DOUBLE-DIFFUSIVE CONVECTION IN POROUS MEDIA WITH SORET EFFECT

Florinda Capone, Roberta De Luca, Maria Vitiello



[email protected]

The onset of double-diffusive convection in horizontal porous layers for the thermo-diffusive Soret phenomenon is widely studied in literature due to the numerous applications in the real world phenomena [2, 3, 5]. In [1] the more general case of a Darcy model including inertia term [6] is considered. Necessary and sufficient conditions guaranteeing the onset of steady or unsteady convection in a closed algebraic form are obtained. Via the Energy Linearization Principle [4], the coincidence between linear and nonlinear (global) stability thresholds of the thermo-solute conduction solution, is proved. References [1] F. Capone, R. De Luca, M. Vitiello, Double-diffusive Soret convection phenomenon in porous media:

effect of Vadasz inertia term. Ric. Mat. DOI: https://doi.org/10.1007/s11587-018-0428-2. [2] N. Deepika, Linear and nonlinear stability of double-diffusive convection with the Soret effect. Trans.

Porous Med 121, 93-108. (2018). [3] D.A. Nield, A. Bejan. Convection in Porous Media, 5th Ed. Springer, Berlin (2017). [4] S. Rionero, Dynamic of thermo-MHD flows via a new approach. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat.

Natur. Rend. Lincei 28, 21-47 (2017). [5] S. Rionero, Soret effects on the onset of convection in rotating porous layers via the “auxiliary system

method”. Ric. Mat. 62(2), 183 (2013). [6] P. Vadasz, Coriolis effect on gravity-driven convection in a rotating porous layer heated from below. Int.

Fluid Mech. 376. 351-375 (1998).

21

REFLECTIONLESS SOLUTIONS FOR SQUARE MATRIX NONLINEAR SCHROEDINGER EQUATION WITH VANISHING BOUNDARY CONDITIONS

Francesco Demontis

Department of Mathematics and Informatics,

University of Cagliari (Italy)

[email protected]

After a quick review of the direct and inverse scattering theory of the focusing Zakharov-Shabat system with symmetric nonvanishing boundary conditions, we derive the reflectionless solutions of the matrix NLS equation with vanishing boundary conditions and four different symmetries by using the Marchenko theory. Since the Marchenko integral kernel has separated variables, the matrix triplet method - consisting of representing the Marchenko integral kernel in a suitable form - allows us to find the exact expressions of the reflectionless solutions in terms of a triplet of matrices. Moreover, since these exact expressions contain matrix exponentials and matrix inverses, computer algebra can be used to “unpack” and graph them. Finally, it is remarkable that these solutions are also veried by direct substitution in the NLS equation. This is a joint work with C. van der Mee (University of Cagliari) and Alyssa Ortiz (University of Colorado at Colorado Springs).

22

ABOUT A CLASS OF CROSS DIFFUSION SYSTEMS ARISING IN CHEMOTAXIS

Laurent Desvillettes

IMJ-PRG,

Universite Paris Diderot (France)

[email protected]

We study a class of cross diffusion systems of the form

where is a decreasing function of . Those systems naturally arise in chemotaxis under specific assumptions on the way cells move in presence of the chemoattractant. We show existence of weak or strong solutions (depending on the dimension), and study the large time behavior of the system. This is a joint work with Y.J. Kim, A. Trescases and C. Yoon.

23

NEW STABILITY RESULTS FOR HYDROMAGNETIC PLANE COUETTE FLOWS

Paolo Falsaperla, Andrea Giacobbe, Giuseppe Mulone

Department of Mathematics and Computer Sciences,

University of Catania (Italy)

[email protected]

The instability of steady laminar flow of an electrically conducting fluid between two infinite parallel plates under a transverse magnetic field has been analyzed by Kakutani [1], Takashima [2] for plane Couette flow. Alexakis et al. [3] studied shear flows with an applied cross-stream magnetic field using dissipative incompressible magnetohydrodynamics. This study incorporates exact solutions, the energy stability method, and exact bounds on the total energy dissipation rate. Recently, Falsaperla et al. [4] proved that the plane Couette and Poiseuille flows are nonlinearly stable with respect to streamwise perturbations for any Reynolds number. They also proved nonlinear stability results for plane Couette and Poiseuille flows with respect to tilted perturbation (2D perturbations with a wave vector not directed along the direction of the basic motion). The aim of this work is to generalize the results of [4] to the hydromagnetic plane Couette flow. We also compare our results with Alexakis et al. [3], Takashima [2] and experiments. References [1] T. Kakutani, J. Phys. Soc. Japan 19, 1041 (1964). [2] M. Takashima, Fluid Dyn. Res. 22, 105 (1998). [3] A. Alexakis, F. Pétrélis, P. J. Morrison, and Charles R. Doering, Phys. of Plasmas 10 (11), 4324 (2003). [4] P. Falsaperla, A. Giacobbe and G. Mulone, Nonlinear stability results for plane Couette and Poiseuille

flows, submitted. (2019).

24

ON THE IMPACT OF SHORT LASER PULSES ON COLD DILUTED PLASMAS

Gaetano Fiore



[email protected]

Applying a recently developed plane hydrodynamical model to the impact of a very short and intense laser pulse onto a cold diluted plasma, we explore its consequences for the motion of the plasma electrons shortly after the beginning of the laser-plasma interaction: where and how long the hydrodynamical description holds, the formation of a plasma wave, the localization of wave-breaking as a function of the initial plasma density and of the laser pulse, and its use for self-injection of electrons in the laser wake-field acceleration mechanism. In our plane model the system of the (Lorentz-Maxwell and continuity) PDEs is reduced into a 1 parameter family of decoupled systems of Hamilton equations in dim 1, and we use Floquet theory to analyze the dynamics of an associated periodic ODE system.

25

MATHEMATICAL MODELING OF DISPERSAL PHENOMENON IN BIOFILMS

Berardino D’Acunto, Luigi Frunzo, Vincenzo Luongo, Maria Rosaria Mattei



[email protected]

The presentation will concern a mathematical model for dispersal phenomenon in multispecies biofilm based on a continuum approach and mass conservation principles. The formation of dispersed cells is modeled by considering a mass balance for the bulk liquid and the biofilm. Diffusion of these cells within the biofilm and in the bulk liquid is described using a diffusion-reaction equation. Notably, biofilm growth is modeled by a hyperbolic partial differential equation while the diffusion process of dispersed cells by a parabolic partial differential equation. The two are mutually connected but governed by different equations that are coupled by two growth rate terms. The complete model takes the following form:

The Mathematical Modelling of three real special cases will be presented. The first is related to experimental observations on starvation induced dispersal [1]. The second considers diffusion of a non-lethal antibiofilm agent which induces dispersal of free cells. The third example considers dispersal induced by a self-produced biocide agent. References [1] D. Schleheck, N. Barraud, J. Klebensberger, J.S. Webb, D. McDougald, S.A. Rice, S. Kjelleberg. (2009)

Pseudomonas aeruginosa PAO1 preferentially grows as aggregates in liquid batch cultures and disperses upon starvation PloS one, 4, 5.

26

SPATIAL PATTERNS AND BISTABILITY IN A CROSS-DIFFUSIVE FITZHUGH-NAGUMO SYSTEM

Gaetana Gambino, Maria Carmela Lombardo, Gianfranco Rubino, Marco Sammartino


University of Palermo (Italy)

[email protected]

The FitzHugh-Nagumo model, initially derived as a mathematical simplification of the Hodgkin-Huxley model to describe the flow of an electric current through the surface membrane of a nerve fiber [1, 2], supports a rich dynamics: tuning the system parameters it exhibits monostability, excitability or bistability [3]. In this talk the effect on Turing pattern formation of the coupling between the FitzHugh-Nagumo kinetics with linear cross diffusion will be addressed. The cross diffusion is proved to be crucial for pattern formation when the FitzHugh-Nagumo system is excitable and it is also responsible of a previously unnoticed Turing mechanism: out-of-phase patterns arise when the inhibitor rapidly diffuse away from the activator but its random diffusion is almost slow. The pattern selection problem in the monostable case is solved performing a close to equilibrium asymptotic weakly nonlinear analysis, which show the existence of square and super-squares when the bifurcation takes place through a multiplicity-two eigenvalue without resonance [4]. In the bistable case large amplitude patterns emerge due to the interaction of the Turing instabilities on the two homogeneous steady states branches of an imperfect pitchfork bifurcation. In order to capture these subcritical structures, the weakly nonlinear analysis is revised in the neighborhood of the cusp point, next to the nascent bistability, where the zero mode of the homogeneous perturbation becomes active and interacts with the spatial critical modes [5]. The resulting bifurcation diagrams reveal large domains of coexisting stable different structures and localized patterns are numerically obtained in these regions. References [1] Hodgkin A.L., Huxley A.F.: A quantitative description of membrane current and its application to

conduction and excitation in nerve. J. Physiol. 117 n.4, 500–544 (1952). [2] FitzHugh R.: Thresholds and plateaus in the Hodgkin-Huxley nerve equations. J. Gen. Physiol. 43,

867-896 (1960). [3] Hagberg A., Meron E.: Pattern formation in non-gradient reaction-diffusion systems: the effects of front

bifurcations. Nonlinearity 7 n.3, 805–835 (1994). [4] Gambino G., Lombardo M. C., Rubino G., Sammartino M.: Pattern selection in the 2D FitzHugh–

Nagumo model. Ricerche di Matematica, First Online (2018). [5] Borckmans P., Dewel G.,De Wit A., Dulos E., Boissonade J., Gauffre F., De Kepper, P.: Diffusive

Instabilities and Chemical Reactions. Internat. J. Bifur. Chaos 12 n.11, pp. 2307–2332 (2002).

