77.. Simulating simple fluidsSimulating simple fluidsphys.ubbcluj.ro/~tbeu/MD/C7.pdf · Allen, M....

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Titus BeuUniversity “Babes-Bolyai”Department of Theoretical and Computational PhysicsCluj-Napoca, Romania

7. 7. Simulating simple fluidsSimulating simple fluids

Titus Beu 2011

Bibliography

Thermodynamic properties

Periodic boundary conditions

Initial configuration

Thermostats

Application

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Rapaport, D.C., The Art of Molecular Dynamics Simulation. Second Edition (Cambridge University Press, 2004).

Leach, A. R., Molecular Modelling. Principles and applications, Second edition (Prentice Hall, 2001) .

Frenkel , D., Smit, B., Understanding Molecular Simulation. From Algorithms to Applications (Academic Press, 2002).

Allen, M. P., Tildesley, D. J., Computer Simulation of Liquids (Clarendon Press, Oxford, 1991).

Sadus, R.J., Molecular Simulation of Fluids. Applications to Physical Systems, Second Edition (Elsevier, 1999).

Titus Beu 2011

System temperature – equipartition theorem → each degree of freedom kBT/2:

Pressure – virial formula:

For a pair potential:

Replacing T:

Etot = Ekin + Epot should be conserved throughout a simulation

T and P fluctuate – should be averaged over several time steps

B kin2

3

k ET

N=

B

1

1

3

N

i i

i

PV Nk T=

= + ⋅∑r F

B

1

3

N

ij ij

i j

PV Nk T<

= + ⋅∑r f

kin2

3

N

ij ij

i j

P EN

ρ

<

= + ⋅∑r f

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Macroscopic systems: N = 1021 −1023 particles (Avogadro’s number)

Typical bulk systems: N = 1021 → N2/3 = 1014 (1 in 107) surface particles

Tractable simulations: N = 106 → N2/3 = 104 (1 in 102) surface particles

Behaviour of "small" systems is dominated by surface effects

Minimizing surface effects for bulk systems:

Finite simulation box + Periodic Boundary Conditions (PBC)

The system is bounded, but free of physical walls

Enables simulations using a relatively small number of representative particleswhich experience forces as if they were in bulk fluid

The simplest simulation box – cubic [−L, L] × [−L, L] × [−L, L]

Limitation of PBC caused by the suppression of fluctuations with λ > L:

Not possible to simulate liquid-gas critical points – fluctuations are macroscopic

First order transitions appear to be of higher order

Titus Beu 2011

Simulation box

Defined to contain a manageable number of particles

Eliminate surface effects – space-filling array of identical copies of the simulation box

Real and “image” particles move synchronously

Aspects to be tackled:

Correcting the coordinates of the particles leaving the simulation box to conserve their total number

Reducing the no. of interactions(theoretically infinite) – minimum image criterion

Simulation box

−L L

−L

L

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Correcting particle coordinates

Should a particle leave the box, an image particle enters through the opposite boundary

The entering particle is identified with the exiting one – replaces it with corrected coordinates

Correction of position:

if x < −L then x’ = x + 2L

if x > +L then x’ = x − 2L

L – half-size of simulation box

Equivalently:

If |x| > L then x’ = x − sign(L,x)

Similar conditions along y and z

Simulation box

−L L

−L

L

Titus Beu 2011

Reducing the number of interactions

A short-range potential can be

characterized by a cut-off distance Rcut

For interatomic distances rij > Rcut

interactions can be neglected

For a box half-size L > Rcut any particle ilies within Rcut with at most one of all periodic images of particle j

Minimum image criterion – for a given particle interactions are to be considered only with the closest instances of all other particles

Correction of interatomic distance:

if xij < −L then xij’ = xij + 2L

if xij > +L then xij’ = xij − 2L

Tremendous CPU economy

−L L > Rcut

−L

L

Rcut

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//===========================================================================

void ForcesL(int iopRun, float epsilon, float sigma, float rcut, float Lbox,float x[], float y[], float z[],

float Fx[], float Fy[], float Fz[], int natm,float &Epot, float &virial)

//---------------------------------------------------------------------------// Returns forces for the Lennard-Jones 12-6 potential

// Energies in eV, forces in eV/Angs, distances in Angs{

float factE, factF, rcut2, sigma2;float dx, dy, dz, sr2, sr6, fpr, fxi, fyi, fzi, r2, Lbox2;

int iatm, jatm;

if (iopRun == 2) {Lbox2 = 2.e0 * Lbox; // total box size

rcut = min(rcut,Lbox);}

factE = 4.e0 * epsilon; factF = 48.e0 * epsilon;sigma2 = sigma * sigma; rcut2 = rcut * rcut;

Epot = 0.e0;

for (iatm=1; iatm<=natm; iatm++) Fx[iatm] = Fy[iatm] = Fz[iatm] = 0.e0;

//===========================================================================

void ForcesL(int iopRun, float epsilon, float sigma, float rcut, float Lbox,float x[], float y[], float z[],


//---------------------------------------------------------------------------// Returns forces for the Lennard-Jones 12-6 potential


float factE, factF, rcut2, sigma2;float dx, dy, dz, sr2, sr6, fpr, fxi, fyi, fzi, r2, Lbox2;

int iatm, jatm;



factE = 4.e0 * epsilon; factF = 48.e0 * epsilon;sigma2 = sigma * sigma; rcut2 = rcut * rcut;

