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;
    HydroProp* 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, 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;
        //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;
    
    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* 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;

    Mat6x6d Xi, D;

    cr->setCOR(rod);

    cr->setXi(Xid);

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

    cr->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^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:	2787
Committed:	Mon Jun 5 18:24:45 2006 UTC (18 years, 1 month ago) by gezelter
File size:	15475 byte(s)
Log Message:	Massive changes for GB code with multiple ellipsoid types (a la Cleaver's paper). Also, changes in hydrodynamics code to make HydroProp a somewhat smarter class (rather than just a struct).
#	Content
1	/*
2	* Copyright (c) 2005 The University of Notre Dame. All Rights Reserved.
3	*
4	* The University of Notre Dame grants you ("Licensee") a
5	* non-exclusive, royalty free, license to use, modify and
6	* redistribute this software in source and binary code form, provided
7	* that the following conditions are met:
8	*
9	* 1. Acknowledgement of the program authors must be made in any
10	* publication of scientific results based in part on use of the
11	* program. An acceptable form of acknowledgement is citation of
12	* the article in which the program was described (Matthew
13	* A. Meineke, Charles F. Vardeman II, Teng Lin, Christopher
14	* J. Fennell and J. Daniel Gezelter, "OOPSE: An Object-Oriented
15	* Parallel Simulation Engine for Molecular Dynamics,"
16	* J. Comput. Chem. 26, pp. 252-271 (2005))
17	*
18	* 2. Redistributions of source code must retain the above copyright
19	* notice, this list of conditions and the following disclaimer.
20	*
21	* 3. Redistributions in binary form must reproduce the above copyright
22	* notice, this list of conditions and the following disclaimer in the
23	* documentation and/or other materials provided with the
24	* distribution.
25	*
26	* This software is provided "AS IS," without a warranty of any
27	* kind. All express or implied conditions, representations and
28	* warranties, including any implied warranty of merchantability,
29	* fitness for a particular purpose or non-infringement, are hereby
30	* excluded. The University of Notre Dame and its licensors shall not
31	* be liable for any damages suffered by licensee as a result of
32	* using, modifying or distributing the software or its
33	* derivatives. In no event will the University of Notre Dame or its
34	* licensors be liable for any lost revenue, profit or data, or for
35	* direct, indirect, special, consequential, incidental or punitive
36	* damages, however caused and regardless of the theory of liability,
37	* arising out of the use of or inability to use software, even if the
38	* University of Notre Dame has been advised of the possibility of
39	* such damages.
40	*/
41
42	#include "applications/hydrodynamics/ApproximationModel.hpp"
43	#include "math/LU.hpp"
44	#include "math/DynamicRectMatrix.hpp"
45	#include "math/SquareMatrix3.hpp"
46	#include "utils/OOPSEConstant.hpp"
47	#include "hydrodynamics/Sphere.hpp"
48	#include "hydrodynamics/Ellipsoid.hpp"
49	#include "applications/hydrodynamics/CompositeShape.hpp"
50	#include "math/LU.hpp"
51	#include "utils/simError.h"
52	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	ApproximationModel::ApproximationModel(StuntDouble* sd, SimInfo* info): HydrodynamicsModel(sd, info){