27

TRANSITION TO TURBULENCE IN THE WEAKLY STRATIFIED KOLMOGOROV FLOW

Francesco Gargano, Giacomo Ponetti, Marco Sammartino, Vincenzo Sciacca



[email protected]

The Kolmogorov flow is a two-dimensional incompressible viscous flow driven by a streamwise monochromatic force. It was introduced by Kolmogorov as a toy-model capable of easing the mathematical difficulties of the full Navier-Stokes equations but still possessing the turbulent regimes typical of the Navier-Stokes solutions. In this talk we shall investigate the various bifurcations leading from laminar solutions toward weakly chaotic states, extending the results presented in [1] where the density of the flow is not stratified. New chaotic states are detected by computing the Lyapunov exponents and analyzed in terms of enstrophy and palinstrophy growth phases [2]. On the other hand, in the density stratified Kolmogorov flow, the bifurcations leading to chaotic states have not been studied. Adopting the Boussinesq approximation according to which the base density profile has a linear relationship with the temperature decreasing from the bottom to the top of the fluid, we shall investigate how this stabilizing effect influences the bifurcations that occur at low Reynolds numbers in the range of small Richardson numbers. Besides the obvious observation that higher Reynolds numbers are required to trigger the instabilities, we shall see that, by increasing the temperature gradient, i.e. the Richardson number, new structures form in the flow, inducing a richer variety of states leading eventually to the chaotic attractors [2]. References [1] D. Armbruster, B. Nicolaenko, N. Smaoui, and P. Chossat, Symmetries and dynamics for 2-D Navier-

Stokes flow, Physica D 95, 81–93 (1996). [2] F. Gargano, G. Ponetti, M. Sammartino, and V. Sciacca, Route to chaos in the weakly stratified

Kolmogorov flow, Phys. Fluids 31, 024106 (2019).

28

THERMAL CONVECTION IN A ROTATING HORIZONTALLY ISOTROPIC POROUS MEDIUM WITH LTNE

Florinda Capone, Maurizio Gentile



[email protected]

Thermal convection of a fluid filling an anisotropic porous medium, uniformly rotating about a vertical axis, with local thermal non equilibrium, is studied. The linear and nonlinear stability analysis are performed. In particular, the coincidence between linear instability and nonlinear (global) stability thresholds is proved.

29

INCLINED CONVECTION IN A POROUS BRINKMAN LAYER: LINEAR INSTABILITY AND NONLINEAR STABILITY

Paolo Falsaperla, Andrea Giacobbe, Giuseppe Mulone



[email protected]

We investigate the stability of the basic stationary solution of a model for thermal convection in an inclined porous layer when the fluid motion obeys to the Darcy-Brinkman law. Inertial effects are also taken into consideration, and different physical boundary conditions are imposed. The model is an extension of the work by Rees and Bassom, where the Darcy’s law is adopted. In this model the basic motion is a combination of hyperbolic and polynomial functions. We will present a numerical investigation of the linear instability of such basic motion for three-dimensional perturbations; we will give estimates of nonlinear stability thresholds solving a maximum problem for an energy Lyapunov functional. For longitudinal perturbations we will prove the coincidence of linear and nonlinear critical Rayleigh numbers. These types of fluid flows have applications to geophysics, engineering and many other areas (Straughan, Nield and Bejan and references therein). References [1] Rees DAS, Bassom AP. 2000 The onset of Darcy-Benard convection in an inclined layer heated from

below. Acta Mech. 144 (1-2), 103?118. [2] Nield DA, Bejan A. 2017 Convection in Porous Media. Springer, New York, 5th Edition. [3] Straughan B. 2004 The Energy Method, Stability, and Nonlinear Convection, Springer-Verlag: Ser. In

Appl. Math. Sci., 91, New-York, 2nd Ed. [4] Straughan B. 2008 Stability, and wave motion in porous media, volume 165 of Appl. Math. Sci.

Springer, New York. [5] Falsaperla P., Mulone G., 2018 Thermal convection in an inclined porous layer with Brinkman law.

Ric. Mat. p. 1-17, ISSN: 0035-5038, doi: 10.1007/s11587-018- 0371-2. [6] Falsaperla P., Giacobbe A., Mulone G, 2019 Inclined convection in a porous Brinkman layer: linear

instability and nonlinear stability, submitted.

30

AGGREGATION PHENOMENA AND WELL-POSEDNESS FOR A MULTIPLE SCLEROSIS MODEL

Valeria Giunta



[email protected]

Multiple Sclerosis (MS) is an inflammatory disorder that affects the central nervous system causing severe and progressive physical and neurological impairment. MS is characterized by myelin damage and loss, resulting in the formation of dense, scar-like tissue called plaques. In [4] and [1] a mathematical model was developed which is able to reproduce many of the typical pathological hallmarks of the disease. The aim of the present talk is twofold. First we shall study the aggregation phenomena described by the reaction-diffusion-chemotaxis model introduced in [1]. In particular, we shall investigate the conditions which yield the appearance of stationary non constant radially symmetric solutions and, using numerical values of the parameters taken from the experimental literature, we shall show that the model supports the formation of stationary patterns that closely reproduce the concentric lesions observed in clinical practice, see [2]. Second we shall investigate the qualitative properties (like existence and uniqueness in the appropriate function space) of the solutions of the model. We shall in fact show how the inclusion of the volume filling sensitivity term is able to prevent finite-time blow-up of the solutions, see [5]. Joint work with L. Desvillettes (Université Paris Diderot, France), M.C. Lombardo (University of Palermo, Italy) and M. Sammartino (University of Palermo, Italy). References [1] M.C. Lombardo, R. Barresi, E. Bilotta, F. Gargano, P. Pantano, and M. Sammartino. Demyelination

patterns in a mathematical model of multiple sclerosis. Journal of Mathematical Biology, 75(2):373-417, 2017.

[2] E. Bilotta, F. Gargano, V. Giunta, M. C. Lombardo., P. Pantano, and M. Sammartino. Eckhaus and zigzag instability in a chemotaxis model of multiple sclerosis. Atti della Accademia Peloritana dei Pericolanti-Classe di Scienze Fisiche, Matematiche e Naturali 96.S3 (2018): 9.

[3] T. Hillen and K.J. Painter. A user’s guide to PDE models for chemotaxis. Journal of Mathematical Biology, 58(1-2):183?217, 2009.

[4] R.H. Khonsari and V. Calvez. The origins of concentric demyelination: Self- organization in the human brain. PLoS ONE, 2(1), 2007.

[5] L. Desvillettes, V. Giunta. Well-posedness for a Multiple Sclerosis model, in preparation, 2019.

31

MEMBRANES AND VESICLES

Henri Gouin, Sergey Gavrilyuk

CNRS,

Aix-Marseille University (France)

[email protected]

Membranes are an important subject of study in physical chemistry and biology. They can be considered as material surfaces with a surface energy depending on the curvature tensor. Usually, mathematical models developed in the literature consider the dependence of surface energy only on mean curvature with an added linear term for Gauss curvature [1, 2]. Therefore, for closed surfaces the Gauss curvature term can be eliminated because of the Gauss-Bonnet theorem. In [3], the dependence on the mean and Gaussian curvatures was considered in statics and under a restrictive assumption of the membrane inextensibility. Thanks to the principle of virtual working, the equations of motion and boundary conditions governing the fluid membranes subject to general dynamical bending are derived without the membrane inextensibility assumption. We obtain the dynamic “shape equation” (equation for the membrane surface) and the dynamic conditions on the contact line generalizing the classical Young-Dupré condition. References [1] W. Helfrich: Elastic properties of lipid bilayers: theory and possible experiments, Z. Naturforsch. C 28,

693–703 (1973). [2] B. Alberts, A. Johnson, J. Lewis, M. Raff, K. Roberts, P. Walter: Molecular biology of the cell, Garland

Science, New York (2002). [3] R. Russo, E.G. Virga: Adhesive borders of liquid membranes. Proceedings of the Royal Society of

London A 455, 4145-4168 (1999). [4] H. Gouin: Vesicle Model with Bending Energy Revisited, Acta Applicandae Mathematicae 132, 347-358

(2014) & arXiv:1510.04824. [5] S. Gavrilyuk, H. Gouin: Dynamics and boundary conditions for membranes whose surface energy

depends on the mean and Gaussian curvatures, Mathematics and Mechanics of Complex Systems, In press (2019) & arXiv:1812.06646.

