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;
    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, RealType viscosity, RealType temperature, HydroProps& 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;
        //Xiorr += -U[i] * Cij * U[j] + (6 * viscosity * volume) * I;    
        Xiorr += -U[i] * Cij * U[j]; 
      }
    }
    
    const RealType 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<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 ;
    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, RealType viscosity, RealType temperature, HydroProps& 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 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;
            //Xirr += -U[i] * Cij * U[j] + (6 * viscosity * volume) * I;            
        Xirr += -U[i] * Cij * U[j];
      }
    }
    
    const RealType convertConstant = 6.023; //convert poise.angstrom to amu/fs
    Xitt *= convertConstant;
    Xitr *= convertConstant;
    Xirr *= convertConstant;
    
    RealType 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<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;

    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:	2774
Committed:	Thu May 25 17:02:00 2006 UTC (18 years, 2 months ago) by tim
File size:	15411 byte(s)
Log Message:	Fix a type promotion problem
#	User	Rev	Content
1	tim	2634	/*
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	2768	#include "hydrodynamics/Sphere.hpp"
48			#include "hydrodynamics/Ellipsoid.hpp"
49	tim	2634	#include "applications/hydrodynamics/CompositeShape.hpp"
50			#include "math/LU.hpp"
51	tim	2675	#include "utils/simError.h"
52	tim	2634	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	2768	ApproximationModel::ApproximationModel(StuntDouble* sd, SimInfo* info): HydrodynamicsModel(sd, info){
61			}
62
63			void ApproximationModel::init() {
64	tim	2634	if (!createBeads(beads_)) {
65	tim	2675	sprintf(painCave.errMsg, "ApproximationModel::init() : Can not create beads\n");
66			painCave.isFatal = 1;
67			simError();
68	tim	2634	}
69	gezelter	2768
70			}
71
72	tim	2773	bool ApproximationModel::calcHydroProps(Shape* shape, RealType viscosity, RealType temperature) {
73	gezelter	2768
74	tim	2634	bool ret = true;
75			HydroProps cr;
76			HydroProps cd;
77			calcHydroPropsAtCR(beads_, viscosity, temperature, cr);
78	tim	2749	//calcHydroPropsAtCD(beads_, viscosity, temperature, cd);
79	tim	2634	setCR(cr);
80			setCD(cd);
81
82			return true;
83	gezelter	2768	}
84
85	tim	2773	bool ApproximationModel::calcHydroPropsAtCR(std::vector<BeadParam>& beads, RealType viscosity, RealType temperature, HydroProps& cr) {
86	gezelter	2768
87	tim	2634	int nbeads = beads.size();
88	tim	2773	DynamicRectMatrix<RealType> B(3nbeads, 3nbeads);
89			DynamicRectMatrix<RealType> C(3nbeads, 3nbeads);
90	tim	2634	Mat3x3d I;
91			I(0, 0) = 1.0;
92			I(1, 1) = 1.0;
93			I(2, 2) = 1.0;
94
95			for (std::size_t i = 0; i < nbeads; ++i) {
96	gezelter	2768	for (std::size_t j = 0; j < nbeads; ++j) {
97			Mat3x3d Tij;
98	tim	2634	if (i != j ) {
99	gezelter	2768	Vector3d Rij = beads[i].pos - beads[j].pos;
