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lammps/src/ASPHERE/pair_gayberne.cpp
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pair_gayberne.cpp
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/* ----------------------------------------------------------------------
LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
http://lammps.sandia.gov, Sandia National Laboratories
Steve Plimpton, sjplimp@sandia.gov
Copyright (2003) Sandia Corporation. Under the terms of Contract
DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
certain rights in this software. This software is distributed under
the GNU General Public License.
See the README file in the top-level LAMMPS directory.
------------------------------------------------------------------------- */
/* ----------------------------------------------------------------------
Contributing author: Mike Brown (SNL)
------------------------------------------------------------------------- */
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include "pair_gayberne.h"
#include "math_extra.h"
#include "atom.h"
#include "atom_vec_ellipsoid.h"
#include "comm.h"
#include "force.h"
#include "neighbor.h"
#include "neigh_list.h"
#include "integrate.h"
#include "citeme.h"
#include "memory.h"
#include "error.h"
using namespace LAMMPS_NS;
static const char cite_pair_gayberne[] =
"pair gayberne command:\n\n"
"@Article{Brown09,\n"
" author = {W. M. Brown, M. K. Petersen, S. J. Plimpton, and G. S. Grest},\n"
" title = {Liquid crystal nanodroplets in solution},\n"
" journal = {J.~Chem.~Phys.},\n"
" year = 2009,\n"
" volume = 130,\n"
" pages = {044901}\n"
"}\n\n";
/* ---------------------------------------------------------------------- */
PairGayBerne::PairGayBerne(LAMMPS *lmp) : Pair(lmp)
{
if (lmp->citeme) lmp->citeme->add(cite_pair_gayberne);
single_enable = 0;
writedata = 1;
}
/* ----------------------------------------------------------------------
free all arrays
------------------------------------------------------------------------- */
PairGayBerne::~PairGayBerne()
{
if (allocated) {
memory->destroy(setflag);
memory->destroy(cutsq);
memory->destroy(form);
memory->destroy(epsilon);
memory->destroy(sigma);
memory->destroy(shape1);
memory->destroy(shape2);
memory->destroy(well);
memory->destroy(cut);
memory->destroy(lj1);
memory->destroy(lj2);
memory->destroy(lj3);
memory->destroy(lj4);
memory->destroy(offset);
delete [] lshape;
delete [] setwell;
}
}
/* ---------------------------------------------------------------------- */
void PairGayBerne::compute(int eflag, int vflag)
{
int i,j,ii,jj,inum,jnum,itype,jtype;
double evdwl,one_eng,rsq,r2inv,r6inv,forcelj,factor_lj;
double fforce[3],ttor[3],rtor[3],r12[3];
double a1[3][3],b1[3][3],g1[3][3],a2[3][3],b2[3][3],g2[3][3],temp[3][3];
int *ilist,*jlist,*numneigh,**firstneigh;
double *iquat,*jquat;
evdwl = 0.0;
if (eflag || vflag) ev_setup(eflag,vflag);
else evflag = vflag_fdotr = 0;
AtomVecEllipsoid::Bonus *bonus = avec->bonus;
int *ellipsoid = atom->ellipsoid;
double **x = atom->x;
double **f = atom->f;
double **tor = atom->torque;
int *type = atom->type;
int nlocal = atom->nlocal;
double *special_lj = force->special_lj;
int newton_pair = force->newton_pair;
inum = list->inum;
ilist = list->ilist;
numneigh = list->numneigh;
firstneigh = list->firstneigh;
// loop over neighbors of my atoms
for (ii = 0; ii < inum; ii++) {
i = ilist[ii];
itype = type[i];
if (form[itype][itype] == ELLIPSE_ELLIPSE) {
iquat = bonus[ellipsoid[i]].quat;