32

CONSISTENT BGK MODELS FOR GAS MIXTURES AND HYDRODYNAMIC EQUATIONS

Maria Groppi

Department of Mathematical, Physical and Computer Sciences,


[email protected]

Kinetic BGK models are often used in various applications in rarefied gas dynamics and plasma physics, because of the complexity of nonlinear Boltzmann-type kinetic equations describing the dynamics of multicomponent gases. In this talk, some consistent relaxation time-approximation models of BGK-type for inert gas mixtures are presented and their main properties are discussed [1, 2]. Consistency means three basic properties: correct reproduction of conservation laws, H-theorem and uniqueness of equilibrium solution. The main peculiarities of the presented BGK models will be highlighted with reference to their continuum limits obtained by Chapman-Enskog expansions [3]. In particular, it will be shown that a recent BGK model [2], reproducing the structure of the Boltzmann collision operator for mixtures and well suited to deal with various intermolecular collisional potentials, can lead in the hydrodynamic limit, in a proper collision dominated regime, to multitemperature and multivelocity Euler and Navier Stokes closures. Joint work with M. Bisi, G. Martalò, and G. Spiga, Department of Mathematical, Physical and Computer Sciences, University of Parma. References [1] M. Groppi, G. Russo, G. Stracquadanio, Semi-Lagrangian approximation of BGK models for inert and

reactive gas mixtures, in “From Particle Systems to Partial Differential Equations V”, Springer Proceedings in Mathematics and Statistics 258, Patricia Gonçalves and Ana Jacinta Soares (Eds.) (2018), p. 53-80.

[2] A.V. Bobylev, M. Bisi, M. Groppi, G. Spiga, I.F. Potapenko, A general consistent BGK model for gas mixtures, Kinet. Relat. Models 11 (2018), 1377–1393.

[3] M. Bisi, A.V. Bobylev, M. Groppi, G. Spiga, Hydrodynamic Equations from a BGK Model for Inert Gas Mixtures, AIP Conference Proceedings, RGD 31 2018, in press.

33

ON THE SECOND-ORDER EXTENSIONS OF FIRST-ORDER COLLECTIVE MODELS

Seung Yeal Ha

Department of Mathematical Sciences,

Seoul National University (Korea)

[email protected]

Self-organization of complex systems has received lots of attention in scientific disciplines such as applied mathematics, biology, control theory of multi-agent system, statistical physics due to many recent applications in cooperative robot system, unmanned aerial vehicles such as drones and sensor networks etc. In literature, first-order models have been used in the collective modeling of complex system from the beginning. In this talk, we will discuss how to lift first-order models to second-order ones by preserving emergent dynamics and reduction to the first-order model in some limiting situation. This talk is based on joint works with Dohyun Kim (NIMS).

34

FROM THE RELATIVISTIC MIXTURE OF GASES TO THE RELATIVISTIC CUCKER-SMALE FLOCKING: MATHEMATICAL ANALYSIS

Jeongho Kim

Department of Mathematical Sciences,

Seoul National University (Korea)

[email protected]

We present a mathematical properties of the relativistic correction for the CS flocking model introduced in the previous talk by Prof. Tommaso Ruggeri. More precisely, we provide a sufficient framework leading to the exponential flocking of the relativistic CS model in terms of communication weights. We also show that the relativistic CS model reduces to the classical CS model, as the speed of light c tends to infinity in any finite- time interval. For the analytical simplicity, we also present the approximated relativistic CS model, in which

term in the equation was ignored. Then, with this simplified model, we provide the kinetic and hydrodynamic description of it, as well as their emergent behaviors. This work was collaborated with Prof. Tommaso Ruggeri and Prof. Seung-Yeal Ha.

35

ON WELL-POSEDNESS OF WEAK SOLUTIONS

Tai-Ping Liu

Institute of Mathematics, Academia Sinica (Taiwan) and

Department of Mathematics, Stanford University (USA)

[email protected]

The traditional interpretation of Hadamard's Well-posedness notion for differential equations is too strong for incompressible Euler equations and even for compressible Euler equations. Method of convex integration has produced multiple solutions with a given initial data. The problem arises for the weak solutions. On the other hand, there is the well-posedness theory for the weak solutions for system of hyperbolic conservation laws. In this talk, historical perspective will be given and recent work of Shih-Hsien Yu and the author on the well-posedness of weak solutions for compressible Navier-Stokes equation will be reported. In particular, we propose that a new notion of well-posedness is necessary. This new notion seems to be physically and analytically natural.

36

COHERENT STRUCTURES IN A CHEMOTAXIS MODEL OF ACUTE INFLAMMATION

Maria Carmela Lombardo, Valeria Giunta, Marco Sammartino



[email protected]

The aim of this talk is to introduce and study a reaction-diffusion-chemotaxis model that describes the initial stages of a wide class of inflammatory diseases. Inflammation is the response to outside insults, aimed at eliminating the threat and promote tissue repair and healing. It is a highly complex process, characterized by the action of both pro- and anti-inflammatory agents that work synergistically to ensure a quick restoration of tissue health. Inflammation is also believed to play a central role in the pathophysiology of many common disorders, including some degenerative patologies, such as Alzheimer’s, atherosclerosis and Multiple Sclerosis. In the last years several mathematical modeling approaches have been adopted to provide insights on the major pathological processes involved in inflammation [1, 2]. Despite the increasing interest in this area, there are only few models that incorporate spatial aspects in the description of inflammation driven diseases [3, 4, 5]. We shall design a model describing the spatio-temporal dynamics of a population of immune cells and of two different types of signaling molecules: a pro-inflammatory chemokine, which is the chemoattractant for the immune cells, and an anti-inflammatory cytokine, which acts, on a longer time scale, as an inhibitor of the inflammatory state [6]. We are interested in the model capability of reproducing aggregation phenomena leading to the formation of localized patches of inflammatory activity. To this end we investigate the conditions on the system parameters that determine the excitation of Turing and wave instabilities. The investigation is conducted by considering biologically realistic values of the introduced parameters, all of which are taken from the existing literature. We shall show that, varying the control parameters, the model is able to reproduce qualitatively different pathological scenarios: a diffused inflammatory state of the type observed in many cutaneous rashes, the formation of stationary patches of inflammation and the ring-shaped skin rashes observed in Erythema Annulare Centrifugum (EAC), a very aggressive form of cutaneous eruption [7]. For large values of both the anti-inflammatory time scale and the chemotaxis coefficient, the analysis yields the presence of large regions in the parameters space where a wave instability occurs, corresponding to the formation of oscillating-in-time spatial patterns, that qualitatively reproduce the periodic appearance of localized skin eruptions characteristic of the Recurrent Erythema Multiforme (REM) [8]. Therefore, the present model proposes a possible mechanism for explaining the insurgence of recurrent inflammations, whose etiology is still unknown. The proposed system also displays a cascade of successive bifurcations leading to chaotic behavior, already observed in existing chemotaxis models. The mechanism of the observed route-to-chaos and its relationship with self-organized criticality of macrophages will be discussed. Finally the issue of localized pattern will be addressed: we shall show the presence, in a well-defined region of the parameter space called the pinning region, of a multiplicity of bifurcating branches of localized states, whose bifurcation diagram is organized in a characteristic snakes-and-ladders structure, called homoclinic snaking [9]. The bifurcation structure and the stability properties of the localised solutions will be investigated, both theoretically and numerically, in the strongly nonlinear regime as the control parameter is varied away from the primary bifurcation value.

37

References [1] Painter, K.J. Mathematical models for chemotaxis and their applications in self-organisation

phenomena (2018) Journal of Theoretical Biology. Article in Press. [2] Ramirez-Zuniga, I., Rubin, J.E., Swigon, D., Clermont, G. Mathematical modeling of energy

consumption in the acute inflammatory response (2019) Journal of Theoretical Biology, 460, pp. 101-114.

[3] Penner, K., Ermentrout, B., Swigon, D. Pattern formation in a model of acute inflammation (2012) SIAM Journal on Applied Dynamical Systems, 11 (2), pp. 629-660.

[4] Chalmers, A.D., Cohen, A., Bursill, C.A., Myerscough, M.R. Bifurcation and dynamics in a mathematical model of early atherosclerosis: How acute inflammation drives lesion development (2015) Journal of Mathematical Biology, 71 (6-7), pp. 1451-1480.

[5] Lombardo, M.C., Barresi, R., Bilotta, E., Gargano, F., Pantano, P., Sammartino, M. Demyelination patterns in a mathematical model of multiple sclerosis (2017) Journal of Mathematical Biology, 75 (2), pp. 373-417.

[6] Giunta, V., Lombardo, M.C., Sammartino, M. Pattern formation and transition to chaos in a mathematical model of acute inflammation (2019) submitted.

[7] Bilotta, E., Gargano, F., Giunta, V., Lombardo, M.C., Pantano, P., Sammartino, M. Axisymmetric solutions for a chemotaxis model of Multiple Sclerosis (2018) Ricerche di Matematica, pp. 1-14. Article in Press.

[8] Lerch, M., Mainetti, C., Terziroli Beretta-Piccoli, B., Harr, T. Current Perspectives on Erythema Multiforme (2018) Clinical Reviews in Allergy and Immunology, 54 (1), pp. 177-184.

[9] Knobloch, E. Spatial localization in dissipative systems (2015) Annual Review of Condensed Matter Physics, 6 (1), pp. 325-359.

38

BIOSORPTION OF HEAVY METALS IN A NITRIFYING BIOFILM




[email protected]

A mathematical model for heavy metals interaction in a nitrifying multispecies biofilm is proposed. The model is based on a continuum approach and mass conservation principles. A diffusion-reaction equation describes the dynamics of a toxic heavy metal within the multispecies biofilm system. Two systems of hyperbolic partial differential equations define the binding sites evolution during biofilm growth. The latter is governed by a system of hyperbolic equations for microbial species growth and a nonlinear ordinary differential equation describing the biofilm thickness evolution as a free boundary problem. The substrate diffusion-reaction within the biofilm is described with an additional system of parabolic partial differential equations. The model is applied to a case study reproducing a biofilm devoted to municipal wastewater treatment. Numerical simulations confirm the model consistency and highlight the adaptive behaviour of such complex microbial community.

