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E-raamat: Statistical Thermodynamics and Stochastic Kinetics: An Introduction for Engineers

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(University of Minnesota)
  • Formaat: EPUB+DRM
  • Ilmumisaeg: 01-Dec-2011
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781139234856
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Statistical Thermodynamics and Stochastic Kinetics: An Introduction for EngineersSuurem pilt
  • Formaat: EPUB+DRM
  • Ilmumisaeg: 01-Dec-2011
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781139234856
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"Presenting the key principles of thermodynamics from a microscopic point of view, this book provides engineers with the knowledge they need to apply thermodynamics and solve engineering challenges at the molecular level. It clearly explains the concernsof entropy and free energy, emphasising key concepts used in equilibrium applications, whilst stochastic processes, such as stochastic reaction kinetics, are also covered. It provides a classical microscopic interpretation of thermodynamic concepts whichis key for engineers, rather than focusing on more esoteric concepts of statistical thermodynamics and quantum mechanics. Coverage of molecular dynamics and Monte Carlo simulations as natural extensions of the theoretical treatment of statistical thermodynamics is also included, teaching readers how to use computer simulations and thus enabling them to understand and engineer the microcosm. Featuring many worked examples and over 100 end-of-chapter exercises, it is ideal for use in the classroom as well as for self-study"--

Arvustused

"Incorporating many worked examples and more than 100 end-of-chapter exercises, the book should be valuable for classroom learning as well as for self-study" - Chemical Engineering Progress, April 2012

