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;
              Tij = ((1.0 + sumSigma2OverRij2/3.0) * I + (1.0 - sumSigma2OverRij2) * 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;
          Tij = ((1.0 + sumSigma2OverRij2/3.0) * I + (1.0 - sumSigma2OverRij2) * 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:	2773
Committed:	Thu May 25 16:27:27 2006 UTC (19 years, 5 months ago) by tim
File size:	15311 byte(s)
Log Message:	replace double with RealType
#	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	gezelter	2768	Tij = ((1.0 + sumSigma2OverRij2/3.0) * I + (1.0 - sumSigma2OverRij2) * tmpMat ) / constant;
107	tim	2634	}else {
108	tim	2773	RealType constant = 1.0 / (6.0 * NumericConstant::PI * viscosity * beads[i].radius);
109	gezelter	2768	Tij(0, 0) = constant;
110			Tij(1, 1) = constant;
111			Tij(2, 2) = constant;
112	tim	2634	}
113			B.setSubMatrix(i3, j3, Tij);
114	gezelter	2768	}
115	tim	2634	}
116	gezelter	2768
117	tim	2634	//invert B Matrix
118			invertMatrix(B, C);
119	tim	2650
120	tim	2634	//prepare U Matrix relative to arbitrary origin O(0.0, 0.0, 0.0)
121			std::vector<Mat3x3d> U;
122			for (int i = 0; i < nbeads; ++i) {
123	gezelter	2768	Mat3x3d currU;
124			currU.setupSkewMat(beads[i].pos);
125			U.push_back(currU);
126	tim	2634	}
127
128			//calculate Xi matrix at arbitrary origin O
129			Mat3x3d Xiott;
130			Mat3x3d Xiorr;
131			Mat3x3d Xiotr;
132	gezelter	2768
133	tim	2634	//calculate the total volume
134	gezelter	2768
135	tim	2773	RealType volume = 0.0;
136	tim	2634	for (std::vector<BeadParam>::iterator iter = beads.begin(); iter != beads.end(); ++iter) {
137	gezelter	2768	volume += 4.0/3.0 * NumericConstant::PI * pow((*iter).radius,3);
138	tim	2634	}
139	gezelter	2768
140			for (std::size_t i = 0; i < nbeads; ++i) {
141			for (std::size_t j = 0; j < nbeads; ++j) {
142			Mat3x3d Cij;
143			C.getSubMatrix(i3, j3, Cij);
144	tim	2634
145	gezelter	2768	Xiott += Cij;
146			Xiotr += U[i] * Cij;
147			//Xiorr += -U[i] * Cij * U[j] + (6 * viscosity * volume) * I;
148			Xiorr += -U[i] * Cij * U[j];
149			}
150	tim	2634	}
151	gezelter	2768
152	tim	2773	const RealType convertConstant = 6.023; //convert poise.angstrom to amu/fs
153	tim	2634	Xiott *= convertConstant;
154			Xiotr *= convertConstant;
155			Xiorr *= convertConstant;
156
157
158	gezelter	2768
159	tim	2634	Mat3x3d tmp;
160			Mat3x3d tmpInv;
161			Vector3d tmpVec;
162			tmp(0, 0) = Xiott(1, 1) + Xiott(2, 2);
163			tmp(0, 1) = - Xiott(0, 1);
164			tmp(0, 2) = -Xiott(0, 2);
165			tmp(1, 0) = -Xiott(0, 1);
166			tmp(1, 1) = Xiott(0, 0) + Xiott(2, 2);
167			tmp(1, 2) = -Xiott(1, 2);
168			tmp(2, 0) = -Xiott(0, 2);
169			tmp(2, 1) = -Xiott(1, 2);
170			tmp(2, 2) = Xiott(1, 1) + Xiott(0, 0);
171			tmpVec[0] = Xiotr(2, 1) - Xiotr(1, 2);
172			tmpVec[1] = Xiotr(0, 2) - Xiotr(2, 0);
173			tmpVec[2] = Xiotr(1, 0) - Xiotr(0, 1);
174			tmpInv = tmp.inverse();
175			Vector3d ror = tmpInv * tmpVec; //center of resistance
176			Mat3x3d Uor;
177			Uor.setupSkewMat(ror);
178
179			Mat3x3d Xirtt;
180			Mat3x3d Xirrr;
181			Mat3x3d Xirtr;
182
183			Xirtt = Xiott;
184			Xirtr = (Xiotr - Uor * Xiott);