39

ON THE EVOLUTION OF FRACTIONAL DIFFUSIVE WAVES

Armando Consiglio, Francesco Mainardi

Department of Physics and Astronomy,


[email protected]

In physics, process involving the phenomena of diffusion and wave propagation have great relevance; these physical processes are governed, from a mathematical point of view, by partial differential equations of order 1 and 2 in time. It is known that, whereas the diffusion equation describes a process where the disturbance spreads infinitely fast, the wave-front velocity of the disturbance is finite for the wave equation. By introducing a fractional derivative of order α in time with , we are lead to processes that, in mathematical physics, we may refer to as fractional diffusive waves. The use of the Laplace transform in the analysis of the Cauchy and Signalling problems leads to a special function of the Wright type, nowadays known as M-Wright function. In this work we want to show that the time-fractional diffusion-wave equation interpolates between the two different responses, studying and simulating both the situations in which the data function (initial signal) is a Dirac delta generalized function, that leads to the fundamental solution, and the one in which the data function (initial signal) is provided by a box-function. In the latter case the solutions are obtained by a convolution of the Green function with the initial data function. Acknowledgments The work of FM has been carried out in the framework of the activities of the National Group of Mathematical Physics (INdAM-GNFM). References [1] Yu. Luchko and F. Mainardi, Cauchy and signaling problems for the time-fractional diffusion-wave

equation, ASME Journal of Vibration and Acoustics 136 No 5 (2014), 050904/1–7. DOI: 10.1115/1.4026892; E-print arXiv:1609.05443.

[2] F. Mainardi, The fundamental solutions for the fractional diffusion-wave equation, Applied Mathematics Letters 9 No 6 (1996), 23–28.

40

GENERALIZED SIMPLE WAVES FOR HYPERBOLIC SYSTEMS

Natale Manganaro

MIFT,


[email protected]

Simple wave solutions are of great interest for nonlinear wave problems. Such a class of solutions are admitted by first order quasilinear hyperbolic systems in the homogeneous case and they are useful for solving different problems of interest in the applications as, for instance, Riemann problems. Unfortunately simple waves are not usually admitted by hyperbolic systems when dissipative effects are taken into account (non-homogeneous case). Within the theoretical framework of the method of differential constraints, here we describe a possible strategy aimed at generalizing simple wave solutions for nonhomogeneous hyperbolic systems. An example of interest in fluid dynamics is presented.

41

WEAK SOLUTIONS TO THE NAVIER-STOKES EQUATIONS WITH NON DECAYING DATA

Paolo Maremonti

Department of Mathematics and Physics,

University of Campania “L. Vanvitelli” (Italy)

[email protected]

In [1] we investigate on the Navier-Stokes initial boundary value problem in 3D-exterior domains with non decaying initial data. We are interested to prove the existence of weak solutions defined for all for large non decaying initial data. We extend the technique already developed in the paper [2] to the 3D-exterior domains. This special problem is part of the peculiar literature related to the solutions global in time with non finite energy, that in the last decade has attracted the interest of some authors. We believe that this literature can be referred to two different branches. One branch looks for the existence of solutions to the problem in the class of the physically reasonable steady solutions of the Navier-Stokes equations. The relevant and physically meaning question is the investigation on a steady fluid motion physically reasonable, governed by the Navier-Stokes equations, that can be seen as limit of an unsteady motion or converse if the steady motion can have the transition to an unsteady motion. Another branch, nevertheless physically interesting, looks for non decaying solutions in connection with the turbulence problems. In this case a priori for the kinetic field or its translated

, with assigned vector , no sort of limit property at infinity is possible to assume. In connection with the second question, we are able to prove the following result (the symbol denotes the initial data and the symbol completion of with respect to for some Theorem - For all , there exists a suitable weak solution to the initial boundary value problem in an exterior domain. Moreover, the initial data is assumed continuously in the norm of . References [1] P. Maremonti and S. Shimizu, Global existence of weak solutions to 3-D Navier–Stokes IBVP with non-

decaying initial data in exterior domains. Submitted for the publication. [2] P. Maremonti and S. Shimizu, Global existence of solutions to 2-D Navier–Stokes flow with non-

decaying initial data in half-plane, J. Differential equations, 265 (2018) 5352-5383, doi.org/10.1016/j.jde.2018.07.004.

42

ANALYSIS OF EVAPORATION-CONDENSATION PROBLEMS FOR A BINARY GAS MIXTURE

Marzia Bisi, Maria Groppi, Giorgio Martalò

Department of Mathematical, Physical and Computer Sciences,


[email protected]

Kinetic theory is the classical framework to describe the dynamics of rarefied gases. However, some particular problems in this context can be initially investigated at the hydrodynamic level by means of macroscopic equations instead of kinetic ones. Hydrodynamic equations can be conceived as a model system providing qualitative indications about kinetic solutions, even when the two approaches give solutions that do not coincide accurately. A special class of 1-dimensional stationary problems is constituted by the half space problem of evaporation and condensation, that has been widely investigated for a single component gas [1]. By using typical qualitative methods of dynamical systems theory, we will discuss from a mathematical point of view the main features of the evaporation-condensation problem for a binary mixture of rarefied gases modeled by a set of Navier-Stokes equations [2], obtained as hydrodynamic limit of a recent BGK description [3] by classical Chapman-Enskog theory. Some numerical result about evaporation-condensation solutions for a mixture of noble gases will be presented and discussed. References [1] A. V. Bobylev, S. Ostmo and T. Ytrehus, Qualitative analysis of the Navier-Stokes equations for

evaporation-condensation problems, Phys. Fluids 8(7), 1764-1773 (1996). [2] M. Bisi, A. Bobylev, M. Groppi and G. Spiga, Hydrodynamic Equations from a BGK Model for Inert

Gas Mixtures, in AIP Conf. Proc., in press. [3] A. V. Bobylev, M. Bisi, M. Groppi, G. Spiga and I. F. Potapenko, A general consistent BGK model for

gas mixtures, Kinet. Relat. Mod. 11(6) (2018).

43

MODELING CELL MOTILITY IN BIOFILMS




[email protected]

The establishment of mixed species biofilms results from the interplay of different factors, such as mass transfer, detachment forces, communication (typically via quorum sensing), and metabolic cooperation or competition. Recent advances in microbial ecology have identified motility as one of the main mediators of the development and shape of multispecies communities. Indeed, motile cells with high kinetic energy and acting as invaders can lead to the dissolution of heterologous biofilms and re-population of the matrix or can result in the development of several beneficial phenotypes. To fill in the gap in modeling the establishment of such mixed species communities mediated by the invasion process, a one-dimensional continuous model is developed by considering two state variables representing the planktonic and sessile phenotypes and reproducing the transition from one state to the other. Different planktonic cell motion behaviors can be described, as well as by including regulatory regimes triggered by the external chemical dynamics. The proposed model is solved numerically to simulate biofilm evolution during biologically relevant conditions and provides interesting insights towards the qualitative and quantitative understanding of biofilm dynamics and ecology.

44

COMPARISON OF SHOCK STRUCTURE BEHAVIOURS FOR INCREASING ORDER OF CLOSURES

Andrea Mentrelli, Tommaso Ruggeri



[email protected]

Linear closure of the moment equations has been for a long time the standard closure in Extended Thermodynamics. The resulting limited hyperbolicity domain, which restricted the applicability of the theory to a relatively small neighborhood of the equilibrium, and its validity only for monatomic gases, were weaknesses of the theory that hampered its adoption in practical applications. After the theory was pushed beyond its long-standing boundaries with the extension to polyatomic gases, very recently Brini and Ruggeri have shown that the maximum entropy principle with a second order closure allows for an extension also of the hyperbolicity region, proving that the theory has still much to offer. We discuss how the maximum entropy principle with second and higher order closures allow to predict shock structure solutions closer to those predicted by the kinetic theory and in much closer agreement with the experiments, with respect to the classical linear closure, further increasing the appeal of the theory.

45

NEW NONLINEAR STABILITY RESULTS FOR PLANE COUETTE AND POISEUILLE FLOWS

Giuseppe Mulone



[email protected]

An overview of linear instability and nonlinear stability results for laminar flows in fluid-dynamics is given. Plane Couette and Poiseuille flows are nonlinearly stable with respect to streamwise perturbations for any Reynolds number Re (see [3]). In this case the coefficient of time-decay of the energy is , and it is a bound from above of the time-decay of streamwise perturbations of linearized equations. Plane Couette and Poiseuille flows are linearly and nonlinearly energy stable if the Reynolds number Re is less than:

when a perturbation is a tilted perturbation in the direction which forms an angle with the direction of the motion and does not depend on . is the critical Reynolds number for spanwise perturbations which is evaluated at the wave number , being any positive wavelength. By taking the minimum of with respect to , we obtain the critical energy Reynolds number: for plane Couette flow:

and for plane Poiseuille flow: (in particular, for we have the classical values for Couette for Poiseuille flow). Here the non-dimensional interval between the planes bounding the channel is . In particular, these results improve those obtained by Joseph [2], who found for streamwise perturbations a critical nonlinear value of in the Couette case, and those obtained by Joseph and Carmi who found the value for plane Poiseuille flow for streamwise perturbations. If we fix some wavelengths from the experimental data of Prigent et al. [4], and the numerical simulations of Barkley and Tuckerman [6], Tsukahara et al. [5], the critical Reynolds numbers we obtain are in a very good agreement both with the experiments and the numerical simulation. These results partially solve the Couette-Sommerferld paradox. References [1] W. M'F. Orr, Proc. Roy. Irish Acad. A 27 9-68 and 69-138 (1907). [2] D. D. Joseph, J. Fluid Mech. 33 part 3, 617-621 (1966). [3] K. Moffatt, in Whither turbulence, J. Lumley (ed), Springer, 250-257 (1990). [4] A. Prigent, G. Grégoire, H. Chaté and O. Dauchot, Physica D 174 100-113 (2003). [5] T. Tsukahara, Y. Seki, H. Kawamura and D. Tochio, In Proc. 4th Intl Symp. On Turbulence and Shear

Flow Phenomena, pp. 935-940 (2005). [6] D. Barkley and L. S. Tuckerman, J. Fluid Mech. 576 109-137 (2007). [7] P. Falsaperla, A. Giacobbe and G. Mulone, Nonlinear stability results for plane Couette and Poiseuille

flows, submitted (2019).

