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. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 *
 * 2. 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.
 *
 * SUPPORT OPEN SCIENCE!  If you use OpenMD or its source code in your
 * research, please cite the appropriate papers when you publish your
 * work.  Good starting points are:
 *                                                                      
 * [1]  Meineke, et al., J. Comp. Chem. 26, 252-271 (2005).             
 * [2]  Fennell & Gezelter, J. Chem. Phys. 124, 234104 (2006).          
 * [3]  Sun, Lin & Gezelter, J. Chem. Phys. 128, 24107 (2008).          
 * [4]  Kuang & Gezelter,  J. Chem. Phys. 133, 164101 (2010).
 * [5]  Vardeman, Stocker & Gezelter, J. Chem. Theory Comput. 7, 834 (2011).
 */

#include "applications/hydrodynamics/ApproximationModel.hpp" 
#include "math/LU.hpp"
#include "math/DynamicRectMatrix.hpp"
#include "math/SquareMatrix3.hpp"
#include "utils/PhysicalConstants.hpp"
#include "hydrodynamics/Sphere.hpp"
#include "hydrodynamics/Ellipsoid.hpp"
#include "applications/hydrodynamics/CompositeShape.hpp"
#include "math/LU.hpp"
#include "utils/simError.h"
namespace OpenMD {
/**
 * Reference:
 * Beatriz Carrasco and Jose Gracia de la Torre, Hydrodynamic Properties of Rigid Particles:
 * Comparison of Different Modeling and Computational Procedures. 
 * Biophysical Journal, 75(6), 3044, 1999
 */

  ApproximationModel::ApproximationModel(StuntDouble* sd, SimInfo* info): HydrodynamicsModel(sd, info){    
  }
  
  void ApproximationModel::init() {
    if (!createBeads(beads_)) {
      sprintf(painCave.errMsg, "ApproximationModel::init() : Can not create beads\n");
      painCave.isFatal = 1;
      simError();        
    }
    
  }
  
  bool ApproximationModel::calcHydroProps(Shape* shape, RealType viscosity, RealType temperature) {
    
    bool ret = true;
    HydroProp* cr = new HydroProp();
    HydroProp* cd = new HydroProp();
    calcHydroPropsAtCR(beads_, viscosity, temperature, cr);
    calcHydroPropsAtCD(beads_, viscosity, temperature, cd);
    setCR(cr);
    setCD(cd);
    return true;    
  }
  
  bool ApproximationModel::calcHydroPropsAtCR(std::vector<BeadParam>& beads, RealType viscosity, RealType temperature, HydroProp* cr) {
    
    unsigned 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 (unsigned int i = 0; i < nbeads; ++i) {
      Mat3x3d currU;
      currU.setupSkewMat(beads[i].pos);
      U.push_back(currU);
    }
    
    //calculate Xi matrix at arbitrary origin O
    Mat3x3d Xiott;
    Mat3x3d Xiorr;
    Mat3x3d Xiotr;
    
    //calculate the total volume
    
    RealType volume = 0.0;
    for (std::vector<BeadParam>::iterator iter = beads.begin(); iter != beads.end(); ++iter) {
      volume += 4.0/3.0 * NumericConstant::PI * pow((*iter).radius,3);
    }
    
    for (std::size_t i = 0; i < nbeads; ++i) {
      for (std::size_t j = 0; j < nbeads; ++j) {
        Mat3x3d Cij;
        C.getSubMatrix(i*3, j*3, Cij);
        
        Xiott += Cij;
        Xiotr += U[i] * Cij;
        // uncorrected here.  Volume correction is added after we assemble Xiorr
        Xiorr += -U[i] * Cij * U[j]; 
      }
    }

    // add the volume correction
    Xiorr += (RealType(6.0) * viscosity * volume) * I;    
    
    Xiott *= PhysicalConstants::viscoConvert;
    Xiotr *= PhysicalConstants::viscoConvert;
    Xiorr *= PhysicalConstants::viscoConvert;
    