MathExtra::quat_to_mat_trans(iquat,a1);
MathExtra::diag_times3(well[itype],a1,temp);
MathExtra::transpose_times3(a1,temp,b1);
MathExtra::diag_times3(shape2[itype],a1,temp);
MathExtra::transpose_times3(a1,temp,g1);
}
jlist = firstneigh[i];
jnum = numneigh[i];
for (jj = 0; jj < jnum; jj++) {
j = jlist[jj];
factor_lj = special_lj[sbmask(j)];
j &= NEIGHMASK;
// r12 = center to center vector
r12[0] = x[j][0]-x[i][0];
r12[1] = x[j][1]-x[i][1];
r12[2] = x[j][2]-x[i][2];
rsq = MathExtra::dot3(r12,r12);
jtype = type[j];
// compute if less than cutoff
if (rsq < cutsq[itype][jtype]) {
switch (form[itype][jtype]) {
case SPHERE_SPHERE:
r2inv = 1.0/rsq;
r6inv = r2inv*r2inv*r2inv;
forcelj = r6inv * (lj1[itype][jtype]*r6inv - lj2[itype][jtype]);
forcelj *= -r2inv;
if (eflag) one_eng =
r6inv*(r6inv*lj3[itype][jtype]-lj4[itype][jtype]) -
offset[itype][jtype];
fforce[0] = r12[0]*forcelj;
fforce[1] = r12[1]*forcelj;
fforce[2] = r12[2]*forcelj;
ttor[0] = ttor[1] = ttor[2] = 0.0;
rtor[0] = rtor[1] = rtor[2] = 0.0;
break;
case SPHERE_ELLIPSE:
jquat = bonus[ellipsoid[j]].quat;
MathExtra::quat_to_mat_trans(jquat,a2);
MathExtra::diag_times3(well[jtype],a2,temp);
MathExtra::transpose_times3(a2,temp,b2);
MathExtra::diag_times3(shape2[jtype],a2,temp);
MathExtra::transpose_times3(a2,temp,g2);
one_eng = gayberne_lj(j,i,a2,b2,g2,r12,rsq,fforce,rtor);
ttor[0] = ttor[1] = ttor[2] = 0.0;
break;
case ELLIPSE_SPHERE:
one_eng = gayberne_lj(i,j,a1,b1,g1,r12,rsq,fforce,ttor);
rtor[0] = rtor[1] = rtor[2] = 0.0;
break;
default:
jquat = bonus[ellipsoid[j]].quat;
MathExtra::quat_to_mat_trans(jquat,a2);
MathExtra::diag_times3(well[jtype],a2,temp);
MathExtra::transpose_times3(a2,temp,b2);
MathExtra::diag_times3(shape2[jtype],a2,temp);
MathExtra::transpose_times3(a2,temp,g2);
one_eng = gayberne_analytic(i,j,a1,a2,b1,b2,g1,g2,r12,rsq,
fforce,ttor,rtor);
break;
}
fforce[0] *= factor_lj;
fforce[1] *= factor_lj;
fforce[2] *= factor_lj;
ttor[0] *= factor_lj;
ttor[1] *= factor_lj;
ttor[2] *= factor_lj;
f[i][0] += fforce[0];
f[i][1] += fforce[1];
f[i][2] += fforce[2];
tor[i][0] += ttor[0];
tor[i][1] += ttor[1];
tor[i][2] += ttor[2];
if (newton_pair || j < nlocal) {
rtor[0] *= factor_lj;
rtor[1] *= factor_lj;
rtor[2] *= factor_lj;
f[j][0] -= fforce[0];
f[j][1] -= fforce[1];
f[j][2] -= fforce[2];
tor[j][0] += rtor[0];
tor[j][1] += rtor[1];
tor[j][2] += rtor[2];
}
if (eflag) evdwl = factor_lj*one_eng;
if (evflag) ev_tally_xyz(i,j,nlocal,newton_pair,
evdwl,0.0,fforce[0],fforce[1],fforce[2],
-r12[0],-r12[1],-r12[2]);
}
}
}
if (vflag_fdotr) virial_fdotr_compute();
}
/* ----------------------------------------------------------------------
allocate all arrays
------------------------------------------------------------------------- */
void PairGayBerne::allocate()
{
allocated = 1;
int n = atom->ntypes;
memory->create(setflag,n+1,n+1,"pair:setflag");
for (int i = 1; i <= n; i++)
for (int j = i; j <= n; j++)
setflag[i][j] = 0;
memory->create(cutsq,n+1,n+1,"pair:cutsq");
memory->create(form,n+1,n+1,"pair:form");
memory->create(epsilon,n+1,n+1,"pair:epsilon");
memory->create(sigma,n+1,n+1,"pair:sigma");
memory->create(shape1,n+1,3,"pair:shape1");
memory->create(shape2,n+1,3,"pair:shape2");
memory->create(well,n+1,3,"pair:well");
memory->create(cut,n+1,n+1,"pair:cut");
memory->create(lj1,n+1,n+1,"pair:lj1");
memory->create(lj2,n+1,n+1,"pair:lj2");
memory->create(lj3,n+1,n+1,"pair:lj3");
memory->create(lj4,n+1,n+1,"pair:lj4");
memory->create(offset,n+1,n+1,"pair:offset");
lshape = new double[n+1];
setwell = new int[n+1];
