applications/hydrodynamics/ApproximationModel.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/ApproximationModel.hpp" 
#include "math/LU.hpp"
#include "math/DynamicRectMatrix.hpp"
#include "math/SquareMatrix3.hpp"
#include "utils/OOPSEConstant.hpp"
#include "applications/hydrodynamics/Spheric.hpp"
#include "applications/hydrodynamics/Ellipsoid.hpp"
#include "applications/hydrodynamics/CompositeShape.hpp"
#include "math/LU.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
 */

ApproximationModel::ApproximationModel(StuntDouble* sd, SimInfo* info): HydrodynamicsModel(sd, info){
/*
    DynamicProperty::const_iterator iter;

    iter = extraParams.find("Viscosity");
    if (iter != extraParams.end()) {
        boost::any param = iter->second;
        viscosity = boost::any_cast<double>(param);
    }else {
        std::cout << "ApproximationModel Error\n" ;
    }

    iter = extraParams.find("Temperature");
    if (iter != extraParams.end()) {
        boost::any param = iter->second;
        temperature = boost::any_cast<double>(param);
    }else {
        std::cout << "ApproximationModel Error\n" ;
    }    
*/
}

bool ApproximationModel::calcHydroProps(Spheric* spheric, double viscosity, double temperature) {
    return internalCalcHydroProps(static_cast<Shape*>(spheric), viscosity, temperature);
}

bool ApproximationModel::calcHydroProps(Ellipsoid* ellipsoid, double viscosity, double temperature) {
    return internalCalcHydroProps(static_cast<Shape*>(ellipsoid), viscosity, temperature);
}
bool ApproximationModel::calcHydroProps(CompositeShape* compositeShape, double viscosity, double temperature) {
    return internalCalcHydroProps(static_cast<Shape*>(compositeShape), viscosity, temperature);
}

 
bool ApproximationModel::internalCalcHydroProps(Shape* shape, double viscosity, double temperature) {
    if (!createBeads(beads_)) {
        std::cout << "can not create beads" << std::endl;
        return false;
    }

    bool ret = true;
    HydroProps cr;
    HydroProps cd;
    calcHydroPropsAtCR(beads_, viscosity, temperature, cr);
    calcHydroPropsAtCD(beads_, viscosity, temperature, cd);
    setCR(cr);
    setCD(cd);
    
    return true;    
}

bool ApproximationModel::calcHydroPropsAtCR(std::vector<BeadParam>& beads, double viscosity, double temperature, HydroProps& cr) {

    int nbeads = beads.size();
    DynamicRectMatrix<double> B(3*nbeads, 3*nbeads);
    DynamicRectMatrix<double> C(3*nbeads, 3*nbeads);
    Mat3x3d I;
    I(0, 0) = 1.0;
    I(1, 1) = 1.0;
    I(2, 2) = 1.0;
    
    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(Rij, Rij) / rij2;
                double constant = 8.0 * NumericConstant::PI * viscosity * rij;
                Tij = ((1.0 + sumSigma2OverRij2/3.0) * I + (1.0 - sumSigma2OverRij2) * tmpMat ) / constant;
            }else {
                double constant = 1.0 / (6.0 * NumericConstant::PI * viscosity * 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 Xiott;
    Mat3x3d Xiorr;
    Mat3x3d Xiotr;

    //calculate the total volume

    double volume = 0.0;
    for (std::vector<BeadParam>::iterator iter = beads.begin(); iter != beads.end(); ++iter) {
        volume += 4.0/3.0 * NumericConstant::PI * pow((*iter).radius,3);
    }
        
    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);
            
            Xiott += Cij;
            Xiotr += U[i] * Cij;
            Xiorr += -U[i] * Cij * U[j] + (6 * viscosity * volume) * I;            
        }
    }

    const double convertConstant = 6.023; //convert poise.angstrom to amu/fs
    Xiott *= convertConstant;
    Xiotr *= convertConstant;
    Xiorr *= convertConstant;
    

