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/* |
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* Copyright (c) 2005 The University of Notre Dame. All Rights Reserved. |
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* |
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* The University of Notre Dame grants you ("Licensee") a |
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* non-exclusive, royalty free, license to use, modify and |
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* redistribute this software in source and binary code form, provided |
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* that the following conditions are met: |
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* |
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* 1. Redistributions of source code must retain the above copyright |
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* notice, this list of conditions and the following disclaimer. |
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* |
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* 2. Redistributions in binary form must reproduce the above copyright |
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* notice, this list of conditions and the following disclaimer in the |
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* documentation and/or other materials provided with the |
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* distribution. |
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* |
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* This software is provided "AS IS," without a warranty of any |
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* kind. All express or implied conditions, representations and |
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* warranties, including any implied warranty of merchantability, |
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* fitness for a particular purpose or non-infringement, are hereby |
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* excluded. The University of Notre Dame and its licensors shall not |
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* be liable for any damages suffered by licensee as a result of |
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* using, modifying or distributing the software or its |
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* derivatives. In no event will the University of Notre Dame or its |
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* licensors be liable for any lost revenue, profit or data, or for |
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* direct, indirect, special, consequential, incidental or punitive |
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* damages, however caused and regardless of the theory of liability, |
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* arising out of the use of or inability to use software, even if the |
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* University of Notre Dame has been advised of the possibility of |
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* such damages. |
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* |
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* SUPPORT OPEN SCIENCE! If you use OpenMD or its source code in your |
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* research, please cite the appropriate papers when you publish your |
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* work. Good starting points are: |
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* |
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* [1] Meineke, et al., J. Comp. Chem. 26, 252-271 (2005). |
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* [2] Fennell & Gezelter, J. Chem. Phys. 124, 234104 (2006). |
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* [3] Sun, Lin & Gezelter, J. Chem. Phys. 128, 24107 (2008). |
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* [4] Kuang & Gezelter, J. Chem. Phys. 133, 164101 (2010). |
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* [5] Vardeman, Stocker & Gezelter, J. Chem. Theory Comput. 7, 834 (2011). |
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*/ |
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|
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#include "applications/hydrodynamics/ApproximationModel.hpp" |
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#include "math/LU.hpp" |
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#include "math/DynamicRectMatrix.hpp" |
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#include "math/SquareMatrix3.hpp" |
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#include "utils/PhysicalConstants.hpp" |
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#include "hydrodynamics/Sphere.hpp" |
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#include "hydrodynamics/Ellipsoid.hpp" |
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#include "applications/hydrodynamics/CompositeShape.hpp" |
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#include "math/LU.hpp" |
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#include "utils/simError.h" |
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namespace OpenMD { |
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/** |
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* Reference: |
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* Beatriz Carrasco and Jose Gracia de la Torre, Hydrodynamic Properties of Rigid Particles: |
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* Comparison of Different Modeling and Computational Procedures. |
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* Biophysical Journal, 75(6), 3044, 1999 |
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*/ |
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|
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ApproximationModel::ApproximationModel(StuntDouble* sd, SimInfo* info): HydrodynamicsModel(sd, info){ |
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} |
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|
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void ApproximationModel::init() { |
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if (!createBeads(beads_)) { |
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sprintf(painCave.errMsg, "ApproximationModel::init() : Can not create beads\n"); |
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painCave.isFatal = 1; |
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simError(); |
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} |
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|
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} |
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|
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bool ApproximationModel::calcHydroProps(Shape* shape, RealType viscosity, RealType temperature) { |
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|
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HydroProp* cr = new HydroProp(); |
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HydroProp* cd = new HydroProp(); |
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calcHydroPropsAtCR(beads_, viscosity, temperature, cr); |
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calcHydroPropsAtCD(beads_, viscosity, temperature, cd); |
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setCR(cr); |
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setCD(cd); |
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return true; |
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} |
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|