for (int i = 1; i <= n; i++) setwell[i] = 0;
}
/* ----------------------------------------------------------------------
global settings
------------------------------------------------------------------------- */
void PairGayBerne::settings(int narg, char **arg)
{
if (narg != 4) error->all(FLERR,"Illegal pair_style command");
gamma = force->numeric(FLERR,arg[0]);
upsilon = force->numeric(FLERR,arg[1])/2.0;
mu = force->numeric(FLERR,arg[2]);
cut_global = force->numeric(FLERR,arg[3]);
// reset cutoffs that have been explicitly set
if (allocated) {
int i,j;
for (i = 1; i <= atom->ntypes; i++)
for (j = i+1; j <= atom->ntypes; j++)
if (setflag[i][j]) cut[i][j] = cut_global;
}
}
/* ----------------------------------------------------------------------
set coeffs for one or more type pairs
------------------------------------------------------------------------- */
void PairGayBerne::coeff(int narg, char **arg)
{
if (narg < 10 || narg > 11)
error->all(FLERR,"Incorrect args for pair coefficients");
if (!allocated) allocate();
int ilo,ihi,jlo,jhi;
force->bounds(arg[0],atom->ntypes,ilo,ihi);
force->bounds(arg[1],atom->ntypes,jlo,jhi);
double epsilon_one = force->numeric(FLERR,arg[2]);
double sigma_one = force->numeric(FLERR,arg[3]);
double eia_one = force->numeric(FLERR,arg[4]);
double eib_one = force->numeric(FLERR,arg[5]);
double eic_one = force->numeric(FLERR,arg[6]);
double eja_one = force->numeric(FLERR,arg[7]);
double ejb_one = force->numeric(FLERR,arg[8]);
double ejc_one = force->numeric(FLERR,arg[9]);
double cut_one = cut_global;
if (narg == 11) cut_one = force->numeric(FLERR,arg[10]);
int count = 0;
for (int i = ilo; i <= ihi; i++) {
for (int j = MAX(jlo,i); j <= jhi; j++) {
epsilon[i][j] = epsilon_one;
sigma[i][j] = sigma_one;
cut[i][j] = cut_one;
if (eia_one != 0.0 || eib_one != 0.0 || eic_one != 0.0) {
well[i][0] = pow(eia_one,-1.0/mu);
well[i][1] = pow(eib_one,-1.0/mu);
well[i][2] = pow(eic_one,-1.0/mu);
if (eia_one == eib_one && eib_one == eic_one) setwell[i] = 2;
else setwell[i] = 1;
}
if (eja_one != 0.0 || ejb_one != 0.0 || ejc_one != 0.0) {
well[j][0] = pow(eja_one,-1.0/mu);
well[j][1] = pow(ejb_one,-1.0/mu);
well[j][2] = pow(ejc_one,-1.0/mu);
if (eja_one == ejb_one && ejb_one == ejc_one) setwell[j] = 2;
else setwell[j] = 1;
}
setflag[i][j] = 1;
count++;
}
}
if (count == 0) error->all(FLERR,"Incorrect args for pair coefficients");
}
/* ----------------------------------------------------------------------
init specific to this pair style
------------------------------------------------------------------------- */
void PairGayBerne::init_style()
{
avec = (AtomVecEllipsoid *) atom->style_match("ellipsoid");
if (!avec) error->all(FLERR,"Pair gayberne requires atom style ellipsoid");
neighbor->request(this,instance_me);
// per-type shape precalculations
// require that atom shapes are identical within each type
// if shape = 0 for point particle, set shape = 1 as required by Gay-Berne
for (int i = 1; i <= atom->ntypes; i++) {
if (!atom->shape_consistency(i,shape1[i][0],shape1[i][1],shape1[i][2]))
error->all(FLERR,
"Pair gayberne requires atoms with same type have same shape");
if (shape1[i][0] == 0.0)
shape1[i][0] = shape1[i][1] = shape1[i][2] = 1.0;
shape2[i][0] = shape1[i][0]*shape1[i][0];
shape2[i][1] = shape1[i][1]*shape1[i][1];
shape2[i][2] = shape1[i][2]*shape1[i][2];
lshape[i] = (shape1[i][0]*shape1[i][1]+shape1[i][2]*shape1[i][2]) *
sqrt(shape1[i][0]*shape1[i][1]);
}
}
/* ----------------------------------------------------------------------