46

NUMERICAL SOLUTIONS OF THE SEMICLASSICAL BOLTZMANN EQUATION FOR BIPOLAR CHARGE TRANSPORT IN GRAPHENE

Giovanni Nastasi



[email protected]

Charge transport in suspended monolayer graphene is simulated by a numerical deterministic approach, based on a discontinuous Galerkin (DG) method, for solving the semiclassical Boltzmann equation for electrons. Both the conduction and valence bands are included and the inter-band scatterings are taken into account. The use of a Direct Simulation Monte Carlo (DSMC) approach, which properly describes the inter-band scatterings, is computationally very expensive because the valence band is very populated and a huge number of particles is needed. Also the choice of simulating holes instead of electrons does not overcome the problem because there is a certain degree of ambiguity in the generation and recombination terms of electron hole pairs. Often, direct solutions of the Boltzmann equations with a DSMC neglect the inter-band scatterings on the basis of physical arguments. The DG approach does not suffer from the previous drawbacks and requires a reasonable computing effort. It is found out that the inclusion of the inter-band scatterings produces huge variations in the average values, as the current, with zero Fermi energy while, as expected, the effect of the inter- band scattering becomes negligible by increasing the absolute value of the Fermi energy. If the presence of an oxide substrate is also included then it is necessary to add the scatterings of the charge carriers with the impurities and the phonons of the substrate, besides the interaction mechanisms already present in the graphene layer. It results that the presence of a substrate leads to a degradation of the electron and hole mobility. References [1] M. Coco, A. Majorana, G. Nastasi, V. Romano, High-field mobility in graphene on substrate with a

proper inclusion of the Pauli exclusion principle, Atti Accad. Pelorit. Pericol. Cl. Sci. Fis. Mat. Nat. (in press).

[2] M. Coco, A. Majorana, V. Romano, Cross validation of discontinuous Galerkin method and Monte Carlo simulations of charge transport in graphene on substrate, Ricerche mat., 66, 201–220 (2017).

[3] A. Majorana, G. Nastasi, V. Romano, Simulation of Bipolar Charge Transport in Graphene by Using a Discontinuous Galerkin Method, Commun. Comput. Phys., Vol. 26, No. 1, pp. 114-134 (2019).

[4] G. Nastasi, V. Romano, Improved mobility models for charge transport in graphene, Commun. Appl. Ind. Math. (in press).

[5] V. Romano, A. Majorana, M. Coco, DSMC method consistent with the Pauli exclusion principle and comparison with deterministic solutions for charge transport in graphene, J. Comput. Phys., 302, 267–284 (2015).

47

ANAEROBIC DIGESTION IN PLUG-FLOW REACTORS: A MATHEMATICAL MODEL

Daniele Bernardo Panaro, Florinda Capone, Maria Rosaria Mattei, Vincenzo Luongo, Luigi Frunzo

Department of Mathematics and Applications "Renato Caccioppoli",


[email protected]

Most of the existing models on Anaerobic Digestion of waste biomasses are based on nonlinear ordinary differential equations describing the biological activities of bacteria living in continuous stirred tank reactors. The perfect mixing ensured by this reactor configuration results in the possibility of neglecting any functional dependence of biological activities on space. In many real cases, the conversion of solid waste biomasses is carried out in plug-flow reactors, where the position along the reactor strongly affects biological activities and reactor performances. A new mathematical model describing the anaerobic bioconversion of solid wastes in a plug-flow reactor is here presented. The model is based on mass balance considerations for different state variables and results in nonlinear partial differential equations accounting for the convection-diffusion-reaction of particulate and dissolved compounds within the bioreactor. Numerical simulations are performed to show model consistency.

48

A 16 MOMENTS MODEL IN RELATIVISTIC EXTENDED THERMODYNAMICS OF RAREFIED POLYATOMIC GAS

Maria Cristina Carrisi, Sebastiano Pennisi

Department of Mathematics and Informatics,

University of Cagliari (Italy)

[email protected]

We aim to discuss here the following set of balance equations for the description of relativistic polyatomic gases:

(1)

In [1], the authors considered only first the two of these equations and the traceless part of (1)3, i.e., ; the reason behind this choice was that they wanted to find, in the non relativistic limit and

in the monoatomic limit, the results of the 14 moments models of the articles [2]-[6]. In the present article we investigate what happens if we don’t take away the trace of (1)3. In this way one obtains a 15 moments model and we want to investigate it. But, in the meanwhile, another 15 moments model [7] has been produced in the classical context. To avoid confusion between these two models we prefer to consider both of them compacted in only one and in the relativistic context, even if at the cost of obtaining a 16 moments model. For this reason we include (1)4 in the field equations; these are expressed in terms of the tensors

(2)

where is the rotational energy of a molecule, its vibration energy and . We will calculate the non relativistic limit of the full set of eqs. (1), finding a 16 moments model for classical extended thermodynamics of polyatomic gases. It encloses two important subsystems: the natural extension of [1] which is obtained neglecting eq. (1)4 and the model [7] which comes out by neglecting the trace of eq. (1)3. After that, we will impose the Maximum Entropy Principle for these field equations and compare the results with those of [1]. The resulting system is hyperbolic for every timelike congruence and this property assures that the characteristic velocities don’t exceed the speed of light.

49

References [1] S. Pennisi, T. Ruggeri, Relativistic Extended thermodynamics of rarefied polyatomic gas, Annals of

Physics, 377 (2017), 414-445, doi: 10.1016/j.aop.2016.12.012. [2] Arima, T.; Taniguchi, S.; Ruggeri, T.; Sugiyama, M. Extended Thermodynamics of dense gases.

Continuum Mech. Thermodyn. 2012, 24, 271–292. [3] M.C. Carrisi, S. Pennisi, T. Ruggeri, Monatomic Limit of Relativistic Extended Thermodynamics of

Polyatomic Gas, Continuum Mech. Thermodyn., doi: 10.1007/s00161- 018-0694-y, (2018). [4] T. Ruggeri, M. Sugiyama, Rational Extended Thermodynamics beyond the Monatomic Gas, Springer,

Cham Heidelberg New York Dorderecht London (2015). [5] Liu, I.-S.; Muller, I.; Ruggeri, T. Relativistic thermodynamics of gases. Ann. Phys. (N.Y.) 1986, 169,

191–219. [6] Muller, I.; Ruggeri, T. Rational Extended Thermodynamics, 2nd ed.; Springer Tracts in Natural

Philosophy. Springer, New York, NY, USA, 1998. [7] Arima, T.; Taniguchi, S.; Ruggeri, T.; Sugiyama, M. Extended thermodynamics of rarefied polyatomic

gases: 15-field theory incorporating relaxation processes of molecular rotation and vibration. Entropy 2018, 20, 301-321. DOI: 10.3390/e20040301.

50

HOPF BIFURCATIONS IN THERMAL MHD AND SPECTRUM INSTABILITY DRIVEN BY PERTURBATIONS TO PRINCIPAL ENTRIES

Salvatore Rionero


Fellowship Accademia Nazionale dei Lincei, Roma (Italy)

[email protected]

The transition from a steady state to an unsteady oscillatory state (Hopf bifurcation) is a scenario: i) “less continuous” than the transition from a steady state to a (close) steady state (steady

bifurcation); ii) more detectable and impressive from the physical point of view.

Further, an Hopf bifurcation is a limit cycle candidate, of known frequency, to the nonlinear system at stark. Let

be the spectrum equation. The new approach for the onset of bifurcation is based on a suitable use of each instability condition

expecially for characterizing the occurring of unsteady bifurcations (Hopf, steady-Hopf, unsteady aperiodic, …). In thermal MHD, at growth of the Chandrasekhar number measuring the growth of the magnetic field in which the electrically conducting fluid is embedded an Hopf bifurcation can occur only when the Prandtl number is less than the Prandtl magnetic number. Calling Hopf bifurcation number the threshold

that has to reach for the occurring of an Hopf bifurcation, we, via the new approach, show that , in the free-free case, is given by

and analogous values are furnished for different cases. In particular spectrum instabilities driven by perturbations to the principal entries and applications to convection in multicomponent fluid layers are analyzed.