    Mat3x3d tmp;
    Mat3x3d tmpInv;
    Vector3d tmpVec;
    tmp(0, 0) = Xiott(1, 1) + Xiott(2, 2);
    tmp(0, 1) = - Xiott(0, 1);
    tmp(0, 2) = -Xiott(0, 2);
    tmp(1, 0) = -Xiott(0, 1);
    tmp(1, 1) = Xiott(0, 0)  + Xiott(2, 2);
    tmp(1, 2) = -Xiott(1, 2);
    tmp(2, 0) = -Xiott(0, 2);
    tmp(2, 1) = -Xiott(1, 2);
    tmp(2, 2) = Xiott(1, 1) + Xiott(0, 0);
    tmpVec[0] = Xiotr(2, 1) - Xiotr(1, 2);
    tmpVec[1] = Xiotr(0, 2) - Xiotr(2, 0);
    tmpVec[2] = Xiotr(1, 0) - Xiotr(0, 1);
    tmpInv = tmp.inverse();    
    Vector3d ror = tmpInv * tmpVec; //center of resistance
    Mat3x3d Uor;
    Uor.setupSkewMat(ror);
    
    Mat3x3d Xirtt;
    Mat3x3d Xirrr;
    Mat3x3d Xirtr;

    Xirtt = Xiott;
    Xirtr = (Xiotr - Uor * Xiott);
    Xirrr = Xiorr - Uor * Xiott * Uor + Xiotr * Uor - Uor * Xiotr.transpose();
    

    SquareMatrix<double,6> Xir6x6;
    SquareMatrix<double,6> Dr6x6;

    Xir6x6.setSubMatrix(0, 0, Xirtt);
    Xir6x6.setSubMatrix(0, 3, Xirtr.transpose());
    Xir6x6.setSubMatrix(3, 0, Xirtr);
    Xir6x6.setSubMatrix(3, 3, Xirrr);

    invertMatrix(Xir6x6, Dr6x6);
    Mat3x3d Drtt;
    Mat3x3d Drtr;
    Mat3x3d Drrt;
    Mat3x3d Drrr;
    Dr6x6.getSubMatrix(0, 0, Drtt);
    Dr6x6.getSubMatrix(0, 3, Drrt);
    Dr6x6.getSubMatrix(3, 0, Drtr);
    Dr6x6.getSubMatrix(3, 3, Drrr);
    double kt = OOPSEConstant::kB * temperature ;
    Drtt *= kt;
    Drrt *= kt;
    Drtr *= kt;
    Drrr *= kt;
    Xirtt *= OOPSEConstant::kb * temperature;
    Xirtr *= OOPSEConstant::kb * temperature;
    Xirrr *= OOPSEConstant::kb * temperature;
    

    cr.center = ror;
    cr.Xi.setSubMatrix(0, 0, Xirtt);
    cr.Xi.setSubMatrix(0, 3, Xirtr);
    cr.Xi.setSubMatrix(3, 0, Xirtr);
    cr.Xi.setSubMatrix(3, 3, Xirrr);
    cr.D.setSubMatrix(0, 0, Drtt);
    cr.D.setSubMatrix(0, 3, Drrt);
    cr.D.setSubMatrix(3, 0, Drtr);
    cr.D.setSubMatrix(3, 3, Drrr);    
    
    std::cout << "-----------------------------------------\n";
    std::cout << "center of resistance :" << std::endl;
    std::cout << ror << std::endl;
    std::cout << "resistant tensor at center of resistance" << std::endl;
    std::cout << "translation:" << std::endl;
    std::cout << Xirtt << std::endl;
    std::cout << "translation-rotation:" << std::endl;
    std::cout << Xirtr << std::endl;
    std::cout << "rotation:" << std::endl;
    std::cout << Xirrr << std::endl; 
    std::cout << "diffusion tensor at center of resistance" << std::endl;
    std::cout << "translation:" << std::endl;
    std::cout << Drtt << std::endl;
    std::cout << "rotation-translation:" << std::endl;
    std::cout << Drrt << std::endl;
    std::cout << "translation-rotation:" << std::endl;
    std::cout << Drtr << std::endl;
    std::cout << "rotation:" << std::endl;
    std::cout << Drrr << std::endl;    
    std::cout << "-----------------------------------------\n";

    return true;
}

bool ApproximationModel::calcHydroPropsAtCD(std::vector<BeadParam>& beads, double viscosity, double temperature, HydroProps& cr) {

    int nbeads = beads.size();
    DynamicRectMatrix<double> B(3*nbeads, 3*nbeads);
    DynamicRectMatrix<double> C(3*nbeads, 3*nbeads);
    Mat3x3d I;
    I(0, 0) = 1.0;
    I(1, 1) = 1.0;
    I(2, 2) = 1.0;
    
