/* calc scalar functions of (M^inf)^-1 in F for unequal spheres
* INPUT
* r := x_b - x_a
* aa, ab : radius of particle a and b
* OUTPUT
* scalar_f [8] : scalar functions in dimensional form!
* 0, 1, 2, 3 : (XA11, XA12, XA21, XA22)
* 4, 5, 6, 7 : (YA11, YA12, YA21, YA22)
*/
void
scalars_minv_f_poly (double r, double aa, double ab,
double *scalar_f)
{
double scalar[11];
// (12)-interaction
// scalar[] is in the dimensional form (not the SD scaling)
scalars_nonewald_poly (0, /* F version */
r, aa, ab, scalar);
double xa12, ya12;
xa12 = scalar [0];
ya12 = scalar [1];
// (21)-interaction
double xa21, ya21;
/* note:
* [xy]a12 = [xy]a21 in dimensional form by symmetry
* therefore, we do not need to calculate (21)-interaction explicitly
*/
xa21 = xa12;
ya21 = ya12;
// self part
double xa11, ya11;
xa11 = 1.0 / aa;
ya11 = 1.0 / aa;
double xa22, ya22;
xa22 = 1.0 / ab;
ya22 = 1.0 / ab;
double det;
// XA part
double XA11, XA12, XA21, XA22;
det = xa11*xa22 - xa12*xa21;
XA11 = xa22 / det;
XA12 = -xa12 / det;
XA21 = -xa21 / det;
XA22 = xa11 / det;
// YA part
double YA11, YA12, YA21, YA22;
det = ya11*ya22 - ya12*ya21;
YA11 = ya22 / det;
YA12 = -ya12 / det;
YA21 = -ya21 / det;
YA22 = ya11 / det;
scalar_f [0] = XA11;
scalar_f [1] = XA12;
scalar_f [2] = XA21;
scalar_f [3] = XA22;
scalar_f [4] = YA11;
scalar_f [5] = YA12;
scalar_f [6] = YA21;
scalar_f [7] = YA22;
}
/* calc U_i += M(i,j) . F_j
* INPUT
* sys : struct BD_imp
* flag_noHI : 1 == no HI
* 0 == with HI
* i, j : particle indices
* f[3] : force on particle j
* OUTPUT
* u[3] := M(i,j).f[], the velocity of particle i
*/
static void
mobility_F_atimes (struct stokes *sys, int flag_noHI,
int i, int j,
const double *f,
double *u)
{
// zero clear
u[0] = 0;
u[1] = 0;
u[2] = 0;
double ai;
double aj;
if (sys->a == NULL)
{
ai = 1.0;
aj = 1.0;
}
else
{
ai = sys->a[i];
aj = sys->a[j];
}
if (i == j)
{
// self
double self_a = 1.0;
matrix_f_atimes (f, u,
0.0, 0.0, 0.0,
self_a, self_a); // a part
}
else if (flag_noHI == 0)
{
double mob [22];
double xx
= sys->pos [j*3 ]
- sys->pos [i*3 ];
double yy
= sys->pos [j*3+1]
- sys->pos [i*3+1];
double zz
= sys->pos [j*3+2]
- sys->pos [i*3+2];
double rr = xx * xx + yy * yy + zz * zz;
double r = sqrt (rr);
double rmin = (ai + aj) * sys->rmin;
if (r < rmin) r = rmin;
double ex = xx / r;
double ey = yy / r;
double ez = zz / r;
// polydisperse code
scalars_nonewald_poly (0, // F version
r,
ai, aj,
mob);
scalars_mob_poly_scale_SD (0, // F version
ai,
mob);
// now mob is in the SD form
// note that interaction (i,j) should be for (U[i], F[j])
matrix_f_atimes (f, u,
ex, ey, ez,
mob[0], mob[1]); // xa, ya
}
/* convert the resultant velocity into the Global scaling
*/
u[0] /= ai;
u[1] /= ai;
u[2] /= ai;
}
/* calc scalar functions of (M^inf)^-1 in FT for unequal spheres
* INPUT
* r := x_b - x_a
* aa, ab : radius of particle a and b
* OUTPUT
* scalar_ft [20] : scalar functions in dimensional form!
