transfer fas uas saint-petersburg state university computational physics introduction physical basis...

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SAINT-PETERSBURG STATE UNIVERSITY COMPUTATIONAL PHYSICS

Introduction

Physical basis

Molecular dynamics

Temperature and thermostatNumerical integration. Verlet algorithmAnalyze dataAbstract view of MD algorithms

System simulation

Full atomic systemUnited atoms system

ProblemsIdeaAlgorithm

Conclusion


MedicinePharmaceutics

TechnologyNematics

Visualization of micro structure


Molecular dynamics is a standard computational technique used in condensed matter physics, material science, chemistry, and other fields, consisting of following the temporal evolution of a

system of N particles, interacting with each other by a certain law.

F = ma Newton’s law (1)

Rewrite (1) in a more detail form:

Newton’s law (2)

i – number of atom, mi – atom mass, ri – radius-vector of atom,

Fi – resultant force


Resultant force is a sum of two components:

(3)

U – potential energy of the system, - force determined by interactions with molecules of surroundings.

Interaction between not connected with each other atoms can be described with the use of Lennard-Jones potential:

(4)

, A, B - constants


Thermostat – algorithm which takes into account energy exchange effects and keeps necessary temperature.

Collision thermostat Berendsen thermostat

Reciprocatingfriction

The deviation oftemperature. Landau-Teller

equation.

The kinetic

energy change


1

2

3

New coordinates of atoms

Forces

Velocities of atoms

Integration step = 1 – 1.5 fs


Visualization

Correlation functions(statistical mechanics)

reaction probabilities(chemistry)


Initialize Positions/Velocitiestemperature/collision conditions/structure

Calculate and Sum Forces for Each Atom

Apply Thermostat/Volume Change

Move Atoms Ahead One Step ( sec)

(Verlet Algorithm)

Analyze Data

12101510


Theoretical problem definition! Hypothesis

Mathematical problem definition! System of equations

Numerical problem definition! Numerical method


Consider the transfer using two types of molecules: Heptane and Benzene.

Heptane ( ) Benzene ( )167HС 66HС

To minimize the time of calculation keeping a realistic aspect of modeling


" + " calculation time is less " – " system is more abstract


Straight removing/appearance of all hydrogens will lead the system to have a big jump of energy and temperature so it will be needed much time to relax the system

The appeared hydrogens must have there one velocities, but the range of them is unknown the values must be optimal in respect to relaxation time

It is incomprehensible how to change interaction potentials between atoms


Gradual appearance/disappearance of atoms of hydrogens

No big jump of energy and temperature, a smooth transition dependent on a step

Velocities of appeared hydrogens may be equal to velocities of carbons because the distance between them is very small

Values of interaction potentials will go up/ go down according to an increase/decrease of bonds between atoms


Modeling Full atomic system

To shorten

the bond on part Full atomic systemwith other

characteristics

Modeling United atoms

system

Full atomic systemwith other

characteristics

Bonds moving-outon part

N

1

N

1

N times

N times


Theoretical problem definition! Hypothesis

Mathematical problem definition! System of equations

Numerical problem definition! Numerical method


C

C

C

C

C

C

C

H H H H H H

HH

H H H H H HH

H

C C

C C

C C

H H

H H

H H


C'

C'

C'

C'

C'

C'

C'

C' C'

C' C'

C' C'

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