    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 = PhysicalConstants::kb * temperature ; // in kcal mol^-1
    Drtt *= kt;
    Drrt *= kt;
    Drtr *= kt;
    Drrr *= kt;
    //Xirtt *= PhysicalConstants::kb * temperature;
    //Xirtr *= PhysicalConstants::kb * temperature;
    //Xirrr *= PhysicalConstants::kb * temperature;
    
    Mat6x6d Xi, D;

    cr->setCOR(ror);

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

    cr->setXi(Xi);

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

    cr->setD(D);
    
    std::cout << "-----------------------------------------\n";
    std::cout << "center of resistance :" << std::endl;
    std::cout << ror << std::endl;
    std::cout << "resistant tensor at center of resistance" << std::endl;
    std::cout << "translation:" << std::endl;
    std::cout << Xirtt << std::endl;
    std::cout << "translation-rotation:" << std::endl;
    std::cout << Xirtr << std::endl;
    std::cout << "rotation:" << std::endl;
    std::cout << Xirrr << std::endl; 
    std::cout << "diffusion tensor at center of resistance" << std::endl;
    std::cout << "translation:" << std::endl;
    std::cout << Drtt << std::endl;
    std::cout << "rotation-translation:" << std::endl;
    std::cout << Drrt << std::endl;
    std::cout << "translation-rotation:" << std::endl;
    std::cout << Drtr << std::endl;
    std::cout << "rotation:" << std::endl;
    std::cout << Drrr << std::endl;    
    std::cout << "-----------------------------------------\n";

    return true;
}
  
  bool ApproximationModel::calcHydroPropsAtCD(std::vector<BeadParam>& beads, RealType viscosity, RealType temperature, HydroProp* cd) {
    
    unsigned 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 (unsigned int i = 0; i < nbeads; ++i) {
      Mat3x3d currU;
      currU.setupSkewMat(beads[i].pos);
      U.push_back(currU);
    }
    
    //calculate Xi matrix at arbitrary origin O
    Mat3x3d Xitt;
    Mat3x3d Xirr;
    Mat3x3d Xitr;

    //calculate the total volume

    RealType volume = 0.0;
    for (std::vector<BeadParam>::iterator iter = beads.begin(); iter != beads.end(); ++iter) {
      volume += 4.0/3.0 * NumericConstant::PI * pow((*iter).radius,3);
    }
    
    for (std::size_t i = 0; i < nbeads; ++i) {
      for (std::size_t j = 0; j < nbeads; ++j) {
        Mat3x3d Cij;
        C.getSubMatrix(i*3, j*3, Cij);
            
        Xitt += Cij;
        Xitr += U[i] * Cij;
        // uncorrected here.  Volume correction is added after we assemble Xiorr
        Xirr += -U[i] * Cij * U[j];
      }
    }
    // add the volume correction here:
    Xirr += (RealType(6.0) * viscosity * volume) * I;    
    
    Xitt *= PhysicalConstants::viscoConvert;
    Xitr *= PhysicalConstants::viscoConvert;
    Xirr *= PhysicalConstants::viscoConvert;
    
    RealType kt = PhysicalConstants::kb * temperature; // in kcal mol^-1
    
    Mat3x3d Dott; //translational diffusion tensor at arbitrary origin O
    Mat3x3d Dorr; //rotational diffusion tensor at arbitrary origin O
    Mat3x3d Dotr; //translation-rotation couplingl diffusion tensor at arbitrary origin O
    
    const static Mat3x3d zeroMat(0.0);
    
    Mat3x3d XittInv(0.0);
    XittInv = Xitt.inverse();
    
    Mat3x3d XirrInv;
    XirrInv = Xirr.inverse();

    Mat3x3d tmp;
    Mat3x3d tmpInv;
    tmp = Xitt - Xitr.transpose() * XirrInv * Xitr;
    tmpInv = tmp.inverse();