Epot = 0.e0;


Titus Beu 2011

for (iatm=1; iatm<=natm-1; iatm++) {

for (jatm=iatm+1; jatm<=natm; jatm++) {dx = x[iatm] - x[jatm];

dy = y[iatm] - y[jatm];dz = z[iatm] - z[jatm];

if (iopRun == 2) { // minimum image criterion

if (dx > Lbox) dx -= Lbox2; else if (dx < -Lbox) dx += Lbox2;if (dy > Lbox) dy -= Lbox2; else if (dy < -Lbox) dy += Lbox2;

if (dz > Lbox) dz -= Lbox2; else if (dz < -Lbox) dz += Lbox2;}

r2 = dx*dx + dy*dy + dz*dz;if (r2 < rcut2) {

sr2 = sigma2 / r2;sr6 = sr2 * sr2 * sr2;

fpr = factF * sr6 * (sr6 - 0.5e0) / r2; // f/r

fxi = fpr * dx;fyi = fpr * dy;

fzi = fpr * dz;Fx[iatm] += fxi; Fx[jatm] -= fxi;

Fy[iatm] += fyi; Fy[jatm] -= fyi;Fz[iatm] += fzi; Fz[jatm] -= fzi;

Epot += factE * sr6 * (sr6 - 1.e0);

virial += fpr * r2;}

}}

if (iopRun == 2) { Epot /= natm; virial /= natm; }}







r2 = dx*dx + dy*dy + dz*dz;if (r2 < rcut2) {

sr2 = sigma2 / r2;sr6 = sr2 * sr2 * sr2;

fpr = factF * sr6 * (sr6 - 0.5e0) / r2; // f/r

fxi = fpr * dx;fyi = fpr * dy;

fzi = fpr * dz;Fx[iatm] += fxi; Fx[jatm] -= fxi;

Fy[iatm] += fyi; Fy[jatm] -= fyi;Fz[iatm] += fzi; Fz[jatm] -= fzi;

Epot += factE * sr6 * (sr6 - 1.e0);

virial += fpr * r2;}

}}


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//===========================================================================

void ForcesB(int iopRun, float kfor, float req, float rcut, float Lbox,float x[], float y[], float z[],


//---------------------------------------------------------------------------// Returns harmonic forces for bonded interactions


float factE, factF, Ecut;float dr, dx, dy, dz, fpr, fxi, fyi, fzi, r, Lbox2;

int iatm, jatm;



factE = 0.5e0 * kfor;factF = -kfor;

dr = rcut - req;Ecut = factE * dr * dr; // E(rcut)

Epot = 0.e0;


//===========================================================================

void ForcesB(int iopRun, float kfor, float req, float rcut, float Lbox,float x[], float y[], float z[],


//---------------------------------------------------------------------------// Returns harmonic forces for bonded interactions


float factE, factF, Ecut;float dr, dx, dy, dz, fpr, fxi, fyi, fzi, r, Lbox2;

int iatm, jatm;



factE = 0.5e0 * kfor;factF = -kfor;

dr = rcut - req;Ecut = factE * dr * dr; // E(rcut)

Epot = 0.e0;


Titus Beu 2011







r = sqrt(dx*dx + dy*dy + dz*dz);

if (r <= rcut) {dr = r - req;

fpr = factF * dr / r; // f/rfxi = fpr * dx;

fyi = fpr * dy;fzi = fpr * dz;

Fx[iatm] += fxi; Fx[jatm] -= fxi;Fy[iatm] += fyi; Fy[jatm] -= fyi;

Fz[iatm] += fzi; Fz[jatm] -= fzi;

Epot += factE * dr * dr - Ecut;virial += factF * dr * r;

}}

}








r = sqrt(dx*dx + dy*dy + dz*dz);

if (r <= rcut) {dr = r - req;

fpr = factF * dr / r; // f/rfxi = fpr * dx;

fyi = fpr * dy;fzi = fpr * dz;

Fx[iatm] += fxi; Fx[jatm] -= fxi;Fy[iatm] += fyi; Fy[jatm] -= fyi;

Fz[iatm] += fzi; Fz[jatm] -= fzi;

Epot += factE * dr * dr - Ecut;virial += factF * dr * r;

}}

}


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//===========================================================================

void Verlet(int iopRun, float amass, float fpar, float rpar, float rcut,float Lbox, float dt,

float x[], float y[], float z[],float vx[], float vy[], float vz[],

float ax[], float ay[], float az[], int natm,float &Ekin, float &Epot, float &virial, int fopt)

//---------------------------------------------------------------------------// x[Angs], v[Angs/psec], a[Angs/psec*psec], F[eV/Angs], E[eV]

{float dt2;

int iatm;

dt2 = 0.5e0 * dt;for (iatm=1; iatm<=natm; iatm++) {

vx[iatm] += ax[iatm] * dt2; // v(t+dt/2)vy[iatm] += ay[iatm] * dt2;

vz[iatm] += az[iatm] * dt2;x[iatm] += vx[iatm] * dt; // r(t+dt)

y[iatm] += vy[iatm] * dt;z[iatm] += vz[iatm] * dt;

