| 查看: 1625 | 回复: 22 | |||
| 【奖励】 本帖被评价18次，作者pkusiyuan增加金币 14.4 个 | |||
[资源]
Statistical Physics of Liquids at Freezing and Beyond
|
|||
|
Preface page xiii Acknowledgements xvi 1 Statistical physics of liquids 1 1.1 Basic statistical mechanics 3 1.1.1 Thermodynamic functions 3 1.1.2 The classical N-particle system 6 1.1.3 The BBGKY hierarchy equations 7 1.1.4 The Boltzmann equation 9 1.2 Equilibrium properties 11 1.2.1 The Gibbs H-theorem 12 1.2.2 The equilibrium ensembles 14 1.2.3 The static structure factor 19 1.2.4 Integral equations for g(r) 24 1.3 Time correlation functions 36 1.3.1 The density correlation function 38 1.3.2 The self-correlation function 41 1.3.3 The linear response function 47 1.4 Brownian motion 50 1.4.1 The Langevin equation 50 1.4.2 The Stokes–Einstein relation 53 Appendix to Chapter 1 55 A1.1 The Gibbs inequality 55 A1.2 The force–force correlation 55 A1.3 Brownian motion 56 A1.3.1 The noise correlation 56 A1.3.2 Evaluation of the integrals 57 2 The freezing transition 58 2.1 The density-functional approach 58 2.1.1 A thermodynamic extremum principle 60 vii viii Contents 2.1.2 An approximate free-energy functional 64 2.1.3 The Ramakrishnan–Yussouff model 68 2.2 Weighted density functionals 72 2.2.1 The modified weighted-density approximation 75 2.2.2 Gaussian density profiles 76 2.2.3 The hard-sphere system 78 2.3 Fundamental measure theory 85 2.3.1 Density-independent weight functions 86 2.3.2 The free-energy functional 88 2.4 Applications to other systems 90 2.4.1 Long-range interaction potentials 91 2.4.2 The solid–liquid interface 99 Appendix to Chapter 2 105 A2.1 Correlation functions for the inhomogeneous solid 105 A2.2 The Ramakrishnan–Yussouff model 106 A2.3 The weighted-density-functional approximation 109 A2.4 The modified weighted-density-functional approximation 113 A2.5 The Gaussian density profiles and phonon model 115 3 Crystal nucleation 117 3.1 Classical nucleation theory 117 3.1.1 The free-energy barrier 118 3.1.2 The nucleation rate 121 3.1.3 Heterogeneous nucleation 129 3.2 A simple nonclassical model 131 3.2.1 The critical nucleus 133 3.2.2 The free-energy barrier 134 3.3 The density-functional approach 137 3.3.1 The square-gradient approximation 137 3.3.2 The critical nucleus 141 3.3.3 The weighted-density-functional approach 145 3.4 Computer-simulation studies 150 3.4.1 Comparisons with CNT predictions 152 3.4.2 The structure of the nucleus 155 Appendix to Chapter 3 160 A3.1 The schematic model for nucleation 160 A3.1.1 Critical nucleus 160 A3.1.2 The free-energy barrier 161 A3.2 The excess free energy in the DFT model 162 4 The supercooled liquid 164 4.1 The liquid–glass transition 164 4.1.1 Characteristic temperatures of the glassy state 165 Contents ix 4.1.2 The free-volume model 170 4.1.3 Self-diffusion and the Stokes–Einstein relation 171 4.2 Glass formation vs. crystallization 175 4.2.1 The minimum cooling rate 176 4.2.2 The kinetic spinodal and the Kauzmann paradox 177 4.3 The landscape paradigm 181 4.3.1 The potential-energy landscape 182 4.3.2 The free-energy landscape 188 4.4 Dynamical heterogeneities 192 4.4.1 Computer-simulation