51

MATHEMATICAL MODELING OF CHARGE TRANSPORT IN GRAPHENE

Vittorio Romano



[email protected]

The last years have witnessed a great interest for 2D-materials due to their promising applications. The most investigated one is graphene which is considered as a potential new material to exploit in nano-electronic and optoelectronic devices. Charge transport in graphene can be described with several degrees of physical complexity. At quantum level an accurate model is represented by the Wigner equation but in several cases its semiclassical limit, the Boltzmann equation, constitutes a fully acceptable model. However, the numerical difficulties encountered in the direct solution of both the Wigner and the semiclassical Boltzmann equation has prompted the development of hydrodynamical, energy transport and drift diffusion models, in view of the design of a future generation of electron devices where graphene replaces standard semiconductors like silicon and gallium arsenide. Moreover, thermal effects in low dimensional structures play a relevant role and, therefore, also phonon transport must be included. Interesting new mathematical issues related to the peculiar features of graphene arise. The main aspects will be discussed and recent results [1-10] illustrated in the perspective of future developments, in particular the optimization of graphene field effect transistors. References [1] L. Luca, V. Romano, Quantum corrected hydrodynamic models for charge transport in graphene,

Annals of Physics 406, 30-53 (2019). [2] A. Majorana, G. Nastasi, V. Romano, Simulation of bipolar charge transport in graphene by using a

discontinuous Galerkin method, Comm in Comp. Physics 26, 114-134 (2019). [3] L. Luca, V. Romano, Comparing linear and nonlinear hydrodynamical models for charge transport in

graphene based on the Maximum Entropy Principle, Int. J. of Non-Linear Mech. (2018). [4] M. Coco, V. Romano, Simulation of Electron–Phonon Coupling and Heating Dynamics in Suspended

Monolayer Graphene Including All the Phonon Branches, J. Heat Transfer 140, 092404 (2018). [5] M. Coco, A. Majorana, V. Romano, Cross validation of discontinuous Galerkin method and Monte

Carlo simulations of charge transport in graphene on substrate, Ricerche di Mat., 66, 201— 220, 2017.

[6] G. Mascali, V. Romano, Charge transport in graphene including thermal effects, SIAM J. Applied Math. Vol 77 (2), 593-613 (2017).

[7] M. Coco, G. Mascali, V. Romano, Monte Carlo Analysis of Thermal Effects in Monolayer Graphene, J. Of Computational and Theoretical Transport 45(7), 540-553, 2016.

[8] A. Majorana, G. Mascali, V. Romano, Charge transport and mobility in monolayer graphene, J. Math. Industry 7:4, https://doi.org/10.1186/s13362-016-0027-3 , 2016.

[9] V. Romano, A. Majorana, M. Coco, DSMC method consistent with the Pauli exclusion principle and comparison with deterministic solutions for charge transport in graphene, J. Comput. Phys.302, 267-284, 2015.

[10] V. D. Camiola, V. Romano, Hydrodynamical Model for Charge Transport in Graphene, J. Stat. Phys. 157, 1114-1137, 2014.

52

RESONANT TURING PATTERNS IN THE FITZHUGH-NAGUMO MODEL WITH CROSS DIFFUSION

Gaetana Gambino, Maria Carmela Lombardo, Gianfranco Rubino, Marco Sammartino



[email protected]

In this talk we shall describe the formation of resonant spatial structures in the FitzHugh-Nagumo (FN) system [2, 5]:

where the linear cross diffusion effect is considered [6]. In the parameters region where the above system supports bistability of the homogeneous steady states, diffusive instabilities lead to the emergence of subcritical large amplitude patterns. In this case the classical weakly nonlinear analysis, as e.g. given in [3], fails. Therefore, to describe the resulting structures, we take into account the coupling of the zero mode with the spatial unstable mode. We will also study the interaction of the patterns emerging from the two different homogeneous equilibria: on a 2D spatial domain, if the unstable interacting modes satisfy some resonant conditions [1], complex quasiperiodic structures emerge. The selection of these superlattice patterns [4] is addressed via normal form reduction. We show that the numerical simulations of the reaction-diffusion system corroborate the predictions obtained through the normal form. References [1] Bachir M., Sonnino G., Tlidi M.: Predicted formation of localized superlattices in spatially distributed

reaction-diffusion solutions. Physical Review E, 86, 045103(R), (2012). [2] FitzHugh R.: Impulses and physiological states in theoretical models of nerve membrane. Biophysical

Journal, 1(6):445-466, (1961). [3] Gambino G., Lombardo M.C., Rubino G., Sammartino M., Pattern selection in the 2D FitzHugh-

Nagumo model. Ricerche di Matematica 10.1007/s11587-018-0424-6, (2018). [4] Judd S.L., Silber M.: Simple and superlattice Turing patterns in reaction-diffusion systems: bifurcation,

bistability, and parameter collapse. Physica D, 136:45-65, (2000). [5] Metens S., Borckmans P., and Dewel G., Large amplitude patterns in bistable reaction-diffusion

systems. 10.1007/978-94-011-4247-2, (2000). [6] Zemskov E.P., Epstein I.R., Muntean A.: Oscillatory pulses in FitzHugh-Nagumo type systems with

cross-diffusion. Mathematical Medicine and Biology, 28(2):217-226, (2011).

53

FROM THE RELATIVISTIC MIXTURE OF GASES TO THE RELATIVISTIC CUCKER-SMALE FLOCKING

Tommaso Ruggeri



[email protected]

We present a relativistic model for a mixture of Euler gases with multi temperatures. For the proposed relativistic model, we explicitly determine production terms resulting from the interchange of energy-momentum between the constituents via the entropy principle. We use the analogy with the homogeneous solutions of a mixture of gases and the thermomechanical Cucker-Smale flocking model in a classical setting (Ha, S.-Y., Ruggeri, T.: Emergent dynamics of a thermodynamically consistent particle model. Arch. Rational Mech. Anal. 223, 1397–1425 (2017)) to derive a relativistic counterpart of the TCS model. Moreover, we employ the theory of principal subsystem to derive the relativistic Cucker-Smale model. In the next talk Jeongho Kim will present the mathematical analysis for the derived relativistic CS model. This is a jointly work with Seung-Yeal Ha and Jeongho Kim.

54

HELMHOLTZ-TYPE SOLITARY SOLUTIONS IN NON-LINEAR ELASTODYNAMICS

Giuseppe Saccomandi

Department of Engineering,

University of Perugia (Italy)

[email protected]

The nonlinear equations descriptive of transverse wave propagation in an isotropic, incompressible, elastic solid on an elastic foundation support interesting class of solitary solutions [1, 2, 4]. The aim of the present talk is to discuss some of such solutions and their stability illustrating some connections with nonlinear optics via a NLS reduction [3]. References: [1] Rogers, Colin, Giuseppe Saccomandi, and Luigi Vergori “Helmholtz-Type Solitary Solutions in

Quasilinear Elastodynamics” submitted. [2] Rogers, Colin, Giuseppe Saccomandi, and Luigi Vergori. "Cnoidal and gausson phenomena in nonlinear

elastodynamics." Acta Mechanica 229.8 (2018): 3489-3500. [3] Rogers, Colin, Giuseppe Saccomandi, and Luigi Vergori. "Nonlinear elastodynamics of materials with

strong ellipticity condition: Carroll-type solutions." Wave Motion 56 (2015): 147- 164. [4] Rogers, Colin, Giuseppe Saccomandi, and Luigi Vergori "Carroll-type deformations in nonlinear

elastodynamics." Journal of Physics A: Mathematical and Theoretical 47.20 (2014): 205204.

55

VISCOUS MHD VORTICITY-CURRENT EQUATIONS WITH DATA IN L1(R2)

Marco Sammartino

Department of Engineering,


[email protected]

In this talk we shall consider the 2D viscous MHD equations:

where is the fluid velocity, is the pressure, is the magnetic field, and are respectively the viscosity and the resistivity. Introducing the vorticity and the current density

one can write the MHD equations in the vorticity-current formulation:

(1)

(2)

where and are written, in terms of and , through the Biot-Savart law:

with

The initial condition for (1) and (2) are

(3)

(4)

We shall prove the following result: Theorem 1. Suppose . Then Eqs. (1)-(2) with initial data given by (3)-(4), admit, globally in time, a unique solution and . Moreover and are smooth for and, in particular,

, for each . This is joint work with V. Sciacca and M. Schonbek.

56

EXTENSION OF THE AUXILIARY EQUATION METHOD BY MEANS OF HYPERELLIPTIC FUNCTIONS

Michele Sciacca

Department of Agricultural, Food and Forest Sciences,


[email protected]

The interest to find exact solutions of (partial) differential equations is an old problem which has involved many researchers over the years. Among the different methods, I consider the auxiliary equation method, which uses an auxiliary equation, whose solutions are known, to find some exact solutions of the (partial) differential equation under investigation. Some years ago a direct method was proposed, which uses the hyperelliptic functions [1–5]. Here I generalize this method and I show that it can be also applied to non-autonomous differential equation (for instance to non- autonoums Korteweg de Vries). References [1] H.F. Baker, Multiply Periodic Functions, Cambridge Univ. Press, 1907. [2] E.D. Belokolos, V.Z. Enolskii, J. Math. Sci. 106 (6) (2001) 3395. [3] E.D. Belokolos, V.Z. Enolskii, J. Math. Sci. 108 (2002) 295. [4] T. Brugarino, M. Sciacca, Phys. Lett. A 372 (2008) 1836. [5] Y. Feng, Y. Dong, Q. Ding, H. Zhang, Appl. Math. Comp. 215 (2010) 3868.

