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/* |
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* Copyright (c) 2008 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. Acknowledgement of the program authors must be made in any |
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* publication of scientific results based in part on use of the |
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* program. An acceptable form of acknowledgement is citation of |
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* the article in which the program was described (Matthew |
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* A. Meineke, Charles F. Vardeman II, Teng Lin, Christopher |
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* J. Fennell and J. Daniel Gezelter, "OOPSE: An Object-Oriented |
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* Parallel Simulation Engine for Molecular Dynamics," |
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* J. Comput. Chem. 26, pp. 252-271 (2005)) |
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* |
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* 2. 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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* 3. 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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#include <fstream> |
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#include <iostream> |
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#include "integrators/SMIPDForceManager.hpp" |
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#include "math/CholeskyDecomposition.hpp" |
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#include "utils/OOPSEConstant.hpp" |
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#include "hydrodynamics/Sphere.hpp" |
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#include "hydrodynamics/Ellipsoid.hpp" |
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#include "utils/ElementsTable.hpp" |
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#include "math/ConvexHull.hpp" |
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#include "math/Triangle.hpp" |
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|
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|
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namespace oopse { |
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|
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SMIPDForceManager::SMIPDForceManager(SimInfo* info) : ForceManager(info), forceTolerance_(1e-6), maxIterNum_(4) { |
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simParams = info->getSimParams(); |
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veloMunge = new Velocitizer(info); |
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|
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// Create Hull, Convex Hull for now, other options later. |
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surfaceMesh_ = new ConvexHull(); |
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|
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|
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|
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/* Check that the simulation has target pressure and target |
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temperature set*/ |
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|
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if (!simParams->haveTargetTemp()) { |
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sprintf(painCave.errMsg, "You can't use the SMIPDynamics integrator without a targetTemp!\n"); |
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painCave.isFatal = 1; |
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painCave.severity = OOPSE_ERROR; |
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simError(); |
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} else { |
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targetTemp_ = simParams->getTargetTemp(); |
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} |
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|
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if (!simParams->haveTargetPressure()) { |
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sprintf(painCave.errMsg, "SMIPDynamics error: You can't use the SMIPD integrator\n" |
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" without a targetPressure!\n"); |
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|
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painCave.isFatal = 1; |
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simError(); |
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} else { |
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targetPressure_ = simParams->getTargetPressure()/OOPSEConstant::pressureConvert; |
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} |
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|
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|
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if (simParams->getUsePeriodicBoundaryConditions()) { |
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sprintf(painCave.errMsg, "SMIPDynamics error: You can't use the SMIPD integrator\n" |
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" with periodic boundary conditions !\n"); |
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|
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painCave.isFatal = 1; |
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simError(); |
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} |
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|
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if (!simParams->haveViscosity()) { |
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sprintf(painCave.errMsg, "You can't use SMIPDynamics without a viscosity!\n"); |
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painCave.isFatal = 1; |
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painCave.severity = OOPSE_ERROR; |
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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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|
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//Compute initial hull |
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/* |
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surfaceMesh_->computeHull(localSites_); |