}

switch(fopt) { // F(t+dt)case 0:

ForcesL(iopRun,fpar,rpar,rcut,Lbox,x,y,z,ax,ay,az,natm,Epot,virial);break;

case 1:ForcesB(iopRun,fpar,rpar,rcut,Lbox,x,y,z,ax,ay,az,natm,Epot,virial);

}

//===========================================================================

void Verlet(int iopRun, float amass, float fpar, float rpar, float rcut,float Lbox, float dt,


float ax[], float ay[], float az[], int natm,float &Ekin, float &Epot, float &virial, int fopt)

//---------------------------------------------------------------------------// x[Angs], v[Angs/psec], a[Angs/psec*psec], F[eV/Angs], E[eV]

{float dt2;

int iatm;

dt2 = 0.5e0 * dt;for (iatm=1; iatm<=natm; iatm++) {

vx[iatm] += ax[iatm] * dt2; // v(t+dt/2)vy[iatm] += ay[iatm] * dt2;

vz[iatm] += az[iatm] * dt2;x[iatm] += vx[iatm] * dt; // r(t+dt)

y[iatm] += vy[iatm] * dt;z[iatm] += vz[iatm] * dt;

}

switch(fopt) { // F(t+dt)case 0:

ForcesL(iopRun,fpar,rpar,rcut,Lbox,x,y,z,ax,ay,az,natm,Epot,virial);break;

case 1:ForcesB(iopRun,fpar,rpar,rcut,Lbox,x,y,z,ax,ay,az,natm,Epot,virial);

}

Titus Beu 2011

Ekin = 0.e0;

for (iatm=1; iatm<=natm; iatm++) {ax[iatm] /= amass; // a(t+dt)

ay[iatm] /= amass;az[iatm] /= amass;

vx[iatm] += ax[iatm] * dt2; // v(t+dt)vy[iatm] += ay[iatm] * dt2;

vz[iatm] += az[iatm] * dt2;Ekin += vx[iatm]*vx[iatm] + vy[iatm]*vy[iatm] + vz[iatm]*vz[iatm];

}Ekin *= 0.5e0 * amass;

if (iopRun == 2) Ekin /= natm;

}

Ekin = 0.e0;

for (iatm=1; iatm<=natm; iatm++) {ax[iatm] /= amass; // a(t+dt)

ay[iatm] /= amass;az[iatm] /= amass;

vx[iatm] += ax[iatm] * dt2; // v(t+dt)vy[iatm] += ay[iatm] * dt2;

vz[iatm] += az[iatm] * dt2;Ekin += vx[iatm]*vx[iatm] + vy[iatm]*vy[iatm] + vz[iatm]*vz[iatm];

}Ekin *= 0.5e0 * amass;

if (iopRun == 2) Ekin /= natm;

}

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//===========================================================================

void BoundCond0(float Lbox, float x[], float y[], float z[], int natm)//---------------------------------------------------------------------------

// Adjusts the atomic coordinates for periodic boundary conditions//---------------------------------------------------------------------------

{float Lbox2;

int iatm;

Lbox2 = 2.e0 * Lbox; // total box sizefor (iatm=1; iatm<=natm; iatm++) {

if (x[iatm] > Lbox) x[iatm] -= Lbox2; elseif (x[iatm] < -Lbox) x[iatm] += Lbox2;

if (y[iatm] > Lbox) y[iatm] -= Lbox2; elseif (y[iatm] < -Lbox) y[iatm] += Lbox2;

if (z[iatm] > Lbox) z[iatm] -= Lbox2; elseif (z[iatm] < -Lbox) z[iatm] += Lbox2;

}}

//===========================================================================

void BoundCond0(float Lbox, float x[], float y[], float z[], int natm)//---------------------------------------------------------------------------

// Adjusts the atomic coordinates for periodic boundary conditions//---------------------------------------------------------------------------

{float Lbox2;

int iatm;

Lbox2 = 2.e0 * Lbox; // total box sizefor (iatm=1; iatm<=natm; iatm++) {

if (x[iatm] > Lbox) x[iatm] -= Lbox2; elseif (x[iatm] < -Lbox) x[iatm] += Lbox2;

if (y[iatm] > Lbox) y[iatm] -= Lbox2; elseif (y[iatm] < -Lbox) y[iatm] += Lbox2;

if (z[iatm] > Lbox) z[iatm] -= Lbox2; elseif (z[iatm] < -Lbox) z[iatm] += Lbox2;

}}

Titus Beu 2011

//===========================================================================

void BoundCond(float Lbox, float x[], float y[], float z[], float xPBC[], float yPBC[], float zPBC[], int natm)

//---------------------------------------------------------------------------// Adjusts the atomic coordinates for periodic boundary conditions.

// Stores the total PBC corrections in xPBC[iatm], yPBC[iatm] and zPBC[iatm]// to be used in computing diffusion coefficients.

