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Novel Methods in Soft Matter Simulations : Lecture Notes in Physics - Mikko Karttunen

Novel Methods in Soft Matter Simulations

Lecture Notes in Physics

By: Mikko Karttunen (Editor), Ilpo Vattulainen (Editor), Ari Lukkarinen (Editor)

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Published: October 2004
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Soft matter and biological systems pose many challenges for theoretical, experimental and computational research. From the computational point of view, these many-body systems cover variations in relevant time and length scales over many orders of magnitude. Indeed, the macroscopic properties of materials and complex fluids are ultimately to be deduced from the dynamics of the microsopic, molecular level. In these lectures, internationally renowned experts offer a tutorial presentation of novel approaches for bridging these space and time scales in realistic simulations. This volume addresses graduate students and nonspecialist researchers from related areas seeking a high-level but accessible introduction to the state of the art in soft matter simulations.

Introductionp. 1
Applications of Dissipative Particle Dynamics CRobert D. Grootp. 5
Why Mesoscopic Simulation?p. 5
Introduction to DPDp. 6
Forcesp. 7
Simulation Techniquesp. 9
Parameterisationp. 10
Generalisations and Alternativesp. 12
Block Copolymer Mesophase Separationp. 14
Polymers in Meltp. 14
Expected and Simulated Phase Diagramp. 16
Evolution Pathwaysp. 20
Importance of Hydrodynamicsp. 21
Polymers and Membranes Interacting with Surfactant Solutionsp. 25
Polymers and Surfactants in Solutionp. 25
Biomembrane Morphologyp. 30
Biomembrane Deformation and Rupturep. 34
Conclusionsp. 36
Simulating the Dynamics of Mesoscopic Systemsp. 39
Introductionp. 39
Renormalizing Static Propertiesp. 40
Time-Scalesp. 41
Absolutely Minimal Mesoscopic Dynamicsp. 43
Modelling the Solvent with an Andersen Thermostatp. 44
Langevin Dynamics of a Gaussian Chainp. 45
Brownian Dynamicsp. 47
The Dynamics of a Colloidal Suspensionp. 47
What Does Minimal Dynamics Teach Usp. 52
More Realistic Solvent Dynamics - Hydrodynamicsp. 52
The Importance of Hydrodynamicsp. 52
Putting Back the Hydrodynamicsp. 54
Dissipative Particle Dynamics and the Lowe-Andersen Thermostatp. 55
Parametrically Correct Solvent Modellingp. 57
Concluding Remarksp. 58
An Example Problem - A Long Polymer Chain in an External Potentialp. 59
Renormalizing the Static Properties of the Ideal Chainp. 59
Long Polymer Dynamics from Short Model Polymersp. 61
Results for the Test Problemp. 64
What Do We Learn from This Examplep. 66
General Conclusionsp. 66
p. 69
Introductionp. 69
The Theory of Coarse-Graining in a Nutshellp. 70
Example: A Colloidal Suspensionp. 72
Microscopic Level: Classical Mechanicsp. 72
Mesoscopic Level 1: Hydrodynamicsp. 74
Mesoscopic Level 2: Fokker-Planckp. 76
Mesoscopic Level 3: Smoluchowskip. 77
Mesoscopic Level 4: Fickp. 78
Macroscopic Level: Thermodynamicsp. 78
The Mathematics of the Theory of Coarse-Grainingp. 79
The Microscopic Levelp. 80
Liouville Theoremp. 80
Equilibrium at the Microscopic Levelp. 81
The Mesoscopic Levelp. 82
Exact Equation for P(x, t)p. 84
The Fokker-Planck Equationp. 86
Example: Smoluchowski Levelp. 88
How to Compute the Objects in the FPE from a MD Simulation?p. 89
GENERIC Structure of the Fokker-Planck Equationp. 92
Properties of L and Mp. 94
GENERIC Stochastic Differential Equationp. 96
The Size of the Fluctuations and the Deterministic Equationsp. 97
Fluid Particle Models for Simulating Complex Fluidsp. 99
Soft Fluid Particlesp. 102
Complex Fluidsp. 111
Summaryp. 112
Mesoscopic Multi-particle Collision Model for Fluid Flow and Molecular Dynamicsp. 116
Introductionp. 116
Multi-particle Collision Model for Fluid Flowp. 117
Evolution Equationp. 120
H-Theoremp. 121
Hydrodynamic Equations and Transport Propertiesp. 126
Evolution Equations for Mean Dynamical Variablesp. 126
Kinetic Equations for Conserved Variablesp. 128
General Form of the Kinetic Equationp. 132
Hydrodynamic Equationsp. 133
Simulations of Fluid Flowp. 135
Mesoscopic Model for Solute Molecular Dynamicsp. 136
Simulations of Hybrid Dynamicsp. 138
Brownian Motionp. 138
Cluster Dynamicsp. 142
Polymer Dynamicsp. 144
Complex Fluidsp. 146
Conclusion and Perspectivesp. 147
Molecular Dynamics of Complex Systems: Non-Hamiltonian, Constrained, Quantum-Classicalp. 150
Introductionp. 150
Non-Hamiltonian Molecular Dynamicsp. 150
Nosé-Hoover """"Demonstration""""p. 150
Invariant Measure for Non-Hamiltonian Dynamical Systemsp. 152
Liouville Equation and Its Stationary Solutionsp. 154
The Correct Rules to Construct the Equilibrium Ensemble of Extended Variables Dynamical Systemsp. 156
