38 |
|
* University of Notre Dame has been advised of the possibility of |
39 |
|
* such damages. |
40 |
|
*/ |
41 |
+ |
#include "applications/hydrodynamics/HydrodynamicsModel.hpp" |
42 |
+ |
#include "applications/hydrodynamics/Spheric.hpp" |
43 |
+ |
#include "applications/hydrodynamics/Ellipsoid.hpp" |
44 |
+ |
#include "applications/hydrodynamics/CompositeShape.hpp" |
45 |
|
|
42 |
– |
#include "applications/hydrodynamics/HydrodynamicsModel.hpp" |
43 |
– |
#include "math/LU.hpp" |
44 |
– |
#include "math/DynamicRectMatrix.hpp" |
45 |
– |
#include "math/SquareMatrix3.hpp" |
46 |
– |
#include "utils/OOPSEConstant.hpp" |
46 |
|
namespace oopse { |
48 |
– |
/** |
49 |
– |
* Reference: |
50 |
– |
* Beatriz Carrasco and Jose Gracia de la Torre, Hydrodynamic Properties of Rigid Particles: |
51 |
– |
* Comparison of Different Modeling and Computational Procedures. |
52 |
– |
* Biophysical Journal, 75(6), 3044, 1999 |
53 |
– |
*/ |
47 |
|
|
48 |
< |
HydrodynamicsModel::HydrodynamicsModel(StuntDouble* sd, const DynamicProperty& extraParams) : sd_(sd){ |
49 |
< |
DynamicProperty::const_iterator iter; |
48 |
> |
bool HydrodynamicsModel::calcHydroProps(Spheric* spheric, double viscosity, double temperature) { |
49 |
> |
return false; |
50 |
> |
} |
51 |
|
|
52 |
< |
iter = extraParams.find("Viscosity"); |
53 |
< |
if (iter != extraParams.end()) { |
54 |
< |
boost::any param = iter->second; |
61 |
< |
viscosity_ = boost::any_cast<double>(param); |
62 |
< |
}else { |
63 |
< |
std::cout << "HydrodynamicsModel Error\n" ; |
64 |
< |
} |
52 |
> |
bool HydrodynamicsModel::calcHydroProps(Ellipsoid* ellipsoid, double viscosity, double temperature) { |
53 |
> |
return false; |
54 |
> |
} |
55 |
|
|
56 |
< |
iter = extraParams.find("Temperature"); |
57 |
< |
if (iter != extraParams.end()) { |
68 |
< |
boost::any param = iter->second; |
69 |
< |
temperature_ = boost::any_cast<double>(param); |
70 |
< |
}else { |
71 |
< |
std::cout << "HydrodynamicsModel Error\n" ; |
72 |
< |
} |
56 |
> |
bool HydrodynamicsModel::calcHydroProps(CompositeShape* compositexShape, double viscosity, double temperature) { |
57 |
> |
return false; |
58 |
|
} |
74 |
– |
|
75 |
– |
bool HydrodynamicsModel::calcHydrodyanmicsProps() { |
76 |
– |
if (!createBeads(beads_)) { |
77 |
– |
std::cout << "can not create beads" << std::endl; |
78 |
– |
return false; |
79 |
– |
} |
59 |
|
|
60 |
< |
//calcResistanceTensor(); |
61 |
< |
calcDiffusionTensor(); |
60 |
> |
void HydrodynamicsModel::writeHydroProps(std::ostream& os) { |
61 |
> |
|
62 |
|
|
63 |
< |
/* |
85 |
< |
int nbeads = beads_.size(); |
86 |
< |
DynamicRectMatrix<double> B(3*nbeads, 3*nbeads); |
87 |
< |
DynamicRectMatrix<double> C(3*nbeads, 3*nbeads); |
88 |
< |
Mat3x3d I; |
89 |
< |
I(0, 0) = 1.0; |
90 |
< |
I(1, 1) = 1.0; |
91 |
< |
I(2, 2) = 1.0; |
63 |
> |
os << sd_->getType() << "\t"; |
64 |
|
|
65 |
< |
for (std::size_t i = 0; i < nbeads; ++i) { |
66 |
< |
for (std::size_t j = 0; j < nbeads; ++j) { |
95 |
< |
Mat3x3d Tij; |
96 |
< |
if (i != j ) { |
97 |
< |
Vector3d Rij = beads_[i].pos - beads_[j].pos; |
98 |
< |
double rij = Rij.length(); |
99 |
< |
double rij2 = rij * rij; |
100 |
< |
double sumSigma2OverRij2 = ((beads_[i].radius*beads_[i].radius) + (beads_[i].radius*beads_[i].radius)) / rij2; |
101 |
< |
Mat3x3d tmpMat; |
102 |
< |
tmpMat = outProduct(Rij, Rij) / rij2; |
103 |
< |
double constant = 8.0 * NumericConstant::PI * viscosity_ * rij; |
104 |
< |
Tij = ((1.0 + sumSigma2OverRij2/3.0) * I + (1.0 - sumSigma2OverRij2) * tmpMat ) / constant; |
105 |
< |
}else { |
106 |
< |
double constant = 1.0 / (6.0 * NumericConstant::PI * viscosity_ * beads_[i].radius); |
107 |
< |
Tij(0, 0) = constant; |
108 |
< |
Tij(1, 1) = constant; |
109 |