//---------------------------------------------------------------------------{

float Lbox2;int iatm;

Lbox2 = 2.e0 * Lbox; // total box size

for (iatm=1; iatm<=natm; iatm++) {if (x[iatm] > Lbox) { x[iatm] -= Lbox2; xPBC[iatm] -= Lbox2; } else

if (x[iatm] < -Lbox) { x[iatm] += Lbox2; xPBC[iatm] += Lbox2; }if (y[iatm] > Lbox) { y[iatm] -= Lbox2; yPBC[iatm] -= Lbox2; } else

if (y[iatm] < -Lbox) { y[iatm] += Lbox2; yPBC[iatm] += Lbox2; }if (z[iatm] > Lbox) { z[iatm] -= Lbox2; zPBC[iatm] -= Lbox2; } else

if (z[iatm] < -Lbox) { z[iatm] += Lbox2; zPBC[iatm] += Lbox2; }}

}

//===========================================================================

void BoundCond(float Lbox, float x[], float y[], float z[], float xPBC[], float yPBC[], float zPBC[], int natm)

//---------------------------------------------------------------------------// Adjusts the atomic coordinates for periodic boundary conditions.

// Stores the total PBC corrections in xPBC[iatm], yPBC[iatm] and zPBC[iatm]// to be used in computing diffusion coefficients.

//---------------------------------------------------------------------------{

float Lbox2;int iatm;

Lbox2 = 2.e0 * Lbox; // total box size

for (iatm=1; iatm<=natm; iatm++) {if (x[iatm] > Lbox) { x[iatm] -= Lbox2; xPBC[iatm] -= Lbox2; } else

if (x[iatm] < -Lbox) { x[iatm] += Lbox2; xPBC[iatm] += Lbox2; }if (y[iatm] > Lbox) { y[iatm] -= Lbox2; yPBC[iatm] -= Lbox2; } else

if (y[iatm] < -Lbox) { y[iatm] += Lbox2; yPBC[iatm] += Lbox2; }if (z[iatm] > Lbox) { z[iatm] -= Lbox2; zPBC[iatm] -= Lbox2; } else

if (z[iatm] < -Lbox) { z[iatm] += Lbox2; zPBC[iatm] += Lbox2; }}

}

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Initial configuration in NVE and NVT simulations needs to:

be homogeneous (not necessarily random)

satisfy a given density

Simple choice – regular arrangement on rectangular mesh – density easy to control

Volume of simulation box for N particles of mass m and density ρ: V = Nm/ρ

Half-size of cubic box centred at the origin: L = V1/3/2

N = n1/3 particles → cubic grid with n equidistant nodes in each direction (h = 2L/n):

xi = −L + (i − 1/2)h, i = 1,n

yj = −L + (j − 1/2)h, j = 1,n

zk = −L + (k − 1/2)h, k = 1,n

Each particle can be assigned a randomly oriented velocity of equal absolute value:

B3v k T m=

Titus Beu 2011

//===========================================================================

void InitFluid(int iopInit, char aname[2], float amass,float dens, float Temp, float &Lbox,


float ax[], float ay[], float az[], int natm)//---------------------------------------------------------------------------

// Arranges atoms on a cubic grid (natm**(1/3) atoms along each direction)// and assigns them randomly oriented velocities corresponding to Temp.

// Simulation box: [-Lbox,Lbox] x [-Lbox,Lbox] x [-Lbox,Lbox]//---------------------------------------------------------------------------

{float Ekin, h, Vbox, xi, yj, zk;

int i, iatm, j, k, ngrid;

ngrid = Nint(pow(natm,(1.e0/3.e0))); // total no. of atoms must be a cubeif (Nint(pow(ngrid,3)) != natm) {

printf("InitFluid: pow(ngrid,3) != natm\n");getch(); exit(1);

}

Vbox = natm * amass / dens; // simulation box volumeLbox = 0.5e0 * pow(Vbox,(1.e0/3.e0)); // simulation box half-size

//===========================================================================

void InitFluid(int iopInit, char aname[2], float amass,float dens, float Temp, float &Lbox,


float ax[], float ay[], float az[], int natm)//---------------------------------------------------------------------------

// Arranges atoms on a cubic grid (natm**(1/3) atoms along each direction)// and assigns them randomly oriented velocities corresponding to Temp.

// Simulation box: [-Lbox,Lbox] x [-Lbox,Lbox] x [-Lbox,Lbox]//---------------------------------------------------------------------------

{float Ekin, h, Vbox, xi, yj, zk;

int i, iatm, j, k, ngrid;

ngrid = Nint(pow(natm,(1.e0/3.e0))); // total no. of atoms must be a cubeif (Nint(pow(ngrid,3)) != natm) {

printf("InitFluid: pow(ngrid,3) != natm\n");getch(); exit(1);

}

Vbox = natm * amass / dens; // simulation box volumeLbox = 0.5e0 * pow(Vbox,(1.e0/3.e0)); // simulation box half-size

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h = 2.e0 * Lbox / ngrid;

iatm = 0;for (i=1; i<=ngrid; i++) {

xi = -Lbox + (i - 0.5) * h;for (j=1; j<=ngrid; j++) {

yj = -Lbox + (j - 0.5) * h;for (k=1; k<=ngrid; k++) {

zk = -Lbox + (k - 0.5) * h;iatm = iatm + 1;

x[iatm] = xi; y[iatm] = yj; z[iatm] = zk;}

}}

Ekin = 1.5e0 * natm * Temp;