    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(Rij, Rij) / rij2;
                double constant = 8.0 * NumericConstant::PI * viscosity * rij;
                Tij = ((1.0 + sumSigma2OverRij2/3.0) * I + (1.0 - sumSigma2OverRij2) * tmpMat ) / constant;
            }else {
                double constant = 1.0 / (6.0 * NumericConstant::PI * viscosity * 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;

    //calculate the total volume

    double volume = 0.0;
    for (std::vector<BeadParam>::iterator iter = beads.begin(); iter != beads.end(); ++iter) {
        volume += 4.0/3.0 * NumericConstant::PI * pow((*iter).radius,3);
    }
        
    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;
            Xitr += U[i] * Cij;
            Xirr += -U[i] * Cij * U[j] + (6 * viscosity * volume) * I;            
        }
    }

    const double convertConstant = 6.023; //convert poise.angstrom to amu/fs
    Xitt *= convertConstant;
    Xitr *= convertConstant;
    Xirr *= convertConstant;

    double kt = OOPSEConstant::kB * temperature;

    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

    const static Mat3x3d zeroMat(0.0);
    
    Mat3x3d XittInv(0.0);
    XittInv = Xitt.inverse();
    
    Mat3x3d XirrInv;
    XirrInv = Xirr.inverse();

    Mat3x3d tmp;
    Mat3x3d tmpInv;
    tmp = Xitt - Xitr.transpose() * XirrInv * Xitr;
    tmpInv = tmp.inverse();

    Dott = tmpInv;
    Dotr = -XirrInv * Xitr * tmpInv;
    
    tmp = Xirr - Xitr * XittInv * Xitr.transpose();    
    tmpInv = tmp.inverse();
    
    Dorr = tmpInv;

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

    tmpInv = tmp.inverse();
    
    Vector3d rod = tmpInv * 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;

    SquareMatrix<double, 6> Dd;
    Dd.setSubMatrix(0, 0, Ddtt);
    Dd.setSubMatrix(0, 3, Ddtr.transpose());
    Dd.setSubMatrix(3, 0, Ddtr);
    Dd.setSubMatrix(3, 3, Ddrr);    
    SquareMatrix<double, 6> Xid;
    Ddtt *= kt;
    Ddtr *=kt;
    Ddrr *= kt;
    invertMatrix(Dd, Xid);


    //Xidtt in units of kcal*fs*mol^-1*Ang^-2
    //Xid /= OOPSEConstant::energyConvert;
    Xid *= OOPSEConstant::kb * temperature;

    cr.center = rod;
    cr.D.setSubMatrix(0, 0, Ddtt);
    cr.D.setSubMatrix(0, 3, Ddtr);
    cr.D.setSubMatrix(3, 0, Ddtr);
    cr.D.setSubMatrix(3, 3, Ddrr);
    cr.Xi = Xid;

    std::cout << "viscosity = " << viscosity << std::endl;
    std::cout << "temperature = " << temperature << std::endl;
    std::cout << "center of diffusion :" << std::endl;
    std::cout << rod << std::endl;
    std::cout << "diffusion tensor at center of diffusion " << std::endl;
    std::cout << "translation(A^2/fs) :" << std::endl;
    std::cout << Ddtt << std::endl;
    std::cout << "translation-rotation(A^3/fs):" << std::endl;
    std::cout << Ddtr << std::endl;
    std::cout << "rotation(A^4/fs):" << std::endl;
    std::cout << Ddrr << std::endl;

    std::cout << "resistance tensor at center of diffusion " << std::endl;
    std::cout << "translation(kcal*fs*mol^-1*Ang^-2) :" << std::endl;