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Area0_ = surfaceMesh_->getArea(); |
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int nTriangles = surfaceMesh_->getNMeshElements(); |
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// variance_ = 2.0 * OOPSEConstant::kb*simParams->getTargetTemp()/simParams->getDt(); |
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gamma_0_ = (NumericConstant::PI * targetPressure_* targetPressure_ * Area0_ * Area0_ * simParams->getDt()) / |
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(4.0 * nTriangles * nTriangles* OOPSEConstant::kb*simParams->getTargetTemp()); |
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//RealType eta0 = gamma_0/ |
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*/ |
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|
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// Build the hydroProp map: |
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std::map<std::string, HydroProp*> hydroPropMap; |
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|
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Molecule* mol; |
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StuntDouble* integrableObject; |
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SimInfo::MoleculeIterator i; |
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Molecule::IntegrableObjectIterator j; |
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bool needHydroPropFile = false; |
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|
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for (mol = info->beginMolecule(i); mol != NULL; |
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mol = info->nextMolecule(i)) { |
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for (integrableObject = mol->beginIntegrableObject(j); |
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integrableObject != NULL; |
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integrableObject = mol->nextIntegrableObject(j)) { |
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|
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if (integrableObject->isRigidBody()) { |
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RigidBody* rb = static_cast<RigidBody*>(integrableObject); |
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if (rb->getNumAtoms() > 1) needHydroPropFile = true; |
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} |
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|
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} |
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} |
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|
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|
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if (needHydroPropFile) { |
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if (simParams->haveHydroPropFile()) { |
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hydroPropMap = parseFrictionFile(simParams->getHydroPropFile()); |
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} else { |
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sprintf( painCave.errMsg, |
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"HydroPropFile must be set to a file name if SMIPDynamics\n" |
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"\tis specified for rigidBodies which contain more than one atom\n" |
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"\tTo create a HydroPropFile, run the \"Hydro\" program.\n\n" |
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"\tFor use with SMIPD, the default viscosity in Hydro should be\n" |
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"\tset to 1.0 because the friction and random forces will be\n" |
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"\tdynamically re-set assuming this is true.\n"); |
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painCave.severity = OOPSE_ERROR; |
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painCave.isFatal = 1; |
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simError(); |
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} |
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|
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for (mol = info->beginMolecule(i); mol != NULL; |
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mol = info->nextMolecule(i)) { |
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for (integrableObject = mol->beginIntegrableObject(j); |
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integrableObject != NULL; |
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integrableObject = mol->nextIntegrableObject(j)) { |
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|
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std::map<std::string, HydroProp*>::iterator iter = hydroPropMap.find(integrableObject->getType()); |
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if (iter != hydroPropMap.end()) { |
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hydroProps_.push_back(iter->second); |
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} else { |
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sprintf( painCave.errMsg, |
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"Can not find resistance tensor for atom [%s]\n", integrableObject->getType().c_str()); |
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painCave.severity = OOPSE_ERROR; |
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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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} else { |
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|
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std::map<std::string, HydroProp*> hydroPropMap; |
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for (mol = info->beginMolecule(i); mol != NULL; |
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mol = info->nextMolecule(i)) { |
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for (integrableObject = mol->beginIntegrableObject(j); |
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integrableObject != NULL; |
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integrableObject = mol->nextIntegrableObject(j)) { |
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Shape* currShape = NULL; |
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|
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if (integrableObject->isAtom()){ |