Heat(amass,vx,vy,vz,natm,Ekin);for (iatm=1; iatm<=natm; iatm++) ax[iatm] = ay[iatm] = az[iatm] = 0.e0;

}

h = 2.e0 * Lbox / ngrid;

iatm = 0;for (i=1; i<=ngrid; i++) {

xi = -Lbox + (i - 0.5) * h;for (j=1; j<=ngrid; j++) {

yj = -Lbox + (j - 0.5) * h;for (k=1; k<=ngrid; k++) {

zk = -Lbox + (k - 0.5) * h;iatm = iatm + 1;

x[iatm] = xi; y[iatm] = yj; z[iatm] = zk;}

}}

Ekin = 1.5e0 * natm * Temp;

Heat(amass,vx,vy,vz,natm,Ekin);for (iatm=1; iatm<=natm; iatm++) ax[iatm] = ay[iatm] = az[iatm] = 0.e0;

}

Titus Beu 2011

Microcanonical (NVE) ensemble does not correspond to the conditions under which most experiments are carried out

Canonical NVT ensemble – system in contact with a heat bath (T0 = const)

Advantage: avoid energy drifts caused by the accumulation of numerical errors

Simple velocity scaling (T0 – desired temperature):

Berendsen thermostat (τ – coupling constant):

2

kin

B

0 kin

1

3

,

i

i

i i

T mvNk

T T v vλ λ

=

′= =

∑

( )0

0

kin

1

1 1

dTT T

dt

Tt

T

τ

δλ

τ

= −

= + −

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//===========================================================================

void Thermostat(float vx[], float vy[], float vz[], int natm,float Temp, float tau, float dt, float &Ekin)

//---------------------------------------------------------------------------// Rescales the velocities and total kinetic energy according to the

// Berendsen thermostat{

float f, Tkin;int iatm;

Tkin = Ekin/1.5e0;

f = sqrt(1.e0 + (dt/tau)*(Temp/Tkin - 1.e0)); // scaling factorfor (iatm=1; iatm<=natm; iatm++) {

vx[iatm] *= f;vy[iatm] *= f;

vz[iatm] *= f;}

Ekin *= f*f;}

//===========================================================================

void Thermostat(float vx[], float vy[], float vz[], int natm,float Temp, float tau, float dt, float &Ekin)

//---------------------------------------------------------------------------// Rescales the velocities and total kinetic energy according to the

// Berendsen thermostat{

float f, Tkin;int iatm;

Tkin = Ekin/1.5e0;

f = sqrt(1.e0 + (dt/tau)*(Temp/Tkin - 1.e0)); // scaling factorfor (iatm=1; iatm<=natm; iatm++) {

vx[iatm] *= f;vy[iatm] *= f;

vz[iatm] *= f;}

Ekin *= f*f;}

Titus Beu 2011

System in contact with a heat bath (T = const)

Gauss’s principle of least constraint: for the constrained motion

The motion is no longer Newtonian

Constrained equations of motion of the molecules:

Lagrange multipliers:

2( / ) mini i i i

i

m m− =∑ a F

Newton/ ,i i i i i i i

m α β= + = +a F v q q q��

2 2

, ,,

,i i i ii i

i i i x i xi i xm I

α βω

⋅ ⋅= − = −∑ ∑∑ ∑

v F ω M

v

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//---------------------------------------------------------------------------

//----------------------------------- MD ------------------------------------//---------------------------------------------------------------------------

#include <winbgim.h>#include "Memalloc.h"

#include "Graphlib.h"#include "Random.h"

#include "Utils.h"#include "Units.h"

#include "Rescal.h"#include "Inout.h"

#include "DataAtom.h"#include "InitConfig.h"

#include "Forces.h"#include "Propag.h"

#include "BoundCond.h"#include "Measure.h"

#include "Spectrum.h"#include "PlotCfg.h"

#include "Plots.h"//---------------------------------------------------------------------------

//---------------------------------------------------------------------------

//----------------------------------- MD ------------------------------------//---------------------------------------------------------------------------

#include <winbgim.h>#include "Memalloc.h"

#include "Graphlib.h"#include "Random.h"

#include "Utils.h"#include "Units.h"

#include "Rescal.h"#include "Inout.h"

#include "DataAtom.h"#include "InitConfig.h"

#include "Forces.h"#include "Propag.h"

#include "BoundCond.h"#include "Measure.h"

#include "Spectrum.h"#include "PlotCfg.h"

#include "Plots.h"//---------------------------------------------------------------------------

Titus Beu 2011

int main()

{char aname[2];

float *x, *y, *z, *vx, *vy, *vz, *vx0, *vy0, *vz0, *ax, *ay, *az;float *Ekin, *Etot, *Pres, *Bmin, *Bmax, *dbond;

float *CorVel, *Intens, *freq;float *Hfunc, *Diff;

float *rHist, *frHist;float *vHist, *fvHist;

float *xPBC, *yPBC, *zPBC;int *atom1, *atom2;

float amass, fpar, rpar, rbnd, rcut, dens, Temp, Lbox, dt, dtOut;float Ekini, EkinAvg, EkinSig, Epoti, EtotAvg, EtotSig;

float Presi, PresAvg, PresSig, virial, t;float BondMin, BondMax, freqMin, freqMax;

float fact, rHistMax, vHistMax;int iatm, iopRun, iopInit, isave, istep, maxbond, fopt;

int natm, nbond, nfreq, nsave, nstep, nstepOut;int nrHist, nvHist, nsum_stat, nsum_rHist, nsum_vHist, nsum_Diff;

int CPUtime, CPUtime0;

int main()