    Mat3x3d Xidtt;
    Mat3x3d Xidrt;
    Mat3x3d Xidtr;
    Mat3x3d Xidrr;
    Xid.getSubMatrix(0, 0, Xidtt);
    Xid.getSubMatrix(0, 3, Xidrt);
    Xid.getSubMatrix(3, 0, Xidtr);
    Xid.getSubMatrix(3, 3, Xidrr);

    std::cout << Xidtt << std::endl;
    std::cout << "rotation-translation (kcal*fs*mol^-1*Ang^-3):" << std::endl;
    std::cout << Xidrt << std::endl;
    std::cout << "translation-rotation(kcal*fs*mol^-1*Ang^-3):" << std::endl;
    std::cout << Xidtr << std::endl;
    std::cout << "rotation(kcal*fs*mol^-1*Ang^-4):" << std::endl;
    std::cout << Xidrr << std::endl;

    return true;
      
}

/*
void ApproximationModel::writeBeads(std::ostream& os) {
    std::vector<BeadParam>::iterator iter;
    os << beads_.size() << std::endl;
    os << "Generated by Hydro" << std::endl;
    for (iter = beads_.begin(); iter != beads_.end(); ++iter) {
        os << iter->atomName << "\t" << iter->pos[0] << "\t" << iter->pos[1] << "\t" << iter->pos[2] << std::endl;
    }