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Atom* atom = static_cast<Atom*>(integrableObject); |
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AtomType* atomType = atom->getAtomType(); |
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if (atomType->isGayBerne()) { |
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DirectionalAtomType* dAtomType = dynamic_cast<DirectionalAtomType*>(atomType); |
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GenericData* data = dAtomType->getPropertyByName("GayBerne"); |
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if (data != NULL) { |
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GayBerneParamGenericData* gayBerneData = dynamic_cast<GayBerneParamGenericData*>(data); |
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|
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if (gayBerneData != NULL) { |
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GayBerneParam gayBerneParam = gayBerneData->getData(); |
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currShape = new Ellipsoid(V3Zero, |
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gayBerneParam.GB_l / 2.0, |
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gayBerneParam.GB_d / 2.0, |
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Mat3x3d::identity()); |
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} else { |
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sprintf( painCave.errMsg, |
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"Can not cast GenericData to GayBerneParam\n"); |
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painCave.severity = OOPSE_ERROR; |
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painCave.isFatal = 1; |
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simError(); |
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} |
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} else { |
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sprintf( painCave.errMsg, "Can not find Parameters for GayBerne\n"); |
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painCave.severity = OOPSE_ERROR; |
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painCave.isFatal = 1; |
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simError(); |
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} |
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} else { |
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if (atomType->isLennardJones()){ |
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GenericData* data = atomType->getPropertyByName("LennardJones"); |
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if (data != NULL) { |
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LJParamGenericData* ljData = dynamic_cast<LJParamGenericData*>(data); |
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if (ljData != NULL) { |
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LJParam ljParam = ljData->getData(); |
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currShape = new Sphere(atom->getPos(), 2.0); |
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} else { |
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sprintf( painCave.errMsg, |
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"Can not cast GenericData to LJParam\n"); |
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painCave.severity = OOPSE_ERROR; |
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painCave.isFatal = 1; |
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simError(); |
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} |
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} |
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} else { |
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int aNum = etab.GetAtomicNum((atom->getType()).c_str()); |
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if (aNum != 0) { |
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currShape = new Sphere(atom->getPos(), 2.0); |
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} else { |
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sprintf( painCave.errMsg, |
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"Could not find atom type in default element.txt\n"); |
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painCave.severity = OOPSE_ERROR; |
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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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HydroProp* currHydroProp = currShape->getHydroProp(1.0,simParams->getTargetTemp()); |
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std::map<std::string, HydroProp*>::iterator iter = hydroPropMap.find(integrableObject->getType()); |
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if (iter != hydroPropMap.end()) |
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hydroProps_.push_back(iter->second); |
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else { |
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currHydroProp->complete(); |
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hydroPropMap.insert(std::map<std::string, HydroProp*>::value_type(integrableObject->getType(), currHydroProp)); |
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hydroProps_.push_back(currHydroProp); |
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} |
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} |
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} |
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} |
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|
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/* Compute hull first time through to get the area of t=0*/ |
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|
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//Build a vector of integrable objects to determine if the are surface atoms |
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for (mol = info_->beginMolecule(i); mol != NULL; mol = info_->nextMolecule(i)) { |
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for (integrableObject = mol->beginIntegrableObject(j); integrableObject != NULL; |
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integrableObject = mol->nextIntegrableObject(j)) { |
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localSites_.push_back(integrableObject); |
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} |