< |
Tij(2, 2) = constant; |
110 |
< |
} |
111 |
< |
B.setSubMatrix(i*3, j*3, Tij); |
112 |
< |
std::cout << Tij << std::endl; |
113 |
< |
} |
114 |
< |
} |
65 |
> |
//center of resistance |
66 |
> |
os << cr_.center[0] << "\t" << cr_.center[1] << "\t" << cr_.center[2] << "\t"; |
67 |
|
|
68 |
< |
std::cout << "B=\n" |
69 |
< |
<< B << std::endl; |
70 |
< |
//invert B Matrix |
71 |
< |
invertMatrix(B, C); |
68 |
> |
//resistance tensor at center of resistance |
69 |
> |
//translation |
70 |
> |
os << cr_.Xi(0, 0) << "\t" << cr_.Xi(0, 1) << "\t" << cr_.Xi(0, 2) << "\t" |
71 |
> |
<< cr_.Xi(1, 0) << "\t" << cr_.Xi(1, 1) << "\t" << cr_.Xi(1, 2) << "\t" |
72 |
> |
<< cr_.Xi(2, 0) << "\t" << cr_.Xi(2, 1) << "\t" << cr_.Xi(2, 2) << "\t"; |
73 |
|
|
74 |
< |
std::cout << "C=\n" |
75 |
< |
<< C << std::endl; |
74 |
> |
//rotation-translation |
75 |
> |
os << cr_.Xi(0, 3) << "\t" << cr_.Xi(0, 4) << "\t" << cr_.Xi(0, 5) << "\t" |
76 |
> |
<< cr_.Xi(1, 3) << "\t" << cr_.Xi(1, 4) << "\t" << cr_.Xi(1, 5) << "\t" |
77 |
> |
<< cr_.Xi(2, 3) << "\t" << cr_.Xi(2, 4) << "\t" << cr_.Xi(2, 5) << "\t"; |
78 |
|
|
79 |
< |
//prepare U Matrix relative to arbitrary origin O(0.0, 0.0, 0.0) |
80 |
< |
std::vector<Mat3x3d> U; |
81 |
< |
for (int i = 0; i < nbeads; ++i) { |
82 |
< |
Mat3x3d currU; |
128 |
< |
currU.setupSkewMat(beads_[i].pos); |
129 |
< |
U.push_back(currU); |
130 |
< |
} |
131 |
< |
|
132 |
< |
//calculate Xi matrix at arbitrary origin O |
133 |
< |
Mat3x3d Xitt; |
134 |
< |
Mat3x3d Xirr; |
135 |
< |
Mat3x3d Xitr; |
79 |
> |
//translation-rotation |
80 |
> |
os << cr_.Xi(3, 0) << "\t" << cr_.Xi(3, 1) << "\t" << cr_.Xi(3, 2) << "\t" |
81 |
> |
<< cr_.Xi(4, 0) << "\t" << cr_.Xi(4, 1) << "\t" << cr_.Xi(4, 2) << "\t" |
82 |
> |
<< cr_.Xi(5, 0) << "\t" << cr_.Xi(5, 1) << "\t" << cr_.Xi(5, 2) << "\t"; |
83 |
|
|
84 |
< |
//calculate the total volume |
84 |
> |
//rotation |
85 |
> |
os << cr_.Xi(3, 3) << "\t" << cr_.Xi(3, 4) << "\t" << cr_.Xi(3, 5) << "\t" |
86 |
> |
<< cr_.Xi(4, 3) << "\t" << cr_.Xi(4, 4) << "\t" << cr_.Xi(4, 5) << "\t" |
87 |
> |
<< cr_.Xi(5, 3) << "\t" << cr_.Xi(5, 4) << "\t" << cr_.Xi(5, 5) << "\t"; |
88 |
|
|
139 |
– |
double volume = 0.0; |
140 |
– |
for (std::vector<BeadParam>::iterator iter = beads_.begin(); iter != beads_.end(); ++iter) { |
141 |
– |
volume += 4.0/3.0 * NumericConstant::PI * pow((*iter).radius,3); |
142 |
– |
} |
143 |
– |
|
144 |
– |
for (std::size_t i = 0; i < nbeads; ++i) { |
145 |
– |
for (std::size_t j = 0; j < nbeads; ++j) { |
146 |
– |
Mat3x3d Cij; |
147 |
– |
C.getSubMatrix(i*3, j*3, Cij); |
148 |
– |
|
149 |
– |
Xitt += Cij; |
150 |
– |
Xitr += U[i] * Cij; |
151 |
– |
//Xirr += -U[i] * Cij * U[j]; |
152 |
– |
Xirr += -U[i] * Cij * U[j] + (0.166*6 * viscosity_ * volume) * I; |
153 |
– |
} |
154 |
– |
} |
89 |
|
|
90 |
< |
//invert Xi to get Diffusion Tensor at arbitrary origin O |
91 |
< |
RectMatrix<double, 6, 6> Xi; |
92 |
< |
RectMatrix<double, 6, 6> Do; |
93 |
< |
Xi.setSubMatrix(0, 0, Xitt); |
94 |
< |
Xi.setSubMatrix(0, 3, Xitr.transpose()); |
161 |
< |
Xi.setSubMatrix(3, 0, Xitr); |
162 |
< |
Xi.setSubMatrix(3, 3, Xirr); |
163 |
< |
//invertMatrix(Xi, Do); |
164 |
< |
double kt = OOPSEConstant::kB * temperature_ * 1.66E-2; |
165 |
< |
//Do *= kt; |
90 |
> |
//diffusion tensor at center of resistance |
91 |
> |
//translation |
92 |
> |
os << cr_.D(0, 0) << "\t" << cr_.D(0, 1) << "\t" << cr_.D(0, 2) << "\t" |
93 |
> |
<< cr_.D(1, 0) << "\t" << cr_.D(1, 1) << "\t" << cr_.D(1, 2) << "\t" |
94 |
> |
<< cr_.D(2, 0) << "\t" << cr_.D(2, 1) << "\t" << cr_.D(2, 2) << "\t"; |
95 |
|
|
96 |
+ |
//rotation-translation |
97 |
+ |
os << cr_.D(0, 3) << "\t" << cr_.D(0, 4) << "\t" << cr_.D(0, 5) << "\t" |
98 |
+ |