100	tim	2773	RealType rij = Rij.length();
101			RealType rij2 = rij * rij;
102			RealType sumSigma2OverRij2 = ((beads[i].radiusbeads[i].radius) + (beads[j].radiusbeads[j].radius)) / rij2;
103	gezelter	2768	Mat3x3d tmpMat;
104			tmpMat = outProduct(Rij, Rij) / rij2;
105	tim	2773	RealType constant = 8.0 * NumericConstant::PI * viscosity * rij;
106	tim	2774	RealType tmp1 = 1.0 + sumSigma2OverRij2/3.0;
107			RealType tmp2 = 1.0 - sumSigma2OverRij2;
108			Tij = (tmp1 * I + tmp2 * tmpMat ) / constant;
109	tim	2634	}else {
110	tim	2773	RealType constant = 1.0 / (6.0 * NumericConstant::PI * viscosity * beads[i].radius);
111	gezelter	2768	Tij(0, 0) = constant;
112			Tij(1, 1) = constant;
113			Tij(2, 2) = constant;
114	tim	2634	}
115			B.setSubMatrix(i3, j3, Tij);
116	gezelter	2768	}
117	tim	2634	}
118	gezelter	2768
119	tim	2634	//invert B Matrix
120			invertMatrix(B, C);
121	tim	2650
122	tim	2634	//prepare U Matrix relative to arbitrary origin O(0.0, 0.0, 0.0)
123			std::vector<Mat3x3d> U;
124			for (int i = 0; i < nbeads; ++i) {
125	gezelter	2768	Mat3x3d currU;
126			currU.setupSkewMat(beads[i].pos);
127			U.push_back(currU);
128	tim	2634	}
129
130			//calculate Xi matrix at arbitrary origin O
131			Mat3x3d Xiott;
132			Mat3x3d Xiorr;
133			Mat3x3d Xiotr;
134	gezelter	2768
135	tim	2634	//calculate the total volume
136	gezelter	2768
137	tim	2773	RealType volume = 0.0;
138	tim	2634	for (std::vector<BeadParam>::iterator iter = beads.begin(); iter != beads.end(); ++iter) {
139	gezelter	2768	volume += 4.0/3.0 * NumericConstant::PI * pow((*iter).radius,3);
140	tim	2634	}
141	gezelter	2768
142			for (std::size_t i = 0; i < nbeads; ++i) {
143			for (std::size_t j = 0; j < nbeads; ++j) {
144			Mat3x3d Cij;
145			C.getSubMatrix(i3, j3, Cij);
146	tim	2634
147	gezelter	2768	Xiott += Cij;
148			Xiotr += U[i] * Cij;
149			//Xiorr += -U[i] * Cij * U[j] + (6 * viscosity * volume) * I;
150			Xiorr += -U[i] * Cij * U[j];
151			}
152	tim	2634	}
153	gezelter	2768
154	tim	2773	const RealType convertConstant = 6.023; //convert poise.angstrom to amu/fs
155	tim	2634	Xiott *= convertConstant;
156			Xiotr *= convertConstant;
157			Xiorr *= convertConstant;
158
159
160	gezelter	2768
161	tim	2634	Mat3x3d tmp;
162			Mat3x3d tmpInv;
163			Vector3d tmpVec;
164			tmp(0, 0) = Xiott(1, 1) + Xiott(2, 2);
165			tmp(0, 1) = - Xiott(0, 1);
166			tmp(0, 2) = -Xiott(0, 2);
167			tmp(1, 0) = -Xiott(0, 1);
168			tmp(1, 1) = Xiott(0, 0) + Xiott(2, 2);
169			tmp(1, 2) = -Xiott(1, 2);
170			tmp(2, 0) = -Xiott(0, 2);
171			tmp(2, 1) = -Xiott(1, 2);
172			tmp(2, 2) = Xiott(1, 1) + Xiott(0, 0);
173			tmpVec[0] = Xiotr(2, 1) - Xiotr(1, 2);
174			tmpVec[1] = Xiotr(0, 2) - Xiotr(2, 0);
175			tmpVec[2] = Xiotr(1, 0) - Xiotr(0, 1);
176			tmpInv = tmp.inverse();
177			Vector3d ror = tmpInv * tmpVec; //center of resistance
178			Mat3x3d Uor;
179			Uor.setupSkewMat(ror);
180
181			Mat3x3d Xirtt;
182			Mat3x3d Xirrr;
183			Mat3x3d Xirtr;
184
185			Xirtt = Xiott;
186			Xirtr = (Xiotr - Uor * Xiott);
187			Xirrr = Xiorr - Uor * Xiott * Uor + Xiotr * Uor - Uor * Xiotr.transpose();
188
189
190	tim	2773	SquareMatrix<RealType,6> Xir6x6;