}
*/


}
Revision:	906
Committed:	Fri Mar 17 23:20:35 2006 UTC (19 years, 7 months ago) by tim
File size:	16333 byte(s)
Log Message:	refactor 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/ApproximationModel.hpp"
43	#include "math/LU.hpp"
44	#include "math/DynamicRectMatrix.hpp"
45	#include "math/SquareMatrix3.hpp"
46	#include "utils/OOPSEConstant.hpp"
47	#include "applications/hydrodynamics/Spheric.hpp"
48	#include "applications/hydrodynamics/Ellipsoid.hpp"
49	#include "applications/hydrodynamics/CompositeShape.hpp"
50	#include "math/LU.hpp"
51	namespace oopse {
52	/**
53	* Reference:
54	* Beatriz Carrasco and Jose Gracia de la Torre, Hydrodynamic Properties of Rigid Particles:
55	* Comparison of Different Modeling and Computational Procedures.
56	* Biophysical Journal, 75(6), 3044, 1999
57	*/
58
59	ApproximationModel::ApproximationModel(StuntDouble* sd, SimInfo* info): HydrodynamicsModel(sd, info){
60	/*
61	DynamicProperty::const_iterator iter;
62
63	iter = extraParams.find("Viscosity");
64	if (iter != extraParams.end()) {
65	boost::any param = iter->second;
66	viscosity = boost::any_cast<double>(param);
67	}else {
68	std::cout << "ApproximationModel Error\n" ;
69	}
70
71	iter = extraParams.find("Temperature");
72	if (iter != extraParams.end()) {
73	boost::any param = iter->second;
74	temperature = boost::any_cast<double>(param);
75	}else {
76	std::cout << "ApproximationModel Error\n" ;
77	}
78	*/
79	}
80
81	bool ApproximationModel::calcHydroProps(Spheric* spheric, double viscosity, double temperature) {
82	return internalCalcHydroProps(static_cast<Shape*>(spheric), viscosity, temperature);
83	}
84
85	bool ApproximationModel::calcHydroProps(Ellipsoid* ellipsoid, double viscosity, double temperature) {
86	return internalCalcHydroProps(static_cast<Shape*>(ellipsoid), viscosity, temperature);
87	}
88	bool ApproximationModel::calcHydroProps(CompositeShape* compositeShape, double viscosity, double temperature) {
89	return internalCalcHydroProps(static_cast<Shape*>(compositeShape), viscosity, temperature);
90	}
91
92
93	bool ApproximationModel::internalCalcHydroProps(Shape* shape, double viscosity, double temperature) {
94	if (!createBeads(beads_)) {
95	std::cout << "can not create beads" << std::endl;
96	return false;
97	}
98
99	bool ret = true;
100	HydroProps cr;
101	HydroProps cd;
102	calcHydroPropsAtCR(beads_, viscosity, temperature, cr);
103	calcHydroPropsAtCD(beads_, viscosity, temperature, cd);
104	setCR(cr);
105	setCD(cd);
106
107	return true;
108	}
109
110	bool ApproximationModel::calcHydroPropsAtCR(std::vector<BeadParam>& beads, double viscosity, double temperature, HydroProps& cr) {
111
112	int nbeads = beads.size();
113	DynamicRectMatrix<double> B(3nbeads, 3nbeads);
114	DynamicRectMatrix<double> C(3nbeads, 3nbeads);
115	Mat3x3d I;
116	I(0, 0) = 1.0;
117	I(1, 1) = 1.0;
118	I(2, 2) = 1.0;
119
120	for (std::size_t i = 0; i < nbeads; ++i) {
121	for (std::size_t j = 0; j < nbeads; ++j) {
122	Mat3x3d Tij;
123	if (i != j ) {
124	Vector3d Rij = beads[i].pos - beads[j].pos;
125	double rij = Rij.length();
126	double rij2 = rij * rij;
127	double sumSigma2OverRij2 = ((beads[i].radiusbeads[i].radius) + (beads[i].radiusbeads[i].radius)) / rij2;
128	Mat3x3d tmpMat;
129	tmpMat = outProduct(Rij, Rij) / rij2;
130	double constant = 8.0 * NumericConstant::PI * viscosity * rij;
131	Tij = ((1.0 + sumSigma2OverRij2/3.0) * I + (1.0 - sumSigma2OverRij2) * tmpMat ) / constant;
132	}else {