    Dott = tmpInv;
    Dotr = -XirrInv * Xitr * tmpInv;
    
    tmp = Xirr - Xitr * XittInv * Xitr.transpose();    
    tmpInv = tmp.inverse();
    
    Dorr = tmpInv;

    //calculate center of diffusion
    tmp(0, 0) = Dorr(1, 1) + Dorr(2, 2);
    tmp(0, 1) = - Dorr(0, 1);
    tmp(0, 2) = -Dorr(0, 2);
    tmp(1, 0) = -Dorr(0, 1);
    tmp(1, 1) = Dorr(0, 0)  + Dorr(2, 2);
    tmp(1, 2) = -Dorr(1, 2);
    tmp(2, 0) = -Dorr(0, 2);
    tmp(2, 1) = -Dorr(1, 2);
    tmp(2, 2) = Dorr(1, 1) + Dorr(0, 0);

    Vector3d tmpVec;
    tmpVec[0] = Dotr(1, 2) - Dotr(2, 1);
    tmpVec[1] = Dotr(2, 0) - Dotr(0, 2);
    tmpVec[2] = Dotr(0, 1) - Dotr(1, 0);

    tmpInv = tmp.inverse();
    
    Vector3d rod = tmpInv * tmpVec;

    //calculate Diffusion Tensor at center of diffusion
    Mat3x3d Uod;
    Uod.setupSkewMat(rod);
    
    Mat3x3d Ddtt; //translational diffusion tensor at diffusion center
    Mat3x3d Ddtr; //rotational diffusion tensor at diffusion center
    Mat3x3d Ddrr; //translation-rotation couplingl diffusion tensor at diffusion tensor
    
    Ddtt = Dott - Uod * Dorr * Uod + Dotr.transpose() * Uod - Uod * Dotr;
    Ddrr = Dorr;
    Ddtr = Dotr + Dorr * Uod;

    SquareMatrix<RealType, 6> Dd;
    Dd.setSubMatrix(0, 0, Ddtt);
    Dd.setSubMatrix(0, 3, Ddtr.transpose());
    Dd.setSubMatrix(3, 0, Ddtr);
    Dd.setSubMatrix(3, 3, Ddrr);    
    SquareMatrix<RealType, 6> Xid;
    Ddtt *= kt;
    Ddtr *=kt;
    Ddrr *= kt;
    invertMatrix(Dd, Xid);


    //Xidtt in units of kcal*fs*mol^-1*Ang^-2
    //Xid /= PhysicalConstants::energyConvert;
    Xid *= PhysicalConstants::kb * temperature;

    Mat6x6d Xi, D;

    cd->setCOR(rod);

    cd->setXi(Xid);

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

    cd->setD(D);

    std::cout << "viscosity = " << viscosity << std::endl;
    std::cout << "temperature = " << temperature << std::endl;
    std::cout << "center of diffusion :" << std::endl;
    std::cout << rod << std::endl;
    std::cout << "diffusion tensor at center of diffusion " << std::endl;
    std::cout << "translation(A^2 / fs) :" << std::endl;
    std::cout << Ddtt << std::endl;
    std::cout << "translation-rotation(A / fs):" << std::endl;
    std::cout << Ddtr << std::endl;
    std::cout << "rotation(fs^-1):" << std::endl;
    std::cout << Ddrr << std::endl;

    std::cout << "resistance tensor at center of diffusion " << std::endl;
    std::cout << "translation(kcal*fs*mol^-1*Ang^-2) :" << std::endl;

    Mat3x3d Xidtt;
    Mat3x3d Xidrt;
    Mat3x3d Xidtr;
    Mat3x3d Xidrr;
    Xid.getSubMatrix(0, 0, Xidtt);
    Xid.getSubMatrix(0, 3, Xidrt);
    Xid.getSubMatrix(3, 0, Xidtr);
    Xid.getSubMatrix(3, 3, Xidrr);

    std::cout << Xidtt << std::endl;
    std::cout << "rotation-translation (kcal*fs*mol^-1*Ang^-1):" << std::endl;
    std::cout << Xidrt << std::endl;
    std::cout << "translation-rotation(kcal*fs*mol^-1*Ang^-1):" << std::endl;
    std::cout << Xidtr << std::endl;
    std::cout << "rotation(kcal*fs*mol^-1):" << std::endl;
    std::cout << Xidrr << std::endl;

    return true;
    