init for one type pair i,j and corresponding j,i
------------------------------------------------------------------------- */
double PairGayBerne::init_one(int i, int j)
{
if (setwell[i] == 0 || setwell[j] == 0)
error->all(FLERR,"Pair gayberne epsilon a,b,c coeffs are not all set");
if (setflag[i][j] == 0) {
epsilon[i][j] = mix_energy(epsilon[i][i],epsilon[j][j],
sigma[i][i],sigma[j][j]);
sigma[i][j] = mix_distance(sigma[i][i],sigma[j][j]);
cut[i][j] = mix_distance(cut[i][i],cut[j][j]);
}
lj1[i][j] = 48.0 * epsilon[i][j] * pow(sigma[i][j],12.0);
lj2[i][j] = 24.0 * epsilon[i][j] * pow(sigma[i][j],6.0);
lj3[i][j] = 4.0 * epsilon[i][j] * pow(sigma[i][j],12.0);
lj4[i][j] = 4.0 * epsilon[i][j] * pow(sigma[i][j],6.0);
if (offset_flag) {
double ratio = sigma[i][j] / cut[i][j];
offset[i][j] = 4.0 * epsilon[i][j] * (pow(ratio,12.0) - pow(ratio,6.0));
} else offset[i][j] = 0.0;
int ishape = 0;
if (shape1[i][0] != shape1[i][1] ||
shape1[i][0] != shape1[i][2] ||
shape1[i][1] != shape1[i][2]) ishape = 1;
if (setwell[i] == 1) ishape = 1;
int jshape = 0;
if (shape1[j][0] != shape1[j][1] ||
shape1[j][0] != shape1[j][2] ||
shape1[j][1] != shape1[j][2]) jshape = 1;
if (setwell[j] == 1) jshape = 1;
if (ishape == 0 && jshape == 0)
form[i][i] = form[j][j] = form[i][j] = form[j][i] = SPHERE_SPHERE;
else if (ishape == 0) {
form[i][i] = SPHERE_SPHERE; form[j][j] = ELLIPSE_ELLIPSE;
form[i][j] = SPHERE_ELLIPSE; form[j][i] = ELLIPSE_SPHERE;
} else if (jshape == 0) {
form[j][j] = SPHERE_SPHERE; form[i][i] = ELLIPSE_ELLIPSE;
form[j][i] = SPHERE_ELLIPSE; form[i][j] = ELLIPSE_SPHERE;
} else
form[i][i] = form[j][j] = form[i][j] = form[j][i] = ELLIPSE_ELLIPSE;
epsilon[j][i] = epsilon[i][j];
sigma[j][i] = sigma[i][j];
lj1[j][i] = lj1[i][j];
lj2[j][i] = lj2[i][j];
lj3[j][i] = lj3[i][j];
lj4[j][i] = lj4[i][j];
offset[j][i] = offset[i][j];
return cut[i][j];
}
/* ----------------------------------------------------------------------
proc 0 writes to restart file
------------------------------------------------------------------------- */
void PairGayBerne::write_restart(FILE *fp)
{
write_restart_settings(fp);
int i,j;
for (i = 1; i <= atom->ntypes; i++) {
fwrite(&setwell[i],sizeof(int),1,fp);
if (setwell[i]) fwrite(&well[i][0],sizeof(double),3,fp);
for (j = i; j <= atom->ntypes; j++) {
fwrite(&setflag[i][j],sizeof(int),1,fp);
if (setflag[i][j]) {
fwrite(&epsilon[i][j],sizeof(double),1,fp);
fwrite(&sigma[i][j],sizeof(double),1,fp);
fwrite(&cut[i][j],sizeof(double),1,fp);
}
}
}
}
/* ----------------------------------------------------------------------
proc 0 reads from restart file, bcasts
------------------------------------------------------------------------- */
void PairGayBerne::read_restart(FILE *fp)
{
read_restart_settings(fp);
allocate();
int i,j;
int me = comm->me;
for (i = 1; i <= atom->ntypes; i++) {
if (me == 0) fread(&setwell[i],sizeof(int),1,fp);
MPI_Bcast(&setwell[i],1,MPI_INT,0,world);
if (setwell[i]) {
if (me == 0) fread(&well[i][0],sizeof(double),3,fp);
MPI_Bcast(&well[i][0],3,MPI_DOUBLE,0,world);
}
for (j = i; j <= atom->ntypes; j++) {
if (me == 0) fread(&setflag[i][j],sizeof(int),1,fp);
MPI_Bcast(&setflag[i][j],1,MPI_INT,0,world);
if (setflag[i][j]) {
if (me == 0) {
fread(&epsilon[i][j],sizeof(double),1,fp);
fread(&sigma[i][j],sizeof(double),1,fp);
fread(&cut[i][j],sizeof(double),1,fp);
}
MPI_Bcast(&epsilon[i][j],1,MPI_DOUBLE,0,world);
MPI_Bcast(&sigma[i][j],1,MPI_DOUBLE,0,world);
MPI_Bcast(&cut[i][j],1,MPI_DOUBLE,0,world);
}
}
}
}
/* ----------------------------------------------------------------------