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bool ApproximationModel::calcHydroPropsAtCR(std::vector<BeadParam>& beads, RealType viscosity, RealType temperature, HydroProp* cr) { |
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|
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unsigned int nbeads = beads.size(); |
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DynamicRectMatrix<RealType> B(3*nbeads, 3*nbeads); |
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DynamicRectMatrix<RealType> C(3*nbeads, 3*nbeads); |
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Mat3x3d I; |
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I(0, 0) = 1.0; |
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I(1, 1) = 1.0; |
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I(2, 2) = 1.0; |
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|
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for (std::size_t i = 0; i < nbeads; ++i) { |
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for (std::size_t j = 0; j < nbeads; ++j) { |
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Mat3x3d Tij; |
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if (i != j ) { |
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Vector3d Rij = beads[i].pos - beads[j].pos; |
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RealType rij = Rij.length(); |
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RealType rij2 = rij * rij; |
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RealType sumSigma2OverRij2 = ((beads[i].radius*beads[i].radius) + (beads[j].radius*beads[j].radius)) / rij2; |
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Mat3x3d tmpMat; |
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tmpMat = outProduct(Rij, Rij) / rij2; |
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RealType constant = 8.0 * NumericConstant::PI * viscosity * rij; |
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RealType tmp1 = 1.0 + sumSigma2OverRij2/3.0; |
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RealType tmp2 = 1.0 - sumSigma2OverRij2; |
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Tij = (tmp1 * I + tmp2 * tmpMat ) / constant; |
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}else { |
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RealType constant = 1.0 / (6.0 * NumericConstant::PI * viscosity * beads[i].radius); |
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Tij(0, 0) = constant; |
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Tij(1, 1) = constant; |
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Tij(2, 2) = constant; |
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} |
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B.setSubMatrix(i*3, j*3, Tij); |
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} |
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} |
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|
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//invert B Matrix |
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invertMatrix(B, C); |
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|
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//prepare U Matrix relative to arbitrary origin O(0.0, 0.0, 0.0) |
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std::vector<Mat3x3d> U; |
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for (unsigned int i = 0; i < nbeads; ++i) { |
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Mat3x3d currU; |
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currU.setupSkewMat(beads[i].pos); |
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U.push_back(currU); |
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} |
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|
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//calculate Xi matrix at arbitrary origin O |
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Mat3x3d Xiott; |
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Mat3x3d Xiorr; |
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Mat3x3d Xiotr; |
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|
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//calculate the total volume |
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|
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RealType volume = 0.0; |
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for (std::vector<BeadParam>::iterator iter = beads.begin(); iter != beads.end(); ++iter) { |
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volume += 4.0/3.0 * NumericConstant::PI * pow((*iter).radius,3); |
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} |
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|
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for (std::size_t i = 0; i < nbeads; ++i) { |
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for (std::size_t j = 0; j < nbeads; ++j) { |
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Mat3x3d Cij; |
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C.getSubMatrix(i*3, j*3, Cij); |
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|
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Xiott += Cij; |
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Xiotr += U[i] * Cij; |
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// uncorrected here. Volume correction is added after we assemble Xiorr |
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Xiorr += -U[i] * Cij * U[j]; |
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} |
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} |
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|
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// add the volume correction |
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Xiorr += (RealType(6.0) * viscosity * volume) * I; |
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|
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Xiott *= PhysicalConstants::viscoConvert; |
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Xiotr *= PhysicalConstants::viscoConvert; |
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Xiorr *= PhysicalConstants::viscoConvert; |
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|
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Mat3x3d tmp; |
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Mat3x3d tmpInv; |
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Vector3d tmpVec; |
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tmp(0, 0) = Xiott(1, 1) + Xiott(2, 2); |
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tmp(0, 1) = - Xiott(0, 1); |
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tmp(0, 2) = -Xiott(0, 2); |
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tmp(1, 0) = -Xiott(0, 1); |
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tmp(1, 1) = Xiott(0, 0) + Xiott(2, 2); |
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tmp(1, 2) = -Xiott(1, 2); |
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tmp(2, 0) = -Xiott(0, 2); |
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tmp(2, 1) = -Xiott(1, 2); |
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tmp(2, 2) = Xiott(1, 1) + Xiott(0, 0); |
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tmpVec[0] = Xiotr(2, 1) - Xiotr(1, 2); |
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tmpVec[1] = Xiotr(0, 2) - Xiotr(2, 0); |
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tmpVec[2] = Xiotr(1, 0) - Xiotr(0, 1); |
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tmpInv = tmp.inverse(); |
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Vector3d ror = tmpInv * tmpVec; //center of resistance |
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Mat3x3d Uor; |