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} |
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|
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|
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} |
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|
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std::map<std::string, HydroProp*> SMIPDForceManager::parseFrictionFile(const std::string& filename) { |
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std::map<std::string, HydroProp*> props; |
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std::ifstream ifs(filename.c_str()); |
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if (ifs.is_open()) { |
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|
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} |
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|
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const unsigned int BufferSize = 65535; |
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char buffer[BufferSize]; |
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while (ifs.getline(buffer, BufferSize)) { |
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HydroProp* currProp = new HydroProp(buffer); |
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props.insert(std::map<std::string, HydroProp*>::value_type(currProp->getName(), currProp)); |
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} |
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|
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return props; |
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} |
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|
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void SMIPDForceManager::postCalculation(bool needStress){ |
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SimInfo::MoleculeIterator i; |
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Molecule::IntegrableObjectIterator j; |
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Molecule* mol; |
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StuntDouble* integrableObject; |
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RealType mass; |
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Vector3d pos; |
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Vector3d frc; |
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Mat3x3d A; |
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Mat3x3d Atrans; |
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Vector3d Tb; |
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Vector3d ji; |
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unsigned int index = 0; |
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int fdf; |
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|
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fdf = 0; |
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|
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/*Compute surface Mesh*/ |
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surfaceMesh_->computeHull(localSites_); |
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|
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/* Get area and number of surface stunt doubles and compute new variance */ |
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RealType area = surfaceMesh_->getArea(); |
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int nSurfaceSDs = surfaceMesh_->getNs(); |
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|
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|
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std::vector<Triangle> sMesh = surfaceMesh_->getMesh(); |
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int nTriangles = sMesh.size(); |
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|
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|
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|
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/* Compute variance for random forces */ |
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|
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|
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|
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|
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std::vector<RealType> randNums = genTriangleForces(nTriangles, 1.0); |
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|
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/* Loop over the mesh faces and apply random force to each of the faces*/ |
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|
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|
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std::vector<Triangle>::iterator face; |
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std::vector<StuntDouble*>::iterator vertex; |
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int thisNumber = 0; |
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for (face = sMesh.begin(); face != sMesh.end(); ++face){ |
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|
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Triangle thisTriangle = *face; |
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std::vector<StuntDouble*> vertexSDs = thisTriangle.getVertices(); |
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RealType thisArea = thisTriangle.getArea(); |
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// RealType sigma_t = sqrt(NumericConstant::PI/2.0)*((targetPressure_)*thisArea) /OOPSEConstant::energyConvert; |
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// gamma_t_ = (NumericConstant::PI * targetPressure_* targetPressure_ * thisArea * thisArea * simParams->getDt()) /(4.0 * OOPSEConstant::kB*simParams->getTargetTemp()); |
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|
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/* Get Random Force */ |
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Vector3d unitNormal = thisTriangle.getNormal(); |
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unitNormal.normalize(); |
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//Vector3d randomForce = -randNums[thisNumber] * sigma_t * unitNormal; |
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Vector3d centroid = thisTriangle.getCentroid(); |
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Vector3d facetVel = thisTriangle.getFacetVelocity(); |
