Free energy computations: a mathematical perspective
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London
Imperial College Press
2010
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XII, 458 S. |
| ISBN: | 9781848162471 1848162472 |
Internformat
MARC
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|---|---|---|---|
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| 020 | |a 1848162472 |c hardcover : alk. paper |9 1-8481-6247-2 | ||
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| 100 | 1 | |a Lelièvre, Tony |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Free energy computations |b a mathematical perspective |c Tony Lelièvre ; Mathias Rousset ; Gabriel Stoltz |
| 264 | 1 | |a London |b Imperial College Press |c 2010 | |
| 300 | |a XII, 458 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Gibbs' free energy | |
| 650 | 4 | |a Statistical physics |x Mathematical models | |
| 650 | 0 | 7 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Freie Energie |0 (DE-588)4155282-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Freie Energie |0 (DE-588)4155282-9 |D s |
| 689 | 0 | 1 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Stoltz, Gabriel |e Verfasser |4 aut | |
| 700 | 1 | |a Rousset, Mathias |e Verfasser |4 aut | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021161113&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-021161113 | ||
Datensatz im Suchindex
| _version_ | 1804143861290762240 |
|---|---|
| adam_text | Titel: Free energy computations
Autor: Lelièvre, Tony
Jahr: 2010
Contents
Preface v
1. Introduction 1
1.1 Computational Statistical physics: some landmarks .... 1
1.1.1 Some Orders of magnitude............. 2
1.1.2 Aims of molecular Simulation............ 3
1.2 Microscopic description of physical Systems........ 6
1.2.1 Interactions ..................... 6
1.2.2 Dynamics of isolated Systems............ 13
1.2.3 Thermodynamic ensembles............. 20
1.3 Free energy and its numerical computation........ 33
1.3.1 Absolute free energy................. 34
1.3.2 Relative free energies................ 37
1.3.3 Free energy and metastability........... 44
1.3.4 Computational techniques............. 51
1.4 Summary of the mathematical tools and structure of the
book.............................. 59
2. Sampling methods 61
2.1 Markov chain methods.................... 63
2.1.1 Some background material on the theory of
Markov chains.................... 64
2.1.2 The Metropolis-Hastings algorithm........ 67
2.1.3 Hybrid Monte-Carlo................. 72
2.1.4 Generalized Metropolis-Hastings variants..... 74
2.2 Continuous stochastic dynamics............... 77
x Free Energy Computations: A Mathematical Perspective
2.2.1 Mathematical background on Markovian continu-
ous processes..................... 78
2.2.2 Overdamped Langevin process........... 86
2.2.3 Langevin process .................. 88
2.2.4 Overdamped limit of the Langevin dynamics ... 97
2.3 Convergence of sampling methods ............. 105
2.3.1 Sampling errors................... 105
2.3.2 Rate of convergence for stochastic processes ... 113
2.4 Methods for alchemical free energy differences....... 118
2.4.1 Free energy perturbation.............. 119
2.4.2 Bridge sampling................... 132
2.5 Histogram methods...................... 138
2.5.1 Principle of histogram methods .......... 138
2.5.2 Extended bridge sampling............. 142
3. Thermodynamic Integration and sampling with constraints 149
3.1 Introduction: The alchemical setting............ 150
3.1.1 General strategy................... 150
3.1.2 Numerical application................ 152
3.2 The reaction coordinate case: configurational space
sampling............................ 154
3.2.1 Reaction coordinate and free energy........ 154
3.2.2 The mean force................... 163
3.2.3 Sampling measures on submanifolds of Rn .... 168
3.2.4 Sampling measures on submanifolds of Rn: dis-
cretization...................... 180
3.2.5 Computing the mean force............. 188
3.2.6 On the efficiency of constrained sampling..... 200
3.3 The reaction coordinate case: Phase space sampling . . . 203
3.3.1 Constrained mechanical Systems.......... 204
3.3.2 Phase space measures for constrained Systems . . 209
3.3.3 Hamilton and Poisson formalisms with
constraints...................... 219
3.3.4 Constrained Langevin processes.......... 227
3.3.5 Numerical implementation............. 232
3.3.6 Thermodynamic Integration with constrained
Langevin processes................. 242
4. Nonequilibrium methods 259
Contents xi
4.1 The Jarzynski equality in the alchemical case....... 260
4.1.1 Markovian nonequilibrium simulations ...... 260
4.1.2 Importance weights of nonequilibrium
simulations...................... 262