proc 0 writes to restart file
------------------------------------------------------------------------- */
void PairGayBerne::write_restart_settings(FILE *fp)
{
fwrite(&gamma,sizeof(double),1,fp);
fwrite(&upsilon,sizeof(double),1,fp);
fwrite(&mu,sizeof(double),1,fp);
fwrite(&cut_global,sizeof(double),1,fp);
fwrite(&offset_flag,sizeof(int),1,fp);
fwrite(&mix_flag,sizeof(int),1,fp);
}
/* ----------------------------------------------------------------------
proc 0 reads from restart file, bcasts
------------------------------------------------------------------------- */
void PairGayBerne::read_restart_settings(FILE *fp)
{
int me = comm->me;
if (me == 0) {
fread(&gamma,sizeof(double),1,fp);
fread(&upsilon,sizeof(double),1,fp);
fread(&mu,sizeof(double),1,fp);
fread(&cut_global,sizeof(double),1,fp);
fread(&offset_flag,sizeof(int),1,fp);
fread(&mix_flag,sizeof(int),1,fp);
}
MPI_Bcast(&gamma,1,MPI_DOUBLE,0,world);
MPI_Bcast(&upsilon,1,MPI_DOUBLE,0,world);
MPI_Bcast(&mu,1,MPI_DOUBLE,0,world);
MPI_Bcast(&cut_global,1,MPI_DOUBLE,0,world);
MPI_Bcast(&offset_flag,1,MPI_INT,0,world);
MPI_Bcast(&mix_flag,1,MPI_INT,0,world);
}
/* ----------------------------------------------------------------------
proc 0 writes to data file
------------------------------------------------------------------------- */
void PairGayBerne::write_data(FILE *fp)
{
for (int i = 1; i <= atom->ntypes; i++)
fprintf(fp,"%d %g %g %g %g %g %g %g %g\n",i,
epsilon[i][i],sigma[i][i],
pow(well[i][0],-mu),pow(well[i][1],-mu),pow(well[i][2],-mu),
pow(well[i][0],-mu),pow(well[i][1],-mu),pow(well[i][2],-mu));
}
/* ----------------------------------------------------------------------
proc 0 writes all pairs to data file
------------------------------------------------------------------------- */
void PairGayBerne::write_data_all(FILE *fp)
{
for (int i = 1; i <= atom->ntypes; i++)
for (int j = i; j <= atom->ntypes; j++)
fprintf(fp,"%d %d %g %g %g %g %g %g %g %g %g\n",i,j,
epsilon[i][i],sigma[i][i],
pow(well[i][0],-mu),pow(well[i][1],-mu),pow(well[i][2],-mu),
pow(well[j][0],-mu),pow(well[j][1],-mu),pow(well[j][2],-mu),
cut[i][j]);
}
/* ----------------------------------------------------------------------
compute analytic energy, force (fforce), and torque (ttor & rtor)
based on rotation matrices a and precomputed matrices b and g
if newton is off, rtor is not calculated for ghost atoms
------------------------------------------------------------------------- */
double PairGayBerne::gayberne_analytic(const int i,const int j,double a1[3][3],
double a2[3][3], double b1[3][3],
double b2[3][3], double g1[3][3],
double g2[3][3], double *r12,
const double rsq, double *fforce,
double *ttor, double *rtor)
{
double tempv[3], tempv2[3];
double temp[3][3];
double temp1,temp2,temp3;
int *type = atom->type;
int newton_pair = force->newton_pair;
int nlocal = atom->nlocal;
double r12hat[3];
MathExtra::normalize3(r12,r12hat);
double r = sqrt(rsq);
// compute distance of closest approach
double g12[3][3];
MathExtra::plus3(g1,g2,g12);
double kappa[3];
int ierror = MathExtra::mldivide3(g12,r12,kappa);
if (ierror) error->all(FLERR,"Bad matrix inversion in mldivide3");
// tempv = G12^-1*r12hat
tempv[0] = kappa[0]/r;
tempv[1] = kappa[1]/r;
tempv[2] = kappa[2]/r;
double sigma12 = MathExtra::dot3(r12hat,tempv);
sigma12 = pow(0.5*sigma12,-0.5);
double h12 = r-sigma12;
// energy
// compute u_r
double varrho = sigma[type[i]][type[j]]/(h12+gamma*sigma[type[i]][type[j]]);
double varrho6 = pow(varrho,6.0);
