applications/hydrodynamics/HydrodynamicsModel.cpp

/*
 * Copyright (c) 2005 The University of Notre Dame. All Rights Reserved.
 *
 * The University of Notre Dame grants you ("Licensee") a
 * non-exclusive, royalty free, license to use, modify and
 * redistribute this software in source and binary code form, provided
 * that the following conditions are met:
 *
 * 1. Acknowledgement of the program authors must be made in any
 *    publication of scientific results based in part on use of the
 *    program.  An acceptable form of acknowledgement is citation of
 *    the article in which the program was described (Matthew
 *    A. Meineke, Charles F. Vardeman II, Teng Lin, Christopher
 *    J. Fennell and J. Daniel Gezelter, "OOPSE: An Object-Oriented
 *    Parallel Simulation Engine for Molecular Dynamics,"
 *    J. Comput. Chem. 26, pp. 252-271 (2005))
 *
 * 2. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 *
 * 3. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the
 *    distribution.
 *
 * This software is provided "AS IS," without a warranty of any
 * kind. All express or implied conditions, representations and
 * warranties, including any implied warranty of merchantability,
 * fitness for a particular purpose or non-infringement, are hereby
 * excluded.  The University of Notre Dame and its licensors shall not
 * be liable for any damages suffered by licensee as a result of
 * using, modifying or distributing the software or its
 * derivatives. In no event will the University of Notre Dame or its
 * licensors be liable for any lost revenue, profit or data, or for
 * direct, indirect, special, consequential, incidental or punitive
 * damages, however caused and regardless of the theory of liability,
 * arising out of the use of or inability to use software, even if the
 * University of Notre Dame has been advised of the possibility of
 * such damages.
 */

#include "applications/hydrodynamics/HydrodynamicsModel.hpp" 
#include "math/LU.hpp"
#include "math/DynamicRectMatrix.hpp"
#include "math/SquareMatrix3.hpp"
namespace oopse {
/**
 * Reference:
 * Beatriz Carrasco and Jose Gracia de la Torre, Hydrodynamic Properties of Rigid Particles:
 * Comparison of Different Modeling and Computational Procedures. 
 * Biophysical Journal, 75(6), 3044, 1999
 */
bool HydrodynamicsModel::calcHydrodyanmicsProps(double eta) {
    if (!createBeads(beads_)) {
        std::cout << "can not create beads" << std::endl;
        return false;
    }
    
    int nbeads = beads_.size();
    DynamicRectMatrix<double> B(3*nbeads, 3*nbeads);
    DynamicRectMatrix<double> C(3*nbeads, 3*nbeads);
    Mat3x3d I;
    for (std::size_t i = 0; i < nbeads; ++i) {
        for (std::size_t j = 0; j < nbeads; ++j) {
            Mat3x3d Tij;
            if (i != j ) {
                Vector3d Rij = beads_[i].pos - beads_[j].pos;
                double rij = Rij.length();
                double rij2 = rij * rij;
                double sumSigma2OverRij2 = ((beads_[i].radius*beads_[i].radius) + (beads_[i].radius*beads_[i].radius)) / rij2;                
                Mat3x3d tmpMat;
                tmpMat = outProduct(beads_[i].pos, beads_[j].pos) / rij2;
                double constant = 8.0 * NumericConstant::PI * eta * rij;
                Tij = ((1.0 + sumSigma2OverRij2/3.0) * I + (1.0 - sumSigma2OverRij2) * tmpMat ) / constant;
            }else {
                double constant = 1.0 / (6.0 * NumericConstant::PI * eta * beads_[i].radius);
                Tij(0, 0) = constant;
                Tij(1, 1) = constant;
                Tij(2, 2) = constant;
            }
            B.setSubMatrix(i*3, j*3, Tij);
        }
    }

    //invert B Matrix
    invertMatrix(B, C);
    
    //prepare U Matrix relative to arbitrary origin O(0.0, 0.0, 0.0)
    std::vector<Mat3x3d> U;
    for (int i = 0; i < nbeads; ++i) {
        Mat3x3d currU;
        currU.setupSkewMat(beads_[i].pos);
        U.push_back(currU);
    }
    