185			Xirrr = Xiorr - Uor * Xiott * Uor + Xiotr * Uor - Uor * Xiotr.transpose();
186
187
188	tim	2773	SquareMatrix<RealType,6> Xir6x6;
189			SquareMatrix<RealType,6> Dr6x6;
190	tim	2634
191			Xir6x6.setSubMatrix(0, 0, Xirtt);
192			Xir6x6.setSubMatrix(0, 3, Xirtr.transpose());
193			Xir6x6.setSubMatrix(3, 0, Xirtr);
194			Xir6x6.setSubMatrix(3, 3, Xirrr);
195
196			invertMatrix(Xir6x6, Dr6x6);
197			Mat3x3d Drtt;
198			Mat3x3d Drtr;
199			Mat3x3d Drrt;
200			Mat3x3d Drrr;
201			Dr6x6.getSubMatrix(0, 0, Drtt);
202			Dr6x6.getSubMatrix(0, 3, Drrt);
203			Dr6x6.getSubMatrix(3, 0, Drtr);
204			Dr6x6.getSubMatrix(3, 3, Drrr);
205	tim	2773	RealType kt = OOPSEConstant::kB * temperature ;
206	tim	2634	Drtt *= kt;
207			Drrt *= kt;
208			Drtr *= kt;
209			Drrr *= kt;
210			Xirtt = OOPSEConstant::kb temperature;
211			Xirtr = OOPSEConstant::kb temperature;
212			Xirrr = OOPSEConstant::kb temperature;
213
214
215			cr.center = ror;
216			cr.Xi.setSubMatrix(0, 0, Xirtt);
217			cr.Xi.setSubMatrix(0, 3, Xirtr);
218			cr.Xi.setSubMatrix(3, 0, Xirtr);
219			cr.Xi.setSubMatrix(3, 3, Xirrr);
220			cr.D.setSubMatrix(0, 0, Drtt);
221			cr.D.setSubMatrix(0, 3, Drrt);
222			cr.D.setSubMatrix(3, 0, Drtr);
223			cr.D.setSubMatrix(3, 3, Drrr);
224
225			std::cout << "-----------------------------------------\n";
226			std::cout << "center of resistance :" << std::endl;
227			std::cout << ror << std::endl;
228			std::cout << "resistant tensor at center of resistance" << std::endl;
229			std::cout << "translation:" << std::endl;
230			std::cout << Xirtt << std::endl;
231			std::cout << "translation-rotation:" << std::endl;
232			std::cout << Xirtr << std::endl;
233			std::cout << "rotation:" << std::endl;
234			std::cout << Xirrr << std::endl;
235			std::cout << "diffusion tensor at center of resistance" << std::endl;
236			std::cout << "translation:" << std::endl;
237			std::cout << Drtt << std::endl;
238			std::cout << "rotation-translation:" << std::endl;
239			std::cout << Drrt << std::endl;
240			std::cout << "translation-rotation:" << std::endl;
241			std::cout << Drtr << std::endl;
242			std::cout << "rotation:" << std::endl;
243			std::cout << Drrr << std::endl;
244			std::cout << "-----------------------------------------\n";
245
246			return true;
247			}
248	gezelter	2768
249	tim	2773	bool ApproximationModel::calcHydroPropsAtCD(std::vector<BeadParam>& beads, RealType viscosity, RealType temperature, HydroProps& cr) {
250	gezelter	2768
251	tim	2634	int nbeads = beads.size();
252	tim	2773	DynamicRectMatrix<RealType> B(3nbeads, 3nbeads);
253			DynamicRectMatrix<RealType> C(3nbeads, 3nbeads);
254	tim	2634	Mat3x3d I;
255			I(0, 0) = 1.0;
256			I(1, 1) = 1.0;
257			I(2, 2) = 1.0;
258
259			for (std::size_t i = 0; i < nbeads; ++i) {
260	gezelter	2768	for (std::size_t j = 0; j < nbeads; ++j) {
261			Mat3x3d Tij;
262			if (i != j ) {
263			Vector3d Rij = beads[i].pos - beads[j].pos;
264	tim	2773	RealType rij = Rij.length();
265			RealType rij2 = rij * rij;
266			RealType sumSigma2OverRij2 = ((beads[i].radiusbeads[i].radius) + (beads[j].radiusbeads[j].radius)) / rij2;
267	gezelter	2768	Mat3x3d tmpMat;
268			tmpMat = outProduct(Rij, Rij) / rij2;