  }

  void ApproximationModel::writeBeads(std::ostream& os) {
    std::vector<BeadParam>::iterator iter;
    os << beads_.size() << std::endl;
    os << "Generated by Hydro" << std::endl;
    for (iter = beads_.begin(); iter != beads_.end(); ++iter) {
      os << iter->atomName << "\t" << iter->pos[0] << "\t" << iter->pos[1] << "\t" << iter->pos[2] << std::endl;
    }
    
  }    
}
Revision:	1767
Committed:	Fri Jul 6 22:01:58 2012 UTC (12 years, 9 months ago) by gezelter
File size:	15823 byte(s)
Log Message:	Various fixes required to compile OpenMD with the MS Visual C++ compiler
#	User	Rev	Content
1	tim	906	/*
2			* Copyright (c) 2005 The University of Notre Dame. All Rights Reserved.
3			*
4			* The University of Notre Dame grants you ("Licensee") a
5			* non-exclusive, royalty free, license to use, modify and
6			* redistribute this software in source and binary code form, provided
7			* that the following conditions are met:
8			*
9	gezelter	1390	* 1. Redistributions of source code must retain the above copyright
10	tim	906	* notice, this list of conditions and the following disclaimer.
11			*
12	gezelter	1390	* 2. Redistributions in binary form must reproduce the above copyright
13	tim	906	* notice, this list of conditions and the following disclaimer in the
14			* documentation and/or other materials provided with the
15			* distribution.
16			*
17			* This software is provided "AS IS," without a warranty of any
18			* kind. All express or implied conditions, representations and
19			* warranties, including any implied warranty of merchantability,
20			* fitness for a particular purpose or non-infringement, are hereby
21			* excluded. The University of Notre Dame and its licensors shall not
22			* be liable for any damages suffered by licensee as a result of
23			* using, modifying or distributing the software or its
24			* derivatives. In no event will the University of Notre Dame or its
25			* licensors be liable for any lost revenue, profit or data, or for
26			* direct, indirect, special, consequential, incidental or punitive
27			* damages, however caused and regardless of the theory of liability,
28			* arising out of the use of or inability to use software, even if the
29			* University of Notre Dame has been advised of the possibility of
30			* such damages.
31	gezelter	1390	*
32			* SUPPORT OPEN SCIENCE! If you use OpenMD or its source code in your
33			* research, please cite the appropriate papers when you publish your
34			* work. Good starting points are:
35			*
36			* [1] Meineke, et al., J. Comp. Chem. 26, 252-271 (2005).
37			* [2] Fennell & Gezelter, J. Chem. Phys. 124, 234104 (2006).
38			* [3] Sun, Lin & Gezelter, J. Chem. Phys. 128, 24107 (2008).
39	gezelter	1665	* [4] Kuang & Gezelter, J. Chem. Phys. 133, 164101 (2010).
40			* [5] Vardeman, Stocker & Gezelter, J. Chem. Theory Comput. 7, 834 (2011).
41	tim	906	*/
42
43			#include "applications/hydrodynamics/ApproximationModel.hpp"
44			#include "math/LU.hpp"
45			#include "math/DynamicRectMatrix.hpp"