<< cr_.D(1, 3) << "\t" << cr_.D(1, 4) << "\t" << cr_.D(1, 5) << "\t" |
99 |
+ |
<< cr_.D(2, 3) << "\t" << cr_.D(2, 4) << "\t" << cr_.D(2, 5) << "\t"; |
100 |
|
|
101 |
< |
Mat3x3d Dott; //translational diffusion tensor at arbitrary origin O |
102 |
< |
Mat3x3d Dorr; //rotational diffusion tensor at arbitrary origin O |
103 |
< |
Mat3x3d Dotr; //translation-rotation couplingl diffusion tensor at arbitrary origin O |
101 |
> |
//translation-rotation |
102 |
> |
os << cr_.D(3, 0) << "\t" << cr_.D(3, 1) << "\t" << cr_.D(3, 2) << "\t" |
103 |
> |
<< cr_.D(4, 0) << "\t" << cr_.D(4, 1) << "\t" << cr_.D(4, 2) << "\t" |
104 |
> |
<< cr_.D(5, 0) << "\t" << cr_.D(5, 1) << "\t" << cr_.D(5, 2) << "\t"; |
105 |
|
|
106 |
< |
const static Mat3x3d zeroMat(0.0); |
107 |
< |
|
108 |
< |
Mat3x3d XittInv(0.0); |
109 |
< |
XittInv = Xitt.inverse(); |
110 |
< |
|
111 |
< |
//Xirr may not be inverted,if it one of the diagonal element is zero, for example |
178 |
< |
//( a11 a12 0) |
179 |
< |
//( a21 a22 0) |
180 |
< |
//( 0 0 0) |
181 |
< |
Mat3x3d XirrInv; |
182 |
< |
XirrInv = Xirr.inverse(); |
106 |
> |
//rotation |
107 |
> |
os << cr_.D(3, 3) << "\t" << cr_.D(3, 4) << "\t" << cr_.D(3, 5) << "\t" |
108 |
> |
<< cr_.D(4, 3) << "\t" << cr_.D(4, 4) << "\t" << cr_.D(4, 5) << "\t" |
109 |
> |
<< cr_.D(5, 3) << "\t" << cr_.D(5, 4) << "\t" << cr_.D(5, 5) << "\t"; |
110 |
> |
|
111 |
> |
//--------------------------------------------------------------------- |
112 |
|
|
113 |
< |
Mat3x3d tmp; |
114 |
< |
Mat3x3d tmpInv; |
186 |
< |
tmp = Xitt - Xitr.transpose() * XirrInv * Xitr; |
187 |
< |
tmpInv = tmp.inverse(); |
113 |
> |
//center of diffusion |
114 |
> |
os << cd_.center[0] << "\t" << cd_.center[1] << "\t" << cd_.center[2] << "\t"; |
115 |
|
|
116 |
< |
Dott = kt * tmpInv; |
117 |
< |
Dotr = -kt*XirrInv * Xitr * tmpInv* 1.0E8; |
116 |
> |
//resistance tensor at center of diffusion |
117 |
> |
//translation |
118 |
> |
os << cd_.Xi(0, 0) << "\t" << cd_.Xi(0, 1) << "\t" << cd_.Xi(0, 2) << "\t" |
119 |
> |
<< cd_.Xi(1, 0) << "\t" << cd_.Xi(1, 1) << "\t" << cd_.Xi(1, 2) << "\t" |
120 |
> |
<< cd_.Xi(2, 0) << "\t" << cd_.Xi(2, 1) << "\t" << cd_.Xi(2, 2) << "\t"; |
121 |
|
|
122 |
< |
tmp = Xirr - Xitr * XittInv * Xitr.transpose(); |
123 |
< |
tmpInv = tmp.inverse(); |
124 |
< |
|
125 |
< |
Dorr = kt * tmpInv*1.0E16; |
122 |
> |
//rotation-translation |
123 |
> |
os << cd_.Xi(0, 3) << "\t" << cd_.Xi(0, 4) << "\t" << cd_.Xi(0, 5) << "\t" |
124 |
> |
<< cd_.Xi(1, 3) << "\t" << cd_.Xi(1, 4) << "\t" << cd_.Xi(1, 5) << "\t" |
125 |
> |
<< cd_.Xi(2, 3) << "\t" << cd_.Xi(2, 4) << "\t" << cd_.Xi(2, 5) << "\t"; |
126 |
|
|
127 |
< |
//Do.getSubMatrix(0, 0 , Dott); |
128 |
< |
//Do.getSubMatrix(3, 0, Dotr); |
129 |
< |
//Do.getSubMatrix(3, 3, Dorr); |
127 |
> |
//translation-rotation |
128 |
> |
os << cd_.Xi(3, 0) << "\t" << cd_.Xi(3, 1) << "\t" << cd_.Xi(3, 2) << "\t" |
129 |
> |
<< cd_.Xi(4, 0) << "\t" << cd_.Xi(4, 1) << "\t" << cd_.Xi(4, 2) << "\t" |
130 |
> |
<< cd_.Xi(5, 0) << "\t" << cd_.Xi(5, 1) << "\t" << cd_.Xi(5, 2) << "\t"; |
131 |
|
|
132 |
< |
//calculate center of diffusion |
133 |
< |
tmp(0, 0) = Dorr(1, 1) + Dorr(2, 2); |
134 |
< |
tmp(0, 1) = - Dorr(0, 1); |
135 |
< |
tmp(0, 2) = -Dorr(0, 2); |
205 |
< |
tmp(1, 0) = -Dorr(0, 1); |
206 |
< |
tmp(1, 1) = Dorr(0, 0) + Dorr(2, 2); |
207 |
< |
tmp(1, 2) = -Dorr(1, 2); |
208 |
< |
tmp(2, 0) = -Dorr(0, 2); |
209 |
< |
tmp(2, 1) = -Dorr(1, 2); |
210 |
< |
tmp(2, 2) = Dorr(1, 1) + Dorr(0, 0); |
132 |
> |
//rotation |
133 |
> |
os << cd_.Xi(3, 3) << "\t" << cd_.Xi(3, 4) << "\t" << cd_.Xi(3, 5) << "\t" |
134 |
> |
<< cd_.Xi(4, 3) << "\t" << cd_.Xi(4, 4) << "\t" << cd_.Xi(4, 5) << "\t" |
135 |
> |
<< cd_.Xi(5, 3) << "\t" << cd_.Xi(5, 4) << "\t" << cd_.Xi(5, 5) << "\t"; |