191			SquareMatrix<RealType,6> Dr6x6;
192	tim	2634
193			Xir6x6.setSubMatrix(0, 0, Xirtt);
194			Xir6x6.setSubMatrix(0, 3, Xirtr.transpose());
195			Xir6x6.setSubMatrix(3, 0, Xirtr);
196			Xir6x6.setSubMatrix(3, 3, Xirrr);
197
198			invertMatrix(Xir6x6, Dr6x6);
199			Mat3x3d Drtt;
200			Mat3x3d Drtr;
201			Mat3x3d Drrt;
202			Mat3x3d Drrr;
203			Dr6x6.getSubMatrix(0, 0, Drtt);
204			Dr6x6.getSubMatrix(0, 3, Drrt);
205			Dr6x6.getSubMatrix(3, 0, Drtr);
206			Dr6x6.getSubMatrix(3, 3, Drrr);
207	tim	2773	RealType kt = OOPSEConstant::kB * temperature ;
208	tim	2634	Drtt *= kt;
209			Drrt *= kt;
210			Drtr *= kt;
211			Drrr *= kt;
212			Xirtt = OOPSEConstant::kb temperature;
213			Xirtr = OOPSEConstant::kb temperature;
214			Xirrr = OOPSEConstant::kb temperature;
215
216
217			cr.center = ror;
218			cr.Xi.setSubMatrix(0, 0, Xirtt);
219			cr.Xi.setSubMatrix(0, 3, Xirtr);
220			cr.Xi.setSubMatrix(3, 0, Xirtr);
221			cr.Xi.setSubMatrix(3, 3, Xirrr);
222			cr.D.setSubMatrix(0, 0, Drtt);
223			cr.D.setSubMatrix(0, 3, Drrt);
224			cr.D.setSubMatrix(3, 0, Drtr);
225			cr.D.setSubMatrix(3, 3, Drrr);
226
227			std::cout << "-----------------------------------------\n";
228			std::cout << "center of resistance :" << std::endl;
229			std::cout << ror << std::endl;
230			std::cout << "resistant tensor at center of resistance" << std::endl;
231			std::cout << "translation:" << std::endl;
232			std::cout << Xirtt << std::endl;
233			std::cout << "translation-rotation:" << std::endl;
234			std::cout << Xirtr << std::endl;
235			std::cout << "rotation:" << std::endl;
236			std::cout << Xirrr << std::endl;
237			std::cout << "diffusion tensor at center of resistance" << std::endl;
238			std::cout << "translation:" << std::endl;
239			std::cout << Drtt << std::endl;
240			std::cout << "rotation-translation:" << std::endl;
241			std::cout << Drrt << std::endl;
242			std::cout << "translation-rotation:" << std::endl;
243			std::cout << Drtr << std::endl;
244			std::cout << "rotation:" << std::endl;
245			std::cout << Drrr << std::endl;
246			std::cout << "-----------------------------------------\n";
247
248			return true;
249			}
250	gezelter	2768
251	tim	2773	bool ApproximationModel::calcHydroPropsAtCD(std::vector<BeadParam>& beads, RealType viscosity, RealType temperature, HydroProps& cr) {
252	gezelter	2768
253	tim	2634	int nbeads = beads.size();
254	tim	2773	DynamicRectMatrix<RealType> B(3nbeads, 3nbeads);
255			DynamicRectMatrix<RealType> C(3nbeads, 3nbeads);
256	tim	2634	Mat3x3d I;
257			I(0, 0) = 1.0;
258			I(1, 1) = 1.0;
259			I(2, 2) = 1.0;
260
261			for (std::size_t i = 0; i < nbeads; ++i) {
262	gezelter	2768	for (std::size_t j = 0; j < nbeads; ++j) {
263			Mat3x3d Tij;
264			if (i != j ) {
265			Vector3d Rij = beads[i].pos - beads[j].pos;
266	tim	2773	RealType rij = Rij.length();
267			RealType rij2 = rij * rij;
268			RealType sumSigma2OverRij2 = ((beads[i].radiusbeads[i].radius) + (beads[j].radiusbeads[j].radius)) / rij2;
269	gezelter	2768	Mat3x3d tmpMat;
270			tmpMat = outProduct(Rij, Rij) / rij2;
271	tim	2773	RealType constant = 8.0 * NumericConstant::PI * viscosity * rij;