46			#include "math/SquareMatrix3.hpp"
47	gezelter	1390	#include "utils/PhysicalConstants.hpp"
48	gezelter	972	#include "hydrodynamics/Sphere.hpp"
49			#include "hydrodynamics/Ellipsoid.hpp"
50	tim	906	#include "applications/hydrodynamics/CompositeShape.hpp"
51			#include "math/LU.hpp"
52	tim	921	#include "utils/simError.h"
53	gezelter	1390	namespace OpenMD {
54	tim	906	/**
55			* Reference:
56			* Beatriz Carrasco and Jose Gracia de la Torre, Hydrodynamic Properties of Rigid Particles:
57			* Comparison of Different Modeling and Computational Procedures.
58			* Biophysical Journal, 75(6), 3044, 1999
59			*/
60
61	gezelter	972	ApproximationModel::ApproximationModel(StuntDouble* sd, SimInfo* info): HydrodynamicsModel(sd, info){
62			}
63
64			void ApproximationModel::init() {
65	tim	906	if (!createBeads(beads_)) {
66	tim	921	sprintf(painCave.errMsg, "ApproximationModel::init() : Can not create beads\n");
67			painCave.isFatal = 1;
68			simError();
69	tim	906	}
70	gezelter	972
71			}
72
73	tim	977	bool ApproximationModel::calcHydroProps(Shape* shape, RealType viscosity, RealType temperature) {
74	gezelter	972
75	tim	906	bool ret = true;
76	xsun	1177	HydroProp* cr = new HydroProp();
77			HydroProp* cd = new HydroProp();
78	tim	906	calcHydroPropsAtCR(beads_, viscosity, temperature, cr);
79	xsun	1177	calcHydroPropsAtCD(beads_, viscosity, temperature, cd);
80	tim	906	setCR(cr);
81			setCD(cd);
82			return true;
83	gezelter	972	}
84
85	gezelter	981	bool ApproximationModel::calcHydroPropsAtCR(std::vector<BeadParam>& beads, RealType viscosity, RealType temperature, HydroProp* cr) {
86	gezelter	972
87	gezelter	1767	unsigned int nbeads = beads.size();
88	tim	977	DynamicRectMatrix<RealType> B(3nbeads, 3nbeads);
89			DynamicRectMatrix<RealType> C(3nbeads, 3nbeads);
90	tim	906	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	972	for (std::size_t j = 0; j < nbeads; ++j) {
97			Mat3x3d Tij;
98	tim	906	if (i != j ) {
99	gezelter	972	Vector3d Rij = beads[i].pos - beads[j].pos;
100	tim	977	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	972	Mat3x3d tmpMat;
104			tmpMat = outProduct(Rij, Rij) / rij2;
105	tim	977	RealType constant = 8.0 * NumericConstant::PI * viscosity * rij;
106	tim	978	RealType tmp1 = 1.0 + sumSigma2OverRij2/3.0;
107			RealType tmp2 = 1.0 - sumSigma2OverRij2;
108			Tij = (tmp1 * I + tmp2 * tmpMat ) / constant;
109	tim	906	}else {
110	tim	977	RealType constant = 1.0 / (6.0 * NumericConstant::PI * viscosity * beads[i].radius);
111	gezelter	972	Tij(0, 0) = constant;
112			Tij(1, 1) = constant;
113			Tij(2, 2) = constant;
114	tim	906	}
115			B.setSubMatrix(i3, j3, Tij);
116	gezelter	972	}
117	tim	906	}
118	gezelter	972
119	tim	906	//invert B Matrix
120			invertMatrix(B, C);
121	tim	910
122	tim	906	//prepare U Matrix relative to arbitrary origin O(0.0, 0.0, 0.0)
123			std::vector<Mat3x3d> U;
124	gezelter	1767	for (unsigned int i = 0; i < nbeads; ++i) {
125	gezelter	972	Mat3x3d currU;
126			currU.setupSkewMat(beads[i].pos);
127			U.push_back(currU);
128	tim	906	}