136 |
|
|
212 |
– |
Vector3d tmpVec; |
213 |
– |
tmpVec[0] = Dotr(1, 2) - Dotr(2, 1); |
214 |
– |
tmpVec[1] = Dotr(2, 0) - Dotr(0, 2); |
215 |
– |
tmpVec[2] = Dotr(0, 1) - Dotr(1, 0); |
137 |
|
|
138 |
< |
tmpInv = tmp.inverse(); |
139 |
< |
|
140 |
< |
Vector3d rod = tmpInv * tmpVec; |
138 |
> |
//diffusion tensor at center of diffusion |
139 |
> |
//translation |
140 |
> |
os << cd_.D(0, 0) << "\t" << cd_.D(0, 1) << "\t" << cd_.D(0, 2) << "\t" |
141 |
> |
<< cd_.D(1, 0) << "\t" << cd_.D(1, 1) << "\t" << cd_.D(1, 2) << "\t" |
142 |
> |
<< cd_.D(2, 0) << "\t" << cd_.D(2, 1) << "\t" << cd_.D(2, 2) << "\t"; |
143 |
|
|
144 |
< |
//calculate Diffusion Tensor at center of diffusion |
145 |
< |
Mat3x3d Uod; |
146 |
< |
Uod.setupSkewMat(rod); |
147 |
< |
|
225 |
< |
Mat3x3d Ddtt; //translational diffusion tensor at diffusion center |
226 |
< |
Mat3x3d Ddtr; //rotational diffusion tensor at diffusion center |
227 |
< |
Mat3x3d Ddrr; //translation-rotation couplingl diffusion tensor at diffusion tensor |
228 |
< |
|
229 |
< |
Ddtt = Dott - Uod * Dorr * Uod + Dotr.transpose() * Uod - Uod * Dotr; |
230 |
< |
Ddrr = Dorr; |
231 |
< |
Ddtr = Dotr + Dorr * Uod; |
232 |
< |
|
233 |
< |
props_.diffCenter = rod; |
234 |
< |
props_.transDiff = Ddtt; |
235 |
< |
props_.transRotDiff = Ddtr; |
236 |
< |
props_.rotDiff = Ddrr; |
237 |
< |
*/ |
238 |
< |
return true; |
239 |
< |
} |
144 |
> |
//rotation-translation |
145 |
> |
os << cd_.D(0, 3) << "\t" << cd_.D(0, 4) << "\t" << cd_.D(0, 5) << "\t" |
146 |
> |
<< cd_.D(1, 3) << "\t" << cd_.D(1, 4) << "\t" << cd_.D(1, 5) << "\t" |
147 |
> |
<< cd_.D(2, 3) << "\t" << cd_.D(2, 4) << "\t" << cd_.D(2, 5) << "\t"; |
148 |
|
|
149 |
< |
void HydrodynamicsModel::calcResistanceTensor() { |
150 |
< |
|
151 |
< |
int nbeads = beads_.size(); |
152 |
< |
DynamicRectMatrix<double> B(3*nbeads, 3*nbeads); |
245 |
< |
DynamicRectMatrix<double> C(3*nbeads, 3*nbeads); |
246 |
< |
Mat3x3d I; |
247 |
< |
I(0, 0) = 1.0; |
248 |
< |
I(1, 1) = 1.0; |
249 |
< |
I(2, 2) = 1.0; |
250 |
< |
|
251 |
< |
for (std::size_t i = 0; i < nbeads; ++i) { |
252 |
< |
for (std::size_t j = 0; j < nbeads; ++j) { |
253 |
< |
Mat3x3d Tij; |
254 |
< |
if (i != j ) { |
255 |
< |
Vector3d Rij = beads_[i].pos - beads_[j].pos; |
256 |
< |
double rij = Rij.length(); |
257 |
< |
double rij2 = rij * rij; |
258 |
< |
double sumSigma2OverRij2 = ((beads_[i].radius*beads_[i].radius) + (beads_[i].radius*beads_[i].radius)) / rij2; |
259 |
< |
Mat3x3d tmpMat; |
260 |
< |
tmpMat = outProduct(Rij, Rij) / rij2; |
261 |
< |
double constant = 8.0 * NumericConstant::PI * viscosity_ * rij; |
262 |
< |
Tij = ((1.0 + sumSigma2OverRij2/3.0) * I + (1.0 - sumSigma2OverRij2) * tmpMat ) / constant; |
263 |
< |
}else { |
264 |
< |
double constant = 1.0 / (6.0 * NumericConstant::PI * viscosity_ * beads_[i].radius); |
265 |
< |
Tij(0, 0) = constant; |
266 |
< |
Tij(1, 1) = constant; |
267 |
< |
Tij(2, 2) = constant; |
268 |
< |
} |
269 |
< |
B.setSubMatrix(i*3, j*3, Tij); |
270 |
< |
} |
271 |
< |
} |
149 |
> |
//translation-rotation |
150 |
> |
os << cd_.D(3, 0) << "\t" << cd_.D(3, 1) << "\t" << cd_.D(3, 2) << "\t" |
151 |
> |
<< cd_.D(4, 0) << "\t" << cd_.D(4, 1) << "\t" << cd_.D(4, 2) << "\t" |
152 |
> |
<< cd_.D(5, 0) << "\t" << cd_.D(5, 1) << "\t" << cd_.D(5, 2) << "\t"; |
153 |
|
|
154 |
< |
|
155 |
< |
//invert B Matrix |
156 |
< |
invertMatrix(B, C); |
157 |
< |
|
277 |
< |
//prepare U Matrix relative to arbitrary origin O(0.0, 0.0, 0.0) |
278 |
< |
std::vector<Mat3x3d> U; |
279 |
< |
for (int i = 0; i < nbeads; ++i) { |
280 |
< |
Mat3x3d currU; |
281 |
< |
currU.setupSkewMat(beads_[i].pos); |
282 |
< |
U.push_back(currU); |
283 |
< |
} |
284 |
< |
|
285 |
< |