61	}
62
63	void ApproximationModel::init() {
64	if (!createBeads(beads_)) {
65	sprintf(painCave.errMsg, "ApproximationModel::init() : Can not create beads\n");
66	painCave.isFatal = 1;
67	simError();
68	}
69
70	}
71
72	bool ApproximationModel::calcHydroProps(Shape* shape, RealType viscosity, RealType temperature) {
73
74	bool ret = true;
75	HydroProp* cr;
76	HydroProp* cd;
77	calcHydroPropsAtCR(beads_, viscosity, temperature, cr);
78	//calcHydroPropsAtCD(beads_, viscosity, temperature, cd);
79	setCR(cr);
80	setCD(cd);
81
82	return true;
83	}
84
85	bool ApproximationModel::calcHydroPropsAtCR(std::vector<BeadParam>& beads, RealType viscosity, RealType temperature, HydroProp* cr) {
86
87	int nbeads = beads.size();
88	DynamicRectMatrix<RealType> B(3nbeads, 3nbeads);
89	DynamicRectMatrix<RealType> C(3nbeads, 3nbeads);
90	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	for (std::size_t j = 0; j < nbeads; ++j) {
97	Mat3x3d Tij;
98	if (i != j ) {
99	Vector3d Rij = beads[i].pos - beads[j].pos;
100	RealType rij = Rij.length();
101	RealType rij2 = rij * rij;
102	RealType sumSigma2OverRij2 = ((beads[i].radiusbeads[i].radius) + (beads[j].radiusbeads[j].radius)) / rij2;
103	Mat3x3d tmpMat;
104	tmpMat = outProduct(Rij, Rij) / rij2;
105	RealType constant = 8.0 * NumericConstant::PI * viscosity * rij;
106	RealType tmp1 = 1.0 + sumSigma2OverRij2/3.0;
107	RealType tmp2 = 1.0 - sumSigma2OverRij2;
108	Tij = (tmp1 * I + tmp2 * tmpMat ) / constant;
109	}else {
110	RealType constant = 1.0 / (6.0 * NumericConstant::PI * viscosity * beads[i].radius);
111	Tij(0, 0) = constant;
112	Tij(1, 1) = constant;
113	Tij(2, 2) = constant;
114	}
115	B.setSubMatrix(i3, j3, Tij);
116	}
117	}
118
119	//invert B Matrix
120	invertMatrix(B, C);
121
122	//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	Mat3x3d currU;
126	currU.setupSkewMat(beads[i].pos);
127	U.push_back(currU);
128	}
129
130	//calculate Xi matrix at arbitrary origin O
131	Mat3x3d Xiott;
132	Mat3x3d Xiorr;
133	Mat3x3d Xiotr;
134
135	//calculate the total volume
136
137	RealType volume = 0.0;
138	for (std::vector<BeadParam>::iterator iter = beads.begin(); iter != beads.end(); ++iter) {
139	volume += 4.0/3.0 * NumericConstant::PI * pow((*iter).radius,3);
140	}
141
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
147	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	}
153
154	const RealType convertConstant = 6.023; //convert poise.angstrom to amu/fs
155	Xiott *= convertConstant;
156	Xiotr *= convertConstant;
157	Xiorr *= convertConstant;
158
159
160
161	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	SquareMatrix<RealType,6> Xir6x6;
191	SquareMatrix<RealType,6> Dr6x6;
192
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	RealType kt = OOPSEConstant::kB * temperature ;
208	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	Mat6x6d Xi, D;
217
218	cr->setCOR(ror);
219
220	Xi.setSubMatrix(0, 0, Xirtt);
221	Xi.setSubMatrix(0, 3, Xirtr);
222	Xi.setSubMatrix(3, 0, Xirtr);
223	Xi.setSubMatrix(3, 3, Xirrr);
224
225	cr->setXi(Xi);
226
227	D.setSubMatrix(0, 0, Drtt);
228	D.setSubMatrix(0, 3, Drrt);
229	D.setSubMatrix(3, 0, Drtr);
230	D.setSubMatrix(3, 3, Drrr);
231
232	cr->setD(D);
233
234	std::cout << "-----------------------------------------\n";
235	std::cout << "center of resistance :" << std::endl;
236	std::cout << ror << std::endl;
237	std::cout << "resistant tensor at center of resistance" << std::endl;
238	std::cout << "translation:" << std::endl;
239	std::cout << Xirtt << std::endl;