129
130			//calculate Xi matrix at arbitrary origin O
131			Mat3x3d Xiott;
132			Mat3x3d Xiorr;
133			Mat3x3d Xiotr;
134	gezelter	972
135	tim	906	//calculate the total volume
136	gezelter	972
137	tim	977	RealType volume = 0.0;
138	tim	906	for (std::vector<BeadParam>::iterator iter = beads.begin(); iter != beads.end(); ++iter) {
139	gezelter	972	volume += 4.0/3.0 * NumericConstant::PI * pow((*iter).radius,3);
140	tim	906	}
141	gezelter	972
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	906
147	gezelter	972	Xiott += Cij;
148			Xiotr += U[i] * Cij;
149	xsun	1208	// uncorrected here. Volume correction is added after we assemble Xiorr
150	gezelter	972	Xiorr += -U[i] * Cij * U[j];
151			}
152	tim	906	}
153	xsun	1208
154			// add the volume correction
155	gezelter	1668	Xiorr += (RealType(6.0) * viscosity * volume) * I;
156	gezelter	972
157	gezelter	1390	Xiott *= PhysicalConstants::viscoConvert;
158			Xiotr *= PhysicalConstants::viscoConvert;
159			Xiorr *= PhysicalConstants::viscoConvert;
160	tim	906
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	tim	977	SquareMatrix<RealType,6> Xir6x6;
191			SquareMatrix<RealType,6> Dr6x6;
192	tim	906
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	gezelter	1390	RealType kt = PhysicalConstants::kb * temperature ; // in kcal mol^-1
208	tim	906	Drtt *= kt;
209			Drrt *= kt;
210			Drtr *= kt;
211			Drrr *= kt;
212	gezelter	1390	//Xirtt = PhysicalConstants::kb temperature;
213			//Xirtr = PhysicalConstants::kb temperature;
214			//Xirrr = PhysicalConstants::kb temperature;
215	tim	906
216	gezelter	981	Mat6x6d Xi, D;
217	tim	906
218	gezelter	981	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	tim	906
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	gezelter	972
258	xsun	1177	bool ApproximationModel::calcHydroPropsAtCD(std::vector<BeadParam>& beads, RealType viscosity, RealType temperature, HydroProp* cd) {
259	gezelter	972
260	gezelter	1767	unsigned int nbeads = beads.size();
261	tim	977	DynamicRectMatrix<RealType> B(3nbeads, 3nbeads);
262			DynamicRectMatrix<RealType> C(3nbeads, 3nbeads);
263	tim	906	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	gezelter	972	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	tim	977	RealType rij = Rij.length();
274			RealType rij2 = rij * rij;
275			RealType sumSigma2OverRij2 = ((beads[i].radiusbeads[i].radius) + (beads[j].radiusbeads[j].radius)) / rij2;
276	gezelter	972	Mat3x3d tmpMat;
277			tmpMat = outProduct(Rij, Rij) / rij2;
278	tim	977	RealType constant = 8.0 * NumericConstant::PI * viscosity * rij;
279	tim	978	RealType tmp1 = 1.0 + sumSigma2OverRij2/3.0;
280			RealType tmp2 = 1.0 - sumSigma2OverRij2;
281			Tij = (tmp1 * I + tmp2 * tmpMat ) / constant;
282	gezelter	972	}else {
283	tim	977	RealType constant = 1.0 / (6.0 * NumericConstant::PI * viscosity * beads[i].radius);
284	gezelter	972	Tij(0, 0) = constant;
285			Tij(1, 1) = constant;
286			Tij(2, 2) = constant;
287	tim	906	}
288	gezelter	972	B.setSubMatrix(i3, j3, Tij);
289			}
290	tim	906	}
291	gezelter	972