269	tim	2773	RealType constant = 8.0 * NumericConstant::PI * viscosity * rij;
270	gezelter	2768	Tij = ((1.0 + sumSigma2OverRij2/3.0) * I + (1.0 - sumSigma2OverRij2) * tmpMat ) / constant;
271			}else {
272	tim	2773	RealType constant = 1.0 / (6.0 * NumericConstant::PI * viscosity * beads[i].radius);
273	gezelter	2768	Tij(0, 0) = constant;
274			Tij(1, 1) = constant;
275			Tij(2, 2) = constant;
276	tim	2634	}
277	gezelter	2768	B.setSubMatrix(i3, j3, Tij);
278			}
279	tim	2634	}
280	gezelter	2768
281	tim	2634	//invert B Matrix
282			invertMatrix(B, C);
283	gezelter	2768
284	tim	2634	//prepare U Matrix relative to arbitrary origin O(0.0, 0.0, 0.0)
285			std::vector<Mat3x3d> U;
286			for (int i = 0; i < nbeads; ++i) {
287	gezelter	2768	Mat3x3d currU;
288			currU.setupSkewMat(beads[i].pos);
289			U.push_back(currU);
290	tim	2634	}
291
292			//calculate Xi matrix at arbitrary origin O
293			Mat3x3d Xitt;
294			Mat3x3d Xirr;
295			Mat3x3d Xitr;
296
297			//calculate the total volume
298
299	tim	2773	RealType volume = 0.0;
300	tim	2634	for (std::vector<BeadParam>::iterator iter = beads.begin(); iter != beads.end(); ++iter) {
301	gezelter	2768	volume += 4.0/3.0 * NumericConstant::PI * pow((*iter).radius,3);
302	tim	2634	}
303	gezelter	2768
304	tim	2634	for (std::size_t i = 0; i < nbeads; ++i) {
305	gezelter	2768	for (std::size_t j = 0; j < nbeads; ++j) {
306			Mat3x3d Cij;
307			C.getSubMatrix(i3, j3, Cij);
308	tim	2634
309	gezelter	2768	Xitt += Cij;
310			Xitr += U[i] * Cij;
311	tim	2749	//Xirr += -U[i] * Cij * U[j] + (6 * viscosity * volume) * I;
312	gezelter	2768	Xirr += -U[i] * Cij * U[j];
313			}
314	tim	2634	}
315	gezelter	2768
316	tim	2773	const RealType convertConstant = 6.023; //convert poise.angstrom to amu/fs
317	tim	2634	Xitt *= convertConstant;
318			Xitr *= convertConstant;
319			Xirr *= convertConstant;
320	gezelter	2768
321	tim	2773	RealType kt = OOPSEConstant::kB * temperature;
322	gezelter	2768
323	tim	2634	Mat3x3d Dott; //translational diffusion tensor at arbitrary origin O
324			Mat3x3d Dorr; //rotational diffusion tensor at arbitrary origin O
325			Mat3x3d Dotr; //translation-rotation couplingl diffusion tensor at arbitrary origin O
326	gezelter	2768
327	tim	2634	const static Mat3x3d zeroMat(0.0);
328
329			Mat3x3d XittInv(0.0);
330			XittInv = Xitt.inverse();
331
332			Mat3x3d XirrInv;
333			XirrInv = Xirr.inverse();
334
335			Mat3x3d tmp;
336			Mat3x3d tmpInv;
337			tmp = Xitt - Xitr.transpose() * XirrInv * Xitr;
338			tmpInv = tmp.inverse();
339
340			Dott = tmpInv;
341			Dotr = -XirrInv * Xitr * tmpInv;
342
343			tmp = Xirr - Xitr * XittInv * Xitr.transpose();
344			tmpInv = tmp.inverse();
345
346			Dorr = tmpInv;
347
348			//calculate center of diffusion
349			tmp(0, 0) = Dorr(1, 1) + Dorr(2, 2);
350			tmp(0, 1) = - Dorr(0, 1);
351			tmp(0, 2) = -Dorr(0, 2);
352			tmp(1, 0) = -Dorr(0, 1);
353			tmp(1, 1) = Dorr(0, 0) + Dorr(2, 2);
354			tmp(1, 2) = -Dorr(1, 2);
355			tmp(2, 0) = -Dorr(0, 2);
356			tmp(2, 1) = -Dorr(1, 2);
357			tmp(2, 2) = Dorr(1, 1) + Dorr(0, 0);
358
359			Vector3d tmpVec;
360			tmpVec[0] = Dotr(1, 2) - Dotr(2, 1);
361			tmpVec[1] = Dotr(2, 0) - Dotr(0, 2);