//calculate Xi matrix at arbitrary origin O |
286 |
< |
Mat3x3d Xiott; |
287 |
< |
Mat3x3d Xiorr; |
288 |
< |
Mat3x3d Xiotr; |
289 |
< |
|
290 |
< |
//calculate the total volume |
291 |
< |
|
292 |
< |
double volume = 0.0; |
293 |
< |
for (std::vector<BeadParam>::iterator iter = beads_.begin(); iter != beads_.end(); ++iter) { |
294 |
< |
volume += 4.0/3.0 * NumericConstant::PI * pow((*iter).radius,3); |
295 |
< |
} |
296 |
< |
|
297 |
< |
for (std::size_t i = 0; i < nbeads; ++i) { |
298 |
< |
for (std::size_t j = 0; j < nbeads; ++j) { |
299 |
< |
Mat3x3d Cij; |
300 |
< |
C.getSubMatrix(i*3, j*3, Cij); |
301 |
< |
|
302 |
< |
Xiott += Cij; |
303 |
< |
Xiotr += U[i] * Cij; |
304 |
< |
//Xiorr += -U[i] * Cij * U[j]; |
305 |
< |
Xiorr += -U[i] * Cij * U[j] + (6 * viscosity_ * volume) * I; |
306 |
< |
} |
307 |
< |
} |
308 |
< |
|
309 |
< |
Mat3x3d tmp; |
310 |
< |
Mat3x3d tmpInv; |
311 |
< |
Vector3d tmpVec; |
312 |
< |
tmp(0, 0) = Xiott(1, 1) + Xiott(2, 2); |
313 |
< |
tmp(0, 1) = - Xiott(0, 1); |
314 |
< |
tmp(0, 2) = -Xiott(0, 2); |
315 |
< |
tmp(1, 0) = -Xiott(0, 1); |
316 |
< |
tmp(1, 1) = Xiott(0, 0) + Xiott(2, 2); |
317 |
< |
tmp(1, 2) = -Xiott(1, 2); |
318 |
< |
tmp(2, 0) = -Xiott(0, 2); |
319 |
< |
tmp(2, 1) = -Xiott(1, 2); |
320 |
< |
tmp(2, 2) = Xiott(1, 1) + Xiott(0, 0); |
321 |
< |
tmpVec[0] = Xiotr(2, 1) - Xiotr(1, 2); |
322 |
< |
tmpVec[1] = Xiotr(0, 2) - Xiotr(2, 0); |
323 |
< |
tmpVec[2] = Xiotr(1, 0) - Xiotr(0, 1); |
324 |
< |
tmpInv = tmp.inverse(); |
325 |
< |
Vector3d ror = tmpInv * tmpVec; //center of resistance |
326 |
< |
Mat3x3d Uor; |
327 |
< |
Uor.setupSkewMat(ror); |
328 |
< |
|
329 |
< |
Mat3x3d Xirtt; |
330 |
< |
Mat3x3d Xirrr; |
331 |
< |
Mat3x3d Xirtr; |
154 |
> |
//rotation |
155 |
> |
os << cd_.D(3, 3) << "\t" << cd_.D(3, 4) << "\t" << cd_.D(3, 5) << "\t" |
156 |
> |
<< cd_.D(4, 3) << "\t" << cd_.D(4, 4) << "\t" << cd_.D(4, 5) << "\t" |
157 |
> |
<< cd_.D(5, 3) << "\t" << cd_.D(5, 4) << "\t" << cd_.D(5, 5) << "\n"; |
158 |
|
|
333 |
– |
Xirtt = Xiott; |
334 |
– |
Xirtr = (Xiotr - Uor * Xiott) * 1E-8; |
335 |
– |
Xirrr = Xiorr - Uor * Xiott * Uor + Xiotr * Uor - Uor * Xiotr.transpose() * 1E-16; |
336 |
– |
/* |
337 |
– |
SquareMatrix<double,6> Xir6x6; |
338 |
– |
SquareMatrix<double,6> Dr6x6; |
159 |
|
|
340 |
– |
Xir6x6.setSubMatrix(0, 0, Xirtt); |
341 |
– |
Xir6x6.setSubMatrix(0, 3, Xirtr.transpose()); |
342 |
– |
Xir6x6.setSubMatrix(3, 0, Xirtr); |
343 |
– |
Xir6x6.setSubMatrix(3, 3, Xirrr); |
344 |
– |
|
345 |
– |
invertMatrix(Xir6x6, Dr6x6); |
346 |
– |
Mat3x3d Drtt; |
347 |
– |
Mat3x3d Drtr; |
348 |
– |
Mat3x3d Drrr; |
349 |
– |
Dr6x6.getSubMatrix(0, 0, Drtt); |
350 |
– |
Dr6x6.getSubMatrix(3, 0, Drtr); |
351 |
– |
Dr6x6.getSubMatrix(3, 3, Drrr); |
352 |
– |
double kt = OOPSEConstant::kB * temperature_ * 1.66E-2; |
353 |
– |
Drtt *= kt; |
354 |
– |
Drtr *= kt*1E8; |
355 |
– |
Drrr *= kt*1E16; |
356 |
– |
*/ |
357 |
– |
|
358 |
– |
const static Mat3x3d zeroMat(0.0); |
359 |
– |
|
360 |
– |
|
361 |
– |
|
362 |
– |
Mat3x3d XirttInv(0.0); |
363 |
– |
XirttInv = Xirtt.inverse(); |
364 |
– |
|
365 |
– |
//Xirr may not be inverted,if it one of the diagonal element is zero, for example |
366 |
– |
//( a11 a12 0) |
367 |
– |
//( a21 a22 0) |
368 |
– |
//( 0 0 0) |
369 |
– |
Mat3x3d XirrrInv; |
370 |
– |
XirrrInv = Xirrr.inverse(); |
371 |
– |
tmp = Xirtt - Xirtr.transpose() * XirrrInv * Xirtr; |
372 |
– |
tmpInv = tmp.inverse(); |
373 |
– |
|
374 |
– |
Mat3x3d Drtt; |
375 |
– |
Mat3x3d Drtr; |
376 |
– |
Mat3x3d Drrr; |
377 |
– |
double kt = OOPSEConstant::kB * temperature_ * 1.66E-2; |
378 |
– |
Drtt = kt * tmpInv; |
379 |
– |
Drtr = -kt*XirrrInv * Xirtr * tmpInv* 1.0E8; |
380 |
– |
|
381 |
– |
tmp = Xirrr - Xirtr * XirttInv * Xirtr.transpose(); |