133	double constant = 1.0 / (6.0 * NumericConstant::PI * viscosity * beads[i].radius);
134	Tij(0, 0) = constant;
135	Tij(1, 1) = constant;
136	Tij(2, 2) = constant;
137	}
138	B.setSubMatrix(i3, j3, Tij);
139	}
140	}
141
142	//invert B Matrix
143	invertMatrix(B, C);
144
145	//prepare U Matrix relative to arbitrary origin O(0.0, 0.0, 0.0)
146	std::vector<Mat3x3d> U;
147	for (int i = 0; i < nbeads; ++i) {
148	Mat3x3d currU;
149	currU.setupSkewMat(beads[i].pos);
150	U.push_back(currU);
151	}
152
153	//calculate Xi matrix at arbitrary origin O
154	Mat3x3d Xiott;
155	Mat3x3d Xiorr;
156	Mat3x3d Xiotr;
157
158	//calculate the total volume
159
160	double volume = 0.0;
161	for (std::vector<BeadParam>::iterator iter = beads.begin(); iter != beads.end(); ++iter) {
162	volume += 4.0/3.0 * NumericConstant::PI * pow((*iter).radius,3);
163	}
164
165	for (std::size_t i = 0; i < nbeads; ++i) {
166	for (std::size_t j = 0; j < nbeads; ++j) {
167	Mat3x3d Cij;
168	C.getSubMatrix(i3, j3, Cij);
169
170	Xiott += Cij;
171	Xiotr += U[i] * Cij;
172	Xiorr += -U[i] * Cij * U[j] + (6 * viscosity * volume) * I;
173	}
174	}
175
176	const double convertConstant = 6.023; //convert poise.angstrom to amu/fs
177	Xiott *= convertConstant;
178	Xiotr *= convertConstant;
179	Xiorr *= convertConstant;
180
181
182
183	Mat3x3d tmp;
184	Mat3x3d tmpInv;
185	Vector3d tmpVec;
186	tmp(0, 0) = Xiott(1, 1) + Xiott(2, 2);
187	tmp(0, 1) = - Xiott(0, 1);
188	tmp(0, 2) = -Xiott(0, 2);
189	tmp(1, 0) = -Xiott(0, 1);
190	tmp(1, 1) = Xiott(0, 0) + Xiott(2, 2);
191	tmp(1, 2) = -Xiott(1, 2);
192	tmp(2, 0) = -Xiott(0, 2);
193	tmp(2, 1) = -Xiott(1, 2);
194	tmp(2, 2) = Xiott(1, 1) + Xiott(0, 0);
195	tmpVec[0] = Xiotr(2, 1) - Xiotr(1, 2);
196	tmpVec[1] = Xiotr(0, 2) - Xiotr(2, 0);
197	tmpVec[2] = Xiotr(1, 0) - Xiotr(0, 1);
198	tmpInv = tmp.inverse();
199	Vector3d ror = tmpInv * tmpVec; //center of resistance
200	Mat3x3d Uor;
201	Uor.setupSkewMat(ror);
202
203	Mat3x3d Xirtt;
204	Mat3x3d Xirrr;
205	Mat3x3d Xirtr;
206
207	Xirtt = Xiott;
208	Xirtr = (Xiotr - Uor * Xiott);
209	Xirrr = Xiorr - Uor * Xiott * Uor + Xiotr * Uor - Uor * Xiotr.transpose();
210
211
212	SquareMatrix<double,6> Xir6x6;
213	SquareMatrix<double,6> Dr6x6;
214
215	Xir6x6.setSubMatrix(0, 0, Xirtt);
216	Xir6x6.setSubMatrix(0, 3, Xirtr.transpose());
217	Xir6x6.setSubMatrix(3, 0, Xirtr);
218	Xir6x6.setSubMatrix(3, 3, Xirrr);
219
220	invertMatrix(Xir6x6, Dr6x6);
221	Mat3x3d Drtt;
222	Mat3x3d Drtr;
223	Mat3x3d Drrt;
224	Mat3x3d Drrr;
225	Dr6x6.getSubMatrix(0, 0, Drtt);
226	Dr6x6.getSubMatrix(0, 3, Drrt);
227	Dr6x6.getSubMatrix(3, 0, Drtr);
228	Dr6x6.getSubMatrix(3, 3, Drrr);
229	double kt = OOPSEConstant::kB * temperature ;
230	Drtt *= kt;
231	Drrt *= kt;
232	Drtr *= kt;
233	Drrr *= kt;
234	Xirtt = OOPSEConstant::kb temperature;
235	Xirtr = OOPSEConstant::kb temperature;
236	Xirrr = OOPSEConstant::kb temperature;
237
238
239	cr.center = ror;
240	cr.Xi.setSubMatrix(0, 0, Xirtt);
241	cr.Xi.setSubMatrix(0, 3, Xirtr);
242	cr.Xi.setSubMatrix(3, 0, Xirtr);
243	cr.Xi.setSubMatrix(3, 3, Xirrr);
244	cr.D.setSubMatrix(0, 0, Drtt);
245	cr.D.setSubMatrix(0, 3, Drrt);
246	cr.D.setSubMatrix(3, 0, Drtr);
247	cr.D.setSubMatrix(3, 3, Drrr);
248
249	std::cout << "-----------------------------------------\n";
250	std::cout << "center of resistance :" << std::endl;
251	std::cout << ror << std::endl;
252	std::cout << "resistant tensor at center of resistance" << std::endl;
253	std::cout << "translation:" << std::endl;
254	std::cout << Xirtt << std::endl;
255	std::cout << "translation-rotation:" << std::endl;