240	std::cout << "translation-rotation:" << std::endl;
241	std::cout << Xirtr << std::endl;
242	std::cout << "rotation:" << std::endl;
243	std::cout << Xirrr << std::endl;
244	std::cout << "diffusion tensor at center of resistance" << std::endl;
245	std::cout << "translation:" << std::endl;
246	std::cout << Drtt << std::endl;
247	std::cout << "rotation-translation:" << std::endl;
248	std::cout << Drrt << std::endl;
249	std::cout << "translation-rotation:" << std::endl;
250	std::cout << Drtr << std::endl;
251	std::cout << "rotation:" << std::endl;
252	std::cout << Drrr << std::endl;
253	std::cout << "-----------------------------------------\n";
254
255	return true;
256	}
257
258	bool ApproximationModel::calcHydroPropsAtCD(std::vector<BeadParam>& beads, RealType viscosity, RealType temperature, HydroProp* cr) {
259
260	int nbeads = beads.size();
261	DynamicRectMatrix<RealType> B(3nbeads, 3nbeads);
262	DynamicRectMatrix<RealType> C(3nbeads, 3nbeads);
263	Mat3x3d I;
264	I(0, 0) = 1.0;
265	I(1, 1) = 1.0;
266	I(2, 2) = 1.0;
267
268	for (std::size_t i = 0; i < nbeads; ++i) {
269	for (std::size_t j = 0; j < nbeads; ++j) {
270	Mat3x3d Tij;
271	if (i != j ) {
272	Vector3d Rij = beads[i].pos - beads[j].pos;
273	RealType rij = Rij.length();
274	RealType rij2 = rij * rij;
275	RealType sumSigma2OverRij2 = ((beads[i].radiusbeads[i].radius) + (beads[j].radiusbeads[j].radius)) / rij2;
276	Mat3x3d tmpMat;
277	tmpMat = outProduct(Rij, Rij) / rij2;
278	RealType constant = 8.0 * NumericConstant::PI * viscosity * rij;
279	RealType tmp1 = 1.0 + sumSigma2OverRij2/3.0;
280	RealType tmp2 = 1.0 - sumSigma2OverRij2;
281	Tij = (tmp1 * I + tmp2 * tmpMat ) / constant;
282	}else {
283	RealType constant = 1.0 / (6.0 * NumericConstant::PI * viscosity * beads[i].radius);
284	Tij(0, 0) = constant;
285	Tij(1, 1) = constant;
286	Tij(2, 2) = constant;
287	}
288	B.setSubMatrix(i3, j3, Tij);
289	}
290	}
291
292	//invert B Matrix
293	invertMatrix(B, C);
294
295	//prepare U Matrix relative to arbitrary origin O(0.0, 0.0, 0.0)
296	std::vector<Mat3x3d> U;
297	for (int i = 0; i < nbeads; ++i) {
298	Mat3x3d currU;
299	currU.setupSkewMat(beads[i].pos);
300	U.push_back(currU);
301	}
302
303	//calculate Xi matrix at arbitrary origin O
304	Mat3x3d Xitt;
305	Mat3x3d Xirr;
306	Mat3x3d Xitr;
307
308	//calculate the total volume
309
310	RealType volume = 0.0;
311	for (std::vector<BeadParam>::iterator iter = beads.begin(); iter != beads.end(); ++iter) {
312	volume += 4.0/3.0 * NumericConstant::PI * pow((*iter).radius,3);
313	}
314
315	for (std::size_t i = 0; i < nbeads; ++i) {
316	for (std::size_t j = 0; j < nbeads; ++j) {
317	Mat3x3d Cij;
318	C.getSubMatrix(i3, j3, Cij);
319
320	Xitt += Cij;
321	Xitr += U[i] * Cij;
322	//Xirr += -U[i] * Cij * U[j] + (6 * viscosity * volume) * I;
323	Xirr += -U[i] * Cij * U[j];
324	}
325	}
326
327	const RealType convertConstant = 6.023; //convert poise.angstrom to amu/fs
328	Xitt *= convertConstant;
329	Xitr *= convertConstant;
330	Xirr *= convertConstant;
331
332	RealType kt = OOPSEConstant::kB * temperature;
333
334	Mat3x3d Dott; //translational diffusion tensor at arbitrary origin O
335	Mat3x3d Dorr; //rotational diffusion tensor at arbitrary origin O
336	Mat3x3d Dotr; //translation-rotation couplingl diffusion tensor at arbitrary origin O
337
338	const static Mat3x3d zeroMat(0.0);
339
340	Mat3x3d XittInv(0.0);
341	XittInv = Xitt.inverse();
342
343	Mat3x3d XirrInv;
344	XirrInv = Xirr.inverse();
345
346	Mat3x3d tmp;
347	Mat3x3d tmpInv;
348	tmp = Xitt - Xitr.transpose() * XirrInv * Xitr;
349	tmpInv = tmp.inverse();
350