382 |
– |
tmpInv = tmp.inverse(); |
383 |
– |
|
384 |
– |
Drrr = kt * tmpInv*1.0E16; |
385 |
– |
|
386 |
– |
std::cout << "-----------------------------------------\n"; |
387 |
– |
std::cout << "center of resistance :" << std::endl; |
388 |
– |
std::cout << ror << std::endl; |
389 |
– |
std::cout << "resistant tensor at center of resistance" << std::endl; |
390 |
– |
std::cout << "translation:" << std::endl; |
391 |
– |
std::cout << Xirtt << std::endl; |
392 |
– |
std::cout << "translation-rotation:" << std::endl; |
393 |
– |
std::cout << Xirtr << std::endl; |
394 |
– |
std::cout << "rotation:" << std::endl; |
395 |
– |
std::cout << Xirrr << std::endl; |
396 |
– |
std::cout << "diffusion tensor at center of resistance" << std::endl; |
397 |
– |
std::cout << "translation:" << std::endl; |
398 |
– |
std::cout << Drtt << std::endl; |
399 |
– |
std::cout << "translation-rotation:" << std::endl; |
400 |
– |
std::cout << Drtr << std::endl; |
401 |
– |
std::cout << "rotation:" << std::endl; |
402 |
– |
std::cout << Drrr << std::endl; |
403 |
– |
std::cout << "-----------------------------------------\n"; |
404 |
– |
|
160 |
|
} |
161 |
|
|
407 |
– |
void HydrodynamicsModel::calcDiffusionTensor() { |
408 |
– |
int nbeads = beads_.size(); |
409 |
– |
DynamicRectMatrix<double> B(3*nbeads, 3*nbeads); |
410 |
– |
DynamicRectMatrix<double> C(3*nbeads, 3*nbeads); |
411 |
– |
Mat3x3d I; |
412 |
– |
I(0, 0) = 1.0; |
413 |
– |
I(1, 1) = 1.0; |
414 |
– |
I(2, 2) = 1.0; |
415 |
– |
|
416 |
– |
for (std::size_t i = 0; i < nbeads; ++i) { |
417 |
– |
for (std::size_t j = 0; j < nbeads; ++j) { |
418 |
– |
Mat3x3d Tij; |
419 |
– |
if (i != j ) { |
420 |
– |
Vector3d Rij = beads_[i].pos - beads_[j].pos; |
421 |
– |
double rij = Rij.length(); |
422 |
– |
double rij2 = rij * rij; |
423 |
– |
double sumSigma2OverRij2 = ((beads_[i].radius*beads_[i].radius) + (beads_[i].radius*beads_[i].radius)) / rij2; |
424 |
– |
Mat3x3d tmpMat; |
425 |
– |
tmpMat = outProduct(Rij, Rij) / rij2; |
426 |
– |
double constant = 8.0 * NumericConstant::PI * viscosity_ * rij; |
427 |
– |
Tij = ((1.0 + sumSigma2OverRij2/3.0) * I + (1.0 - sumSigma2OverRij2) * tmpMat ) / constant; |
428 |
– |
}else { |
429 |
– |
double constant = 1.0 / (6.0 * NumericConstant::PI * viscosity_ * beads_[i].radius); |
430 |
– |
Tij(0, 0) = constant; |
431 |
– |
Tij(1, 1) = constant; |
432 |
– |
Tij(2, 2) = constant; |
433 |
– |
} |
434 |
– |
B.setSubMatrix(i*3, j*3, Tij); |
435 |
– |
} |
436 |
– |
} |
437 |
– |
|
438 |
– |
//invert B Matrix |
439 |
– |
invertMatrix(B, C); |
440 |
– |
|
441 |
– |
//prepare U Matrix relative to arbitrary origin O(0.0, 0.0, 0.0) |
442 |
– |
std::vector<Mat3x3d> U; |
443 |
– |
for (int i = 0; i < nbeads; ++i) { |
444 |
– |
Mat3x3d currU; |
445 |
– |
currU.setupSkewMat(beads_[i].pos); |
446 |
– |
U.push_back(currU); |
447 |
– |
} |
448 |
– |
|
449 |
– |
//calculate Xi matrix at arbitrary origin O |
450 |
– |
Mat3x3d Xitt; |
451 |
– |
Mat3x3d Xirr; |
452 |
– |
Mat3x3d Xitr; |
453 |
– |
|
454 |
– |
//calculate the total volume |
455 |
– |
|
456 |
– |
double volume = 0.0; |
457 |
– |
for (std::vector<BeadParam>::iterator iter = beads_.begin(); iter != beads_.end(); ++iter) { |
458 |
– |
volume += 4.0/3.0 * NumericConstant::PI * pow((*iter).radius,3); |
459 |
– |
} |
460 |
– |
|
461 |
– |
for (std::size_t i = 0; i < nbeads; ++i) { |
462 |
– |
for (std::size_t j = 0; j < nbeads; ++j) { |
463 |
– |
Mat3x3d Cij; |
464 |
– |
C.getSubMatrix(i*3, j*3, Cij); |
465 |
– |
|
466 |
– |
Xitt += Cij; |
467 |
– |
Xitr += U[i] * Cij; |
468 |
– |
//Xirr += -U[i] * Cij * U[j]; |
469 |
– |
Xirr += -U[i] * Cij * U[j] + (6 * viscosity_ * volume) * I; |
470 |
– |
} |
471 |
– |
} |
472 |
– |
|
473 |
– |
