Simulation of - ii.uib.nomatthey/ttp5/ttp_protomol_presentation4.pdf · system of positiv e charged...

MD

Sim

ulationofC

oulomb

Crystals

Thierry

Matthey,para//ab,U

NIF

OB

,University

ofBergen

c�

Thierry

Matthey,F

evikM

etting,August30,2002.

MD

Sim

ulationofC

oulomb

Crystals

1/??

What

areC

oulomb

crystals?�

Asystem

ofpositivecharged

ions(1-����

)trapped

bya

magnetic

field.

++

+

�

Acandidate

forQ

uantumP

rocessors.

�

Apossibility

tostudy

stronglycoupled

systems

with

onlypositive

charges.

c�

Thierry

Matthey,F

evikM

etting,August30,2002.

MD

Sim

ulationofC

oulomb

Crystals

2/??

Experim

ents

Left:M

onocomponent,sphere.

Right:

Bicom

ponent,string,Ca ���

(Blue),M

g ��

(Red).

c�

Thierry

Matthey,F

evikM

etting,August30,2002.

MD

Sim

ulationofC

oulomb

Crystals

3/??

Physicalm

odel���

Quantum

Mechanics

and ����

signifi-cant.

��� K

�

ClassicalA

pproximation�

Classical

Molecular

Dynam

ics(N

ewton’s

equationofm

otion)

c�

Thierry

Matthey,F

evikM

etting,August30,2002.

MD

Sim

ulationofC

oulomb

Crystals

4/??

Physicalm

odel(cont.)

Q2

Q1

Rm

,q

�

Coul �

����� � �����

� �

Trap ��

!

.

�

Coul ��

Trap�

!�#"$% ������'& ��� ()* �+.

NB

:Independentof ��

.

c�

Thierry

Matthey,F

evikM

etting,August30,2002.

MD

Sim

ulationofC

oulomb

Crystals

5/??

Research

�Investigation

ofthestructure

anddynam

icsofso-

calledions

trappedin

aelectric

andm

agneticfield

(PaulTrap)

with

1- ��,�

ions.

�

Radial

distributionand

shellstructure

(ornot)

ofm

ono-and

bicomponent(C

a ���

andA �-�

)crystals.

�

Dynam

icalfeaturesoffinite

temperature

(�� K).

�

Future

work:

Fulltreatm

entofquantaleffects.

c�

Thierry

Matthey,F

evikM

etting,August30,2002.

MD

Sim

ulationofC

oulomb

Crystals

6/??

Molecular

Dynam

ics(M

D)

�. /

/ 0 12.3 04 � 1�.3 04657 // 0

12.3 04

(1)

// 07 �83 5

equlibrium4

(2)

1�. � 59.;:

(3)

:��<=>�?@

.BA�CDFE. G

. GDHHHHH HHHHH 12.D HHHHH HHHHH I

�J ?@. A� �. 12 .

(4)

c�

Thierry

Matthey,F

evikM

etting,August30,2002.

MD

Sim

ulationofC

oulomb

Crystals

7/??

Molecular

Dynam

ics(M

D)

(cont.)

New

ton’sequation

ofmotion

solvedby

thenum

ericalLeap-Frog

method

with

Nose-H

oovertherm

ostat:

KML� ���KMLON �� 5

P0� "$$% � L5

7 LKML N �� ())*

(5)/7 L� ��

/ 0

�Q "

$$$% ?@. A� �.3 K L� ��.4 5

R SJTU ()))*

(6)

2 L� ��2 LIP0KVL� ��

(7)

7 L� ��7 LIP0 /7 L� ��

/ 0W

(8)

c�

Thierry

Matthey,F

evikM

etting,August30,2002.

MD

Sim

ulationofC

oulomb

Crystals

8/??

PR

OT

OM

OL

–a

moleculardynam

icsfram

ework

�A

nobject-oriented

component

basedfram

ework

form

oleculardynam

icssim

ulations.

�

Designed

forhigh

flexibility,easyextendibility

andm

aintenance,andhigh

performance

demands,in-

cludingparallelization.

�

Supportofm

ultipletim

e-steppingintegration.

�

Fastelectrostatic

forceevaluation

algorithms

likeplain

Ew

ald(X3 S

+�4 ),P

article-Mesh-E

wald

(X3 SYZ[ S4 ),and

Multigrid

summ

ation(X3 S

4 ).

c�

Thierry

Matthey,F

evikM

etting,August30,2002.

MD

Sim

ulationofC

oulomb

Crystals

9/??

PR

OT

OM

OL

–a

moleculardynam

icsfram

ework

(cont.)

libparallel, libforceslibbase, libtopology

libintegrators

libfrontendC

omponent

Fram

ework

Class Library

Middle Layer

Front−

end

Back−

end

c�

Thierry

Matthey,F

evikM

etting,August30,2002.

MD

Sim

ulationofC

oulomb

Crystals

10/??

Fronthem

isphereofthe

outershell

Left:S

ystemofa

20,288C

a

\]^ .R

ight:S

ystemofa

10,144C

a

\]^ _a`b

and10,144

A c\d^ _aebsystem

.

c�

Thierry

Matthey,F

evikM

etting,August30,2002.

MD

Sim

ulationofC

oulomb

Crystals

11/??

Radialdistrib

utionofm

ono-andbicom

ponentcrystals

050

100150

200250

0 1 2 3 4 5 6

Radius (µm

)

Density

0100

200300

4000

0.5 1

1.5 2

2.5 3

Radius (µm

)

Density

Left:20,288

Ca

\]^

(Blue),

and10,144

Ca

\]^

and10,144

A c\d^

(Green),

and

20,288A c\d^

(Red)

ions.R

ight:100,000

Ca

\]^(B

lue),and

50,000C

a

\]^

and

50,000A c\d^

(Green)

ions.T

heinner

parthasbeen

smoothed.

c�

Thierry

Matthey,F

evikM

etting,August30,2002.

MD

Sim

ulationofC

oulomb

Crystals

12/??

Conclusions

�

Sim

ulationsresult

inclear

outershellstructure

inlarge

bicomponent

ioncrystals

with

identicalGf �

ration.

�

Each

component

haveslightly

differentshellradii

resultingin

aninteresting

“doublestructure”ofeach

shell.

c�

Thierry

Matthey,F

evikM

etting,August30,2002.

MD

Sim

ulationofC

oulomb

Crystals

13/??

Partners

�

JanP

etterH

ansen,University

ofBergen.

�

MichaelD

rewsen,T

heion

Trapgroup,Institute

ofP

hysicsand

Astronom

y,University

ofAarhus.

�

PR

OT

OM

OL

isa

collaborationw

orkw

ithJesus

A.

Izaguirre,CS

E,U

niversityofN

otreD

ame,U

SA

.

c�

Thierry

Matthey,F

evikM

etting,August30,2002.

MD

Sim

ulationofC

oulomb

Crystals

14/??