57

UP-WIND DIFFERENCE APPROXIMATION AND SINGULARITY FORMATION FOR A SLOW EROSION MODEL

Vincenzo Sciacca



[email protected]

We consider a model for a granular flow in the slow erosion limit, introduced in [1, 2], which describes the erosion of a mountain profile caused by small avalanches. The model takes the form of a nonlocal first-order conservation law

where gives the slope of the standing profile of granular matter; is the erosion function and has the meaning of the erosion rate per unit length in space covered by the avalanches; and is a nonlocal, in space, integral operator. The function is defined on , with a singularity at . Well-posedness results was established in [2, 3], for initial data and , with ; and in [4], with

and . No rigorous numerical results are known for this model, excluding the wave-front tracking method in [5]. We propose an up-wind numerical scheme for this problem and show that the approximate solutions generated by the scheme converge to the unique entropy solution. Numerical examples are also presented showing the reliability of the scheme. We study also the finite time singularity formation for the model with the singularity tracking method [6, 7, 8], and we characterize the singularities as shocks in the solution. Joint work with Giuseppe M. Coclite (Polytechnic University of Bari - Italy) and Francesco Gargano (University of Palermo - Italy). References [1] K.P. Hadeler and C. Kuttler. Dynamical models for granular matter. Granular Matter, 2(1):9-18, 1999. [2] W. Shen and T. Y. Zhang. Erosion profile by a global model for granular flow. Arch. Ration. Mech. Anal.

204:837-879, 2012. [3] D. Amadori and W. Shen. An integro-differential conservation law arising in a model of granular flow. J.

of Hyperb. Diff. Eqs., 9(1):105-131, 2012. [4] G.M. Coclite and E. Jannelli. Well-posedness for a slow erosion model. J. of Math. Anal. and Appl.,

456(1):337-355, 2017. [5] D. Amadori and W. Shen. Front tracking approximations for slow erosion. Disc. and Cont. Dyn. Syst.,

32(5):1481-1502, 2012. [6] G. Della Rocca, M.C. Lombardo, M. Sammartino, and V. Sciacca. Singularity tracking for Camassa-

Holm and Prandtls equations. Appl. Numer. Math., 56(8):1108- 1122, 2006. [7] F. Gargano, M. Sammartino, V. Sciacca, and K. W. Cassel. Analysis of complex singularities in high-

Reynolds-number Navier-Stokes solutions. J. Fluid Mech., 747:381-421, 2014. [8] F. Gargano, G. Ponetti, M. Sammartino, and V. Sciacca. Complex singularities in KdV solutions.

Ricerche di Matematica, 65(2):479-490, 2016.

58

RATIONAL EXTENDED THERMODYNAMICS OF A RAREFIED POLYATOMIC GAS WITH RELAXATION PROCESSES OF MOLECULAR ROTATION AND VIBRATION

Masaru Sugiyama

Nagoya Institute of Technology (Japan)

[email protected]

Rational extended thermodynamics (RET) [1, 2] is the theory for describing highly nonequilibrium phenomena that are out of the validity range of thermo-dynamics of irreversible processes. The purpose of the present talk is to show the RET theory of a rarefied polyatomic gas in which molecular rotational and vibrational relaxation processes are treated individually. The theory is justified, at mesoscopic level, by a generalized Boltzmann equation. Its distribution function depends on two internal variables, by which we can study the energy exchange among the different molecular modes of a gas, that is, translational, rotational, and vibrational modes. Then a triple hierarchy of the moment system is necessary, and the system of balance equations is closed via the maximum entropy principle. The production terms in the system, which are suggested by a generalized BGK-type collision term in the Boltzmann equation, are adopted. Firstly, in order to cast a spotlight on the dynamic pressure, a simplified RET theory with seven independent fields (ET7): mass density, velocity, translational energy density, molecular rotational energy density, and the molecular vibrational energy density [3] is explained. Secondly, by taking into account also the viscous stress and the heat flux, the RET theory with 15 independent fields (ET15) is explained [4]. This is a direct generalization of the Navier-Stokes and Fourier (NSF) theory of viscous heat- conducting fluids. In fact, the NSF theory can be derived from the ET15 as a limiting case of small relaxation times via the Maxwellian iteration. The relaxation times introduced in the theory are shown to be related to the shear and bulk viscosities and heat conductivity. Some applications of the RET theories explained above to the ultrasonic waves will be shown in the next talk by T. Arima. This is the joint work with T. Arima and T. Ruggeri [3,4]. References [1] I. Müller and T. Ruggeri: Extended Thermodynamics, (1st edition) Springer 1993; Rational Extended

Thermodynamics, (2nd edition) Springer 1998. [2] T. Ruggeri and M. Sugiyama: Rational Extended Thermodynamics beyond the Monatomic Gas,

Springer 2015. [3] T. Arima, T. Ruggeri and M. Sugiyama: Phys. Rev. E 96 (2017) 042143. [4] T. Arima, T. Ruggeri and M. Sugiyama: Entropy 20 (2018) 301.

59

ON THE SIMILARITY SOLUTION OF STRONG SPHERICAL SHOCK WAVES BASED ON EXTENDED THERMODYNAMICS

Shigeru Taniguchi, Tommaso Ruggeri

National Institute of Technology, Kitakyushu College (Japan)

[email protected]

Rational Extended Thermodynamics (RET) [1, 2] has been developed for analyzing highly non-equilibrium phenomena out of local equilibrium. It has been shown that the RET theory can explain the features of the structure of a plane shock wave in a polyatomic gas in which the internal modes, namely, the rotational or vibrational modes in a molecule relax very slowly and the theoretical predictions by the RET theory agree with experimental data and the predictions by kinetic theory quantitatively [3, 4, 5]. In this talk, we study similarity solutions of a spherical shock wave in rarefied polyatomic gases on the basis of the RET theory with only six independent fields; the mass density, velocity, pressure and dynamic pressure. By adopting the strategy proposed in [6] based on the Lie group theory, we derive a system depending on a similarity variable and numerically solve this system with the boundary conditions for a strong shock [7], In particular, the deviation from the well-known Sedov-von Neumann-Taylor solution is addressed quantitatively and an important role of the dynamic pressure will be discussed [7]. References [1] I. Muller and T. Ruggeri, Rational Extended Thermodynamics (Springer- Verlag, New York, 1998). [2] T. Ruggeri and M. Sugiyama, Rational Extended Thermodynamics beyond the Monatomic Gas

(Springer, Heidelberg, 2015). [3] S. Taniguchi, T. Arima, T. Ruggeri and M. Sugiyama, Phys. Rev. E Vol. 89, 013025 (2014). [4] S. Kosuge and K. Aoki, Phys. Rev. Fluids Vol. 3, 023401 (2018). [5] S. Taniguchi, T. Arima, T. Ruggeri and M. Sugiyama, J. Phys. Conf. Ser. Vol. 1035, 012009 (2018). [6] A. Donato and T. Ruggeri, J. Math. Anal. Appl. Vol. 251, 395 (2000). [7] R. Nagaoka, S. Taniguchi and T. Ruggeri, submitted to AIP Conf. Proc. (2019).

60

MODELLING OF ECOLOGY IN A PHOTOTROPHIC-HETEROTROPHIC BIOFILM

AlbertoTenore, Berardino D’Acunto, Maria Rosaria Mattei, Vincenzo Luongo, Luigi Frunzo

Department of Mathematics and Applications "Renato Caccioppoli",


[email protected]

The work presents a 1D mathematical model for the analysis and prediction of microbial interactions within mixotrophic biofilms composed of microalgae and heterotrophic bacteria. The model combines equations for biomasses growth and decay, diffusion-reaction of substrates, and detachment process. In particular, the colonization of external species invading the biofilm is considered. The biofilm growth is governed by nonlinear hyperbolic PDEs while substrate and invading species dynamics are dominated by semilinear parabolic PDEs. It follows a complex system of PDEs on a free boundary domain. The equations are numerically integrated by using the method of characteristics. The model has been applied to simulate the ecology of a mixotrophic biofilm formed by phototrophic and heterotrophic species. For this purpose, the main factors influencing microbial interactions has been included, light as well as nutrients.

61

KINETIC MODELING OF ALCOHOL CONSUMPTION

Giuseppe Toscani

Department of Mathematics, University of Pavia (Italy) and

IMATI - National Research Council, Pavia (Italy)

[email protected]

In most countries, alcohol consumption distributions have been shown to possess universal features. Their unimodal right-skewed shape is usually modeled in terms of the Lognormal distribution, which is easy to fit, test, and modify. However, empirical distributions often deviate considerably from the Lognormal model, and both Gamma and Weibull distributions appear to better describe the survey data. In this talk we explain the appearance of these distributions by means of classical methods of kinetic theory of multi-agent systems. The microscopic variation of alcohol consumption of agents around a universal social accepted value of consumption, is built up introducing as main criterion for consumption a suitable value function in the spirit of the prospect theory of Kahneman and Twersky. The mathematical properties of the value function then determine the unique macroscopic equilibrium which results to be a generalized Gamma distribution. The modeling of the microscopic kinetic interaction allows to clarify the meaning of the various parameters characterizing the generalized Gamma equilibrium.