351	Dott = tmpInv;
352	Dotr = -XirrInv * Xitr * tmpInv;
353
354	tmp = Xirr - Xitr * XittInv * Xitr.transpose();
355	tmpInv = tmp.inverse();
356
357	Dorr = tmpInv;
358
359	//calculate center of diffusion
360	tmp(0, 0) = Dorr(1, 1) + Dorr(2, 2);
361	tmp(0, 1) = - Dorr(0, 1);
362	tmp(0, 2) = -Dorr(0, 2);
363	tmp(1, 0) = -Dorr(0, 1);
364	tmp(1, 1) = Dorr(0, 0) + Dorr(2, 2);
365	tmp(1, 2) = -Dorr(1, 2);
366	tmp(2, 0) = -Dorr(0, 2);
367	tmp(2, 1) = -Dorr(1, 2);
368	tmp(2, 2) = Dorr(1, 1) + Dorr(0, 0);
369
370	Vector3d tmpVec;
371	tmpVec[0] = Dotr(1, 2) - Dotr(2, 1);
372	tmpVec[1] = Dotr(2, 0) - Dotr(0, 2);
373	tmpVec[2] = Dotr(0, 1) - Dotr(1, 0);
374
375	tmpInv = tmp.inverse();
376
377	Vector3d rod = tmpInv * tmpVec;
378
379	//calculate Diffusion Tensor at center of diffusion
380	Mat3x3d Uod;
381	Uod.setupSkewMat(rod);
382
383	Mat3x3d Ddtt; //translational diffusion tensor at diffusion center
384	Mat3x3d Ddtr; //rotational diffusion tensor at diffusion center
385	Mat3x3d Ddrr; //translation-rotation couplingl diffusion tensor at diffusion tensor
386
387	Ddtt = Dott - Uod * Dorr * Uod + Dotr.transpose() * Uod - Uod * Dotr;
388	Ddrr = Dorr;
389	Ddtr = Dotr + Dorr * Uod;
390
391	SquareMatrix<RealType, 6> Dd;
392	Dd.setSubMatrix(0, 0, Ddtt);
393	Dd.setSubMatrix(0, 3, Ddtr.transpose());
394	Dd.setSubMatrix(3, 0, Ddtr);
395	Dd.setSubMatrix(3, 3, Ddrr);
396	SquareMatrix<RealType, 6> Xid;
397	Ddtt *= kt;
398	Ddtr *=kt;
399	Ddrr *= kt;
400	invertMatrix(Dd, Xid);
401
402
403
404	//Xidtt in units of kcalfsmol^-1*Ang^-2
405	//Xid /= OOPSEConstant::energyConvert;
406	Xid = OOPSEConstant::kb temperature;
407
408	Mat6x6d Xi, D;
409
410	cr->setCOR(rod);
411
412	cr->setXi(Xid);
413
414	D.setSubMatrix(0, 0, Ddtt);
415	D.setSubMatrix(0, 3, Ddtr);
416	D.setSubMatrix(3, 0, Ddtr);
417	D.setSubMatrix(3, 3, Ddrr);
418
419	cr->setD(D);
420
421	std::cout << "viscosity = " << viscosity << std::endl;
422	std::cout << "temperature = " << temperature << std::endl;
423	std::cout << "center of diffusion :" << std::endl;
424	std::cout << rod << std::endl;
425	std::cout << "diffusion tensor at center of diffusion " << std::endl;
426	std::cout << "translation(A^2/fs) :" << std::endl;
427	std::cout << Ddtt << std::endl;
428	std::cout << "translation-rotation(A^3/fs):" << std::endl;
429	std::cout << Ddtr << std::endl;
430	std::cout << "rotation(A^4/fs):" << std::endl;
431	std::cout << Ddrr << std::endl;
432
433	std::cout << "resistance tensor at center of diffusion " << std::endl;
434	std::cout << "translation(kcalfsmol^-1*Ang^-2) :" << std::endl;
435
436	Mat3x3d Xidtt;
437	Mat3x3d Xidrt;
438	Mat3x3d Xidtr;
439	Mat3x3d Xidrr;
440	Xid.getSubMatrix(0, 0, Xidtt);
441	Xid.getSubMatrix(0, 3, Xidrt);
442	Xid.getSubMatrix(3, 0, Xidtr);
443	Xid.getSubMatrix(3, 3, Xidrr);
444
445	std::cout << Xidtt << std::endl;
446	std::cout << "rotation-translation (kcalfsmol^-1*Ang^-3):" << std::endl;
447	std::cout << Xidrt << std::endl;
448	std::cout << "translation-rotation(kcalfsmol^-1*Ang^-3):" << std::endl;
449	std::cout << Xidtr << std::endl;
450	std::cout << "rotation(kcalfsmol^-1*Ang^-4):" << std::endl;
451	std::cout << Xidrr << std::endl;
452
453	return true;
454
455	}
456
457	void ApproximationModel::writeBeads(std::ostream& os) {
458	std::vector<BeadParam>::iterator iter;
459	os << beads_.size() << std::endl;
460	os << "Generated by Hydro" << std::endl;
461	for (iter = beads_.begin(); iter != beads_.end(); ++iter) {
462	os << iter->atomName << "\t" << iter->pos[0] << "\t" << iter->pos[1] << "\t" << iter->pos[2] << std::endl;
463	}
464
465	}
466	}