results 193 4.4.2 Dynamic length scales 198 5 Dynamics of collective modes 204 5.1 Conservation laws and dissipation 205 5.1.1 The microscopic balance equations 205 5.1.2 Euler equations of hydrodynamics 207 5.1.3 Dissipative equations of hydrodynamics 209 5.1.4 Tagged-particle dynamics 211 5.1.5 Two-component systems 212 5.2 Hydrodynamic correlation functions 215 5.2.1 Self-diffusion 217 5.2.2 Transport coefficients 218 5.3 Linear fluctuating hydrodynamics 225 5.3.1 The generalized Langevin equation 225 5.3.2 The liquid-state dynamics 236 5.4 Hydrodynamics of a solid 246 Appendix to Chapter 5 260 A5.1 The microscopic-balance equations 260 A5.1.1 The Euler equations 263 A5.1.2 The entropy-production rate 264 A5.2 The second fluctuation–dissipation relation 269 6 Nonlinear fluctuating hydrodynamics 271 6.1 Nonlinear Langevin equations 271 6.1.1 Coupling of collective modes 271 6.1.2 Nonlinear Langevin equations 274 6.2 The compressible liquid 287 6.2.1 The one-component fluid 287 6.2.2 The nonlinear diffusion equation 293 6.2.3 A two-component fluid 295 6.2.4 The solid state 300 6.3 Stochastic balance equations 303 6.3.1 Smoluchowski dynamics 303 x Contents 6.3.2 Fokker–Planck dynamics 308 Appendix to Chapter 6 310 A6.1 The coarse-grained free energy 310 7 Renormalization of the dynamics 318 7.1 The Martin–Siggia–Rose theory 319 7.1.1 The MSR action functional 320 7.2 The compressible liquid 327 7.2.1 MSR theory for a compressible liquid 328 7.2.2 Correlation and response functions 330 7.3 Renormalization 334 7.3.1 Fluctuation–dissipation relations 335 7.3.2 Nonperturbative results 339 7.3.3 One-loop renormalization 343 Appendix to Chapter 7 348 A7.1 The Jacobian of MSR fields 350 A7.2 The MSR field theory 351 A7.3 Invariance of the MSR action 355 A7.4 The memory-function approach 357 A7.4.1 The projection-operator method 358 A7.4.2 The mode-coupling approximation 361 8 The ergodic–nonergodic transition 363 8.1 Mode-coupling theory 363 8.1.1 The schematic model 365 8.1.2 Effects of structure on dynamics 369 8.1.3 Tagged-particle dynamics 376 8.1.4 Dynamical heterogeneities and MCT 383 8.1.5 Linking DFT with MCT 388 8.1.6 Dynamic density-functional theory 391 8.2 Evidence from experiments 400 8.2.1 Testing with schematic MCT 400 8.2.2 Glass transition in colloids 406 8.2.3 Molecular-dynamics simulations 407 8.2.4 Discussion 409 8.3 Ergodicity-restoring mechanisms 411 8.3.1 Ergodic behavior in the NFH model 412 8.3.2 The hydrodynamic limit 414 8.3.3 Numerical solution of NFH equations 417 8.4 Spin-glass models 419 8.4.1 The p-spin interaction model 420 8.4.2 MCT and mean-field theories 426 Contents xi Appendix to Chapter 8 430 A8.1 Calculation of the spring constant 430 A8.2 Field-theoretic treatment of the DDFT model 432 A8.3 The one-loop result for ˆv ˆv(0, 0) 442 9 The nonequilibrium dynamics 443 9.1 The nonequilibrium state 443 9.1.1 A generalized fluctuation–dissipation relation 443 9.1.2 Computer-simulation studies 444 9.2 The effective temperature 449 9.2.1 The phenomenological approach 451 9.2.2 A simple thermometer 451 9.3 A mean-field model 456 9.3.1 The mode-coupling