62

THE EXTENDED THERMODYNAMICS FOR A.C AND D.C. DYNAMIC HIGH-FIELD TRANSPORT IN GRAPHENE

Massimo Trovato



[email protected]

Using the maximum entropy principle (MEP) [1], we present a general theory to describe ac and dc high-field transport in monolayer graphene [2] within a dynamical context. In particular:

i) The connections between the conductivity effective mass and the introduction of a Lorentz factor for the system, and, more generally, the analogies between the monolayer graphene and other physical systems in which we have a saturation velocity for the charge carriers are explicitly explained.

ii) By keeping unchanged the modulus of the group velocity, we show that the external field and the scattering processes can only align or randomize its direction with respect to the applied field. Here, we prove that the alternation and the competition between these processes, together with the effects of linear band structure, can lead to the onset of negative differential mobility (NDM) for both the average velocity and for other deviatoric moments of higher order.

iii) By using the small-signal analysis, the nature and the characteristics of the collisional processes can be easily investigated. We show that the electron transport is characterized by the streaming motion regime due to the combined action of the electric field and scattering phenomena. The streaming motion is also present in correspondence of a very few collisional events and it extends to larger values of the external field than for the usual semiconductors.

In general, by using the present approach, the effects imputable to a linear band structure, the role of conductivity effective mass of carriers, and their connection with the coupling between the driving field and the dissipation phenomena are analyzed both qualitatively and quantitatively for different electron densities. We conclude that, under conditions very far from thermal equilibrium, the HD results are found to compare well with those obtained by analogous MC simulations. Consequently, the overall agreement is used to validate the theoretical approach and to provide a systematic physical insight into the microscopic dynamics. Therefore, the present HD-MEP method can be fruitfully applied to describe transport properties in graphene with the relevant following advantages: (a) to provide a closed analytical approach and a reduced computational effort with respect to other competitive numerical methods at a kinetic level; (b) to investigate and classify in a systematic way the behavior of the macroscopic moments in ac and dc dynamic conditions; (c) to distinguish the different regimes of transport by identifying, from an analysis of collisional frequencies, the dominant scattering mechanisms for a given range of electric field. References [1] I. Müller, T. Ruggeri, Rational Extended Thermodynamics: Springer Tracts in Natural Philosophy, Vol.

37, (Springer-Verlag New York) (1998). [2] M. Trovato, P. Falsaperla, L. Reggiani, Maximum-entropy principle for a.c. and d.c. dynamic high-field

transport in monolayer graphene (2019), to appear on Journal of Applied Physics.

63

UNCERTAINTY AND SENSITIVITY ANALYSIS FOR BACTERIAL INVASION IN MULTI-SPECIES BIOFILMS

Andrea Trucchia, Luigi Frunzo, Maria Rosaria Mattei, Vincenzo Luongo, Mélanie C. Rochoux

BCAM - Basque Center for Applied Mathematics (Spain)

[email protected]

In this work, we present a probabilistic analysis of a detailed one-dimensional continuum biofilm model which explicitly accounts for planktonic bacterial invasion in a multi-species biofilm. The objective of the presented research is i) to quantify and understand how the uncertainty in the new parameters of the invasion sub-model influences the biofilm model predictions and ii) to spot which parameters are the most important factors with respect to the biofilm model response. A surrogate of the biofilm model is trained using an experimental design with limited size. A comparison of different types of surrogates (generalized Polynomial Chaos expansion -gPC, Gaussian process model - GP) is performed; results show that the best performance (measured in terms of the Q_2 predictive coefficient) is retrieved using a Least-Angle Regression (LAR) gPC-type expansion, where a sparse polynomial basis is constructed to reduce the problem size and where the basis coordinates are obtained using a regularized least-square minimization. The resulting LAR gPC-expansion is found to capture the raise in complexity of the biofilm structure due to niche formation. Sobol’ sensitivity indices show the prevalence in the invasion sub-model of the maximum colonization rate of autotrophic bacteria on biofilm composition.

64

INSTABILITY, WEAK TURBULENCE AND CHAOS IN POROUS MEDIA

Peter Vadasz

Department of Mechanical Engineering,

Northern Arizona University (USA)

[email protected]

A review of the research on the instability of steady state convection in a porous layer heated from below is presented. The latter leads to chaos (weak turbulence) and the possibility of controlling this transition from steady convection to chaos is considered. The governing equations consisting of the continuity, the extended Darcy, and the energy equations subject to the assumption of local thermal equilibrium and the Boussinesq approximation are converted into a set of three nonlinear ordinary differential equations by assuming two-dimensional convection and expansion of the dependent variables into a truncated spectrum of modes. Solutions to the resulting set of equations via analytical (weak nonlinear), computational (Adomian decomposition) as well as numerical (Runge-Kutta-Verner) methods are presented and compared to each other. The analytical solution for the transition point to chaos is identical to the computational and numerical solutions in the neighborhood of a convective fixed point and deviates from the accurate computational and numerical solutions as the initial conditions deviate from the neighborhood of a convective fixed point. The control of this transition is also discussed.

65

LINEARLY DEGENERATE SYSTEMS OF PDES AND INTERACTING WAVES

Raffaele Vitolo

Department of Mathematics and Physics,

University of Salento, Lecce (Italy)

[email protected]

In this talk we will review recent results on the theory of linearly degenerate (or completely exceptional) quasilinear systems of first-order PDEs in two independent variables. We will show that a wide family of such systems is determined by the requirement that there exists a Hamiltonian formulation of a distinguished type. In the 3-component case, such systems are all integrable and are related to the Zakharov-Manakov system of 3 interacting waves. This nontrivial map yields a correspondence between solutions that will be discussed.

66

GLOBAL ANALYSIS OF MATHEMATICAL MODELS FOR NONLOCAL EPIDEMIC DISEASES

Wendi Wang

School of Mathematics and Statistics,

Southwest University (China)

[email protected]

The mathematical models of dengue fever and lyme disease are presented, which are described by nonlocal reaction-diffusion equations. The basic reproduction numbers of disease transmission are derived and are shown to be the threshold values of disease invasion. The influences of population mobility and spatial heterogeneity on disease outbreaks are also analyzed by numerical simulation.

67

THE RIEMANN PROBLEM OF RELATIVISTIC EULER EQUATIONS

Qinghua Xiao

Wuhan Institute of Physics and Mathematics,

Chinese Academy of Sciences (China)

[email protected]

We study the Riemann problem of relativistic Euler equations with Synge energy for rarefied monatomic gas and polyatomic gas. Constitutive equations of these relativistic Euler equations are related to the modified Bessel functions of the second kind. We provide detailed investigation of basic hyperbolic qualities and properties of elementary waves for the relativistic Euler equations, especially for the properties of shock waves for the relativistic Euler equations describing the rarefied monatomic gas and some polyatomic gas. Mathematical theory of the Riemann problem for these relativistic Euler equations, which is analogous to the corresponding theory of the classical Euler equations, is rigorously provided. This is a joint work with Prof. Tommaso Ruggeri and Prof. Huijiang Zhao.

68

LIST OF SPEAKERS IN ALPHABETICAL ORDER (A - L)

Arima, Takashi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 9

Barbera, Elvira . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 10

Bisi, Marzia. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 11

Brini, Francesca . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 12

Brull, Stéphane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 13

Buonomo, Bruno . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 14

Capone, Florinda . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 15

Consolo, Giancarlo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 16

D’Acunto, Berardino . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .pag. 17

Dafermos, Costantine M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 18

De Angelis, Monica . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 19

De Falco, Vittorio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 20

De Luca, Roberta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 21

Demontis, Francesco . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 22

Desvillettes, Laurent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 23

Falsaperla, Paolo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 24

Fiore, Gaetano . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 25

Frunzo, Luigi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 26

Gambino, Gaetana . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 27

Gargano, Francesco . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 28

Gentile, Maurizio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 29

Giacobbe, Andrea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 30

Giunta, Valeria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 31

Gouin, Henri . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .pag. 32

Groppi, Maria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 33

Ha, Seung-Yeal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 34

Kim, Jeongho. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 35

Liu, Tai-Ping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 36

Lombardo, Maria Carmela . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 37

Luongo, Vincenzo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 39

Mainardi, Francesco . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 40

Manganaro, Natale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 41

Maremonti, Paolo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 42

Martalò, Giorgio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 43

Mattei, Maria Rosaria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 44

Mentrelli, Andrea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 45

Mulone, Giuseppe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 46

Nastasi, Giovanni . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 47

Panaro, Daniele B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 48

Pennisi, Sebastiano . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 49

Rionero, Salvatore . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 51

Romano, Vittorio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 52

Rubino, Gianfranco . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 53

Ruggeri, Tommaso . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 54

Saccomandi, Giuseppe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 55

Sammartino, Marco . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 56

Sciacca, Michele . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 57

Sciacca, Vincenzo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 58

Sugiyama, Masaru . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 59

Taniguchi, Shigeru . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 60

Tenore, Alberto . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 61

Toscani, Giuseppe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 62

Trovato, Massimo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 63

Trucchia, Andrea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 64

Vadasz, Peter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .pag. 65

Vitolo, Raffaele . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .pag. 66

Wang, Wendi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 67

Xiao, Qinghua . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag. 68

LIST OF SPEAKERS IN ALPHABETICAL ORDER (M - Z)

WASCOM 2019

Documents

Book of Abstracts Wascom19 - Wascom 2019 – XX International … · WASCOM 2019 Monday, June 10th 08.30 - 09.00 REGISTRATION 09.00 - 09.30 Opening CHAIRMAN: TOMMASO RUGGERI 09.30