    //calculate Xi matrix at arbitrary origin O
    Mat3x3d Xitt;
    Mat3x3d Xirr;
    Mat3x3d Xitr;
        
    for (std::size_t i = 0; i < nbeads; ++i) {
        for (std::size_t j = 0; j < nbeads; ++j) {
            Mat3x3d Cij;
            C.getSubMatrix(i*3, j*3, Cij);
            
            Xitt += Cij;
            Xirr += U[i] * Cij;
            Xitr += U[i] * Cij * U[j];            
        }
    }

    //invert Xi to get Diffusion Tensor at arbitrary origin O
    RectMatrix<double, 6, 6> Xi;    
    RectMatrix<double, 6, 6> Do;
    Xi.setSubMatrix(0, 0, Xitt);
    Xi.setSubMatrix(0, 3, Xitr.transpose());
    Xi.setSubMatrix(3, 0, Xitr);
    Xi.setSubMatrix(3, 3, Xitt);
    invertMatrix(Xi, Do);

    Mat3x3d Dott; //translational diffusion tensor at arbitrary origin O
    Mat3x3d Dorr; //rotational diffusion tensor at arbitrary origin O
    Mat3x3d Dotr; //translation-rotation couplingl diffusion tensor at arbitrary origin O
    Do.getSubMatrix(0, 0 , Dott);
    Do.getSubMatrix(3, 0, Dotr);
    Do.getSubMatrix(3, 3, Dorr);

    //calculate center of diffusion
    Mat3x3d tmpMat;
    tmpMat(0, 0) = Dorr(1, 1) + Dorr(2, 2);
    tmpMat(0, 1) = - Dorr(0, 1);
    tmpMat(0, 2) = -Dorr(0, 2);
    tmpMat(1, 0) = -Dorr(0, 1);
    tmpMat(1, 1) = Dorr(0, 0)  + Dorr(2, 2);
    tmpMat(1, 2) = -Dorr(1, 2);
    tmpMat(2, 0) = -Dorr(0, 2);
    tmpMat(2, 1) = -Dorr(1, 2);
    tmpMat(2, 2) = Dorr(1, 1) + Dorr(0, 0);

    Vector3d tmpVec;
    tmpVec[0] = Dotr(1, 2) - Dotr(2, 1);
    tmpVec[1] = Dotr(2, 0) - Dotr(0, 2);
    tmpVec[2] = Dotr(0, 1) - Dotr(1, 0);
        
    Vector3d rod = tmpMat.inverse() * tmpVec;

    //calculate Diffusion Tensor at center of diffusion
    Mat3x3d Uod;
    Uod.setupSkewMat(rod);
    
    Mat3x3d Ddtt; //translational diffusion tensor at diffusion center
    Mat3x3d Ddtr; //rotational diffusion tensor at diffusion center
    Mat3x3d Ddrr; //translation-rotation couplingl diffusion tensor at diffusion tensor
    
    Ddtt = Dott - Uod * Dorr * Uod + Dotr.transpose() * Uod - Uod * Dotr;
    Ddrr = Dorr;
    Ddtr = Dotr + Dorr * Uod;
    
    props_.diffCenter = rod;
    props_.transDiff = Ddtt;
    props_.transRotDiff = Ddtr;
    props_.rotDiff = Ddrr;

