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ОбложкаBerendsen H.J.C. Simulating the physical world: hierarchical modeling from quantum mechanics to fluid dynamics. - Cambridge: Cambridge University Press, 2007. - xxvii, 596 p.: ill. - Ref.: p.557-585. - Ind.: p.587-596. - ISBN 978-0-521-83527-5
Шифр: (И/В3-В45) 02
 

Место хранения: 02 | Отделение ГПНТБ СО РАН | Новосибирск

Оглавление / Contents
 
Preface ........................................................ xi
Symbols, units and constants ................................... xv

Part I  A Modeling Hierarchy for Simulations .................... 1
1  Introduction ................................................. 3
   1.1  What is this book about? ................................ 3
   1.2  A modeling hierarchy .................................... 9
   1.3  Trajectories and distributions ......................... 13
   1.4  Further reading ........................................ 14
2  Quantum mechanics: principles and relativistic effects ...... 19
   2.1  The wave character of particles ........................ 19
   2.2  Non-relativistic single free particle .................. 23
   2.3  Relativistic energy relations for a free particle ...... 25
   2.4  Electrodynamic interactions ............................ 31
   2.5  Fermions, bosons and the parity rule ................... 36
3  From quantum to classical mechanics: when and how ........... 39
   3.1  Introduction ........................................... 39
   3.2  From quantum to classical dynamics ..................... 42
   3.3  Path integral quantum mechanics ........................ 44
   3.4  Quantum hydrodynamics .................................. 64
   3.5  Quantum corrections to classical behavior .............. 70
4  Quantum chemistry: solving the time-independent
   Schrödinger equation ........................................ 77
   4.1  Introduction ........................................... 77
   4.2  Stationary solutions of the TDSE ....................... 78
   4.3  The few-particle problem ............................... 79
   4.4  The Born-Oppenheimer approximation ..................... 97
   4.5  The many-electron problem of quantum chemistry ......... 98
   4.6  Hartree-Fock methods ................................... 99
   4.7  Density functional theory ............................. 102
   4.8  Excited-state quantum mechanics ....................... 105
   4.9  Approximate quantum methods ........................... 106
   4.10 Nuclear quantum states ................................ 107
5  Dynamics of mixed quantum/classical systems ................ 109
   5.1  Introduction .......................................... 109
   5.2  Quantum dynamics in a non-stationary potential ........ 114
   5.3  Embedding in a classical environment .................. 129
6  Molecular dynamics ......................................... 139
   6.1  Introduction .......................................... 139
   6.2  Boundary conditions of the system ..................... 140
   6.3  Force field descriptions .............................. 149
   6.4  Solving the equations of motion ....................... 189
   6.5  Controlling the system ................................ 194
   6.6  Replica exchange method ............................... 204
   6.7  Applications of molecular dynamics .................... 207
7  Free  energy, entropy and potential of mean force .......... 211
   7.1  Introduction .......................................... 211
   7.2  Free energy determination by spatial integration ...... 213
   7.3  Thermodynamic potentials and particle insertion ....... 218
   7.4  Free energy by perturbation and integration ........... 221
   7.5  Free energy and potentials of mean force .............. 227
   7.6  Reconstruction of free energy from PMF ................ 231
   7.7  Methods to derive the potential of mean force ......... 234
   7.8  Free energy from non-equilibrium processes ............ 239
8  Stochastic dynamics: reducing degrees of freedom ........... 249
   8.1  Distinguishing relevant degrees of freedom ............ 249
   8.2  The generalized Langevin equation ..................... 251
   8.3  The potential of mean force ........................... 255
   8.4  Superatom approach .................................... 256
   8.5  The fluctuation-dissipation theorem ................... 257
   8.6  Langevin dynamics ..................................... 263
   8.7  Brownian dynamics ..................................... 268
   8.8  Probability distributions and Fokker-Planck
        equations ............................................. 269
   8.9  Smart Monte Carlo methods ............................. 272
   8.10 How to obtain the friction tensor ..................... 274
9  Coarse graining from particles to fluid dynamics ........... 279
   9.1  Introduction .......................................... 279
   9.2  The macroscopic equations of fluid dynamics ........... 281
   9.3  Coarse graining in space .............................. 288
   9.4  Conclusion ............................................ 295
10 Mesoscopic continuum dynamics .............................. 297
   10.1 Introduction .......................................... 297
   10.2 Connection to irreversible thermodynamics ............. 298
   10.3 The mean field approach to the chemical potential ..... 301
11 Dissipative particle dynamics .............................. 305
   11.1 Representing continuum equations by particles ......... 307
   11.2 Prescribing fluid parameters .......................... 308
   11.3 Numerical solutions ................................... 309
   11.4 Applications .......................................... 309