{char aname[2];

float *x, *y, *z, *vx, *vy, *vz, *vx0, *vy0, *vz0, *ax, *ay, *az;float *Ekin, *Etot, *Pres, *Bmin, *Bmax, *dbond;

float *CorVel, *Intens, *freq;float *Hfunc, *Diff;

float *rHist, *frHist;float *vHist, *fvHist;

float *xPBC, *yPBC, *zPBC;int *atom1, *atom2;

float amass, fpar, rpar, rbnd, rcut, dens, Temp, Lbox, dt, dtOut;float Ekini, EkinAvg, EkinSig, Epoti, EtotAvg, EtotSig;

float Presi, PresAvg, PresSig, virial, t;float BondMin, BondMax, freqMin, freqMax;

float fact, rHistMax, vHistMax;int iatm, iopRun, iopInit, isave, istep, maxbond, fopt;

int natm, nbond, nfreq, nsave, nstep, nstepOut;int nrHist, nvHist, nsum_stat, nsum_rHist, nsum_vHist, nsum_Diff;

int CPUtime, CPUtime0;

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initwindow(1100,700);

Input(iopRun,iopInit,aname,dens,Temp,dt,natm,nstep,nstepOut);

DataAtom(aname,amass,fpar,rpar,rbnd,rcut,fopt);

dtOut = dt * nstepOut;

nsave = nstep / nstepOut;nstep = nsave * nstepOut;

maxbond = natm*(natm-1)/2; // max. no. of bondsnrHist = 100; rHistMax = 20.e0;

nvHist = 100; vHistMax = 3.e0 * sqrt(3.e0*Temp / amass);

x = Vector(1,natm); y = Vector(1,natm); z = Vector(1,natm);vx = Vector(1,natm); vy = Vector(1,natm); vz = Vector(1,natm);

vx0 = Vector(1,natm); vy0 = Vector(1,natm); vz0 = Vector(1,natm);ax = Vector(1,natm); ay = Vector(1,natm); az = Vector(1,natm);

Ekin = Vector(1,nsave); Etot = Vector(1,nsave); Pres = Vector(1,nsave);dbond = Vector(1,maxbond); Bmin = Vector(1,nsave); Bmax = Vector(1,nsave);

CorVel = Vector(1,nsave); Intens = Vector(1,nsave); freq = Vector(1,nsave);Hfunc = Vector(1,nsave); Diff = Vector(1,nsave);

rHist = Vector(1,nrHist); frHist = Vector(1,nrHist);vHist = Vector(1,nvHist); fvHist = Vector(1,nvHist);

xPBC = Vector(1,natm); yPBC = Vector(1,natm); zPBC = Vector(1,natm);atom1 = IVector(1,maxbond); atom2 = IVector(1,maxbond);

Randomize();

initwindow(1100,700);

Input(iopRun,iopInit,aname,dens,Temp,dt,natm,nstep,nstepOut);

DataAtom(aname,amass,fpar,rpar,rbnd,rcut,fopt);

dtOut = dt * nstepOut;

nsave = nstep / nstepOut;nstep = nsave * nstepOut;

maxbond = natm*(natm-1)/2; // max. no. of bondsnrHist = 100; rHistMax = 20.e0;

nvHist = 100; vHistMax = 3.e0 * sqrt(3.e0*Temp / amass);

x = Vector(1,natm); y = Vector(1,natm); z = Vector(1,natm);vx = Vector(1,natm); vy = Vector(1,natm); vz = Vector(1,natm);

vx0 = Vector(1,natm); vy0 = Vector(1,natm); vz0 = Vector(1,natm);ax = Vector(1,natm); ay = Vector(1,natm); az = Vector(1,natm);

Ekin = Vector(1,nsave); Etot = Vector(1,nsave); Pres = Vector(1,nsave);dbond = Vector(1,maxbond); Bmin = Vector(1,nsave); Bmax = Vector(1,nsave);

CorVel = Vector(1,nsave); Intens = Vector(1,nsave); freq = Vector(1,nsave);Hfunc = Vector(1,nsave); Diff = Vector(1,nsave);

rHist = Vector(1,nrHist); frHist = Vector(1,nrHist);vHist = Vector(1,nvHist); fvHist = Vector(1,nvHist);

xPBC = Vector(1,natm); yPBC = Vector(1,natm); zPBC = Vector(1,natm);atom1 = IVector(1,maxbond); atom2 = IVector(1,maxbond);

Randomize();

Titus Beu 2011

switch (iopRun) { // initialize configuration

case 0:case 1:

InitClus(iopInit,aname,amass,rpar,Temp,x,y,z,vx,vy,vz,ax,ay,az,natm);

break;case 2:

