You are a scientist working at Los Alamos National Labs during WWII and your job is to
Question:
You are a scientist working at Los Alamos National Labs during WWII and your job is to study the stability of an atomic material consisting of Argon atoms. You will initialize a uniform 2D lattice of 25 Argon atoms and plot it using the built in Matlab scatter function (Part I), compute the potential energy and forces of the system using the supplied Matlab function vanderWaals (Part II), move each atom 5000 times using an algorithm called molecular dynamics (Part III) and finally summarize the energetic and structural results for your boss Edward Teller (Part IV).
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% Author: MJ Schnieders
% Date: April 19th, 2013
% Function: vanDerWaalsForces.m
% Purpose: Compute the van der Waals energy and forces for Argon atoms.
% Input:
% x - a vector of x-coordinates (Angstroms)
% y - a vector of y-coordinates (Angstroms)
% Output:
% energy - the potential energy (Kcal/mole)
% fx - the x-component of the force (Kcal/mole/Angstrom)
% fy - the y-component of the force (Kcal/mole/Angstrom)
%
function [energy, fx, fy] = vanderWaals(x, y)
eps4 = 0.2824 * 4.0;
rmin = 3.361;
rmin6 = rmin^6;
rmin12 = rmin^12;
nAtoms = length(x);
% Zero out energy.
energy = 0;
% Zero out forces.
fx = zeros(1,nAtoms);
fy = zeros(1,nAtoms);
% Loop over atoms to accumulate energy and forces.
for i=1:nAtoms
xi = x(i);
yi = y(i);
% Loop over atoms whose index is greater than i.
for j=i+1:nAtoms
% Compute separation distance (Angstroms).
dx = xi - x(j);
dy = yi - y(j);
r = sqrt(dx*dx + dy*dy);
% Compute interaction energy.
ir = 1.0/r;
ir6 = ir^6;
ir12 = ir6*ir6;
e = eps4*(rmin12*ir12 - rmin6*ir6);
energy = energy + e;
% Compute equal and opposite forces, includeing chain rule term.
ir7 = ir6*ir;
ir13 = ir12*ir;
de = eps4*(6.0*rmin6*ir7 - 12.0*rmin12*ir13);
dxr = de*dx/r;
dyr = de*dy/r;
fx(i) = fx(i) - dxr;
fy(i) = fy(i) - dyr;
fx(j) = fx(j) + dxr;
fy(j) = fy(j) + dyr;
end
end
end
Expert Answer:
