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 "hydrodynamics/Sphere.hpp"
#include "hydrodynamics/Ellipsoid.hpp"
#include "applications/hydrodynamics/CompositeShape.hpp"
#include "math/LU.hpp"
#include "utils/simError.h"
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){    
  }
  
  void ApproximationModel::init() {
    if (!createBeads(beads_)) {
      sprintf(painCave.errMsg, "ApproximationModel::init() : Can not create beads\n");
      painCave.isFatal = 1;
      simError();        
    }
    
  }
  
  bool ApproximationModel::calcHydroProps(Shape* shape, RealType viscosity, RealType temperature) {
    
    bool ret = true;
    HydroProp* cr = new HydroProp();
    HydroProp* cd = new HydroProp();
    calcHydroPropsAtCR(beads_, viscosity, temperature, cr);
    calcHydroPropsAtCD(beads_, viscosity, temperature, cd);
    setCR(cr);
    setCD(cd);
    return true;    
  }
  
  bool ApproximationModel::calcHydroPropsAtCR(std::vector<BeadParam>& beads, RealType viscosity, RealType temperature, HydroProp* cr) {
    
    int nbeads = beads.size();
    DynamicRectMatrix<RealType> B(3*nbeads, 3*nbeads);
    DynamicRectMatrix<RealType> 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;
              RealType rij = Rij.length();
              RealType rij2 = rij * rij;
              RealType sumSigma2OverRij2 = ((beads[i].radius*beads[i].radius) + (beads[j].radius*beads[j].radius)) / rij2;                
              Mat3x3d tmpMat;
              tmpMat = outProduct(Rij, Rij) / rij2;
              RealType constant = 8.0 * NumericConstant::PI * viscosity * rij;
              RealType tmp1 = 1.0 + sumSigma2OverRij2/3.0;
              RealType tmp2 = 1.0 - sumSigma2OverRij2;
              Tij = (tmp1 * I + tmp2 * tmpMat ) / constant;
            }else {
              RealType 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
    
    RealType 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;
        // uncorrected here.  Volume correction is added after we assemble Xiorr
        Xiorr += -U[i] * Cij * U[j]; 
      }
    }

    // add the volume correction
    Xiorr += (6.0 * viscosity * volume) * I;    
    
    const RealType convertConstant = 1.439326479e4; //converts Poise angstroms
                                                    // to kcal fs mol^-1 Angstrom^-1

    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<RealType,6> Xir6x6;
    SquareMatrix<RealType,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);
    RealType kt = OOPSEConstant::kb * temperature ; // in kcal mol^-1
    Drtt *= kt;
    Drrt *= kt;
    Drtr *= kt;
    Drrr *= kt;
    //Xirtt *= OOPSEConstant::kb * temperature;
    //Xirtr *= OOPSEConstant::kb * temperature;
    //Xirrr *= OOPSEConstant::kb * temperature;
    
    Mat6x6d Xi, D;

    cr->setCOR(ror);

    Xi.setSubMatrix(0, 0, Xirtt);
    Xi.setSubMatrix(0, 3, Xirtr);
    Xi.setSubMatrix(3, 0, Xirtr);
    Xi.setSubMatrix(3, 3, Xirrr);

    cr->setXi(Xi);

    D.setSubMatrix(0, 0, Drtt);
    D.setSubMatrix(0, 3, Drrt);
    D.setSubMatrix(3, 0, Drtr);
    D.setSubMatrix(3, 3, Drrr);    

    cr->setD(D);
    
    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, RealType viscosity, RealType temperature, HydroProp* cd) {
    
    int nbeads = beads.size();
    DynamicRectMatrix<RealType> B(3*nbeads, 3*nbeads);
    DynamicRectMatrix<RealType> 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;
          RealType rij = Rij.length();
          RealType rij2 = rij * rij;
          RealType sumSigma2OverRij2 = ((beads[i].radius*beads[i].radius) + (beads[j].radius*beads[j].radius)) / rij2;                
          Mat3x3d tmpMat;
          tmpMat = outProduct(Rij, Rij) / rij2;
          RealType constant = 8.0 * NumericConstant::PI * viscosity * rij;
          RealType tmp1 = 1.0 + sumSigma2OverRij2/3.0;
          RealType tmp2 = 1.0 - sumSigma2OverRij2;
          Tij = (tmp1 * I + tmp2 * tmpMat ) / constant;
        }else {
          RealType 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

    RealType 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;
        // uncorrected here.  Volume correction is added after we assemble Xiorr
        Xirr += -U[i] * Cij * U[j];
      }
    }
    // add the volume correction here:
    Xirr += (6.0 * viscosity * volume) * I;    
    
    const RealType convertConstant = 1.439326479e4; //converts Poise angstroms
                                                    // to kcal fs mol^-1 Angstrom^-1
    Xitt *= convertConstant;
    Xitr *= convertConstant;
    Xirr *= convertConstant;
    
    RealType kt = OOPSEConstant::kb * temperature; // in kcal mol^-1
    
    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<RealType, 6> Dd;
    Dd.setSubMatrix(0, 0, Ddtt);
    Dd.setSubMatrix(0, 3, Ddtr.transpose());
    Dd.setSubMatrix(3, 0, Ddtr);
    Dd.setSubMatrix(3, 3, Ddrr);    
    SquareMatrix<RealType, 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;

    Mat6x6d Xi, D;

    cd->setCOR(rod);

    cd->setXi(Xid);

    D.setSubMatrix(0, 0, Ddtt);
    D.setSubMatrix(0, 3, Ddtr);
    D.setSubMatrix(3, 0, Ddtr);
    D.setSubMatrix(3, 3, Ddrr);

    cd->setD(D);

    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 / fs):" << std::endl;
    std::cout << Ddtr << std::endl;
    std::cout << "rotation(fs^-1):" << 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^-1):" << std::endl;
    std::cout << Xidrt << std::endl;
    std::cout << "translation-rotation(kcal*fs*mol^-1*Ang^-1):" << std::endl;
    std::cout << Xidtr << std::endl;
    std::cout << "rotation(kcal*fs*mol^-1):" << 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:	1208
Committed:	Wed Jan 16 20:19:28 2008 UTC (17 years, 9 months ago) by xsun
File size:	15860 byte(s)
Log Message:	Changes to do hydrodynamics modeling and to explain a diff file
#	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	gezelter	972	#include "hydrodynamics/Sphere.hpp"
48			#include "hydrodynamics/Ellipsoid.hpp"
49	tim	906	#include "applications/hydrodynamics/CompositeShape.hpp"
50			#include "math/LU.hpp"
51	tim	921	#include "utils/simError.h"
52	tim	906	namespace oopse {
53			/**
54			* Reference:
55			* Beatriz Carrasco and Jose Gracia de la Torre, Hydrodynamic Properties of Rigid Particles:
56			* Comparison of Different Modeling and Computational Procedures.
57			* Biophysical Journal, 75(6), 3044, 1999
58			*/
59
60	gezelter	972	ApproximationModel::ApproximationModel(StuntDouble* sd, SimInfo* info): HydrodynamicsModel(sd, info){
61			}
62
63			void ApproximationModel::init() {
64	tim	906	if (!createBeads(beads_)) {
65	tim	921	sprintf(painCave.errMsg, "ApproximationModel::init() : Can not create beads\n");
66			painCave.isFatal = 1;
67			simError();
68	tim	906	}
69	gezelter	972
70			}
71
72	tim	977	bool ApproximationModel::calcHydroProps(Shape* shape, RealType viscosity, RealType temperature) {
73	gezelter	972
74	tim	906	bool ret = true;
75	xsun	1177	HydroProp* cr = new HydroProp();
76			HydroProp* cd = new HydroProp();
77	tim	906	calcHydroPropsAtCR(beads_, viscosity, temperature, cr);
78	xsun	1177	calcHydroPropsAtCD(beads_, viscosity, temperature, cd);
79	tim	906	setCR(cr);
80			setCD(cd);
81			return true;
82	gezelter	972	}
83
84	gezelter	981	bool ApproximationModel::calcHydroPropsAtCR(std::vector<BeadParam>& beads, RealType viscosity, RealType temperature, HydroProp* cr) {
85	gezelter	972
86	tim	906	int nbeads = beads.size();
87	tim	977	DynamicRectMatrix<RealType> B(3nbeads, 3nbeads);
88			DynamicRectMatrix<RealType> C(3nbeads, 3nbeads);
89	tim	906	Mat3x3d I;
90			I(0, 0) = 1.0;
91			I(1, 1) = 1.0;
92			I(2, 2) = 1.0;
93
94			for (std::size_t i = 0; i < nbeads; ++i) {
95	gezelter	972	for (std::size_t j = 0; j < nbeads; ++j) {
96			Mat3x3d Tij;
97	tim	906	if (i != j ) {
98	gezelter	972	Vector3d Rij = beads[i].pos - beads[j].pos;
99	tim	977	RealType rij = Rij.length();
100			RealType rij2 = rij * rij;
101			RealType sumSigma2OverRij2 = ((beads[i].radiusbeads[i].radius) + (beads[j].radiusbeads[j].radius)) / rij2;
102	gezelter	972	Mat3x3d tmpMat;
103			tmpMat = outProduct(Rij, Rij) / rij2;
104	tim	977	RealType constant = 8.0 * NumericConstant::PI * viscosity * rij;
105	tim	978	RealType tmp1 = 1.0 + sumSigma2OverRij2/3.0;
106			RealType tmp2 = 1.0 - sumSigma2OverRij2;
107			Tij = (tmp1 * I + tmp2 * tmpMat ) / constant;
108	tim	906	}else {
109	tim	977	RealType constant = 1.0 / (6.0 * NumericConstant::PI * viscosity * beads[i].radius);
110	gezelter	972	Tij(0, 0) = constant;
111			Tij(1, 1) = constant;
112			Tij(2, 2) = constant;
113	tim	906	}
114			B.setSubMatrix(i3, j3, Tij);
115	gezelter	972	}
116	tim	906	}
117	gezelter	972
118	tim	906	//invert B Matrix
119			invertMatrix(B, C);
120	tim	910
121	tim	906	//prepare U Matrix relative to arbitrary origin O(0.0, 0.0, 0.0)
122			std::vector<Mat3x3d> U;
123			for (int i = 0; i < nbeads; ++i) {
124	gezelter	972	Mat3x3d currU;
125			currU.setupSkewMat(beads[i].pos);
126			U.push_back(currU);
127	tim	906	}
128
129			//calculate Xi matrix at arbitrary origin O
130			Mat3x3d Xiott;
131			Mat3x3d Xiorr;
132			Mat3x3d Xiotr;
133	gezelter	972
134	tim	906	//calculate the total volume
135	gezelter	972
136	tim	977	RealType volume = 0.0;
137	tim	906	for (std::vector<BeadParam>::iterator iter = beads.begin(); iter != beads.end(); ++iter) {
138	gezelter	972	volume += 4.0/3.0 * NumericConstant::PI * pow((*iter).radius,3);
139	tim	906	}
140	gezelter	972
141			for (std::size_t i = 0; i < nbeads; ++i) {
142			for (std::size_t j = 0; j < nbeads; ++j) {
143			Mat3x3d Cij;
144			C.getSubMatrix(i3, j3, Cij);
145	tim	906
146	gezelter	972	Xiott += Cij;
147			Xiotr += U[i] * Cij;
148	xsun	1208	// uncorrected here. Volume correction is added after we assemble Xiorr
149	gezelter	972	Xiorr += -U[i] * Cij * U[j];
150			}
151	tim	906	}
152	xsun	1208
153			// add the volume correction
154			Xiorr += (6.0 * viscosity * volume) * I;
155	gezelter	972
156	xsun	1208	const RealType convertConstant = 1.439326479e4; //converts Poise angstroms
157			// to kcal fs mol^-1 Angstrom^-1
158
159	tim	906	Xiott *= convertConstant;
160			Xiotr *= convertConstant;
161			Xiorr *= convertConstant;
162
163			Mat3x3d tmp;
164			Mat3x3d tmpInv;
165			Vector3d tmpVec;
166			tmp(0, 0) = Xiott(1, 1) + Xiott(2, 2);
167			tmp(0, 1) = - Xiott(0, 1);
168			tmp(0, 2) = -Xiott(0, 2);
169			tmp(1, 0) = -Xiott(0, 1);
170			tmp(1, 1) = Xiott(0, 0) + Xiott(2, 2);
171			tmp(1, 2) = -Xiott(1, 2);
172			tmp(2, 0) = -Xiott(0, 2);
173			tmp(2, 1) = -Xiott(1, 2);
174			tmp(2, 2) = Xiott(1, 1) + Xiott(0, 0);
175			tmpVec[0] = Xiotr(2, 1) - Xiotr(1, 2);
176			tmpVec[1] = Xiotr(0, 2) - Xiotr(2, 0);
177			tmpVec[2] = Xiotr(1, 0) - Xiotr(0, 1);
178			tmpInv = tmp.inverse();
179			Vector3d ror = tmpInv * tmpVec; //center of resistance
180			Mat3x3d Uor;
181			Uor.setupSkewMat(ror);
182
183			Mat3x3d Xirtt;
184			Mat3x3d Xirrr;
185			Mat3x3d Xirtr;
186
187			Xirtt = Xiott;
188			Xirtr = (Xiotr - Uor * Xiott);
189			Xirrr = Xiorr - Uor * Xiott * Uor + Xiotr * Uor - Uor * Xiotr.transpose();
190
191
192	tim	977	SquareMatrix<RealType,6> Xir6x6;
193			SquareMatrix<RealType,6> Dr6x6;
194	tim	906
195			Xir6x6.setSubMatrix(0, 0, Xirtt);
196			Xir6x6.setSubMatrix(0, 3, Xirtr.transpose());
197			Xir6x6.setSubMatrix(3, 0, Xirtr);
198			Xir6x6.setSubMatrix(3, 3, Xirrr);
199
200			invertMatrix(Xir6x6, Dr6x6);
201			Mat3x3d Drtt;
202			Mat3x3d Drtr;
203			Mat3x3d Drrt;
204			Mat3x3d Drrr;
205			Dr6x6.getSubMatrix(0, 0, Drtt);
206			Dr6x6.getSubMatrix(0, 3, Drrt);
207			Dr6x6.getSubMatrix(3, 0, Drtr);
208			Dr6x6.getSubMatrix(3, 3, Drrr);
209	xsun	1208	RealType kt = OOPSEConstant::kb * temperature ; // in kcal mol^-1
210	tim	906	Drtt *= kt;
211			Drrt *= kt;
212			Drtr *= kt;
213			Drrr *= kt;
214	xsun	1208	//Xirtt = OOPSEConstant::kb temperature;
215			//Xirtr = OOPSEConstant::kb temperature;
216			//Xirrr = OOPSEConstant::kb temperature;
217	tim	906
218	gezelter	981	Mat6x6d Xi, D;
219	tim	906
220	gezelter	981	cr->setCOR(ror);
221
222			Xi.setSubMatrix(0, 0, Xirtt);
223			Xi.setSubMatrix(0, 3, Xirtr);
224			Xi.setSubMatrix(3, 0, Xirtr);
225			Xi.setSubMatrix(3, 3, Xirrr);
226
227			cr->setXi(Xi);
228
229			D.setSubMatrix(0, 0, Drtt);
230			D.setSubMatrix(0, 3, Drrt);
231			D.setSubMatrix(3, 0, Drtr);
232			D.setSubMatrix(3, 3, Drrr);
233
234			cr->setD(D);
235	tim	906
236			std::cout << "-----------------------------------------\n";
237			std::cout << "center of resistance :" << std::endl;
238			std::cout << ror << std::endl;
239			std::cout << "resistant tensor at center of resistance" << std::endl;
240			std::cout << "translation:" << std::endl;
241			std::cout << Xirtt << std::endl;
242			std::cout << "translation-rotation:" << std::endl;
243			std::cout << Xirtr << std::endl;
244			std::cout << "rotation:" << std::endl;
245			std::cout << Xirrr << std::endl;
246			std::cout << "diffusion tensor at center of resistance" << std::endl;
247			std::cout << "translation:" << std::endl;
248			std::cout << Drtt << std::endl;
249			std::cout << "rotation-translation:" << std::endl;
250			std::cout << Drrt << std::endl;
251			std::cout << "translation-rotation:" << std::endl;
252			std::cout << Drtr << std::endl;
253			std::cout << "rotation:" << std::endl;
254			std::cout << Drrr << std::endl;
255			std::cout << "-----------------------------------------\n";
256
257			return true;
258			}
259	gezelter	972
260	xsun	1177	bool ApproximationModel::calcHydroPropsAtCD(std::vector<BeadParam>& beads, RealType viscosity, RealType temperature, HydroProp* cd) {
261	gezelter	972
262	tim	906	int nbeads = beads.size();
263	tim	977	DynamicRectMatrix<RealType> B(3nbeads, 3nbeads);
264			DynamicRectMatrix<RealType> C(3nbeads, 3nbeads);
265	tim	906	Mat3x3d I;
266			I(0, 0) = 1.0;
267			I(1, 1) = 1.0;
268			I(2, 2) = 1.0;
269
270			for (std::size_t i = 0; i < nbeads; ++i) {
271	gezelter	972	for (std::size_t j = 0; j < nbeads; ++j) {
272			Mat3x3d Tij;
273			if (i != j ) {
274			Vector3d Rij = beads[i].pos - beads[j].pos;
275	tim	977	RealType rij = Rij.length();
276			RealType rij2 = rij * rij;
277			RealType sumSigma2OverRij2 = ((beads[i].radiusbeads[i].radius) + (beads[j].radiusbeads[j].radius)) / rij2;
278	gezelter	972	Mat3x3d tmpMat;
279			tmpMat = outProduct(Rij, Rij) / rij2;
280	tim	977	RealType constant = 8.0 * NumericConstant::PI * viscosity * rij;
281	tim	978	RealType tmp1 = 1.0 + sumSigma2OverRij2/3.0;
282			RealType tmp2 = 1.0 - sumSigma2OverRij2;
283			Tij = (tmp1 * I + tmp2 * tmpMat ) / constant;
284	gezelter	972	}else {
285	tim	977	RealType constant = 1.0 / (6.0 * NumericConstant::PI * viscosity * beads[i].radius);
286	gezelter	972	Tij(0, 0) = constant;
287			Tij(1, 1) = constant;
288			Tij(2, 2) = constant;
289	tim	906	}
290	gezelter	972	B.setSubMatrix(i3, j3, Tij);
291			}
292	tim	906	}
293	gezelter	972
294	tim	906	//invert B Matrix
295			invertMatrix(B, C);
296	gezelter	972
297	tim	906	//prepare U Matrix relative to arbitrary origin O(0.0, 0.0, 0.0)
298			std::vector<Mat3x3d> U;
299			for (int i = 0; i < nbeads; ++i) {
300	gezelter	972	Mat3x3d currU;
301			currU.setupSkewMat(beads[i].pos);
302			U.push_back(currU);
303	tim	906	}
304
305			//calculate Xi matrix at arbitrary origin O
306			Mat3x3d Xitt;
307			Mat3x3d Xirr;
308			Mat3x3d Xitr;
309
310			//calculate the total volume
311
312	tim	977	RealType volume = 0.0;
313	tim	906	for (std::vector<BeadParam>::iterator iter = beads.begin(); iter != beads.end(); ++iter) {
314	gezelter	972	volume += 4.0/3.0 * NumericConstant::PI * pow((*iter).radius,3);
315	tim	906	}
316	gezelter	972
317	tim	906	for (std::size_t i = 0; i < nbeads; ++i) {
318	gezelter	972	for (std::size_t j = 0; j < nbeads; ++j) {
319			Mat3x3d Cij;
320			C.getSubMatrix(i3, j3, Cij);
321	tim	906
322	gezelter	972	Xitt += Cij;
323			Xitr += U[i] * Cij;
324	xsun	1208	// uncorrected here. Volume correction is added after we assemble Xiorr
325	gezelter	972	Xirr += -U[i] * Cij * U[j];
326			}
327	tim	906	}
328	xsun	1208	// add the volume correction here:
329			Xirr += (6.0 * viscosity * volume) * I;
330	gezelter	972
331	xsun	1208	const RealType convertConstant = 1.439326479e4; //converts Poise angstroms
332			// to kcal fs mol^-1 Angstrom^-1
333	tim	906	Xitt *= convertConstant;
334			Xitr *= convertConstant;
335			Xirr *= convertConstant;
336	gezelter	972
337	xsun	1208	RealType kt = OOPSEConstant::kb * temperature; // in kcal mol^-1
338	gezelter	972
339	tim	906	Mat3x3d Dott; //translational diffusion tensor at arbitrary origin O
340			Mat3x3d Dorr; //rotational diffusion tensor at arbitrary origin O
341			Mat3x3d Dotr; //translation-rotation couplingl diffusion tensor at arbitrary origin O
342	gezelter	972
343	tim	906	const static Mat3x3d zeroMat(0.0);
344
345			Mat3x3d XittInv(0.0);
346			XittInv = Xitt.inverse();
347
348			Mat3x3d XirrInv;
349			XirrInv = Xirr.inverse();
350
351			Mat3x3d tmp;
352			Mat3x3d tmpInv;
353			tmp = Xitt - Xitr.transpose() * XirrInv * Xitr;
354			tmpInv = tmp.inverse();
355
356			Dott = tmpInv;
357			Dotr = -XirrInv * Xitr * tmpInv;
358
359			tmp = Xirr - Xitr * XittInv * Xitr.transpose();
360			tmpInv = tmp.inverse();
361
362			Dorr = tmpInv;
363
364			//calculate center of diffusion
365			tmp(0, 0) = Dorr(1, 1) + Dorr(2, 2);
366			tmp(0, 1) = - Dorr(0, 1);
367			tmp(0, 2) = -Dorr(0, 2);
368			tmp(1, 0) = -Dorr(0, 1);
369			tmp(1, 1) = Dorr(0, 0) + Dorr(2, 2);
370			tmp(1, 2) = -Dorr(1, 2);
371			tmp(2, 0) = -Dorr(0, 2);
372			tmp(2, 1) = -Dorr(1, 2);
373			tmp(2, 2) = Dorr(1, 1) + Dorr(0, 0);
374
375			Vector3d tmpVec;
376			tmpVec[0] = Dotr(1, 2) - Dotr(2, 1);
377			tmpVec[1] = Dotr(2, 0) - Dotr(0, 2);
378			tmpVec[2] = Dotr(0, 1) - Dotr(1, 0);
379
380			tmpInv = tmp.inverse();
381
382			Vector3d rod = tmpInv * tmpVec;
383
384			//calculate Diffusion Tensor at center of diffusion
385			Mat3x3d Uod;