292	tim	906	//invert B Matrix
293			invertMatrix(B, C);
294	gezelter	972
295	tim	906	//prepare U Matrix relative to arbitrary origin O(0.0, 0.0, 0.0)
296			std::vector<Mat3x3d> U;
297	gezelter	1767	for (unsigned int i = 0; i < nbeads; ++i) {
298	gezelter	972	Mat3x3d currU;
299			currU.setupSkewMat(beads[i].pos);
300			U.push_back(currU);
301	tim	906	}
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	tim	977	RealType volume = 0.0;
311	tim	906	for (std::vector<BeadParam>::iterator iter = beads.begin(); iter != beads.end(); ++iter) {
312	gezelter	972	volume += 4.0/3.0 * NumericConstant::PI * pow((*iter).radius,3);
313	tim	906	}
314	gezelter	972
315	tim	906	for (std::size_t i = 0; i < nbeads; ++i) {
316	gezelter	972	for (std::size_t j = 0; j < nbeads; ++j) {
317			Mat3x3d Cij;
318			C.getSubMatrix(i3, j3, Cij);
319	tim	906
320	gezelter	972	Xitt += Cij;
321			Xitr += U[i] * Cij;
322	xsun	1208	// uncorrected here. Volume correction is added after we assemble Xiorr
323	gezelter	972	Xirr += -U[i] * Cij * U[j];
324			}
325	tim	906	}
326	xsun	1208	// add the volume correction here:
327	gezelter	1668	Xirr += (RealType(6.0) * viscosity * volume) * I;
328	gezelter	972
329	gezelter	1390	Xitt *= PhysicalConstants::viscoConvert;
330			Xitr *= PhysicalConstants::viscoConvert;
331			Xirr *= PhysicalConstants::viscoConvert;
332	gezelter	972
333	gezelter	1390	RealType kt = PhysicalConstants::kb * temperature; // in kcal mol^-1
334	gezelter	972
335	tim	906	Mat3x3d Dott; //translational diffusion tensor at arbitrary origin O
336			Mat3x3d Dorr; //rotational diffusion tensor at arbitrary origin O
337			Mat3x3d Dotr; //translation-rotation couplingl diffusion tensor at arbitrary origin O
338	gezelter	972
339	tim	906	const static Mat3x3d zeroMat(0.0);
340
341			Mat3x3d XittInv(0.0);
342			XittInv = Xitt.inverse();
343
344			Mat3x3d XirrInv;
345			XirrInv = Xirr.inverse();
346
347			Mat3x3d tmp;
348			Mat3x3d tmpInv;
349			tmp = Xitt - Xitr.transpose() * XirrInv * Xitr;
350			tmpInv = tmp.inverse();
351
352			Dott = tmpInv;
353			Dotr = -XirrInv * Xitr * tmpInv;
354
355			tmp = Xirr - Xitr * XittInv * Xitr.transpose();
356			tmpInv = tmp.inverse();
357
358			Dorr = tmpInv;
359
360			//calculate center of diffusion
361			tmp(0, 0) = Dorr(1, 1) + Dorr(2, 2);
362			tmp(0, 1) = - Dorr(0, 1);
363			tmp(0, 2) = -Dorr(0, 2);
364			tmp(1, 0) = -Dorr(0, 1);
365			tmp(1, 1) = Dorr(0, 0) + Dorr(2, 2);
366			tmp(1, 2) = -Dorr(1, 2);
367			tmp(2, 0) = -Dorr(0, 2);
368			tmp(2, 1) = -Dorr(1, 2);
369			tmp(2, 2) = Dorr(1, 1) + Dorr(0, 0);
370
371			Vector3d tmpVec;
372			tmpVec[0] = Dotr(1, 2) - Dotr(2, 1);
373			tmpVec[1] = Dotr(2, 0) - Dotr(0, 2);
374			tmpVec[2] = Dotr(0, 1) - Dotr(1, 0);
375
376			tmpInv = tmp.inverse();
377
378			Vector3d rod = tmpInv * tmpVec;
379
380			//calculate Diffusion Tensor at center of diffusion
381			Mat3x3d Uod;
382			Uod.setupSkewMat(rod);
383
384			Mat3x3d Ddtt; //translational diffusion tensor at diffusion center
385			Mat3x3d Ddtr; //rotational diffusion tensor at diffusion center