272	tim	2774	RealType tmp1 = 1.0 + sumSigma2OverRij2/3.0;
273			RealType tmp2 = 1.0 - sumSigma2OverRij2;
274			Tij = (tmp1 * I + tmp2 * tmpMat ) / constant;
275	gezelter	2768	}else {
276	tim	2773	RealType constant = 1.0 / (6.0 * NumericConstant::PI * viscosity * beads[i].radius);
277	gezelter	2768	Tij(0, 0) = constant;
278			Tij(1, 1) = constant;
279			Tij(2, 2) = constant;
280	tim	2634	}
281	gezelter	2768	B.setSubMatrix(i3, j3, Tij);
282			}
283	tim	2634	}
284	gezelter	2768
285	tim	2634	//invert B Matrix
286			invertMatrix(B, C);
287	gezelter	2768
288	tim	2634	//prepare U Matrix relative to arbitrary origin O(0.0, 0.0, 0.0)
289			std::vector<Mat3x3d> U;
290			for (int i = 0; i < nbeads; ++i) {
291	gezelter	2768	Mat3x3d currU;
292			currU.setupSkewMat(beads[i].pos);
293			U.push_back(currU);
294	tim	2634	}
295
296			//calculate Xi matrix at arbitrary origin O
297			Mat3x3d Xitt;
298			Mat3x3d Xirr;
299			Mat3x3d Xitr;
300
301			//calculate the total volume
302
303	tim	2773	RealType volume = 0.0;
304	tim	2634	for (std::vector<BeadParam>::iterator iter = beads.begin(); iter != beads.end(); ++iter) {
305	gezelter	2768	volume += 4.0/3.0 * NumericConstant::PI * pow((*iter).radius,3);
306	tim	2634	}
307	gezelter	2768
308	tim	2634	for (std::size_t i = 0; i < nbeads; ++i) {
309	gezelter	2768	for (std::size_t j = 0; j < nbeads; ++j) {
310			Mat3x3d Cij;
311			C.getSubMatrix(i3, j3, Cij);
312	tim	2634
313	gezelter	2768	Xitt += Cij;
314			Xitr += U[i] * Cij;
315	tim	2749	//Xirr += -U[i] * Cij * U[j] + (6 * viscosity * volume) * I;
316	gezelter	2768	Xirr += -U[i] * Cij * U[j];
317			}
318	tim	2634	}
319	gezelter	2768
320	tim	2773	const RealType convertConstant = 6.023; //convert poise.angstrom to amu/fs
321	tim	2634	Xitt *= convertConstant;
322			Xitr *= convertConstant;
323			Xirr *= convertConstant;
324	gezelter	2768
325	tim	2773	RealType kt = OOPSEConstant::kB * temperature;
326	gezelter	2768
327	tim	2634	Mat3x3d Dott; //translational diffusion tensor at arbitrary origin O
328			Mat3x3d Dorr; //rotational diffusion tensor at arbitrary origin O
329			Mat3x3d Dotr; //translation-rotation couplingl diffusion tensor at arbitrary origin O
330	gezelter	2768
331	tim	2634	const static Mat3x3d zeroMat(0.0);
332
333			Mat3x3d XittInv(0.0);
334			XittInv = Xitt.inverse();
335
336			Mat3x3d XirrInv;
337			XirrInv = Xirr.inverse();
338
339			Mat3x3d tmp;
340			Mat3x3d tmpInv;
341			tmp = Xitt - Xitr.transpose() * XirrInv * Xitr;
342			tmpInv = tmp.inverse();
343
344			Dott = tmpInv;
345			Dotr = -XirrInv * Xitr * tmpInv;
346
347			tmp = Xirr - Xitr * XittInv * Xitr.transpose();
348			tmpInv = tmp.inverse();
349
350			Dorr = tmpInv;
351
352			//calculate center of diffusion
353			tmp(0, 0) = Dorr(1, 1) + Dorr(2, 2);
354			tmp(0, 1) = - Dorr(0, 1);
355			tmp(0, 2) = -Dorr(0, 2);
356			tmp(1, 0) = -Dorr(0, 1);
357			tmp(1, 1) = Dorr(0, 0) + Dorr(2, 2);
358			tmp(1, 2) = -Dorr(1, 2);
359			tmp(2, 0) = -Dorr(0, 2);
360			tmp(2, 1) = -Dorr(1, 2);
361			tmp(2, 2) = Dorr(1, 1) + Dorr(0, 0);
362
363			Vector3d tmpVec;
364			tmpVec[0] = Dotr(1, 2) - Dotr(2, 1);
365			tmpVec[1] = Dotr(2, 0) - Dotr(0, 2);
366			tmpVec[2] = Dotr(0, 1) - Dotr(1, 0);
