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, 1 month ago) by tim
File size:	16333 byte(s)
Log Message:	refactor Hydrodynamics module.
#	User	Rev	Content
1	tim	906	/*
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			}