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RealType hydroLength = thisTriangle.getIncircleRadius()*2.0/3.14; |
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|
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RealType f_normal = simParams->getViscosity()*hydroLength*1.439326479e4; |
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RealType extPressure = -(targetPressure_ * thisArea)/OOPSEConstant::energyConvert; |
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RealType randomForce = randNums[thisNumber++] * sqrt(2.0 * f_normal * OOPSEConstant::kb*targetTemp_/simParams->getDt()); |
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|
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RealType dragForce = -f_normal * dot(facetVel, unitNormal); |
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|
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|
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Vector3d langevinForce = (extPressure + randomForce + dragForce) * unitNormal; |
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|
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// Vector3d dragForce = - gamma_t_ * dot(facetVel, unitNormal) * unitNormal / OOPSEConstant::energyConvert; |
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|
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// std::cout << " " << randomForce << " " << f_normal << std::endl; |
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|
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|
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for (vertex = vertexSDs.begin(); vertex != vertexSDs.end(); ++vertex){ |
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if ((*vertex) != NULL){ |
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// mass = integrableObject->getMass(); |
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Vector3d vertexForce = langevinForce/3.0; |
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(*vertex)->addFrc(vertexForce); |
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|
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if ((*vertex)->isDirectional()){ |
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|
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Vector3d vertexPos = (*vertex)->getPos(); |
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Vector3d vertexCentroidVector = vertexPos - centroid; |
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(*vertex)->addTrq(cross(vertexCentroidVector,vertexForce)); |
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} |
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} |
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} |
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} |
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|
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/* Now loop over all surface particles and apply the drag*/ |
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/* |
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std::vector<StuntDouble*> surfaceSDs = surfaceMesh_->getSurfaceAtoms(); |
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for (vertex = surfaceSDs.begin(); vertex != surfaceSDs.end(); ++vertex){ |
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integrableObject = *vertex; |
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mass = integrableObject->getMass(); |
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if (integrableObject->isDirectional()){ |
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|
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// preliminaries for directional objects: |
| 383 |
|
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A = integrableObject->getA(); |
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Atrans = A.transpose(); |
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Vector3d rcrLab = Atrans * hydroProps_[index]->getCOR(); |
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//apply random force and torque at center of resistance |
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Mat3x3d I = integrableObject->getI(); |
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Vector3d omegaBody; |
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|
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// What remains contains velocity explicitly, but the velocity required |
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// is at the full step: v(t + h), while we have initially the velocity |
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// at the half step: v(t + h/2). We need to iterate to converge the |
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// friction force and friction torque vectors. |
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|
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// this is the velocity at the half-step: |
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|
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Vector3d vel =integrableObject->getVel(); |
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Vector3d angMom = integrableObject->getJ(); |
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|
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//estimate velocity at full-step using everything but friction forces: |
| 402 |
|
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frc = integrableObject->getFrc(); |
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Vector3d velStep = vel + (dt2_ /mass * OOPSEConstant::energyConvert) * frc; |
| 405 |
|
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Tb = integrableObject->lab2Body(integrableObject->getTrq()); |
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Vector3d angMomStep = angMom + (dt2_ * OOPSEConstant::energyConvert) * Tb; |
| 408 |
|
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Vector3d omegaLab; |
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Vector3d vcdLab; |
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Vector3d vcdBody; |
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Vector3d frictionForceBody; |
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Vector3d frictionForceLab(0.0); |
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Vector3d oldFFL; // used to test for convergence |
| 415 |
Vector3d frictionTorqueBody(0.0); |
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Vector3d oldFTB; // used to test for convergence |
| 417 |
Vector3d frictionTorqueLab; |
| 418 |
RealType fdot; |