    return true;    
}

void HydrodynamicsModel::writeBeads(std::ostream& os) {

}

void HydrodynamicsModel::writeDiffCenterAndDiffTensor(std::ostream& os) {

}

}
Revision:	891
Committed:	Wed Feb 22 20:35:16 2006 UTC (19 years, 8 months ago) by tim
File size:	6512 byte(s)
Log Message:	Adding Hydrodynamics Module
#	Content
1	/*
2	* Copyright (c) 2005 The University of Notre Dame. All Rights Reserved.
3	*
4	* The University of Notre Dame grants you ("Licensee") a
5	* non-exclusive, royalty free, license to use, modify and
6	* redistribute this software in source and binary code form, provided
7	* that the following conditions are met:
8	*
9	* 1. Acknowledgement of the program authors must be made in any
10	* publication of scientific results based in part on use of the
11	* program. An acceptable form of acknowledgement is citation of
12	* the article in which the program was described (Matthew
13	* A. Meineke, Charles F. Vardeman II, Teng Lin, Christopher
14	* J. Fennell and J. Daniel Gezelter, "OOPSE: An Object-Oriented
15	* Parallel Simulation Engine for Molecular Dynamics,"
16	* J. Comput. Chem. 26, pp. 252-271 (2005))
17	*
18	* 2. Redistributions of source code must retain the above copyright
19	* notice, this list of conditions and the following disclaimer.
20	*
21	* 3. Redistributions in binary form must reproduce the above copyright
22	* notice, this list of conditions and the following disclaimer in the
23	* documentation and/or other materials provided with the
24	* distribution.
25	*
26	* This software is provided "AS IS," without a warranty of any
27	* kind. All express or implied conditions, representations and
28	* warranties, including any implied warranty of merchantability,
29	* fitness for a particular purpose or non-infringement, are hereby
30	* excluded. The University of Notre Dame and its licensors shall not
31	* be liable for any damages suffered by licensee as a result of
32	* using, modifying or distributing the software or its
33	* derivatives. In no event will the University of Notre Dame or its
34	* licensors be liable for any lost revenue, profit or data, or for
35	* direct, indirect, special, consequential, incidental or punitive
36	* damages, however caused and regardless of the theory of liability,
37	* arising out of the use of or inability to use software, even if the
38	* University of Notre Dame has been advised of the possibility of
39	* such damages.
40	*/
41
42	#include "applications/hydrodynamics/HydrodynamicsModel.hpp"
43	#include "math/LU.hpp"
44	#include "math/DynamicRectMatrix.hpp"
45	#include "math/SquareMatrix3.hpp"
46	namespace oopse {
47	/**
48	* Reference:
49	* Beatriz Carrasco and Jose Gracia de la Torre, Hydrodynamic Properties of Rigid Particles:
50	* Comparison of Different Modeling and Computational Procedures.
51	* Biophysical Journal, 75(6), 3044, 1999
52	*/
53	bool HydrodynamicsModel::calcHydrodyanmicsProps(double eta) {
54	if (!createBeads(beads_)) {
55	std::cout << "can not create beads" << std::endl;
56	return false;
57	}
58
59	int nbeads = beads_.size();
60	DynamicRectMatrix<double> B(3nbeads, 3nbeads);
61	DynamicRectMatrix<double> C(3nbeads, 3nbeads);
62	Mat3x3d I;
63	for (std::size_t i = 0; i < nbeads; ++i) {
64	for (std::size_t j = 0; j < nbeads; ++j) {
65	Mat3x3d Tij;