4.1.3 Practical implementation.............. 266
4.1.4 Degeneracy of weights................ 269
4.1.5 Error analysis.................... 275
4.2 Generalized Jarzynski-Crooks fluctuation identity..... 284
4.2.1 Derivation of the identity.............. 285
4.2.2 Relationship with Standard equalities in the
physics and chemistry literature.......... 291
4.2.3 Numerical strategies................. 293
4.3 Nonequilibrium stochastic methods in the reaction coordi-
nate case ........................... 296
4.3.1 Overdamped nonequilibrium dynamics...... 296
4.3.2 Hamiltonian and Langevin nonequilibrium
dynamics....................... 305
4.3.3 Numerical results.................. 323
4.4 Path sampling strategies................... 324
4.4.1 The path ensemble ................. 324
4.4.2 Sampling switching paths.............. 327
5. Adaptive methods 339
5.1 Adaptive algorithms: A general framework ........ 340
5.1.1 Updating formulas.................. 343
5.1.2 Extended dynamics................. 350
5.1.3 Discretization methods............... 353
5.1.4 Classical examples of adaptive methods...... 365
5.1.5 Numerical illustration................ 369
5.2 Convergence of the adaptive biasing force method .... 372
5.2.1 Presentation of the studied ABF dynamics .... 372
5.2.2 Precise Statements of the convergence results . . . 377
5.2.3 Proofs ........................ 390
6. Selection 405
6.1 Replica selection framework................. 407
6.1.1 Weighted replica ensembles............. 407
6.1.2 Resampling strategies................ 413
xii Free Energy Computations: A Mathematical Perspective
6.1.3 Discrete-time version................ 419
6.1.4 Numerical application................ 422
6.2 Selection in adaptive methods................ 424
6.2.1 Motivation for the selection term ......... 424
6.2.2 Numerical application................ 428
Appendix A Most important notation used throughout this book 431
A.l General notation....................... 431
A.2 Physical spaces and energies................. 433
A.3 Spaces with constraints, projection Operators....... 434
A.4 Measures ........................... 436
A.5 Free energy.......................... 438
Bibliography 441
Index 455
|
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| id | DE-604.BV037247743 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:54:23Z |
| institution | BVB |
| isbn | 9781848162471 1848162472 |
| language | English |
| lccn | 2010005252 |
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| physical | XII, 458 S. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
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| publisher | Imperial College Press |
| record_format | marc |
| spelling | Lelièvre, Tony Verfasser aut Free energy computations a mathematical perspective Tony Lelièvre ; Mathias Rousset ; Gabriel Stoltz London Imperial College Press 2010 XII, 458 S. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Mathematisches Modell Gibbs' free energy Statistical physics Mathematical models Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Freie Energie (DE-588)4155282-9 gnd rswk-swf Freie Energie (DE-588)4155282-9 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Stoltz, Gabriel Verfasser aut Rousset, Mathias Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021161113&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lelièvre, Tony Stoltz, Gabriel Rousset, Mathias Free energy computations a mathematical perspective Mathematisches Modell Gibbs' free energy Statistical physics Mathematical models Numerisches Verfahren (DE-588)4128130-5 gnd Freie Energie (DE-588)4155282-9 gnd |
| subject_GND | (DE-588)4128130-5 (DE-588)4155282-9 |
| title | Free energy computations a mathematical perspective |
| title_auth | Free energy computations a mathematical perspective |
| title_exact_search | Free energy computations a mathematical perspective |
| title_full | Free energy computations a mathematical perspective Tony Lelièvre ; Mathias Rousset ; Gabriel Stoltz |
| title_fullStr | Free energy computations a mathematical perspective Tony Lelièvre ; Mathias Rousset ; Gabriel Stoltz |
| title_full_unstemmed | Free energy computations a mathematical perspective Tony Lelièvre ; Mathias Rousset ; Gabriel Stoltz |
| title_short | Free energy computations |
| title_sort | free energy computations a mathematical perspective |
| title_sub | a mathematical perspective |
| topic | Mathematisches Modell Gibbs' free energy Statistical physics Mathematical models Numerisches Verfahren (DE-588)4128130-5 gnd Freie Energie (DE-588)4155282-9 gnd |
| topic_facet | Mathematisches Modell Gibbs' free energy Statistical physics Mathematical models Numerisches Verfahren Freie Energie |
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