InitFluid(iopInit,aname,amass,dens,Temp,Lbox,x,y,z,vx,vy,vz,ax,ay,az,natm);

if (Lbox < rcut) {printf("MD: Lbox < rcut !\n");

getch(); exit(1);}

rHistMax = min(rHistMax,Lbox);SavePDB(aname,x,y,z,natm);

}

Output0(iopRun,iopInit,aname,amass,fpar,rpar,rcut,dens,Lbox,Temp,dt,natm,nstep,nstepOut);

if (iopRun >= 1)

for (iatm=1; iatm<=natm; iatm++) {vx0[iatm] = vx[iatm]; vy0[iatm] = vy[iatm]; vz0[iatm] = vz[iatm];

xPBC[iatm] = yPBC[iatm] = zPBC[iatm] = 0.e0;}

switch (iopRun) { // initialize configuration

case 0:case 1:

InitClus(iopInit,aname,amass,rpar,Temp,x,y,z,vx,vy,vz,ax,ay,az,natm);

break;case 2:

InitFluid(iopInit,aname,amass,dens,Temp,Lbox,x,y,z,vx,vy,vz,ax,ay,az,natm);

if (Lbox < rcut) {printf("MD: Lbox < rcut !\n");

getch(); exit(1);}

rHistMax = min(rHistMax,Lbox);SavePDB(aname,x,y,z,natm);

}

Output0(iopRun,iopInit,aname,amass,fpar,rpar,rcut,dens,Lbox,Temp,dt,natm,nstep,nstepOut);

if (iopRun >= 1)

for (iatm=1; iatm<=natm; iatm++) {vx0[iatm] = vx[iatm]; vy0[iatm] = vy[iatm]; vz0[iatm] = vz[iatm];

xPBC[iatm] = yPBC[iatm] = zPBC[iatm] = 0.e0;}

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CPUtime0 = time(NULL);

t = 0.e0;

nsum_stat = 0;nsum_rHist = 0;

nsum_vHist = 0;nsum_Diff = 0;

for (istep=1; istep<=nstep; istep++) { // MAIN TEMPORAL LOOPt += dt;

Verlet(iopRun,amass,fpar,rpar,rcut,Lbox,dt,x,y,z,vx,vy,vz,ax,ay,az,natm,Ekini,Epoti,virial,fopt);

if (iopRun == 0) { // simmulated annealing

Ekini *= 0.99;Vrescal(amass,vx,vy,vz,natm,Ekini);

}

if (iopRun == 2) {BoundCond(Lbox,x,y,z,xPBC,yPBC,zPBC,natm); // periodic bound. cond.

Thermostat(vx,vy,vz,natm,Temp,10*dt,dt,Ekini);}

if (istep % nstepOut == 0) { // measurements & output

isave = istep / nstepOut;Ekin[isave] = Ekini;

Etot[isave] = Ekini + Epoti;

CPUtime0 = time(NULL);

t = 0.e0;

nsum_stat = 0;nsum_rHist = 0;

nsum_vHist = 0;nsum_Diff = 0;

for (istep=1; istep<=nstep; istep++) { // MAIN TEMPORAL LOOPt += dt;

Verlet(iopRun,amass,fpar,rpar,rcut,Lbox,dt,x,y,z,vx,vy,vz,ax,ay,az,natm,Ekini,Epoti,virial,fopt);

if (iopRun == 0) { // simmulated annealing

Ekini *= 0.99;Vrescal(amass,vx,vy,vz,natm,Ekini);

}

if (iopRun == 2) {BoundCond(Lbox,x,y,z,xPBC,yPBC,zPBC,natm); // periodic bound. cond.

Thermostat(vx,vy,vz,natm,Temp,10*dt,dt,Ekini);}

if (istep % nstepOut == 0) { // measurements & output

isave = istep / nstepOut;Ekin[isave] = Ekini;

Etot[isave] = Ekini + Epoti;

Titus Beu 2011

switch (iopRun) {

case 0: // cluster structureBonds(x,y,z,natm,atom1,atom2,dbond,nbond,rcut,

Bmin[isave],Bmax[isave]);break;

case 1: // cluster spectrumBonds(x,y,z,natm,atom1,atom2,dbond,nbond,rcut,

Bmin[isave],Bmax[isave]);CorVel[isave] = FuncCorr(isave-1,vx,vy,vz,natm);

freqMin = 0.e0; freqMax = 3.e3;Spectrum(CorVel,Intens,freq,freqMin,freqMax,dt*nstepOut,isave,nfreq);

break;case 2: // fluid structure

Presi = dens * (2.e0*Ekini + virial) / 3.e0;Statistics(Ekini,EkinAvg,EkinSig,Etot[isave],EtotAvg,EtotSig,

Presi,PresAvg,PresSig,nsum_stat);DistribV(vx,vy,vz,natm,vHist,fvHist,nvHist,vHistMax,nsum_vHist);

DistribR(Lbox,x,y,z,natm,rHist,frHist,nrHist,rHistMax,nsum_rHist);

Etot[isave] = EtotAvg;Pres[isave] = PresAvg;

Hfunc[isave] = HBoltzmann(vHist,fvHist,nvHist);Diff[isave] = DiffCorV(vx,vy,vz,natm,dt*nstepOut,nsum_Diff);