Part II  Physical and Theoretical Concepts .................... 313
12 Fourier transforms ......................................... 315
   12.1 Definitions and properties ............................ 315
   12.2 Convolution and autocorrelation ....................... 316
   12.3 Operators ............................................. 317
   12.4 Uncertainty relations ................................. 318
   12.5 Examples of functions and transforms .................. 320
   12.6 Discrete Fourier transforms ........................... 323
   12.7 Fast Fourier transforms ............................... 324
   12.8 Autocorrelation and spectral density from FFT ......... 325
   12.9 Multidimensional Fourier transforms ................... 331
13 Electromagnetism ........................................... 335
   13.1 Maxwell's equation for vacuum ......................... 335
   13.2 Maxwell's equation for polarizable matter ............. 336
   13.3 Integrated form of Maxwell's equations ................ 337
   13.4 Potentials ............................................ 337
   13.5 Waves ................................................. 338
   13.6 Energies .............................................. 339
   13.7 Quasi-stationary electrostatics ....................... 340
   13.8 Multipole expansion ................................... 353
   13.9 Potentials and fields in non-periodic systems ......... 362
   13.10 Potentials and fields in periodic systems of
        charges ............................................... 362
14 Vectors, operators and vector spaces ....................... 379
   14.1 Introduction .......................................... 379
   14.2 Definitions ........................................... 380
   14.3 Hilbert spaces of wave functions ...................... 381
   14.4 Operators in Hilbert space ............................ 382
   14.5 Transformations of the basis set ...................... 384
   14.6 Exponential operators and matrices .................... 385
   14.7 Equations of motion ................................... 390
   14.8 The density matrix .................................... 392
15 Lagrangian and Hamiltonian mechanics ....................... 397
   15.1 Introduction .......................................... 397
   15.2 Lagrangian mechanics .................................. 398
   15.3 Hamiltonian mechanics ................................. 399
   15.4 Cyclic coordinates .................................... 400
   15.5 Coordinate transformations ............................ 401
   15.6 Translation and rotation .............................. 403
   15.7 Rigid body motion ..................................... 405
   15.8 Holonomic constraints ................................. 417
16 Review of thermodynamics ................................... 423
   16.1 Introduction and history .............................. 423
   16.2 Definitions ........................................... 425
   16.3 Thermodynamic equilibrium relations ................... 429
   16.4 The second law ........................................ 432
   16.5 Phase behavior ........................................ 433
   16.6 Activities and standard states ........................ 435
   16.7 Reaction equilibria ................................... 437
   16.8 Colligative properties ................................ 441
   16.9 Tabulated thermodynamic quantities .................... 443
   16.10 Thermodynamics of irreversible processes ............. 444
17 Review of statistical mechanics ............................ 453
   17.1 Introduction .......................................... 453
   17.2 Ensembles and the postulates of statistical
        mechanics ............................................. 454
   17.3 Identification of thermodynamical variables ........... 457
   17.4 Other ensembles ....................................... 459
   17.5 Fermi-Dirac, Bose-Einstein and Boltzmann statistics ... 463
   17.6 The classical approximation ........................... 472
   17.7 Pressure and virial ................................... 479
   17.8 Liouville equations in phase space .................... 492
   17.9 Canonical distribution functions ...................... 497
   17.10 The generalized equipartition theorem ................ 502
18 Linear response theory ..................................... 505
   18.1 Introduction .......................................... 505
   18.2 Linear response relations ............................. 506
   18.3 Relation to time correlation functions ................ 511
   18.4 The Einstein relation ................................. 518
   18.5 Non-equilibrium molecular dynamics .................... 519
19 Splines for everything ..................................... 523
   19.1 Introduction .......................................... 523
   19.2 Cubic splines through points .......................... 526
   19.3 Fitting splines ....................................... 530
   19.4 Fitting distribution functions ........................ 536
   19.5 Splines for tabulation ................................ 539
   19.6 Algorithms for spline interpolation ................... 542
   19.7 B-splines ............................................. 548

References .................................................... 557
Index ......................................................... 587

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