Some works involving (multi) fractalsmyrtus.uspnet.usp.br/spsas/presentations/Presentations_05_Apr/05_Food_Consumer... · ESPCA/São Paulo School of Advanced Science Advances in Molecular

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Some works involving (multi) fractals

There is a kind of self similarity attrributes (and sense learning) at different levels…

O Lineal?

O Not lineal?

O Self affinity (similarity)…

But…..is self affinity perceived by our senses

as homogeneous (or otherwise) along the

whole eating experience?

FOR INSTANCE:

O Eating pasta……

We expect the whole duration of our italian

degustation experience will be as our

senses predicted…

The first bite, the second, the third, etc will

taste to pasta, YES…”degraded and more

degraded IN the mouth and latter in our

digestive system….AND NOT……

I buy and eat pasta and…

O Second (or third, etc) bite has the texture of an apple…?!

or a nacho….?! this was obviously not expected….

THERE IS A VERY COMPLEX LEARNING PROCESS IN MANY ASPECTS OF FOOD CONSUPTION.

AND IN MANY WAYS AND WITH TIME, WE CAN PREDICT WHAT IS GOING TO BE LIKE THE NEXT EATING STAGE…

MAY MASTICATION BE A PROCESS FOR GENERATING MULTIFRACTAL

SURFACES?

ESPCA/São Paulo School of Advanced Science

Advances in Molecular Structuring of Food Materials

… watch and learn,

I’ll show you how

you can proceed

with multifractality

MULTIFRACTALITY



O Different patterns (statistically different

scale dependence) merged to form one total

structure

log ε

Fractal dimension

log N

Self-affinity

(monofractal) No self-affinity

Self-affinity

(multifractal)

Different

dependence

behaviours

MULTIFRACTALITY



O A multifractal structure can be considered

as a superposition of homogeneous

monofractal structures.

O Therefore there is not a unique value of DF

but a spectrum (distribution) of self-affinity

dimensions.

Chhabra et al., 1989

MULTIFRACTAL ANALYSIS



O Probability distribution of pixels in ε-sized boxes

ε = 20 km

N = 139 Therefore:




O




O Spectrum D(q) vs q. Multifractal sets can also be characterized

through the scaling of the qth order moments of Pi,ε

distributions

Multifractal




O The measurements of multifractals are mainly

the measurements of a statistical distribution,

which is why the results yield useful information

even if the underlying structure does not show a

self-affine behaviour.

O Thereby: multifractal analysis should be explored

as a first step in order to determine the

statistical behaviour of a pattern or figure.

Plotnick et al., 1996



Plotnick et al., 1996

Multifractal analysis- Applications

In the fields:

Astronomy and Cosmology

Atmospheric Science

Biology and Bioengineering

Chemical Reactions

Civil Engineering and Architecture

Electrical Engineering

Financial forecast

Food Science

Geology and Seismology

Histopathology

Informatics

Linguistics

Music

Pharmaceutical technology

Physics

Textile industry



OUR WORKS



STUDY OF BREAKAGE IN FOOD,

MODELLING BY IMAGE ANALYSIS AND NON-LINEAR DYNAMICS

Evangelina García Armenta

1. Division or separation of an object in different parts after applying a force or stress on it

2. Maximum point of the stress-strain curve

van den Berg et al., 2008



ε

σ

Askeland y Phulé, 2004.

Young´s modulus

E Elasticity

modulus

σ stress

ε strain

Elastic

deformation Microfracture

Breakage point

(catastrophic

failure)

Plastic

deformation

Permanent deformation



ImageJ v.1.47

Parameters: fractal dimension, fracture’s length and lacunarity



Digital image analysis

RESULTS



RESULTS



INFLUENCE OF MOISTURE CONTENT



0,5

0,7

0,9

1,1

1,3

1,5

0 1 2 3 4 5 6 7 8

Frac

tal d

ime

nsi

on

Moisture content(%)

1.01 -1.09

Breakage of fried corn chips (nachos)

INFLUENCE OF MOISTURE CONTENT



Breakage of fried corn chips (nachos)

0

10

20

30

40

50

60

70

80

2 parts 3 parts 4 parts Perforation Crack No breakage

Pe

rce

nt

of

bro

ken

ch

ips

Type of breakage

1%

7%

Moisture content



IMAGE ANALYSIS AS A TOOL FOR

QUANTITATIVELY DESCRIBING THE

SENESCENCE PROCESS IN PRE-

CUT, FRESH PAPAYA (Carica papaya L.)

Gabriela Cáez



Initial 30 min

60 min 90 min

120 min 150 min

180 min 210 min

240 min 4°C 240 min 37°C

240 min 4°C 240 min 37°C

4 ºC



Papaya verde inicial tejido interno 10X Papaya Madura Tejido interno 10X

Papaya verde Tejido interno Expuesto 10X Papaya madura Tejido interno Expuesto 10X

Figura 5. Micrografías confocal. El color verde se asocia a los compuestos tipo carbohidrato de la lámina

media y el color rojo a pigmentos que fluorecen en el rango de la clorofila.