256	std::cout << Xirtr << std::endl;
257	std::cout << "rotation:" << std::endl;
258	std::cout << Xirrr << std::endl;
259	std::cout << "diffusion tensor at center of resistance" << std::endl;
260	std::cout << "translation:" << std::endl;
261	std::cout << Drtt << std::endl;
262	std::cout << "rotation-translation:" << std::endl;
263	std::cout << Drrt << std::endl;
264	std::cout << "translation-rotation:" << std::endl;
265	std::cout << Drtr << std::endl;
266	std::cout << "rotation:" << std::endl;
267	std::cout << Drrr << std::endl;
268	std::cout << "-----------------------------------------\n";
269
270	return true;
271	}
272
273	bool ApproximationModel::calcHydroPropsAtCD(std::vector<BeadParam>& beads, double viscosity, double temperature, HydroProps& cr) {
274
275	int nbeads = beads.size();
276	DynamicRectMatrix<double> B(3nbeads, 3nbeads);
277	DynamicRectMatrix<double> C(3nbeads, 3nbeads);
278	Mat3x3d I;
279	I(0, 0) = 1.0;
280	I(1, 1) = 1.0;
281	I(2, 2) = 1.0;
282
283	for (std::size_t i = 0; i < nbeads; ++i) {
284	for (std::size_t j = 0; j < nbeads; ++j) {
285	Mat3x3d Tij;
286	if (i != j ) {
287	Vector3d Rij = beads[i].pos - beads[j].pos;
288	double rij = Rij.length();
289	double rij2 = rij * rij;
290	double sumSigma2OverRij2 = ((beads[i].radiusbeads[i].radius) + (beads[i].radiusbeads[i].radius)) / rij2;
291	Mat3x3d tmpMat;
292	tmpMat = outProduct(Rij, Rij) / rij2;
293	double constant = 8.0 * NumericConstant::PI * viscosity * rij;
294	Tij = ((1.0 + sumSigma2OverRij2/3.0) * I + (1.0 - sumSigma2OverRij2) * tmpMat ) / constant;
295	}else {
296	double constant = 1.0 / (6.0 * NumericConstant::PI * viscosity * beads[i].radius);
297	Tij(0, 0) = constant;
298	Tij(1, 1) = constant;
299	Tij(2, 2) = constant;
300	}
301	B.setSubMatrix(i3, j3, Tij);
302	}
303	}
304
305	//invert B Matrix
306	invertMatrix(B, C);
307
308	//prepare U Matrix relative to arbitrary origin O(0.0, 0.0, 0.0)
309	std::vector<Mat3x3d> U;
310	for (int i = 0; i < nbeads; ++i) {
311	Mat3x3d currU;
312	currU.setupSkewMat(beads[i].pos);
313	U.push_back(currU);
314	}
315
316	//calculate Xi matrix at arbitrary origin O
317	Mat3x3d Xitt;
318	Mat3x3d Xirr;
319	Mat3x3d Xitr;
320
321	//calculate the total volume
322
323	double volume = 0.0;
324	for (std::vector<BeadParam>::iterator iter = beads.begin(); iter != beads.end(); ++iter) {
325	volume += 4.0/3.0 * NumericConstant::PI * pow((*iter).radius,3);
326	}
327
328	for (std::size_t i = 0; i < nbeads; ++i) {
329	for (std::size_t j = 0; j < nbeads; ++j) {
330	Mat3x3d Cij;
331	C.getSubMatrix(i3, j3, Cij);
332
333	Xitt += Cij;
334	Xitr += U[i] * Cij;
335	Xirr += -U[i] * Cij * U[j] + (6 * viscosity * volume) * I;
336	}
337	}
338
339	const double convertConstant = 6.023; //convert poise.angstrom to amu/fs
340	Xitt *= convertConstant;
341	Xitr *= convertConstant;
342	Xirr *= convertConstant;
343
344	double kt = OOPSEConstant::kB * temperature;
345
346	Mat3x3d Dott; //translational diffusion tensor at arbitrary origin O
347	Mat3x3d Dorr; //rotational diffusion tensor at arbitrary origin O
348	Mat3x3d Dotr; //translation-rotation couplingl diffusion tensor at arbitrary origin O
349
350	const static Mat3x3d zeroMat(0.0);
351
352	Mat3x3d XittInv(0.0);
353	XittInv = Xitt.inverse();
354
355	Mat3x3d XirrInv;
356	XirrInv = Xirr.inverse();
357
358	Mat3x3d tmp;
359	Mat3x3d tmpInv;
360	tmp = Xitt - Xitr.transpose() * XirrInv * Xitr;
361	tmpInv = tmp.inverse();
362
363	Dott = tmpInv;
364	Dotr = -XirrInv * Xitr * tmpInv;