Muu info

Provides engineers with the knowledge they need to apply thermodynamics and solve engineering challenges at the molecular level.
Acknowledgments xiii
1 Introduction
1(10)
1.1 Prologue
1(2)
1.2 If we had only a single lecture in statistical thermodynamics
3(8)
2 Elements of probability and combinatorial theory
11(21)
2.1 Probability theory
11(6)
2.1.1 Useful definitions
12(1)
2.1.2 Probability distributions
13(2)
2.1.3 Mathematical expectation
15(1)
2.1.4 Moments of probability distributions
15(1)
2.1.5 Gaussian probability distribution
16(1)
2.2 Elements of combinatorial analysis
17(2)
2.2.1 Arrangements
17(1)
2.2.2 Permutations
18(1)
2.2.3 Combinations
18(1)
2.3 Distinguishable and indistinguishable particles
19(1)
2.4 Stirling's approximation
20(1)
2.5 Binomial distribution
21(2)
2.6 Multinomial distribution
23(1)
2.7 Exponential and Poisson distributions
23(1)
2.8 One-dimensional random walk
24(2)
2.9 Law of large numbers
26(2)
2.10 Central limit theorem
28(1)
2.11 Further reading
29(1)
2.12 Exercises
29(3)
3 Phase spaces, from classical to quantum mechanics, and back
32(34)
3.1 Classical mechanics
32(11)
3.1.1 Newtonian mechanics
32(3)
3.1.2 Generalized coordinates
35(2)
3.1.3 Lagrangian mechanics
37(3)
3.1.4 Hamiltonian mechanics
40(3)
3.2 Phase space
43(4)
3.2.1 Conservative systems
46(1)
3.3 Quantum mechanics
47(13)
3.3.1 Particle-wave duality
49(9)
3.3.2 Heisenberg's uncertainty principle
58(2)
3.4 From quantum mechanical to classical mechanical phase spaces
60(2)
3.4.1 Born-Oppenheimer approximation
62(1)
3.5 Further reading
62(1)
3.6 Exercises
63(3)
4 Ensemble theory
66(25)
4.1 Distribution function and probability density in phase space
66(3)
4.2 Ensemble average of thermodynamic properties
69(1)
4.3 Ergodic hypothesis
70(1)
4.4 Partition function
71(1)
4.5 Microcanonical ensemble
71(2)
4.6 Thermodynamics from ensembles
73(2)
4.7 S = kB In Ω, or entropy understood
75(4)
4.8 Ω for ideal gases
79(4)
4.9 Ω with quantum uncertainty
83(3)
4.10 Liouville's equation
86(3)
4.11 Further reading
89(1)
4.12 Exercises
89(2)
5 Canonical ensemble
91(19)
5.1 Probability density in phase space
91(4)
5.2 NVT ensemble thermodynamics
95(2)
5.3 Entropy of an NVT system
97(2)
5.4 Thermodynamics of NVT ideal gases
99(4)
5.5 Calculation of absolute partition functions is impossible and unnecessary
103(1)
5.6 Maxwell-Boltzmann velocity distribution
104(3)
5.7 Further reading
107(1)
5.8 Exercises
107(3)
6 Fluctuations and other ensembles
110(14)
6.1 Fluctuations and equivalence of different ensembles
110(3)
6.2 Statistical derivation of the NVT partition function
113(2)
6.3 Grand-canonical and isothermal-isobaric ensembles
115(2)
6.4 Maxima and minima at equilibrium
117(3)
6.5 Reversibility and the second law of thermodynamics
120(2)
6.6 Further reading
122(1)
6.7 Exercises
122(2)
7 Molecules
124(15)
7.1 Molecular degrees of freedom
124(1)
7.2 Diatomic molecules
125(10)
7.2.1 Rigid rotation
130(2)
7.2.2 Vibrations included
132(3)
7.2.3 Subatomic degrees of freedom
135(1)
7.3 Equipartition theorem
135(2)
7.4 Further reading
137(1)
7.5 Exercises
137(2)
8 Non-ideal gases
139(16)
8.1 The virial theorem
140(4)
8.1.1 Application of the virial theorem: equation of state for non-ideal systems
142(2)
8.2 Pairwise interaction potentials
144(5)
8.2.1 Lennard-Jones potential
146(2)
8.2.2 Electrostatic interactions
148(1)
8.2.3 Total intermolecular potential energy
149(1)
8.3 Virial equation of state
149(1)
8.4 van der Waals equation of state
150(3)
8.5 Further reading
153(1)
8.6 Exercises
153(2)
9 Liquids and crystals
155(18)
9.1 Liquids
155(1)
9.2 Molecular distributions
155(3)
9.3 Physical interpretation of pair distribution functions
158(4)
9.4 Thermodynamic properties from pair distribution functions
162(2)
9.5 Solids
164(6)
9.5.1 Heat capacity of monoatomic crystals
164(3)
9.5.2 The Einstein model of the specific heat of crystals
167(2)
9.5.3 The Debye model of the specific heat of crystals
169(1)
9.6 Further reading
170(1)
9.7 Exercises
171(2)
10 Beyond pure, single-component systems
173(17)
10.1 Ideal mixtures
173(4)
10.1.1 Properties of mixing for ideal mixtures
176(1)
10.2 Phase behavior
177(5)
10.2.1 The law of corresponding states
181(1)
10.3 Regular solution theory
182(4)
10.3.1 Binary vapor-liquid equilibria
185(1)
10.4 Chemical reaction equilibria
186(2)
10.5 Further reading
188(1)
10.6 Exercises
188(2)
11 Polymers - Brownian dynamics
190(12)
11.1 Polymers
190(8)
11.1.1 Macromolecular dimensions
190(4)
11.1.2 Rubber elasticity
194(2)
11.1.3 Dynamic models of macromolecules
196(2)
11.2 Brownian dynamics
198(3)
11.3 Further reading
201(1)
11.4 Exercises
201(1)
12 Non-equilibrium thermodynamics
202(13)