367
368			tmpInv = tmp.inverse();
369
370			Vector3d rod = tmpInv * tmpVec;
371
372			//calculate Diffusion Tensor at center of diffusion
373			Mat3x3d Uod;
374			Uod.setupSkewMat(rod);
375
376			Mat3x3d Ddtt; //translational diffusion tensor at diffusion center
377			Mat3x3d Ddtr; //rotational diffusion tensor at diffusion center
378			Mat3x3d Ddrr; //translation-rotation couplingl diffusion tensor at diffusion tensor
379
380			Ddtt = Dott - Uod * Dorr * Uod + Dotr.transpose() * Uod - Uod * Dotr;
381			Ddrr = Dorr;
382			Ddtr = Dotr + Dorr * Uod;
383
384	tim	2773	SquareMatrix<RealType, 6> Dd;
385	tim	2634	Dd.setSubMatrix(0, 0, Ddtt);
386			Dd.setSubMatrix(0, 3, Ddtr.transpose());
387			Dd.setSubMatrix(3, 0, Ddtr);
388			Dd.setSubMatrix(3, 3, Ddrr);
389	tim	2773	SquareMatrix<RealType, 6> Xid;
390	tim	2634	Ddtt *= kt;
391			Ddtr *=kt;
392			Ddrr *= kt;
393			invertMatrix(Dd, Xid);
394
395
396
397			//Xidtt in units of kcalfsmol^-1*Ang^-2
398			//Xid /= OOPSEConstant::energyConvert;
399			Xid = OOPSEConstant::kb temperature;
400
401			cr.center = rod;
402			cr.D.setSubMatrix(0, 0, Ddtt);
403			cr.D.setSubMatrix(0, 3, Ddtr);
404			cr.D.setSubMatrix(3, 0, Ddtr);
405			cr.D.setSubMatrix(3, 3, Ddrr);
406			cr.Xi = Xid;
407
408			std::cout << "viscosity = " << viscosity << std::endl;
409			std::cout << "temperature = " << temperature << std::endl;
410			std::cout << "center of diffusion :" << std::endl;
411			std::cout << rod << std::endl;
412			std::cout << "diffusion tensor at center of diffusion " << std::endl;
413			std::cout << "translation(A^2/fs) :" << std::endl;
414			std::cout << Ddtt << std::endl;
415			std::cout << "translation-rotation(A^3/fs):" << std::endl;
416			std::cout << Ddtr << std::endl;
417			std::cout << "rotation(A^4/fs):" << std::endl;
418			std::cout << Ddrr << std::endl;
419
420			std::cout << "resistance tensor at center of diffusion " << std::endl;
421			std::cout << "translation(kcalfsmol^-1*Ang^-2) :" << std::endl;
422
423			Mat3x3d Xidtt;
424			Mat3x3d Xidrt;
425			Mat3x3d Xidtr;
426			Mat3x3d Xidrr;
427			Xid.getSubMatrix(0, 0, Xidtt);
428			Xid.getSubMatrix(0, 3, Xidrt);
429			Xid.getSubMatrix(3, 0, Xidtr);
430			Xid.getSubMatrix(3, 3, Xidrr);
431
432			std::cout << Xidtt << std::endl;
433			std::cout << "rotation-translation (kcalfsmol^-1*Ang^-3):" << std::endl;
434			std::cout << Xidrt << std::endl;
435			std::cout << "translation-rotation(kcalfsmol^-1*Ang^-3):" << std::endl;
436			std::cout << Xidtr << std::endl;
437			std::cout << "rotation(kcalfsmol^-1*Ang^-4):" << std::endl;
438			std::cout << Xidrr << std::endl;
439
440			return true;
441	gezelter	2768
442			}
443	tim	2634
444	gezelter	2768	void ApproximationModel::writeBeads(std::ostream& os) {
445	tim	2634	std::vector<BeadParam>::iterator iter;
446			os << beads_.size() << std::endl;
447			os << "Generated by Hydro" << std::endl;
448			for (iter = beads_.begin(); iter != beads_.end(); ++iter) {
449	gezelter	2768	os << iter->atomName << "\t" << iter->pos[0] << "\t" << iter->pos[1] << "\t" << iter->pos[2] << std::endl;
450	tim	2634	}
451	gezelter	2768
452			}
453	tim	2634	}