365
366	tmp = Xirr - Xitr * XittInv * Xitr.transpose();
367	tmpInv = tmp.inverse();
368
369	Dorr = tmpInv;
370
371	//calculate center of diffusion
372	tmp(0, 0) = Dorr(1, 1) + Dorr(2, 2);
373	tmp(0, 1) = - Dorr(0, 1);
374	tmp(0, 2) = -Dorr(0, 2);
375	tmp(1, 0) = -Dorr(0, 1);
376	tmp(1, 1) = Dorr(0, 0) + Dorr(2, 2);
377	tmp(1, 2) = -Dorr(1, 2);
378	tmp(2, 0) = -Dorr(0, 2);
379	tmp(2, 1) = -Dorr(1, 2);
380	tmp(2, 2) = Dorr(1, 1) + Dorr(0, 0);
381
382	Vector3d tmpVec;
383	tmpVec[0] = Dotr(1, 2) - Dotr(2, 1);
384	tmpVec[1] = Dotr(2, 0) - Dotr(0, 2);
385	tmpVec[2] = Dotr(0, 1) - Dotr(1, 0);
386
387	tmpInv = tmp.inverse();
388
389	Vector3d rod = tmpInv * tmpVec;
390
391	//calculate Diffusion Tensor at center of diffusion
392	Mat3x3d Uod;
393	Uod.setupSkewMat(rod);
394
395	Mat3x3d Ddtt; //translational diffusion tensor at diffusion center
396	Mat3x3d Ddtr; //rotational diffusion tensor at diffusion center
397	Mat3x3d Ddrr; //translation-rotation couplingl diffusion tensor at diffusion tensor
398
399	Ddtt = Dott - Uod * Dorr * Uod + Dotr.transpose() * Uod - Uod * Dotr;
400	Ddrr = Dorr;
401	Ddtr = Dotr + Dorr * Uod;
402
403	SquareMatrix<double, 6> Dd;
404	Dd.setSubMatrix(0, 0, Ddtt);
405	Dd.setSubMatrix(0, 3, Ddtr.transpose());
406	Dd.setSubMatrix(3, 0, Ddtr);
407	Dd.setSubMatrix(3, 3, Ddrr);
408	SquareMatrix<double, 6> Xid;
409	Ddtt *= kt;
410	Ddtr *=kt;
411	Ddrr *= kt;
412	invertMatrix(Dd, Xid);
413
414
415
416	//Xidtt in units of kcalfsmol^-1*Ang^-2
417	//Xid /= OOPSEConstant::energyConvert;
418	Xid = OOPSEConstant::kb temperature;
419
420	cr.center = rod;
421	cr.D.setSubMatrix(0, 0, Ddtt);
422	cr.D.setSubMatrix(0, 3, Ddtr);
423	cr.D.setSubMatrix(3, 0, Ddtr);
424	cr.D.setSubMatrix(3, 3, Ddrr);
425	cr.Xi = Xid;
426
427	std::cout << "viscosity = " << viscosity << std::endl;
428	std::cout << "temperature = " << temperature << std::endl;
429	std::cout << "center of diffusion :" << std::endl;
430	std::cout << rod << std::endl;
431	std::cout << "diffusion tensor at center of diffusion " << std::endl;
432	std::cout << "translation(A^2/fs) :" << std::endl;
433	std::cout << Ddtt << std::endl;
434	std::cout << "translation-rotation(A^3/fs):" << std::endl;
435	std::cout << Ddtr << std::endl;
436	std::cout << "rotation(A^4/fs):" << std::endl;
437	std::cout << Ddrr << std::endl;
438
439	std::cout << "resistance tensor at center of diffusion " << std::endl;
440	std::cout << "translation(kcalfsmol^-1*Ang^-2) :" << std::endl;
441
442	Mat3x3d Xidtt;
443	Mat3x3d Xidrt;
444	Mat3x3d Xidtr;
445	Mat3x3d Xidrr;
446	Xid.getSubMatrix(0, 0, Xidtt);
447	Xid.getSubMatrix(0, 3, Xidrt);
448	Xid.getSubMatrix(3, 0, Xidtr);
449	Xid.getSubMatrix(3, 3, Xidrr);
450
451	std::cout << Xidtt << std::endl;
452	std::cout << "rotation-translation (kcalfsmol^-1*Ang^-3):" << std::endl;
453	std::cout << Xidrt << std::endl;
454	std::cout << "translation-rotation(kcalfsmol^-1*Ang^-3):" << std::endl;
455	std::cout << Xidtr << std::endl;
456	std::cout << "rotation(kcalfsmol^-1*Ang^-4):" << std::endl;
457	std::cout << Xidrr << std::endl;
458
459	return true;
460
461	}
462
463	/*
464	void ApproximationModel::writeBeads(std::ostream& os) {
465	std::vector<BeadParam>::iterator iter;
466	os << beads_.size() << std::endl;
467	os << "Generated by Hydro" << std::endl;
468	for (iter = beads_.begin(); iter != beads_.end(); ++iter) {
469	os << iter->atomName << "\t" << iter->pos[0] << "\t" << iter->pos[1] << "\t" << iter->pos[2] << std::endl;
470	}
471
472	}
473	*/
474
475
476	}