66	if (i != j ) {
67	Vector3d Rij = beads_[i].pos - beads_[j].pos;
68	double rij = Rij.length();
69	double rij2 = rij * rij;
70	double sumSigma2OverRij2 = ((beads_[i].radiusbeads_[i].radius) + (beads_[i].radiusbeads_[i].radius)) / rij2;
71	Mat3x3d tmpMat;
72	tmpMat = outProduct(beads_[i].pos, beads_[j].pos) / rij2;
73	double constant = 8.0 * NumericConstant::PI * eta * rij;
74	Tij = ((1.0 + sumSigma2OverRij2/3.0) * I + (1.0 - sumSigma2OverRij2) * tmpMat ) / constant;
75	}else {
76	double constant = 1.0 / (6.0 * NumericConstant::PI * eta * beads_[i].radius);
77	Tij(0, 0) = constant;
78	Tij(1, 1) = constant;
79	Tij(2, 2) = constant;
80	}
81	B.setSubMatrix(i3, j3, Tij);
82	}
83	}
84
85	//invert B Matrix
86	invertMatrix(B, C);
87
88	//prepare U Matrix relative to arbitrary origin O(0.0, 0.0, 0.0)
89	std::vector<Mat3x3d> U;
90	for (int i = 0; i < nbeads; ++i) {
91	Mat3x3d currU;
92	currU.setupSkewMat(beads_[i].pos);
93	U.push_back(currU);
94	}
95
96	//calculate Xi matrix at arbitrary origin O
97	Mat3x3d Xitt;
98	Mat3x3d Xirr;
99	Mat3x3d Xitr;
100
101	for (std::size_t i = 0; i < nbeads; ++i) {
102	for (std::size_t j = 0; j < nbeads; ++j) {
103	Mat3x3d Cij;
104	C.getSubMatrix(i3, j3, Cij);
105
106	Xitt += Cij;
107	Xirr += U[i] * Cij;
108	Xitr += U[i] * Cij * U[j];
109	}
110	}
111
112	//invert Xi to get Diffusion Tensor at arbitrary origin O
113	RectMatrix<double, 6, 6> Xi;
114	RectMatrix<double, 6, 6> Do;
115	Xi.setSubMatrix(0, 0, Xitt);
116	Xi.setSubMatrix(0, 3, Xitr.transpose());
117	Xi.setSubMatrix(3, 0, Xitr);
118	Xi.setSubMatrix(3, 3, Xitt);
119	invertMatrix(Xi, Do);
120
121	Mat3x3d Dott; //translational diffusion tensor at arbitrary origin O
122	Mat3x3d Dorr; //rotational diffusion tensor at arbitrary origin O
123	Mat3x3d Dotr; //translation-rotation couplingl diffusion tensor at arbitrary origin O
124	Do.getSubMatrix(0, 0 , Dott);
125	Do.getSubMatrix(3, 0, Dotr);
126	Do.getSubMatrix(3, 3, Dorr);
127
128	//calculate center of diffusion
129	Mat3x3d tmpMat;
130	tmpMat(0, 0) = Dorr(1, 1) + Dorr(2, 2);
131	tmpMat(0, 1) = - Dorr(0, 1);
132	tmpMat(0, 2) = -Dorr(0, 2);
133	tmpMat(1, 0) = -Dorr(0, 1);
134	tmpMat(1, 1) = Dorr(0, 0) + Dorr(2, 2);
135	tmpMat(1, 2) = -Dorr(1, 2);
136	tmpMat(2, 0) = -Dorr(0, 2);
137	tmpMat(2, 1) = -Dorr(1, 2);
138	tmpMat(2, 2) = Dorr(1, 1) + Dorr(0, 0);
139
140	Vector3d tmpVec;
141	tmpVec[0] = Dotr(1, 2) - Dotr(2, 1);
142	tmpVec[1] = Dotr(2, 0) - Dotr(0, 2);
143	tmpVec[2] = Dotr(0, 1) - Dotr(1, 0);
144
145	Vector3d rod = tmpMat.inverse() * tmpVec;
146
147	//calculate Diffusion Tensor at center of diffusion
148	Mat3x3d Uod;
149	Uod.setupSkewMat(rod);
150
151	Mat3x3d Ddtt; //translational diffusion tensor at diffusion center
152	Mat3x3d Ddtr; //rotational diffusion tensor at diffusion center
153	Mat3x3d Ddrr; //translation-rotation couplingl diffusion tensor at diffusion tensor
154
155	Ddtt = Dott - Uod * Dorr * Uod + Dotr.transpose() * Uod - Uod * Dotr;
156	Ddrr = Dorr;
157	Ddtr = Dotr + Dorr * Uod;
158
159	props_.diffCenter = rod;
160	props_.transDiff = Ddtt;
161	props_.transRotDiff = Ddtr;
162	props_.rotDiff = Ddrr;
163
164	return true;
165	}
166
167	void HydrodynamicsModel::writeBeads(std::ostream& os) {
168
169	}
170
171	void HydrodynamicsModel::writeDiffCenterAndDiffTensor(std::ostream& os) {
172
173	}
174
175	}