double varrho12 = varrho6*varrho6;
double u_r = 4.0*epsilon[type[i]][type[j]]*(varrho12-varrho6);
// compute eta_12
double eta = 2.0*lshape[type[i]]*lshape[type[j]];
double det_g12 = MathExtra::det3(g12);
eta = pow(eta/det_g12,upsilon);
// compute chi_12
double b12[3][3];
double iota[3];
MathExtra::plus3(b1,b2,b12);
ierror = MathExtra::mldivide3(b12,r12,iota);
if (ierror) error->all(FLERR,"Bad matrix inversion in mldivide3");
// tempv = G12^-1*r12hat
tempv[0] = iota[0]/r;
tempv[1] = iota[1]/r;
tempv[2] = iota[2]/r;
double chi = MathExtra::dot3(r12hat,tempv);
chi = pow(chi*2.0,mu);
// force
// compute dUr/dr
temp1 = (2.0*varrho12*varrho-varrho6*varrho)/sigma[type[i]][type[j]];
temp1 = temp1*24.0*epsilon[type[i]][type[j]];
double u_slj = temp1*pow(sigma12,3.0)/2.0;
double dUr[3];
temp2 = MathExtra::dot3(kappa,r12hat);
double uslj_rsq = u_slj/rsq;
dUr[0] = temp1*r12hat[0]+uslj_rsq*(kappa[0]-temp2*r12hat[0]);
dUr[1] = temp1*r12hat[1]+uslj_rsq*(kappa[1]-temp2*r12hat[1]);
dUr[2] = temp1*r12hat[2]+uslj_rsq*(kappa[2]-temp2*r12hat[2]);
// compute dChi_12/dr
double dchi[3];
temp1 = MathExtra::dot3(iota,r12hat);
temp2 = -4.0/rsq*mu*pow(chi,(mu-1.0)/mu);
dchi[0] = temp2*(iota[0]-temp1*r12hat[0]);
dchi[1] = temp2*(iota[1]-temp1*r12hat[1]);
dchi[2] = temp2*(iota[2]-temp1*r12hat[2]);
temp1 = -eta*u_r;
temp2 = eta*chi;
fforce[0] = temp1*dchi[0]-temp2*dUr[0];
fforce[1] = temp1*dchi[1]-temp2*dUr[1];
fforce[2] = temp1*dchi[2]-temp2*dUr[2];
// torque for particle 1 and 2
// compute dUr
tempv[0] = -uslj_rsq*kappa[0];
tempv[1] = -uslj_rsq*kappa[1];
tempv[2] = -uslj_rsq*kappa[2];
MathExtra::vecmat(kappa,g1,tempv2);
MathExtra::cross3(tempv,tempv2,dUr);
double dUr2[3];
if (newton_pair || j < nlocal) {
MathExtra::vecmat(kappa,g2,tempv2);
MathExtra::cross3(tempv,tempv2,dUr2);
}
// compute d_chi
MathExtra::vecmat(iota,b1,tempv);
MathExtra::cross3(tempv,iota,dchi);
temp1 = -4.0/rsq;
dchi[0] *= temp1;
dchi[1] *= temp1;
dchi[2] *= temp1;
double dchi2[3];
if (newton_pair || j < nlocal) {
MathExtra::vecmat(iota,b2,tempv);
MathExtra::cross3(tempv,iota,dchi2);
dchi2[0] *= temp1;
dchi2[1] *= temp1;
dchi2[2] *= temp1;
}
// compute d_eta
double deta[3];
deta[0] = deta[1] = deta[2] = 0.0;
compute_eta_torque(g12,a1,shape2[type[i]],temp);
temp1 = -eta*upsilon;
for (int m = 0; m < 3; m++) {
for (int y = 0; y < 3; y++) tempv[y] = temp1*temp[m][y];
MathExtra::cross3(a1[m],tempv,tempv2);
deta[0] += tempv2[0];
deta[1] += tempv2[1];
deta[2] += tempv2[2];
}
// compute d_eta for particle 2
double deta2[3];
if (newton_pair || j < nlocal) {
deta2[0] = deta2[1] = deta2[2] = 0.0;
compute_eta_torque(g12,a2,shape2[type[j]],temp);
for (int m = 0; m < 3; m++) {
for (int y = 0; y < 3; y++) tempv[y] = temp1*temp[m][y];
MathExtra::cross3(a2[m],tempv,tempv2);
deta2[0] += tempv2[0];
deta2[1] += tempv2[1];
deta2[2] += tempv2[2];
}
}
// torque
temp1 = u_r*eta;
temp2 = u_r*chi;
temp3 = chi*eta;
ttor[0] = (temp1*dchi[0]+temp2*deta[0]+temp3*dUr[0]) * -1.0;
ttor[1] = (temp1*dchi[1]+temp2*deta[1]+temp3*dUr[1]) * -1.0;
ttor[2] = (temp1*dchi[2]+temp2*deta[2]+temp3*dUr[2]) * -1.0;
if (newton_pair || j < nlocal) {
rtor[0] = (temp1*dchi2[0]+temp2*deta2[0]+temp3*dUr2[0]) * -1.0;
rtor[1] = (temp1*dchi2[1]+temp2*deta2[1]+temp3*dUr2[1]) * -1.0;
rtor[2] = (temp1*dchi2[2]+temp2*deta2[2]+temp3*dUr2[2]) * -1.0;
}
return temp1*chi;
}
/* ----------------------------------------------------------------------
compute analytic energy, force (fforce), and torque (ttor)
between ellipsoid and lj particle