386			Mat3x3d Ddrr; //translation-rotation couplingl diffusion tensor at diffusion tensor
387
388			Ddtt = Dott - Uod * Dorr * Uod + Dotr.transpose() * Uod - Uod * Dotr;
389			Ddrr = Dorr;
390			Ddtr = Dotr + Dorr * Uod;
391
392	tim	977	SquareMatrix<RealType, 6> Dd;
393	tim	906	Dd.setSubMatrix(0, 0, Ddtt);
394			Dd.setSubMatrix(0, 3, Ddtr.transpose());
395			Dd.setSubMatrix(3, 0, Ddtr);
396			Dd.setSubMatrix(3, 3, Ddrr);
397	tim	977	SquareMatrix<RealType, 6> Xid;
398	tim	906	Ddtt *= kt;
399			Ddtr *=kt;
400			Ddrr *= kt;
401			invertMatrix(Dd, Xid);
402
403
404
405			//Xidtt in units of kcalfsmol^-1*Ang^-2
406	gezelter	1390	//Xid /= PhysicalConstants::energyConvert;
407			Xid = PhysicalConstants::kb temperature;
408	tim	906
409	gezelter	981	Mat6x6d Xi, D;
410	tim	906
411	xsun	1177	cd->setCOR(rod);
412	gezelter	981
413	xsun	1177	cd->setXi(Xid);
414	gezelter	981
415			D.setSubMatrix(0, 0, Ddtt);
416			D.setSubMatrix(0, 3, Ddtr);
417			D.setSubMatrix(3, 0, Ddtr);
418			D.setSubMatrix(3, 3, Ddrr);
419
420	xsun	1177	cd->setD(D);
421	gezelter	981
422	tim	906	std::cout << "viscosity = " << viscosity << std::endl;
423			std::cout << "temperature = " << temperature << std::endl;
424			std::cout << "center of diffusion :" << std::endl;
425			std::cout << rod << std::endl;
426			std::cout << "diffusion tensor at center of diffusion " << std::endl;
427	xsun	1208	std::cout << "translation(A^2 / fs) :" << std::endl;
428	tim	906	std::cout << Ddtt << std::endl;
429	xsun	1208	std::cout << "translation-rotation(A / fs):" << std::endl;
430	tim	906	std::cout << Ddtr << std::endl;
431	xsun	1208	std::cout << "rotation(fs^-1):" << std::endl;
432	tim	906	std::cout << Ddrr << std::endl;
433
434			std::cout << "resistance tensor at center of diffusion " << std::endl;
435			std::cout << "translation(kcalfsmol^-1*Ang^-2) :" << std::endl;
436
437			Mat3x3d Xidtt;
438			Mat3x3d Xidrt;
439			Mat3x3d Xidtr;
440			Mat3x3d Xidrr;
441			Xid.getSubMatrix(0, 0, Xidtt);
442			Xid.getSubMatrix(0, 3, Xidrt);
443			Xid.getSubMatrix(3, 0, Xidtr);
444			Xid.getSubMatrix(3, 3, Xidrr);
445
446			std::cout << Xidtt << std::endl;
447	xsun	1208	std::cout << "rotation-translation (kcalfsmol^-1*Ang^-1):" << std::endl;
448	tim	906	std::cout << Xidrt << std::endl;
449	xsun	1208	std::cout << "translation-rotation(kcalfsmol^-1*Ang^-1):" << std::endl;
450	tim	906	std::cout << Xidtr << std::endl;
451	xsun	1208	std::cout << "rotation(kcalfsmol^-1):" << std::endl;
452	tim	906	std::cout << Xidrr << std::endl;
453
454			return true;
455	gezelter	972
456			}
457	tim	906
458	gezelter	972	void ApproximationModel::writeBeads(std::ostream& os) {
459	tim	906	std::vector<BeadParam>::iterator iter;
460			os << beads_.size() << std::endl;
461			os << "Generated by Hydro" << std::endl;
462			for (iter = beads_.begin(); iter != beads_.end(); ++iter) {
463	gezelter	972	os << iter->atomName << "\t" << iter->pos[0] << "\t" << iter->pos[1] << "\t" << iter->pos[2] << std::endl;
464	tim	906	}
465	gezelter	972
466			}
467	tim	906	}