* 0, 1, 2, 3 : (XA11, XA12, XA21, XA22)
* 4, 5, 6, 7 : (YA11, YA12, YA21, YA22)
* 8, 9,10,11 : (YB11, YB12, YB21, YB22)
* 12,13,14,15 : (XC11, XC12, XC21, XC22)
* 16,17,18,19 : (YC11, YC12, YC21, YC22)
*/
void
scalars_minv_ft_poly (double r, double aa, double ab,
double *scalar_ft)
{
double mat[16];
double scalar[11];
// (12)-interaction
// scalar[] is in the dimensional form (not the SD scaling)
scalars_nonewald_poly (1, // FT version
r, aa, ab, scalar);
double xa12, ya12;
double yb12;
double xc12, yc12;
double aa2 = aa * aa;
double aa3 = aa2 * aa;
xa12 = scalar [0];
ya12 = scalar [1];
yb12 = scalar [2];
xc12 = scalar [3];
yc12 = scalar [4];
// (21)-interaction
double xa21, ya21;
double yb21;
double xc21, yc21;
double ab2 = ab * ab;
double ab3 = ab2 * ab;
/* note:
* [xy]a12 = [xy]a21 in dimensional form by symmetry
* [xy]c12 = [xy]c21 in dimensional form by symmetry
* yb12 = yb21 in dimensional form for M^infty (lack of a dependence)
* therefore, we do not need to calculate (21)-interaction explicitly
*/
xa21 = xa12;
ya21 = ya12;
yb21 = yb12;
xc21 = xc12;
yc21 = yc12;
double xa11, ya11;
xa11 = 1.0 / aa;
ya11 = 1.0 / aa;
double xa22, ya22;
xa22 = 1.0 / ab;
ya22 = 1.0 / ab;
double xc11, yc11;
xc11 = 0.75 / aa3;
yc11 = 0.75 / aa3;
double xc22, yc22;
xc22 = 0.75 / ab3;
yc22 = 0.75 / ab3;
double det;
// XA part
double XA11, XA12, XA21, XA22;
det = xa11*xa22 - xa12*xa21;
XA11 = xa22 / det;
XA12 = -xa12 / det;
XA21 = -xa21 / det;
XA22 = xa11 / det;
// XC part
double XC11, XC12, XC21, XC22;
det = xc11*xc22 - xc12*xc21;
XC11 = xc22 / det;
XC12 = -xc12 / det;
XC21 = -xc21 / det;
XC22 = xc11 / det;
// Y part
double YA11, YA12, YA21, YA22;
double YB11, YB12, YB21, YB22;
double YC11, YC12, YC21, YC22;
mat [0] = ya11; // ya11
mat [1] = ya12; // ya12
mat [2] = 0.0; // -yb11
mat [3] = yb21; // yb21
mat [4] = ya21; // ya21
mat [5] = ya22; // ya22
mat [6] = -yb12; // -yb12
mat [7] = 0.0; // yb22
mat [8] = 0.0; // -yb11
mat [9] = -yb12; // -yb12
mat[10] = yc11; // yc11
mat[11] = yc12; // yc12
mat[12] = yb21; // yb21
mat[13] = 0.0; // yb22
mat[14] = yc21; // yc21
mat[15] = yc22; // yc22
lapack_inv_ (4, mat);
YA11 = mat [0];
YA12 = mat [1];
YA21 = mat [4];
YA22 = mat [5];
YB11 = -mat [8];
YB12 = -mat [9];
YB21 = mat[12];
YB22 = mat[13];
YC11 = mat[10];
YC12 = mat[11];
YC21 = mat[14];
YC22 = mat[15];
scalar_ft [0] = XA11;
scalar_ft [1] = XA12;
scalar_ft [2] = XA21;
scalar_ft [3] = XA22;
scalar_ft [4] = YA11;
scalar_ft [5] = YA12;
scalar_ft [6] = YA21;
scalar_ft [7] = YA22;
scalar_ft [8] = YB11;
scalar_ft [9] = YB12;
scalar_ft[10] = YB21;
scalar_ft[11] = YB22;
scalar_ft[12] = XC11;
scalar_ft[13] = XC12;
scalar_ft[14] = XC21;
scalar_ft[15] = XC22;
scalar_ft[16] = YC11;
scalar_ft[17] = YC12;
scalar_ft[18] = YC21;
scalar_ft[19] = YC22;
}