------------------------------------------------------------------------- */
double PairGayBerne::gayberne_lj(const int i,const int j,double a1[3][3],
double b1[3][3],double g1[3][3],
double *r12,const double rsq,double *fforce,
double *ttor)
{
double tempv[3], tempv2[3];
double temp[3][3];
double temp1,temp2,temp3;
int *type = atom->type;
double r12hat[3];
MathExtra::normalize3(r12,r12hat);
double r = sqrt(rsq);
// compute distance of closest approach
double g12[3][3];
g12[0][0] = g1[0][0]+shape2[type[j]][0];
g12[1][1] = g1[1][1]+shape2[type[j]][0];
g12[2][2] = g1[2][2]+shape2[type[j]][0];
g12[0][1] = g1[0][1]; g12[1][0] = g1[1][0];
g12[0][2] = g1[0][2]; g12[2][0] = g1[2][0];
g12[1][2] = g1[1][2]; g12[2][1] = g1[2][1];
double kappa[3];
int ierror = MathExtra::mldivide3(g12,r12,kappa);
if (ierror) error->all(FLERR,"Bad matrix inversion in mldivide3");
// tempv = G12^-1*r12hat
tempv[0] = kappa[0]/r;
tempv[1] = kappa[1]/r;
tempv[2] = kappa[2]/r;
double sigma12 = MathExtra::dot3(r12hat,tempv);
sigma12 = pow(0.5*sigma12,-0.5);
double h12 = r-sigma12;
// energy
// compute u_r
double varrho = sigma[type[i]][type[j]]/(h12+gamma*sigma[type[i]][type[j]]);
double varrho6 = pow(varrho,6.0);
double varrho12 = varrho6*varrho6;
double u_r = 4.0*epsilon[type[i]][type[j]]*(varrho12-varrho6);
// compute eta_12
double eta = 2.0*lshape[type[i]]*lshape[type[j]];
double det_g12 = MathExtra::det3(g12);
eta = pow(eta/det_g12,upsilon);
// compute chi_12
double b12[3][3];
double iota[3];
b12[0][0] = b1[0][0] + well[type[j]][0];
b12[1][1] = b1[1][1] + well[type[j]][0];
b12[2][2] = b1[2][2] + well[type[j]][0];
b12[0][1] = b1[0][1]; b12[1][0] = b1[1][0];
b12[0][2] = b1[0][2]; b12[2][0] = b1[2][0];
b12[1][2] = b1[1][2]; b12[2][1] = b1[2][1];
ierror = MathExtra::mldivide3(b12,r12,iota);
if (ierror) error->all(FLERR,"Bad matrix inversion in mldivide3");
// tempv = G12^-1*r12hat
tempv[0] = iota[0]/r;
tempv[1] = iota[1]/r;
tempv[2] = iota[2]/r;
double chi = MathExtra::dot3(r12hat,tempv);
chi = pow(chi*2.0,mu);
// force
// compute dUr/dr
temp1 = (2.0*varrho12*varrho-varrho6*varrho)/sigma[type[i]][type[j]];
temp1 = temp1*24.0*epsilon[type[i]][type[j]];
double u_slj = temp1*pow(sigma12,3.0)/2.0;
double dUr[3];
temp2 = MathExtra::dot3(kappa,r12hat);
double uslj_rsq = u_slj/rsq;
dUr[0] = temp1*r12hat[0]+uslj_rsq*(kappa[0]-temp2*r12hat[0]);
dUr[1] = temp1*r12hat[1]+uslj_rsq*(kappa[1]-temp2*r12hat[1]);
dUr[2] = temp1*r12hat[2]+uslj_rsq*(kappa[2]-temp2*r12hat[2]);
// compute dChi_12/dr
double dchi[3];
temp1 = MathExtra::dot3(iota,r12hat);
temp2 = -4.0/rsq*mu*pow(chi,(mu-1.0)/mu);
dchi[0] = temp2*(iota[0]-temp1*r12hat[0]);
dchi[1] = temp2*(iota[1]-temp1*r12hat[1]);
dchi[2] = temp2*(iota[2]-temp1*r12hat[2]);
temp1 = -eta*u_r;
temp2 = eta*chi;
fforce[0] = temp1*dchi[0]-temp2*dUr[0];
fforce[1] = temp1*dchi[1]-temp2*dUr[1];
fforce[2] = temp1*dchi[2]-temp2*dUr[2];
// torque for particle 1 and 2
// compute dUr
tempv[0] = -uslj_rsq*kappa[0];
tempv[1] = -uslj_rsq*kappa[1];
tempv[2] = -uslj_rsq*kappa[2];
MathExtra::vecmat(kappa,g1,tempv2);
MathExtra::cross3(tempv,tempv2,dUr);
// compute d_chi
MathExtra::vecmat(iota,b1,tempv);
MathExtra::cross3(tempv,iota,dchi);
temp1 = -4.0/rsq;
dchi[0] *= temp1;
dchi[1] *= temp1;
dchi[2] *= temp1;
// compute d_eta
double deta[3];
deta[0] = deta[1] = deta[2] = 0.0;
compute_eta_torque(g12,a1,shape2[type[i]],temp);
temp1 = -eta*upsilon;
for (int m = 0; m < 3; m++) {
for (int y = 0; y < 3; y++) tempv[y] = temp1*temp[m][y];
MathExtra::cross3(a1[m],tempv,tempv2);
deta[0] += tempv2[0];
deta[1] += tempv2[1];