12.1 Linear response theory
202(2)
12.2 Time correlation functions
204(4)
12.3 Fluctuation-dissipation theorem
208(2)
12.4 Dielectric relaxation of polymer chains
210(3)
12.5 Further reading
213(1)
12.6 Exercises
214(1)
13 Stochastic processes
215(17)
13.1 Continuous-deterministic reaction kinetics
216(2)
13.2 Away from the thermodynamic limit - chemical master equation
218(7)
13.2.1 Analytic solution of the chemical master equation
221(4)
13.3 Derivation of the master equation for any stochastic process
225(6)
13.3.1 Chapman-Kolmogorov equation
226(1)
13.3.2 Master equation
227(1)
13.3.3 Fokker-Planck equation
228(1)
13.3.4 Langevin equation
229(1)
13.3.5 Chemical Langevin equations
230(1)
13.4 Further reading
231(1)
13.5 Exercises
231(1)
14 Molecular simulations
232(23)
14.1 Tractable exploration of phase space
232(2)
14.2 Computer simulations are tractable mathematics
234(1)
14.3 Introduction to molecular simulation techniques
235(15)
14.3.1 Construction of the molecular model
235(4)
14.3.2 Semi-empirical force field potential
239(3)
14.3.3 System size and geometry
242(1)
14.3.4 Periodic boundary conditions
243(1)
14.3.5 Fortran code for periodic boundary conditions
244(1)
14.3.6 Minimum image convection
245(5)
14.4 How to start a simulation
250(2)
14.5 Non-dimensional simulation parameters
252(1)
14.6 Neighbor lists: a time-saving trick
252(1)
14.7 Further reading
253(1)
14.8 Exercises
254(1)
15 Monte Carlo simulations
255(18)
15.1 Sampling of probability distribution functions
256(1)
15.2 Uniformly random sampling of phase space
257(2)
15.3 Markov chains in Monte Carlo
259(3)
15.4 Importance sampling
262(6)
15.4.1 How to generate states
263(1)
15.4.2 How to accept states
264(2)
15.4.3 Metropolis Monte Carlo pseudo-code
266(1)
15.4.4 Importance sampling with a coin and a die
267(1)
15.4.5 Biased Monte Carlo
268(1)
15.5 Grand canonical Monte Carlo
268(1)
15.6 Gibbs ensemble Monte Carlo for phase equilibria
269(2)
15.7 Further reading
271(1)
15.8 Exercises
272(1)
16 Molecular dynamics simulations
273(14)
16.1 Molecular dynamics simulation of simple fluids
274(1)
16.2 Numerical integration algorithms
274(5)
16.2.1 Predictor-corrector algorithms
276(1)
16.2.2 Verlet algorithms
277(2)
16.3 Selecting the size of the time step
279(1)
16.4 How long to run the simulation?
280(1)
16.5 Molecular dynamics in other ensembles
280(4)
16.5.1 Canonical ensemble molecular dynamics simulations
282(2)
16.6 Constrained and multiple time step dynamics
284(1)
16.7 Further reading
285(1)
16.8 Exercises
286(1)
17 Properties of matter from simulation results
287(8)
17.1 Structural properties
287(2)
17.2 Dynamical information
289(3)
17.2.1 Diffusion coefficient
289(1)
17.2.2 Correlation functions
290(1)
17.2.3 Time correlation functions
291(1)
17.3 Free energy calculations
292(2)
17.3.1 Free energy perturbation methods
292(1)
17.3.2 Histogram methods
293(1)
17.3.3 Thermodynamic integration methods
293(1)
17.4 Further reading
294(1)
17.5 Exercises
294(1)
18 Stochastic simulations of chemical reaction kinetics
295(13)
18.1 Stochastic simulation algorithm
296(1)
18.2 Multiscale algorithms for chemical kinetics
297(3)
18.2.1 Slow-discrete region (I)
299(1)
18.2.2 Slow-continuous region (II)
299(1)
18.2.3 Fast-discrete region (III)
299(1)
18.2.4 Fast-continuous stochastic region (IV)
300(1)
18.2.5 Fast-continuous deterministic region (V)
300(1)
18.3 Hybrid algorithms
300(2)
18.4 Hybrid stochastic algorithm
302(2)
18.4.1 System partitioning
302(1)
18.4.2 Propagation of the fast subsystem - chemical Langevin equations
303(1)
18.4.3 Propagation of the slow subsystem - jump equations
303(1)
18.5 Hy3S - Hybrid stochastic simulations for supercomputers
304(1)
18.6 Multikin - Multiscale kinetics
305(1)
18.7 Further reading
305(1)
18.8 Exercises
306(2)
Appendices
A Physical constants and conversion factors
308(1)
A.1 Physical constants
308(1)
A.2 Conversion factors
308(1)
B Elements of classical thermodynamics
309(3)
B.1 Systems, properties, and states in thermodynamics
309(1)
B.2 Fundamental thermodynamic relations
310(2)
Index 312
Yiannis N. Kaznessis is a Professor in the Department of Engineering and Materials Science at the University of Minnesota, where he has taught statistical thermodynamics since 2001. He has received several awards and recognitions including the Fulbright Award, the US National Science Foundation CAREER Award, the 3M non-Tenured Faculty Award, the IBM Young Faculty Award, the AIChE Computers and Systems Technology Division Outstanding Young Researcher Award and the University of Minnesota College of Science and Engineering Charles Bowers Faculty Teaching Award.
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