The True Statistics of the Nosé-Hoover Ensemblep. 157
New Atomic """"iso""""-stats (NVT, NPT)p. 159
Molecular NPT with Constraintsp. 162
Implementationsp. 167
Reversible Integratorsp. 167
Constraints (SHAKE)p. 172
Concluding Remarks for Non-Hamiltonian Molecular Dynamicsp. 177
Dynamics and (Some) Statistical Mechanics of Quantum-Classical Systemsp. 177
Quantum-Classical Non-adiabatic Dynamicsp. 177
Quantum-Classical Statistical Mechanicsp. 184
Concluding Remarks for Quantum-Classical Systemsp. 188
Hybrid Models: Bridging Particle and Continuum Scales in Hydrodynamic Flow Simulationsp. 190
Introductionp. 190
A Hybrid Model for Diffusionp. 191
Simulations and Resultsp. 193
Transport Properties and Continuity of the Discrete-Continuous Interfacep. 194
Equilibrium Fluctuationsp. 196
A Hybrid Model for the Navier-Stokes Equationp. 201
A Hybrid Model for the Coupling of Gas and Grainsp. 205
Gas Dynamicsp. 206
Particle Dynamicsp. 208
Implementationp. 210
Sedimentationp. 211
Fluidized Bedsp. 213
Experimental Verificationp. 214
Conclusionsp. 215
On the Reduction of Molecular Degrees of Freedom in Computer Simulationsp. 219
Introductionp. 219
Atomistic Force Fieldsp. 220
Parameterization of Force Fieldsp. 224
Reduction of Molecular Degrees of Freedomp. 225
Eliminating Fast Fluctuationsp. 226
Simplifying Molecular Modelsp. 227
Elimination of Explicit Solvent Moleculesp. 227
Effective Potentials and the Inverse Monte Carlo Methodp. 228
Inverse Problem in Statistical Mechanicsp. 228
The Methodp. 229
How to Implement the Method for More General Systemsp. 231
Some Examples and Discussionp. 232
Ab-Initio Effective Potentialsp. 232
Effective Solvent-Mediated Potentialsp. 236
Effective Potentials for Macromoleculesp. 241
Summaryp. 242
Computer Simulations of the Electric Double Layerp. 245
Introductionp. 245
Numerics of the Coulomb Interactionp. 246
Electrostatic Energy for Periodic Systemsp. 248
Precision of the Lekner Summationp. 252
Counterions Close to a Single Charged Wallp. 253
Counterion Density Profilep. 257
Two-Dimensional Liquid and Crystalp. 259
Finite-Size Effectsp. 262
Other Boundary Conditionsp. 263
Charge-Modulated Substratep. 265
Interacting Double Layersp. 270
Concluding Remarksp. 275
Lattice Boltzmann Modeling of Complex Fluids: Colloidal Suspensions and Fluid Mixturesp. 279
Introductionp. 279
Lattice Boltzmann: The Modelp. 280
Elementary Variablesp. 282
Time Evolutionp. 282
The Equilibrium Distributionp. 283
Macroscopic Dynamicsp. 284
Colloidal Suspensionsp. 286
Modeling Solid Particlesp. 286
Colloidal Hydrodynamicsp. 289
Colloids at High Confinementp. 290
Non-ideal Fluids: A Binary Mixturep. 298
The Modelp. 299
Spinodal Decompositionp. 301
Conclusionsp. 306
Reverse Non-equilibrium Molecular Dynamicsp. 310
Introductionp. 310
Introduction: Transport Coefficientsp. 310
Illustration of the RNEMD Method: Calculating Shear Viscosityp. 312
Modification of the RNEMD Method: Thermal Conductivityp. 317
Digression: Features of the RNEMD Methodp. 319
The RNEMD and Higher-Order Transport Coefficients: The Ludwig-Soret Effect as an Examplep. 320
Molecular Fluids and the RNEMD Methodp. 321
A Bibliography of Applications of the RNEMD Methodp. 323
Shear Flow, Viscosityp. 323
Thermal Conductivityp. 323
Thermal Diffusion, Soret Coefficientp. 324
Status and Future Potential of the RNEMD Methodp. 324
Coarse-Graining in Polymer Simulationsp. 327
Introductionp. 327
From Quantum Chemistry to Atomistic Simulationp. 329
The Bonded-Potentialp. 330
The Non-bonded Potentialp. 331
Force Field Optimisationp. 332
Coarse-Graining from Atomistic to Mesoscopic Modelsp. 335
The Super-Atomsp. 336
Definition and Optimisation of the Potentialp. 339
Reverse Mappingp. 347
Relation to Other Coarse-Graining Proceduresp. 349
Lattice Modelsp. 349
Coarse-Graining Further: From Super-Atoms to Blobsp. 354
Conclusionsp. 354
Phase-Field Modeling of Dynamical Interface Phenomena in Fluidsp. 357
Introduction to Coarse-Grainingp. 357
Phase-Field Modelingp. 359
Construction of Free Energyp. 360
The Phase-Fieldp. 361
Sharp Interface Limitp. 364
Dropletsp. 364
Dynamics of Gently Curved Frontsp. 366
Kinetic Rougheningp. 368
Universalityp. 370
Advantages of the Phase-Field Approachp. 371
Alphabet Soup of Modelsp. 372
Application: Kinetic Roughening in Imbibitionp. 374
Backgroundp. 374
Phase-Field Model of Imbibitionp. 375
Evaporation and Gravityp. 379
Capillariesp. 381
Phase-Field Models and Hydrodynamicsp. 382
Summary and Conclusionsp. 384
Indexp. 389
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9783540209164
ISBN-10: 3540209166
Series: Lecture Notes in Physics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 393
Published: October 2004
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 24.77 x 16.51  x 1.91
Weight (kg): 0.78