deta[2] += tempv2[2];
}
// torque
temp1 = u_r*eta;
temp2 = u_r*chi;
temp3 = chi*eta;
ttor[0] = (temp1*dchi[0]+temp2*deta[0]+temp3*dUr[0]) * -1.0;
ttor[1] = (temp1*dchi[1]+temp2*deta[1]+temp3*dUr[1]) * -1.0;
ttor[2] = (temp1*dchi[2]+temp2*deta[2]+temp3*dUr[2]) * -1.0;
return temp1*chi;
}
/* ----------------------------------------------------------------------
torque contribution from eta
computes trace in the last doc equation for the torque derivative
code comes from symbolic solver dump
m is g12, m2 is a_i, s is the shape for the particle
------------------------------------------------------------------------- */
void PairGayBerne::compute_eta_torque(double m[3][3], double m2[3][3],
double *s, double ans[3][3])
{
double den = m[1][0]*m[0][2]*m[2][1]-m[0][0]*m[1][2]*m[2][1]-
m[0][2]*m[2][0]*m[1][1]+m[0][1]*m[2][0]*m[1][2]-
m[1][0]*m[0][1]*m[2][2]+m[0][0]*m[1][1]*m[2][2];
ans[0][0] = s[0]*(m[1][2]*m[0][1]*m2[0][2]+2.0*m[1][1]*m[2][2]*m2[0][0]-
m[1][1]*m2[0][2]*m[0][2]-2.0*m[1][2]*m2[0][0]*m[2][1]+
m2[0][1]*m[0][2]*m[2][1]-m2[0][1]*m[0][1]*m[2][2]-
m[1][0]*m[2][2]*m2[0][1]+m[2][0]*m[1][2]*m2[0][1]+
m[1][0]*m2[0][2]*m[2][1]-m2[0][2]*m[2][0]*m[1][1])/den;
ans[0][1] = s[0]*(m[0][2]*m2[0][0]*m[2][1]-m[2][2]*m2[0][0]*m[0][1]+
2.0*m[0][0]*m[2][2]*m2[0][1]-m[0][0]*m2[0][2]*m[1][2]-
2.0*m[2][0]*m[0][2]*m2[0][1]+m2[0][2]*m[1][0]*m[0][2]-
m[2][2]*m[1][0]*m2[0][0]+m[2][0]*m2[0][0]*m[1][2]+
m[2][0]*m2[0][2]*m[0][1]-m2[0][2]*m[0][0]*m[2][1])/den;
ans[0][2] = s[0]*(m[0][1]*m[1][2]*m2[0][0]-m[0][2]*m2[0][0]*m[1][1]-
m[0][0]*m[1][2]*m2[0][1]+m[1][0]*m[0][2]*m2[0][1]-
m2[0][1]*m[0][0]*m[2][1]-m[2][0]*m[1][1]*m2[0][0]+
2.0*m[1][1]*m[0][0]*m2[0][2]-2.0*m[1][0]*m2[0][2]*m[0][1]+
m[1][0]*m[2][1]*m2[0][0]+m[2][0]*m2[0][1]*m[0][1])/den;
ans[1][0] = s[1]*(-m[1][1]*m2[1][2]*m[0][2]+2.0*m[1][1]*m[2][2]*m2[1][0]+
m[1][2]*m[0][1]*m2[1][2]-2.0*m[1][2]*m2[1][0]*m[2][1]+
m2[1][1]*m[0][2]*m[2][1]-m2[1][1]*m[0][1]*m[2][2]-
m[1][0]*m[2][2]*m2[1][1]+m[2][0]*m[1][2]*m2[1][1]-
m2[1][2]*m[2][0]*m[1][1]+m[1][0]*m2[1][2]*m[2][1])/den;
ans[1][1] = s[1]*(m[0][2]*m2[1][0]*m[2][1]-m[0][1]*m[2][2]*m2[1][0]+
2.0*m[2][2]*m[0][0]*m2[1][1]-m2[1][2]*m[0][0]*m[1][2]-
2.0*m[2][0]*m2[1][1]*m[0][2]-m[1][0]*m[2][2]*m2[1][0]+
m[2][0]*m[1][2]*m2[1][0]+m[1][0]*m2[1][2]*m[0][2]-
m[0][0]*m2[1][2]*m[2][1]+m2[1][2]*m[0][1]*m[2][0])/den;
ans[1][2] = s[1]*(m[0][1]*m[1][2]*m2[1][0]-m[0][2]*m2[1][0]*m[1][1]-
m[0][0]*m[1][2]*m2[1][1]+m[1][0]*m[0][2]*m2[1][1]+
2.0*m[1][1]*m[0][0]*m2[1][2]-m[0][0]*m2[1][1]*m[2][1]+
m[0][1]*m[2][0]*m2[1][1]-m2[1][0]*m[2][0]*m[1][1]-
2.0*m[1][0]*m[0][1]*m2[1][2]+m[1][0]*m2[1][0]*m[2][1])/den;
ans[2][0] = s[2]*(-m[1][1]*m[0][2]*m2[2][2]+m[0][1]*m[1][2]*m2[2][2]+
2.0*m[1][1]*m2[2][0]*m[2][2]-m[0][1]*m2[2][1]*m[2][2]+
m[0][2]*m[2][1]*m2[2][1]-2.0*m2[2][0]*m[2][1]*m[1][2]-
m[1][0]*m2[2][1]*m[2][2]+m[1][2]*m[2][0]*m2[2][1]-
m[1][1]*m[2][0]*m2[2][2]+m[2][1]*m[1][0]*m2[2][2])/den;
ans[2][1] = s[2]*-(m[0][1]*m[2][2]*m2[2][0]-m[0][2]*m2[2][0]*m[2][1]-
2.0*m2[2][1]*m[0][0]*m[2][2]+m[1][2]*m2[2][2]*m[0][0]+
2.0*m2[2][1]*m[0][2]*m[2][0]+m[1][0]*m2[2][0]*m[2][2]-
m[1][0]*m[0][2]*m2[2][2]-m[1][2]*m[2][0]*m2[2][0]+
m[0][0]*m2[2][2]*m[2][1]-m2[2][2]*m[0][1]*m[2][0])/den;
ans[2][2] = s[2]*(m[0][1]*m[1][2]*m2[2][0]-m[0][2]*m2[2][0]*m[1][1]-
m[0][0]*m[1][2]*m2[2][1]+m[1][0]*m[0][2]*m2[2][1]-
m[1][1]*m[2][0]*m2[2][0]-m[2][1]*m2[2][1]*m[0][0]+
2.0*m[1][1]*m2[2][2]*m[0][0]+m[2][1]*m[1][0]*m2[2][0]+
m[2][0]*m[0][1]*m2[2][1]-2.0*m2[2][2]*m[1][0]*m[0][1])/den;
}
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