| 74 |
|
} |
| 75 |
|
|
| 76 |
|
/** |
| 77 |
– |
* calculate the ratio of friction coeffiction constant between ellipsoid and spheric |
| 78 |
– |
* with same volume. |
| 79 |
– |
* @param m |
| 80 |
– |
* @param n |
| 81 |
– |
* @note |
| 77 |
|
* Reference: |
| 83 |
– |
* |
| 84 |
– |
* (1) Victor A. Bloomfield, On-Line Biophysics Textbook, Volume: Separations and Hydrodynamics |
| 85 |
– |
* Chapter 1,Survey of Biomolecular Hydrodynamics |
| 86 |
– |
* http://www.biophysics.org/education/vbloomfield.pdf |
| 78 |
|
* (2) F. Perrin , J. Phys. Radium, [7] 5, 497-511, 1934 |
| 79 |
|
* (3) F. Perrin, J. Phys. Radium, [7] 7, 1-11, 1936 |
| 80 |
|
*/ |
| 81 |
|
bool AnalyticalModel::calcHydroProps(Ellipsoid* ellipsoid, double viscosity, double temperature) { |
| 82 |
< |
double ft; |
| 83 |
< |
double fra; |
| 84 |
< |
double frb; |
| 85 |
< |
double a = ellipsoid->getA(); |
| 86 |
< |
double b = ellipsoid->getB(); |
| 87 |
< |
double q = a/b; //? |
| 88 |
< |
if (q > 1.0) {//prolate |
| 89 |
< |
ft = sqrt(1-q*q)/(pow(q, 2.0/3.0)*log((1 + sqrt(1-q*q))/q)); |
| 90 |
< |
fra = 4*(1-q*q)/(3*(2 - 2*pow(q, 4.0/3.0)/ft)); //not sure |
| 91 |
< |
frb = 4*(1-q*q*q*q) /(3*q*q*(2*pow(q, -2.0/3.0)*(2-q*q)/ft-2)); |
| 92 |
< |
} else {//oblate |
| 93 |
< |
ft = sqrt(1-q*q)/(pow(q, 2.0/3.0)*atan(sqrt(q*q-1))); |
| 94 |
< |
fra = 4*(1-q*q)/(3*(2 - 2*pow(q, 4.0/3.0)/ft)); //not sure |
| 95 |
< |
frb = 4*(1-q*q*q*q) /(3*q*q*(2*pow(q, -2.0/3.0)*(2-q*q)/ft-2)); |
| 82 |
> |
|
| 83 |
> |
double rMajor = ellipsoid->getRMajor(); |
| 84 |
> |
double rMinor = ellipsoid->getRMinor(); |
| 85 |
> |
|
| 86 |
> |
double a = rMinor; |
| 87 |
> |
double b = rMajor; |
| 88 |
> |
double a2 = a * a; |
| 89 |
> |
double b2 = b* b; |
| 90 |
> |
|
| 91 |
> |
double p = a /b; |
| 92 |
> |
double S; |
| 93 |
> |
if (p > 1.0) { //prolate |
| 94 |
> |
S = 2.0/sqrt(a2 - b2) * log((a + sqrt(a2-b2))/b); |
| 95 |
> |
} else { //oblate |
| 96 |
> |
S = 2.0/sqrt(b2 - a2) * atan(sqrt(b2-a2)/a); |
| 97 |
|
} |
| 98 |
< |
|
| 99 |
< |
double radius = pow(a*a*b, 1.0/3.0); |
| 98 |
> |
|
| 99 |
> |
double P = 1.0/(a2 - b2) * (S - 2.0/a); |
| 100 |
> |
double Q = 0.5/(a2-b2) * (2.0*a/b2 - S); |
| 101 |
> |
|
| 102 |
> |
double transMinor = 16.0 * NumericConstant::PI * viscosity * (a2 - b2) /((2.0*a2-b2)*S -2.0*a); |
| 103 |
> |
double transMajor = 32.0 * NumericConstant::PI * viscosity * (a2 - b2) /((2.0*a2-3.0*b2)*S +2.0*a); |
| 104 |
> |
double rotMinor = 32.0/3.0 * NumericConstant::PI * viscosity *(a2 - b2) * b2 /(2.0*a -b2*S); |
| 105 |
> |
double rotMajor = 32.0/3.0 * NumericConstant::PI * viscosity *(a2*a2 - b2*b2)/((2.0*a2-b2)*S-2.0*a); |
| 106 |
> |
|
| 107 |
> |
|
| 108 |
|
HydroProps props; |
| 109 |
< |
double Xitt = 6.0 * NumericConstant::PI * viscosity * radius; |
| 110 |
< |
double Xirr = 8.0 * NumericConstant::PI * viscosity * radius * radius * radius; |
| 111 |
< |
props.Xi(0, 0) = Xitt; |
| 112 |
< |
props.Xi(1, 1) = Xitt; |
| 113 |
< |
props.Xi(2, 2) = Xitt; |
| 114 |
< |
props.Xi(3, 3) = Xirr; |
| 115 |
< |
props.Xi(4, 4) = Xirr; |
| 116 |
< |
props.Xi(5, 5) = Xirr; |
| 109 |
> |
|
| 110 |
> |
props.Xi(0,0) = transMajor; |
| 111 |
> |
props.Xi(1,1) = transMajor; |
| 112 |
> |
props.Xi(2,2) = transMinor; |
| 113 |
> |
props.Xi(3,3) = rotMajor; |
| 114 |
> |
props.Xi(4,4) = rotMajor; |
| 115 |
> |
props.Xi(5,5) = rotMinor; |
| 116 |
|
|
| 117 |
|
const double convertConstant = 6.023; //convert poise.angstrom to amu/fs |
| 118 |
|
props.Xi *= convertConstant; |
| 120 |
– |
props.Xi(0,0) *= ft; |
| 121 |
– |
props.Xi(1,1) *= ft; |
| 122 |
– |
props.Xi(2,2) *= ft; |
| 123 |
– |
props.Xi(3,3) *= fra; |
| 124 |
– |
props.Xi(4,4) *= fra; |
| 125 |
– |
props.Xi(5,5) *= frb; |
| 119 |
|
|
| 120 |
|
Mat6x6d XiCopy = props.Xi; |
| 128 |
– |
XiCopy /= OOPSEConstant::kb * temperature; |
| 121 |
|
invertMatrix(XiCopy, props.D); |
| 122 |
|
double kt = OOPSEConstant::kB * temperature; |
| 123 |
|
props.D *= kt; |
| 124 |
< |
|
| 124 |
> |
props.Xi *= OOPSEConstant::kb * temperature; |
| 125 |
> |
|
| 126 |
|
setCR(props); |
| 127 |
|
setCD(props); |
| 128 |
|
|