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Uor.setupSkewMat(ror); |
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|
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Mat3x3d Xirtt; |
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Mat3x3d Xirrr; |
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Mat3x3d Xirtr; |
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|
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Xirtt = Xiott; |
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Xirtr = (Xiotr - Uor * Xiott); |
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Xirrr = Xiorr - Uor * Xiott * Uor + Xiotr * Uor - Uor * Xiotr.transpose(); |
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|
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|
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SquareMatrix<RealType,6> Xir6x6; |
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SquareMatrix<RealType,6> Dr6x6; |
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|
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Xir6x6.setSubMatrix(0, 0, Xirtt); |
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Xir6x6.setSubMatrix(0, 3, Xirtr.transpose()); |
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Xir6x6.setSubMatrix(3, 0, Xirtr); |
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Xir6x6.setSubMatrix(3, 3, Xirrr); |
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|
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invertMatrix(Xir6x6, Dr6x6); |
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Mat3x3d Drtt; |
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Mat3x3d Drtr; |
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Mat3x3d Drrt; |
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Mat3x3d Drrr; |
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Dr6x6.getSubMatrix(0, 0, Drtt); |
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Dr6x6.getSubMatrix(0, 3, Drrt); |
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Dr6x6.getSubMatrix(3, 0, Drtr); |
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Dr6x6.getSubMatrix(3, 3, Drrr); |
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RealType kt = PhysicalConstants::kb * temperature ; // in kcal mol^-1 |
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Drtt *= kt; |
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Drrt *= kt; |
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Drtr *= kt; |
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Drrr *= kt; |
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//Xirtt *= PhysicalConstants::kb * temperature; |
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//Xirtr *= PhysicalConstants::kb * temperature; |
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//Xirrr *= PhysicalConstants::kb * temperature; |
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|
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Mat6x6d Xi, D; |
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|
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cr->setCOR(ror); |
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|
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Xi.setSubMatrix(0, 0, Xirtt); |
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Xi.setSubMatrix(0, 3, Xirtr); |
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Xi.setSubMatrix(3, 0, Xirtr); |
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Xi.setSubMatrix(3, 3, Xirrr); |
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|
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cr->setXi(Xi); |
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|
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D.setSubMatrix(0, 0, Drtt); |
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D.setSubMatrix(0, 3, Drrt); |
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D.setSubMatrix(3, 0, Drtr); |
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D.setSubMatrix(3, 3, Drrr); |
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|
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cr->setD(D); |
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|
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std::cout << "-----------------------------------------\n"; |
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std::cout << "center of resistance :" << std::endl; |
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std::cout << ror << std::endl; |
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std::cout << "resistant tensor at center of resistance" << std::endl; |
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std::cout << "translation:" << std::endl; |
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std::cout << Xirtt << std::endl; |
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std::cout << "translation-rotation:" << std::endl; |
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std::cout << Xirtr << std::endl; |
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std::cout << "rotation:" << std::endl; |
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std::cout << Xirrr << std::endl; |
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std::cout << "diffusion tensor at center of resistance" << std::endl; |
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std::cout << "translation:" << std::endl; |
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std::cout << Drtt << std::endl; |
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std::cout << "rotation-translation:" << std::endl; |
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std::cout << Drrt << std::endl; |
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std::cout << "translation-rotation:" << std::endl; |
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std::cout << Drtr << std::endl; |
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std::cout << "rotation:" << std::endl; |
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std::cout << Drrr << std::endl; |
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std::cout << "-----------------------------------------\n"; |
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|
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return true; |
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} |
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|
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bool ApproximationModel::calcHydroPropsAtCD(std::vector<BeadParam>& beads, RealType viscosity, RealType temperature, HydroProp* cd) { |
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|
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unsigned int nbeads = beads.size(); |
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DynamicRectMatrix<RealType> B(3*nbeads, 3*nbeads); |
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DynamicRectMatrix<RealType> C(3*nbeads, 3*nbeads); |
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Mat3x3d I; |
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I(0, 0) = 1.0; |
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I(1, 1) = 1.0; |
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I(2, 2) = 1.0; |
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|
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for (std::size_t i = 0; i < nbeads; ++i) { |
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for (std::size_t j = 0; j < nbeads; ++j) { |
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Mat3x3d Tij; |
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if (i != j ) { |
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Vector3d Rij = beads[i].pos - beads[j].pos; |
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RealType rij = Rij.length(); |
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RealType rij2 = rij * rij; |