}

switch (iopRun) {

case 0: // cluster structureBonds(x,y,z,natm,atom1,atom2,dbond,nbond,rcut,

Bmin[isave],Bmax[isave]);break;

case 1: // cluster spectrumBonds(x,y,z,natm,atom1,atom2,dbond,nbond,rcut,

Bmin[isave],Bmax[isave]);CorVel[isave] = FuncCorr(isave-1,vx,vy,vz,natm);

freqMin = 0.e0; freqMax = 3.e3;Spectrum(CorVel,Intens,freq,freqMin,freqMax,dt*nstepOut,isave,nfreq);

break;case 2: // fluid structure

Presi = dens * (2.e0*Ekini + virial) / 3.e0;Statistics(Ekini,EkinAvg,EkinSig,Etot[isave],EtotAvg,EtotSig,

Presi,PresAvg,PresSig,nsum_stat);DistribV(vx,vy,vz,natm,vHist,fvHist,nvHist,vHistMax,nsum_vHist);

DistribR(Lbox,x,y,z,natm,rHist,frHist,nrHist,rHistMax,nsum_rHist);

Etot[isave] = EtotAvg;Pres[isave] = PresAvg;

Hfunc[isave] = HBoltzmann(vHist,fvHist,nvHist);Diff[isave] = DiffCorV(vx,vy,vz,natm,dt*nstepOut,nsum_Diff);

}

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cleardevice();

Output(iopRun,t,Ekin,Etot,Bmin,Bmax,Hfunc,Intens,freq,nsave,isave,nfreq,rHist,frHist,nrHist,vHist,fvHist,nvHist);

PlotCfg(iopRun,Lbox,x,y,atom1,atom2,natm,nbond,0.07e0,0.40e0,0.56e0,0.97e0);Plots(iopRun,Ekin,Etot,Pres,dbond,nbond,Bmin,Bmax,

CorVel,Intens,freq,dtOut,nsave,isave,nfreq,rHist,frHist,nrHist,vHist,fvHist,nvHist,

Hfunc,Diff);

if (iopRun == 0 && isave > 1) { // convergence checkif (fabs(1.e0 - Bmax[isave-1]/Bmax[isave]) <= 1.e-6) break;

}}

}

if (iopRun == 0) SavePDB(aname,x,y,z,natm); // save optimized structureCPUtime = time(NULL);

printf("\nCPU time: %5i sec\n",CPUtime-CPUtime0);getch();

}

cleardevice();

Output(iopRun,t,Ekin,Etot,Bmin,Bmax,Hfunc,Intens,freq,nsave,isave,nfreq,rHist,frHist,nrHist,vHist,fvHist,nvHist);

PlotCfg(iopRun,Lbox,x,y,atom1,atom2,natm,nbond,0.07e0,0.40e0,0.56e0,0.97e0);Plots(iopRun,Ekin,Etot,Pres,dbond,nbond,Bmin,Bmax,

CorVel,Intens,freq,dtOut,nsave,isave,nfreq,rHist,frHist,nrHist,vHist,fvHist,nvHist,

Hfunc,Diff);

if (iopRun == 0 && isave > 1) { // convergence checkif (fabs(1.e0 - Bmax[isave-1]/Bmax[isave]) <= 1.e-6) break;

}}

}

if (iopRun == 0) SavePDB(aname,x,y,z,natm); // save optimized structureCPUtime = time(NULL);

printf("\nCPU time: %5i sec\n",CPUtime-CPUtime0);getch();

}

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2

0343

Ar300.

1.0e-4100000

10002.

2

0343

Ar300.

1.0e-4100000

10002.

md.dat:

Input:

fscanf(in,"%i",&iopRun); // run: 0,1,2 - structure, spectrum, fluid

fscanf(in,"%i",&iopInit); // initialization: 0-from file, 1-spherefscanf(in,"%i",&natm); // no. of atoms

fscanf(in,"%s",aname); // chemical symbolfscanf(in,"%f",&Temp); // kinetic temperature in K

fscanf(in,"%f",&dt); // integration time stepfscanf(in,"%i",&nstep); // no. of time steps

fscanf(in,"%i",&nstepOut); // no. of time steps for outputif (iopRun == 2) fscanf(in,"%f",&dens); // fluid density in g/cmc

fscanf(in,"%i",&iopRun); // run: 0,1,2 - structure, spectrum, fluid

fscanf(in,"%i",&iopInit); // initialization: 0-from file, 1-spherefscanf(in,"%i",&natm); // no. of atoms

fscanf(in,"%s",aname); // chemical symbolfscanf(in,"%f",&Temp); // kinetic temperature in K

fscanf(in,"%f",&dt); // integration time stepfscanf(in,"%i",&nstep); // no. of time steps

fscanf(in,"%i",&nstepOut); // no. of time steps for outputif (iopRun == 2) fscanf(in,"%f",&dens); // fluid density in g/cmc

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istep = 1

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istep = 1000

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istep = 10000

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istep = 100000

77.. Simulating simple fluidsSimulating simple fluidsphys.ubbcluj.ro/~tbeu/MD/C7.pdf · Allen, M....

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Transcript of 77.. Simulating simple fluidsSimulating simple fluidsphys.ubbcluj.ro/~tbeu/MD/C7.pdf · Allen, M....