362			tmpVec[2] = Dotr(0, 1) - Dotr(1, 0);
363
364			tmpInv = tmp.inverse();
365
366			Vector3d rod = tmpInv * tmpVec;
367
368			//calculate Diffusion Tensor at center of diffusion
369			Mat3x3d Uod;
370			Uod.setupSkewMat(rod);
371
372			Mat3x3d Ddtt; //translational diffusion tensor at diffusion center
373			Mat3x3d Ddtr; //rotational diffusion tensor at diffusion center
374			Mat3x3d Ddrr; //translation-rotation couplingl diffusion tensor at diffusion tensor
375
376			Ddtt = Dott - Uod * Dorr * Uod + Dotr.transpose() * Uod - Uod * Dotr;
377			Ddrr = Dorr;
378			Ddtr = Dotr + Dorr * Uod;
379
380	tim	2773	SquareMatrix<RealType, 6> Dd;
381	tim	2634	Dd.setSubMatrix(0, 0, Ddtt);
382			Dd.setSubMatrix(0, 3, Ddtr.transpose());
383			Dd.setSubMatrix(3, 0, Ddtr);
384			Dd.setSubMatrix(3, 3, Ddrr);
385	tim	2773	SquareMatrix<RealType, 6> Xid;
386	tim	2634	Ddtt *= kt;
387			Ddtr *=kt;
388			Ddrr *= kt;
389			invertMatrix(Dd, Xid);
390
391
392
393			//Xidtt in units of kcalfsmol^-1*Ang^-2
394			//Xid /= OOPSEConstant::energyConvert;
395			Xid = OOPSEConstant::kb temperature;
396
397			cr.center = rod;
398			cr.D.setSubMatrix(0, 0, Ddtt);
399			cr.D.setSubMatrix(0, 3, Ddtr);
400			cr.D.setSubMatrix(3, 0, Ddtr);
401			cr.D.setSubMatrix(3, 3, Ddrr);
402			cr.Xi = Xid;
403
404			std::cout << "viscosity = " << viscosity << std::endl;
405			std::cout << "temperature = " << temperature << std::endl;
406			std::cout << "center of diffusion :" << std::endl;
407			std::cout << rod << std::endl;
408			std::cout << "diffusion tensor at center of diffusion " << std::endl;
409			std::cout << "translation(A^2/fs) :" << std::endl;
410			std::cout << Ddtt << std::endl;
411			std::cout << "translation-rotation(A^3/fs):" << std::endl;
412			std::cout << Ddtr << std::endl;
413			std::cout << "rotation(A^4/fs):" << std::endl;
414			std::cout << Ddrr << std::endl;
415
416			std::cout << "resistance tensor at center of diffusion " << std::endl;
417			std::cout << "translation(kcalfsmol^-1*Ang^-2) :" << std::endl;
418
419			Mat3x3d Xidtt;
420			Mat3x3d Xidrt;
421			Mat3x3d Xidtr;
422			Mat3x3d Xidrr;
423			Xid.getSubMatrix(0, 0, Xidtt);
424			Xid.getSubMatrix(0, 3, Xidrt);
425			Xid.getSubMatrix(3, 0, Xidtr);
426			Xid.getSubMatrix(3, 3, Xidrr);
427
428			std::cout << Xidtt << std::endl;
429			std::cout << "rotation-translation (kcalfsmol^-1*Ang^-3):" << std::endl;
430			std::cout << Xidrt << std::endl;
431			std::cout << "translation-rotation(kcalfsmol^-1*Ang^-3):" << std::endl;
432			std::cout << Xidtr << std::endl;
433			std::cout << "rotation(kcalfsmol^-1*Ang^-4):" << std::endl;
434			std::cout << Xidrr << std::endl;
435
436			return true;
437	gezelter	2768
438			}
439	tim	2634
440	gezelter	2768	void ApproximationModel::writeBeads(std::ostream& os) {
441	tim	2634	std::vector<BeadParam>::iterator iter;
442			os << beads_.size() << std::endl;
443			os << "Generated by Hydro" << std::endl;
444			for (iter = beads_.begin(); iter != beads_.end(); ++iter) {
445	gezelter	2768	os << iter->atomName << "\t" << iter->pos[0] << "\t" << iter->pos[1] << "\t" << iter->pos[2] << std::endl;
446	tim	2634	}
447	gezelter	2768
448			}
449	tim	2634	}