//invert Xi to get Diffusion Tensor at arbitrary origin O |
474 |
– |
RectMatrix<double, 6, 6> Xi; |
475 |
– |
RectMatrix<double, 6, 6> Do; |
476 |
– |
Xi.setSubMatrix(0, 0, Xitt); |
477 |
– |
Xi.setSubMatrix(0, 3, Xitr.transpose()); |
478 |
– |
Xi.setSubMatrix(3, 0, Xitr); |
479 |
– |
Xi.setSubMatrix(3, 3, Xirr); |
480 |
– |
//invertMatrix(Xi, Do); |
481 |
– |
//double kt = OOPSEConstant::kB * temperature_ * 1.66E-2; |
482 |
– |
|
483 |
– |
//1 poise = 0.1 N.S/m^2 = 1.661E-3 amu/ (Angstrom*fs) |
484 |
– |
double kt = OOPSEConstant::kB * temperature_ * 1.66E-3; |
485 |
– |
|
486 |
– |
Mat3x3d Dott; //translational diffusion tensor at arbitrary origin O |
487 |
– |
Mat3x3d Dorr; //rotational diffusion tensor at arbitrary origin O |
488 |
– |
Mat3x3d Dotr; //translation-rotation couplingl diffusion tensor at arbitrary origin O |
489 |
– |
|
490 |
– |
const static Mat3x3d zeroMat(0.0); |
491 |
– |
|
492 |
– |
Mat3x3d XittInv(0.0); |
493 |
– |
XittInv = Xitt.inverse(); |
494 |
– |
|
495 |
– |
//Xirr may not be inverted,if it one of the diagonal element is zero, for example |
496 |
– |
//( a11 a12 0) |
497 |
– |
//( a21 a22 0) |
498 |
– |
//( 0 0 0) |
499 |
– |
Mat3x3d XirrInv; |
500 |
– |
XirrInv = Xirr.inverse(); |
501 |
– |
|
502 |
– |
Mat3x3d tmp; |
503 |
– |
Mat3x3d tmpInv; |
504 |
– |
tmp = Xitt - Xitr.transpose() * XirrInv * Xitr; |
505 |
– |
tmpInv = tmp.inverse(); |
506 |
– |
|
507 |
– |
//Dott = kt * tmpInv; //unit in A^2/fs |
508 |
– |
Dott = tmpInv; |
509 |
– |
//Dotr = -kt*XirrInv * Xitr * tmpInv*1E8; |
510 |
– |
//Dotr = -kt*XirrInv * Xitr * tmpInv; |
511 |
– |
Dotr = -XirrInv* Xitr * tmpInv; |
512 |
– |
|
513 |
– |
tmp = Xirr - Xitr * XittInv * Xitr.transpose(); |
514 |
– |
tmpInv = tmp.inverse(); |
515 |
– |
|
516 |
– |
//Dorr = kt * tmpInv*1E16; |
517 |
– |
//Dorr = kt * tmpInv; |
518 |
– |
Dorr = tmpInv; |
519 |
– |
//calculate center of diffusion |
520 |
– |
tmp(0, 0) = Dorr(1, 1) + Dorr(2, 2); |
521 |
– |
tmp(0, 1) = - Dorr(0, 1); |
522 |
– |
tmp(0, 2) = -Dorr(0, 2); |
523 |
– |
tmp(1, 0) = -Dorr(0, 1); |
524 |
– |
tmp(1, 1) = Dorr(0, 0) + Dorr(2, 2); |
525 |
– |
tmp(1, 2) = -Dorr(1, 2); |
526 |
– |
tmp(2, 0) = -Dorr(0, 2); |
527 |
– |
tmp(2, 1) = -Dorr(1, 2); |
528 |
– |
tmp(2, 2) = Dorr(1, 1) + Dorr(0, 0); |
529 |
– |
|
530 |
– |
Vector3d tmpVec; |
531 |
– |
tmpVec[0] = Dotr(1, 2) - Dotr(2, 1); |
532 |
– |
tmpVec[1] = Dotr(2, 0) - Dotr(0, 2); |
533 |
– |
tmpVec[2] = Dotr(0, 1) - Dotr(1, 0); |
534 |
– |
|
535 |
– |
tmpInv = tmp.inverse(); |
536 |
– |
|
537 |
– |
Vector3d rod = tmpInv * tmpVec; |
538 |
– |
|
539 |
– |
//calculate Diffusion Tensor at center of diffusion |
540 |
– |
Mat3x3d Uod; |
541 |
– |
Uod.setupSkewMat(rod); |
542 |
– |
|
543 |
– |
Mat3x3d Ddtt; //translational diffusion tensor at diffusion center |
544 |
– |
Mat3x3d Ddtr; //rotational diffusion tensor at diffusion center |
545 |
– |
Mat3x3d Ddrr; //translation-rotation couplingl diffusion tensor at diffusion tensor |
546 |
– |
|
547 |
– |
Ddtt = Dott - Uod * Dorr * Uod + Dotr.transpose() * Uod - Uod * Dotr; |
548 |
– |
Ddrr = Dorr; |
549 |
– |
Ddtr = Dotr + Dorr * Uod; |
550 |
– |
|
551 |
– |
props_.diffCenter = rod; |
552 |
– |
props_.Ddtt = Ddtt; |
553 |
– |
props_.Ddtr = Ddtr; |
554 |
– |
props_.Ddrr = Ddrr; |
555 |
– |
|
556 |
– |
SquareMatrix<double, 6> Dd; |
557 |
– |
Dd.setSubMatrix(0, 0, Ddtt); |
558 |
– |
Dd.setSubMatrix(0, 3, Ddtr.transpose()); |
559 |
– |
Dd.setSubMatrix(3, 0, Ddtr); |
560 |
– |
Dd.setSubMatrix(3, 3, Ddrr); |
561 |
– |
SquareMatrix<double, 6> Xid; |
562 |
– |
invertMatrix(Dd, Xid); |
563 |
– |
|
564 |
– |
Ddtt *= kt; |
565 |
– |
Ddtr *= kt; |
566 |
– |
Ddrr *= kt; |
567 |
– |
Xid /= 1.66E-3; |
568 |
– |
|
569 |
– |
Xid.getSubMatrix(0, 0, props_.Xidtt); |