386			Uod.setupSkewMat(rod);
387
388			Mat3x3d Ddtt; //translational diffusion tensor at diffusion center
389			Mat3x3d Ddtr; //rotational diffusion tensor at diffusion center
390			Mat3x3d Ddrr; //translation-rotation couplingl diffusion tensor at diffusion tensor
391
392			Ddtt = Dott - Uod * Dorr * Uod + Dotr.transpose() * Uod - Uod * Dotr;
393			Ddrr = Dorr;
394			Ddtr = Dotr + Dorr * Uod;
395
396	tim	977	SquareMatrix<RealType, 6> Dd;
397	tim	906	Dd.setSubMatrix(0, 0, Ddtt);
398			Dd.setSubMatrix(0, 3, Ddtr.transpose());
399			Dd.setSubMatrix(3, 0, Ddtr);
400			Dd.setSubMatrix(3, 3, Ddrr);
401	tim	977	SquareMatrix<RealType, 6> Xid;
402	tim	906	Ddtt *= kt;
403			Ddtr *=kt;
404			Ddrr *= kt;
405			invertMatrix(Dd, Xid);
406
407
408
409			//Xidtt in units of kcalfsmol^-1*Ang^-2
410			//Xid /= OOPSEConstant::energyConvert;
411			Xid = OOPSEConstant::kb temperature;
412
413	gezelter	981	Mat6x6d Xi, D;
414	tim	906
415	xsun	1177	cd->setCOR(rod);
416	gezelter	981
417	xsun	1177	cd->setXi(Xid);
418	gezelter	981
419			D.setSubMatrix(0, 0, Ddtt);
420			D.setSubMatrix(0, 3, Ddtr);
421			D.setSubMatrix(3, 0, Ddtr);
422			D.setSubMatrix(3, 3, Ddrr);
423
424	xsun	1177	cd->setD(D);
425	gezelter	981
426	tim	906	std::cout << "viscosity = " << viscosity << std::endl;
427			std::cout << "temperature = " << temperature << std::endl;
428			std::cout << "center of diffusion :" << std::endl;
429			std::cout << rod << std::endl;
430			std::cout << "diffusion tensor at center of diffusion " << std::endl;
431	xsun	1208	std::cout << "translation(A^2 / fs) :" << std::endl;
432	tim	906	std::cout << Ddtt << std::endl;
433	xsun	1208	std::cout << "translation-rotation(A / fs):" << std::endl;
434	tim	906	std::cout << Ddtr << std::endl;
435	xsun	1208	std::cout << "rotation(fs^-1):" << std::endl;
436	tim	906	std::cout << Ddrr << std::endl;
437
438			std::cout << "resistance tensor at center of diffusion " << std::endl;
439			std::cout << "translation(kcalfsmol^-1*Ang^-2) :" << std::endl;
440
441			Mat3x3d Xidtt;
442			Mat3x3d Xidrt;
443			Mat3x3d Xidtr;
444			Mat3x3d Xidrr;
445			Xid.getSubMatrix(0, 0, Xidtt);
446			Xid.getSubMatrix(0, 3, Xidrt);
447			Xid.getSubMatrix(3, 0, Xidtr);
448			Xid.getSubMatrix(3, 3, Xidrr);
449
450			std::cout << Xidtt << std::endl;
451	xsun	1208	std::cout << "rotation-translation (kcalfsmol^-1*Ang^-1):" << std::endl;
452	tim	906	std::cout << Xidrt << std::endl;
453	xsun	1208	std::cout << "translation-rotation(kcalfsmol^-1*Ang^-1):" << std::endl;
454	tim	906	std::cout << Xidtr << std::endl;
455	xsun	1208	std::cout << "rotation(kcalfsmol^-1):" << std::endl;
456	tim	906	std::cout << Xidrr << std::endl;
457
458			return true;
459	gezelter	972
460			}
461	tim	906
462	gezelter	972	void ApproximationModel::writeBeads(std::ostream& os) {
463	tim	906	std::vector<BeadParam>::iterator iter;
464			os << beads_.size() << std::endl;
465			os << "Generated by Hydro" << std::endl;
466			for (iter = beads_.begin(); iter != beads_.end(); ++iter) {
467	gezelter	972	os << iter->atomName << "\t" << iter->pos[0] << "\t" << iter->pos[1] << "\t" << iter->pos[2] << std::endl;
468	tim	906	}
469	gezelter	972
470			}
471	tim	906	}