approximation 459 9.3.2 The FDT regime 460 9.3.3 The aging regime 465 9.3.4 Quasi-ergodic behavior 469 9.4 Glassy aging dynamics 471 9.4.1 Thermalization 471 9.4.2 Aging dynamics: experiments 473 Appendix to Chapter 9 479 A9.1 The energy of the oscillator 479 A9.2 Evaluation of integrals 481 A9.2.1 Integral IR for the FDT solution 481 A9.2.2 Integrals for the aging solution 482 10 The thermodynamic transition scenario 486 10.1 The entropy crisis 486 10.1.1 The Adam–Gibbs theory 487 10.1.2 Dynamics near TK 488 10.2 First-order transitions 490 10.2.1 Metastable aperiodic structures 491 10.2.2 Random first-order transition theory 494 10.3 Self-generated disorder 498 10.3.1 Effective potential and overlap functions 498 10.3.2 A model calculation 501 10.4 Spontaneous breaking of ergodicity 505 10.4.1 The replica method for self-generated disorder 507 10.4.2 Free energy of the Replicated liquid 509 10.4.3 An example: The φ4 model 514 10.5 The amorphous solid 519 10.5.1 The Mézard–Parisi model 522 xii Contents Appendix to Chapter 10 531 A10.1 Matrix identity 531 A10.2 Matrix identity II 532 A10.3 Computation of the vibrational contribution Iv 533 A10.4 Computation of Tr lnM∗ 536 References 540 Index 558 |
回复此楼» 本帖附件资源列表
-
欢迎监督和反馈：小木虫仅提供交流平台，不对该内容负责。
本内容由用户自主发布，如果其内容涉及到知识产权问题，其责任在于用户本人，如对版权有异议，请联系邮箱：xiaomuchong@tal.com - 附件 1 : Statistical_Physics_of_Liquids_at_Freezing_and_Beyond_-_Shankar_Prasad_Das_-_(_Cambridge_University_Press_-_2011_-_pp.586).pdf
2015-09-16 11:16:48, 4.24 M
» 收录本帖的淘帖专辑推荐
 计算数学与经济统计 |
» 猜你喜欢
化学0703-一志愿211-338分求调剂
已经有9人回复
-
求调剂！生物与医药专硕
已经有8人回复
-
275 求调剂
已经有5人回复
-
一志愿085404，总分291，四级已过，求调剂
已经有10人回复
-
085600专硕材料与化工348分求调剂
已经有12人回复
-
电子信息346
已经有3人回复
-
0703总分331求调剂
已经有21人回复
-
301求调剂
已经有9人回复
-
材料专硕调剂
已经有12人回复
-
327求调剂
已经有9人回复
» 本主题相关价值贴推荐，对您同样有帮助:
- Statistica软件下载
已经有9人回复
- statistica10教程+实例分析 中文简体
已经有47人回复
- 求statistica 统计与图表软件
已经有7人回复
- statistica6
已经有20人回复
- 求助STATISTICA 6.0~~~
已经有11人回复
- 谁会用statistica做PLS分析！
已经有2人回复
- statistica使用手册
已经有50人回复
- StatSoft Statistica软件求助
已经有12人回复
- 应虫友要求，重传statistica教程
已经有21人回复
- 求助statistica软件
已经有2人回复
- 【软件】统计基础与Statistica软件
已经有69人回复
- 【分享】给大家一个Statistica6.0的纳米盘下载资源，已搜索无重复
已经有14人回复
18楼2016-04-24 05:35:20
简单回复
mechtest2楼
2015-09-16 13:03
回复
五星好评 顶一下，感谢分享！
2015-09-16 23:01
回复
五星好评 顶一下，感谢分享！
吠陀4楼
2015-09-17 07:25
回复
五星好评 顶一下，感谢分享！
wjy20115楼
2015-09-17 08:35
回复
五星好评 顶一下，感谢分享！
applaq6楼
2015-09-18 11:25
回复
五星好评 顶一下，感谢分享！
2015-09-27 11:26
回复
五星好评 顶一下，感谢分享！
akaige8楼
2015-10-28 09:14
回复
五星好评 顶一下，感谢分享！
吠陀9楼
2015-12-01 20:42
回复
顶一下，感谢分享！
attractor10楼
2015-12-01 21:56
回复
五星好评 顶一下，感谢分享！
mechtest11楼
2015-12-02 21:18
回复
顶一下，感谢分享！
starrylee12楼
2015-12-31 09:39
回复
五星好评 谢谢分享 发自小木虫Android客户端
fannieyang13楼
2016-02-13 10:35
回复
五星好评 顶一下，感谢分享！
mechtest14楼
2016-02-13 16:38
回复
顶一下，感谢分享！
幸运果15楼
2016-03-01 17:04
回复
五星好评 顶一下，感谢分享！
c2002z16楼
2016-03-15 23:39
回复
五星好评 顶一下，感谢分享！
遗忘消失的灆17楼
2016-04-21 16:37
回复
五星好评 顶一下，感谢分享！
wl177719楼
2016-09-30 13:03
回复
五星好评 顶一下，感谢分享！
lantianbihb20楼
2017-02-25 14:28
回复
五星好评 顶一下，感谢分享！
cryohuang21楼
2017-02-25 15:44
回复
五星好评 顶一下，感谢分享！
wisdomwolf22楼
2019-11-09 16:22
回复
五星好评 顶一下，感谢分享！
ljb19721123楼
2020-08-06 04:19
回复
五星好评 顶一下，感谢分享！ 发自小木虫Android客户端