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RealType sumSigma2OverRij2 = ((beads[i].radius*beads[i].radius) + (beads[j].radius*beads[j].radius)) / rij2; |
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Mat3x3d tmpMat; |
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tmpMat = outProduct(Rij, Rij) / rij2; |
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RealType constant = 8.0 * NumericConstant::PI * viscosity * rij; |
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RealType tmp1 = 1.0 + sumSigma2OverRij2/3.0; |
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RealType tmp2 = 1.0 - sumSigma2OverRij2; |
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Tij = (tmp1 * I + tmp2 * tmpMat ) / constant; |
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}else { |
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RealType constant = 1.0 / (6.0 * NumericConstant::PI * viscosity * beads[i].radius); |
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Tij(0, 0) = constant; |
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Tij(1, 1) = constant; |
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Tij(2, 2) = constant; |
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} |
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B.setSubMatrix(i*3, j*3, Tij); |
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} |
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} |
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|
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//invert B Matrix |
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invertMatrix(B, C); |
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|
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//prepare U Matrix relative to arbitrary origin O(0.0, 0.0, 0.0) |
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std::vector<Mat3x3d> U; |
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for (unsigned int i = 0; i < nbeads; ++i) { |
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Mat3x3d currU; |
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currU.setupSkewMat(beads[i].pos); |
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U.push_back(currU); |
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} |
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|
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//calculate Xi matrix at arbitrary origin O |
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Mat3x3d Xitt; |
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Mat3x3d Xirr; |
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Mat3x3d Xitr; |
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|
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//calculate the total volume |
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|
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RealType volume = 0.0; |
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for (std::vector<BeadParam>::iterator iter = beads.begin(); iter != beads.end(); ++iter) { |
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volume += 4.0/3.0 * NumericConstant::PI * pow((*iter).radius,3); |
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} |
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|
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for (std::size_t i = 0; i < nbeads; ++i) { |
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for (std::size_t j = 0; j < nbeads; ++j) { |
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Mat3x3d Cij; |
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C.getSubMatrix(i*3, j*3, Cij); |
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|
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Xitt += Cij; |
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Xitr += U[i] * Cij; |
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// uncorrected here. Volume correction is added after we assemble Xiorr |
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Xirr += -U[i] * Cij * U[j]; |
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} |
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} |
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// add the volume correction here: |
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Xirr += (RealType(6.0) * viscosity * volume) * I; |
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|
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Xitt *= PhysicalConstants::viscoConvert; |
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Xitr *= PhysicalConstants::viscoConvert; |
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Xirr *= PhysicalConstants::viscoConvert; |
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|
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RealType kt = PhysicalConstants::kb * temperature; // in kcal mol^-1 |
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|
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Mat3x3d Dott; //translational diffusion tensor at arbitrary origin O |
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Mat3x3d Dorr; //rotational diffusion tensor at arbitrary origin O |
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Mat3x3d Dotr; //translation-rotation couplingl diffusion tensor at arbitrary origin O |
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|
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const static Mat3x3d zeroMat(0.0); |
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|
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Mat3x3d XittInv(0.0); |
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XittInv = Xitt.inverse(); |
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|
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Mat3x3d XirrInv; |
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XirrInv = Xirr.inverse(); |
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|
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Mat3x3d tmp; |
| 347 |
Mat3x3d tmpInv; |
| 348 |
tmp = Xitt - Xitr.transpose() * XirrInv * Xitr; |
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tmpInv = tmp.inverse(); |
| 350 |
|
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Dott = tmpInv; |
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Dotr = -XirrInv * Xitr * tmpInv; |
| 353 |
|
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tmp = Xirr - Xitr * XittInv * Xitr.transpose(); |
| 355 |
tmpInv = tmp.inverse(); |
| 356 |
|
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Dorr = tmpInv; |
| 358 |
|
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//calculate center of diffusion |
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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 kcal*fs*mol^-1*Ang^-2 |
| 405 |
//Xid /= PhysicalConstants::energyConvert; |
| 406 |
Xid *= PhysicalConstants::kb * temperature; |
| 407 |
|
| 408 |
Mat6x6d Xi, D; |
| 409 |
|
| 410 |
cd->setCOR(rod); |
| 411 |
|
| 412 |
cd->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 |
cd->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 / fs):" << std::endl; |
| 429 |
std::cout << Ddtr << std::endl; |
| 430 |
std::cout << "rotation(fs^-1):" << std::endl; |
| 431 |
std::cout << Ddrr << std::endl; |
| 432 |
|
| 433 |
std::cout << "resistance tensor at center of diffusion " << std::endl; |
| 434 |
std::cout << "translation(kcal*fs*mol^-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 (kcal*fs*mol^-1*Ang^-1):" << std::endl; |
| 447 |
std::cout << Xidrt << std::endl; |
| 448 |
std::cout << "translation-rotation(kcal*fs*mol^-1*Ang^-1):" << std::endl; |
| 449 |
std::cout << Xidtr << std::endl; |
| 450 |
std::cout << "rotation(kcal*fs*mol^-1):" << 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 |
} |