| 419 |
RealType tdot; |
| 420 |
|
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//iteration starts here: |
| 422 |
|
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for (int k = 0; k < maxIterNum_; k++) { |
| 424 |
|
| 425 |
if (integrableObject->isLinear()) { |
| 426 |
int linearAxis = integrableObject->linearAxis(); |
| 427 |
int l = (linearAxis +1 )%3; |
| 428 |
int m = (linearAxis +2 )%3; |
| 429 |
omegaBody[l] = angMomStep[l] /I(l, l); |
| 430 |
omegaBody[m] = angMomStep[m] /I(m, m); |
| 431 |
|
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} else { |
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omegaBody[0] = angMomStep[0] /I(0, 0); |
| 434 |
omegaBody[1] = angMomStep[1] /I(1, 1); |
| 435 |
omegaBody[2] = angMomStep[2] /I(2, 2); |
| 436 |
} |
| 437 |
|
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omegaLab = Atrans * omegaBody; |
| 439 |
|
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// apply friction force and torque at center of resistance |
| 441 |
|
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vcdLab = velStep + cross(omegaLab, rcrLab); |
| 443 |
vcdBody = A * vcdLab; |
| 444 |
frictionForceBody = -(hydroProps_[index]->getXitt() * vcdBody + hydroProps_[index]->getXirt() * omegaBody); |
| 445 |
oldFFL = frictionForceLab; |
| 446 |
frictionForceLab = Atrans * frictionForceBody; |
| 447 |
oldFTB = frictionTorqueBody; |
| 448 |
frictionTorqueBody = -(hydroProps_[index]->getXitr() * vcdBody + hydroProps_[index]->getXirr() * omegaBody); |
| 449 |
frictionTorqueLab = Atrans * frictionTorqueBody; |
| 450 |
|
| 451 |
// re-estimate velocities at full-step using friction forces: |
| 452 |
|
| 453 |
velStep = vel + (dt2_ / mass * OOPSEConstant::energyConvert) * (frc + frictionForceLab); |
| 454 |
angMomStep = angMom + (dt2_ * OOPSEConstant::energyConvert) * (Tb + frictionTorqueBody); |
| 455 |
|
| 456 |
// check for convergence (if the vectors have converged, fdot and tdot will both be 1.0): |
| 457 |
|
| 458 |
fdot = dot(frictionForceLab, oldFFL) / frictionForceLab.lengthSquare(); |
| 459 |
tdot = dot(frictionTorqueBody, oldFTB) / frictionTorqueBody.lengthSquare(); |
| 460 |
|
| 461 |
if (fabs(1.0 - fdot) <= forceTolerance_ && fabs(1.0 - tdot) <= forceTolerance_) |
| 462 |
break; // iteration ends here |
| 463 |
} |
| 464 |
|
| 465 |
integrableObject->addFrc(frictionForceLab); |
| 466 |
integrableObject->addTrq(frictionTorqueLab + cross(rcrLab, frictionForceLab)); |
| 467 |
|
| 468 |
|
| 469 |
} else { |
| 470 |
//spherical atom |
| 471 |
|
| 472 |
// What remains contains velocity explicitly, but the velocity required |
| 473 |
// is at the full step: v(t + h), while we have initially the velocity |
| 474 |
// at the half step: v(t + h/2). We need to iterate to converge the |
| 475 |
// friction force vector. |
| 476 |
|
| 477 |
// this is the velocity at the half-step: |
| 478 |
|
| 479 |
Vector3d vel =integrableObject->getVel(); |
| 480 |
|
| 481 |
//estimate velocity at full-step using everything but friction forces: |
| 482 |
|
| 483 |
frc = integrableObject->getFrc(); |
| 484 |
Vector3d velStep = vel + (dt2_ / mass * OOPSEConstant::energyConvert) * frc; |
| 485 |
|
| 486 |
Vector3d frictionForce(0.0); |
| 487 |
Vector3d oldFF; // used to test for convergence |
| 488 |
RealType fdot; |
| 489 |
|
| 490 |
//iteration starts here: |
| 491 |
|
| 492 |
for (int k = 0; k < maxIterNum_; k++) { |
| 493 |
|
| 494 |
oldFF = frictionForce; |
| 495 |
frictionForce = -hydroProps_[index]->getXitt() * velStep; |
| 496 |
//frictionForce = -gamma_t*velStep; |
| 497 |
// re-estimate velocities at full-step using friction forces: |
| 498 |
|
| 499 |
velStep = vel + (dt2_ / mass * OOPSEConstant::energyConvert) * (frc + frictionForce); |
| 500 |
|
| 501 |
// check for convergence (if the vector has converged, fdot will be 1.0): |
| 502 |
|
| 503 |
fdot = dot(frictionForce, oldFF) / frictionForce.lengthSquare(); |
| 504 |
|
| 505 |
if (fabs(1.0 - fdot) <= forceTolerance_) |
| 506 |
break; // iteration ends here |
| 507 |
} |
| 508 |
|
| 509 |
integrableObject->addFrc(frictionForce); |
| 510 |
|
| 511 |
|
| 512 |
} |
| 513 |
|
| 514 |
|
| 515 |
} |
| 516 |
*/ |
| 517 |
Snapshot* currSnapshot = info_->getSnapshotManager()->getCurrentSnapshot(); |
| 518 |
currSnapshot->setVolume(surfaceMesh_->getVolume()); |
| 519 |
ForceManager::postCalculation(needStress); |
| 520 |
} |
| 521 |
|
| 522 |
void SMIPDForceManager::genRandomForceAndTorque(Vector3d& force, Vector3d& torque, unsigned int index, RealType variance) { |
| 523 |
|
| 524 |
|
| 525 |
Vector<RealType, 6> Z; |
| 526 |
Vector<RealType, 6> generalForce; |
| 527 |
|
| 528 |
|
| 529 |
Z[0] = randNumGen_.randNorm(0, variance); |
| 530 |
Z[1] = randNumGen_.randNorm(0, variance); |
| 531 |
Z[2] = randNumGen_.randNorm(0, variance); |
| 532 |
Z[3] = randNumGen_.randNorm(0, variance); |
| 533 |
Z[4] = randNumGen_.randNorm(0, variance); |
| 534 |
Z[5] = randNumGen_.randNorm(0, variance); |
| 535 |
|
| 536 |
generalForce = hydroProps_[index]->getS()*Z; |
| 537 |
|
| 538 |
force[0] = generalForce[0]; |
| 539 |
force[1] = generalForce[1]; |
| 540 |
force[2] = generalForce[2]; |
| 541 |
torque[0] = generalForce[3]; |
| 542 |
torque[1] = generalForce[4]; |
| 543 |
torque[2] = generalForce[5]; |
| 544 |
|
| 545 |
} |
| 546 |
std::vector<RealType> SMIPDForceManager::genTriangleForces(int nTriangles, RealType variance) { |
| 547 |
|
| 548 |
// zero fill the random vector before starting: |
| 549 |
std::vector<RealType> gaussRand; |
| 550 |
gaussRand.resize(nTriangles); |
| 551 |
std::fill(gaussRand.begin(), gaussRand.end(), 0.0); |
| 552 |
|
| 553 |
|
| 554 |
|
| 555 |
#ifdef IS_MPI |
| 556 |
if (worldRank == 0) { |
| 557 |
#endif |
| 558 |
for (int i = 0; i < nTriangles; i++) { |
| 559 |
//gaussRand[i] = fabs(randNumGen_.randNorm(0.0, 1.0)); |
| 560 |
gaussRand[i] = randNumGen_.randNorm(0.0, 1.0); |
| 561 |
} |
| 562 |
#ifdef IS_MPI |
| 563 |
} |
| 564 |
#endif |
| 565 |
|
| 566 |
// push these out to the other processors |
| 567 |
|
| 568 |
#ifdef IS_MPI |
| 569 |
if (worldRank == 0) { |
| 570 |
MPI_Bcast(&gaussRand[0], nTriangles, MPI_REAL, 0, MPI_COMM_WORLD); |
| 571 |
} else { |
| 572 |
MPI_Bcast(&gaussRand[0], nTriangles, MPI_REAL, 0, MPI_COMM_WORLD); |
| 573 |
} |
| 574 |
#endif |
| 575 |
|
| 576 |
for (int i = 0; i < nTriangles; i++) { |
| 577 |
gaussRand[i] = gaussRand[i] * variance; |
| 578 |
} |
| 579 |
|
| 580 |
return gaussRand; |
| 581 |
} |
| 582 |
|
| 583 |
|
| 584 |
|
| 585 |
|
| 586 |
|
| 587 |
} |