570 |
– |
Xid.getSubMatrix(0, 3, props_.Xidrt); |
571 |
– |
Xid.getSubMatrix(3, 0, props_.Xidtr); |
572 |
– |
Xid.getSubMatrix(3, 3, props_.Xidrr); |
573 |
– |
|
574 |
– |
/* |
575 |
– |
std::cout << "center of diffusion :" << std::endl; |
576 |
– |
std::cout << rod << std::endl; |
577 |
– |
std::cout << "diffusion tensor at center of diffusion" << std::endl; |
578 |
– |
std::cout << "translation:" << std::endl; |
579 |
– |
std::cout << Ddtt << std::endl; |
580 |
– |
std::cout << "translation-rotation:" << std::endl; |
581 |
– |
std::cout << Ddtr << std::endl; |
582 |
– |
std::cout << "rotation:" << std::endl; |
583 |
– |
std::cout << Ddrr << std::endl; |
584 |
– |
*/ |
585 |
– |
|
162 |
|
} |
587 |
– |
|
588 |
– |
void HydrodynamicsModel::writeBeads(std::ostream& os) { |
589 |
– |
std::vector<BeadParam>::iterator iter; |
590 |
– |
os << beads_.size() << std::endl; |
591 |
– |
os << "Generated by Hydro" << std::endl; |
592 |
– |
for (iter = beads_.begin(); iter != beads_.end(); ++iter) { |
593 |
– |
os << iter->atomName << "\t" << iter->pos[0] << "\t" << iter->pos[1] << "\t" << iter->pos[2] << std::endl; |
594 |
– |
} |
595 |
– |
|
596 |
– |
} |
597 |
– |
|
598 |
– |
void HydrodynamicsModel::writeDiffCenterAndDiffTensor(std::ostream& os) { |
599 |
– |
|
600 |
– |
os << sd_->getType() << "\t"; |
601 |
– |
os << props_.diffCenter[0] << "\t" << props_.diffCenter[1] << "\t" << props_.diffCenter[2] << "\t"; |
602 |
– |
|
603 |
– |
os << props_.Ddtt(0, 0) << "\t" << props_.Ddtt(0, 1) << "\t" << props_.Ddtt(0, 2) << "\t" |
604 |
– |
<< props_.Ddtt(1, 0) << "\t" << props_.Ddtt(1, 1) << "\t" << props_.Ddtt(1, 2) << "\t" |
605 |
– |
<< props_.Ddtt(2, 0) << "\t" << props_.Ddtt(2, 1) << "\t" << props_.Ddtt(2, 2) << "\t"; |
606 |
– |
|
607 |
– |
os << props_.Ddtr(0, 0) << "\t" << props_.Ddtr(0, 1) << "\t" << props_.Ddtr(0, 2) << "\t" |
608 |
– |
<< props_.Ddtr(1, 0) << "\t" << props_.Ddtr(1, 1) << "\t" << props_.Ddtr(1, 2) << "\t" |
609 |
– |
<< props_.Ddtr(2, 0) << "\t" << props_.Ddtr(2, 1) << "\t" << props_.Ddtr(2, 2) << "\t"; |
610 |
– |
|
611 |
– |
os << props_.Ddrr(0, 0) << "\t" << props_.Ddrr(0, 1) << "\t" << props_.Ddrr(0, 2) << "\t" |
612 |
– |
<< props_.Ddrr(1, 0) << "\t" << props_.Ddrr(1, 1) << "\t" << props_.Ddrr(1, 2) << "\t" |
613 |
– |
<< props_.Ddrr(2, 0) << "\t" << props_.Ddrr(2, 1) << "\t" << props_.Ddrr(2, 2) <<"\t"; |
614 |
– |
|
615 |
– |
os << props_.Xidtt(0, 0) << "\t" << props_.Xidtt(0, 1) << "\t" << props_.Xidtt(0, 2) << "\t" |
616 |
– |
<< props_.Xidtt(1, 0) << "\t" << props_.Xidtt(1, 1) << "\t" << props_.Xidtt(1, 2) << "\t" |
617 |
– |
<< props_.Xidtt(2, 0) << "\t" << props_.Xidtt(2, 1) << "\t" << props_.Xidtt(2, 2) << "\t"; |
618 |
– |
|
619 |
– |
os << props_.Xidrt(0, 0) << "\t" << props_.Xidrt(0, 1) << "\t" << props_.Xidrt(0, 2) << "\t" |
620 |
– |
<< props_.Xidrt(1, 0) << "\t" << props_.Xidrt(1, 1) << "\t" << props_.Xidrt(1, 2) << "\t" |
621 |
– |
<< props_.Xidrt(2, 0) << "\t" << props_.Xidrt(2, 1) << "\t" << props_.Xidrt(2, 2) << "\t"; |
622 |
– |
|
623 |
– |
os << props_.Xidtr(0, 0) << "\t" << props_.Xidtr(0, 1) << "\t" << props_.Xidtr(0, 2) << "\t" |
624 |
– |
<< props_.Xidtr(1, 0) << "\t" << props_.Xidtr(1, 1) << "\t" << props_.Xidtr(1, 2) << "\t" |
625 |
– |
<< props_.Xidtr(2, 0) << "\t" << props_.Xidtr(2, 1) << "\t" << props_.Xidtr(2, 2) << "\t"; |
626 |
– |
|
627 |
– |
os << props_.Xidrr(0, 0) << "\t" << props_.Xidrr(0, 1) << "\t" << props_.Xidrr(0, 2) << "\t" |
628 |
– |
<< props_.Xidrr(1, 0) << "\t" << props_.Xidrr(1, 1) << "\t" << props_.Xidrr(1, 2) << "\t" |
629 |
– |
<< props_.Xidrr(2, 0) << "\t" << props_.Xidrr(2, 1) << "\t" << props_.Xidrr(2, 2) << std::endl; |
630 |
– |
|
631 |
– |
} |
632 |
– |
|
633 |
– |
} |