A B

C D

Internal tissue. 10 x Internal tissue. 10 x

Internal tissue. 10 x Internal tissue. 10 x

No

exp

osit

ion

E

xpo

sit

ion

at

20

ºC

an

d 6

0%

RH

Fresh Mature

Confocal

microscopy

Green

and red

emission

spectra



1,4

1,9

2,4

2 2,2 2,4 2,6

F (α

)

α

2

2,2

2,4

2,6

-20 0 20

D (

q)

Q

Fresh papaya

Before exposition After exposition G

ree

n e

mis

sio

n

Re

d e

mis

sio

n

1,4

1,9

2,4

1,8 2,3 2,8

F (α

)

α

2

2,2

2,4

2,6

-20 0 20

D (

q)

Q

0

1

2

0 2 4

F (α

)

α

0

2

4

-20 0 20

D (

q)

Q

1

2

3

1,5 2 2,5

F (α

)

α

1,8

2

2,2

-20 0 20

D (

q)

Q



Mature papaya

Before exposition After exposition G

ree

n e

mis

sio

n

Re

d e

mis

sio

n

0

2

4

1 2 3

F (α

)

α

1,8

2

2,2

2,4

-20 0 20

D (

q)

Q

0

2

4

1 2 3

F (α

)

α

0

2

4

-20 0 20

D (

q)

Q

0

2

4

1 2 3

F (α

)

α

1,8

2

2,2

-20 0 20

D (

q)

Q

0

2

4

0 2 4

F (α

)

α

0

2

4

-20 0 20

D (

q)

Q



OTHER WORKS RELATED WITH NON-LINEAR DYNAMICS

Hydrodynamics of disintegration



a

f (x, y) = [(1.1 + 0.91 (xi cos Q + yi sen Q)), (0.91 (-xi sen Q + yi cos Q))]

Q = (-5.6) / (1+xi2+yi

2)

b

c

e d

-20

-10

0

10

20

30

40

-20 -10 0 10 20 30 40 50 60

Position in "x" axis (pixel)

Po

sit

ion

in

"y"

axis

(p

ixel)

-30

-20

-10

0

10

20

30

-20 -10 0 10 20 30 40 50 60

Position in "x" axis (pixel)

Po

sit

ion

in

"y"

axis

(p

ixel)

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

-1 -0.5 0 0.5 1 1.5 2

Position in "x" axis (mm)

Po

sit

ion

in

"y"

axis

(m

m)





O Attempting to “enter” into the black box

Processes and Fundamentals

Phenomena

Tools Interpretation

Design, equipments and processes

Operating conditions Functionality

Shelf life

Packaging materials, etc.

Beyond the

structure



BUILDING THE BRIDGE

AND BRIDGING….

STRUCTURE

PROCESSING

FUNCTION

INTEGRATED APPROACH

BEYOND THE STRUCTURE

Consequences (and

implications)

http://images.google.com/imgres?imgurl=http://www.microscopy-uk.org.uk/mag/imgoct02/foams.jpg&imgrefurl=http://www.microscopy-uk.org.uk/mag/artoct02/amgallery.html&h=375&w=500&sz=32&hl=es&start=4&um=1&tbnid=tfT_0AULYGEsTM:&tbnh=98&tbnw=130&prev=/images?q=FOAMS&svnum=10&um=1&hl=es&rls=GGLR,GGLR:2005-49,GGLR:en&sa=N

TEAM O Liliana Alamilla

O Gustavo Barbosa-Cánovas

O José Miguel Aguilera

O Ximena Quintanilla

O DaríoTétez

O Domingo Mery

O Jorge Welti

O Jorge Chanona

O Ebner Azuara

O Ignacio Beristain

O Georgina Calderón

O Reynold Farrera

O Humberto Hernández

O Antonio Jiménez

O Cristian Jiménez

O Cynthia Cano

O Amor Monroy

O Miriam Fabela

O Itzel García-Luna

O Josefina Porras

O Evangelina García Armenta

O Brenda Camacho

O Gabriela Cáez

O Fabiola Guzmán

O Verónica Freyre

O Andrea Lezama

O Rosalva Mora

O Alicia Ortiz

O Antonio Pérez-Nieto

O Jaime Vernon

O Enrique Flores

O Luz Alicia Pascual

O Carolina Gumeta

O Sofía Meraz

O Israel Arzate

O Rubí Viveros

O Raúl y Jaime

THANK YOU!

[email protected]



Documents

Some works involving (multi) fractalsmyrtus.uspnet.usp.br/spsas/presentations/Presentations_05_Apr/05_Food_Consumer... · ESPCA/São Paulo School of Advanced Science Advances in Molecular