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Thermal Transport in Low Dimensions: From Statistical Physics to Nanoscale Heat Transfer 1st ed. 2016 [Pehme köide]

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  • Formaat: Paperback / softback, 411 pages, kõrgus x laius: 235x155 mm, kaal: 869 g, 90 Illustrations, color; 27 Illustrations, black and white; XI, 411 p. 117 illus., 90 illus. in color., 1 Paperback / softback
  • Sari: Lecture Notes in Physics 921
  • Ilmumisaeg: 08-Apr-2016
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 3319292595
  • ISBN-13: 9783319292595
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  • Formaat: Paperback / softback, 411 pages, kõrgus x laius: 235x155 mm, kaal: 869 g, 90 Illustrations, color; 27 Illustrations, black and white; XI, 411 p. 117 illus., 90 illus. in color., 1 Paperback / softback
  • Sari: Lecture Notes in Physics 921
  • Ilmumisaeg: 08-Apr-2016
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 3319292595
  • ISBN-13: 9783319292595
Teised raamatud teemal:
Understandingnon-equilibrium properties of classical and quantum many-particle systems is oneof the goals of contemporary statistical mechanics. Besides its own interestfor the theoretical foundations of irreversible thermodynamics(e.g. of the Fourier"s law of heat conduction), this topic is also relevant to developinnovative ideas for nanoscale thermal management with possible future applicationsto nanotechnologies and effective energetic resources.The first part of thevolume (Chapters 1-6) describes the basic models, the phenomenology and thevarious theoretical approaches to understand heat transport in low-dimensionallattices (1D e 2D). The methods described will include equilibrium and nonequilibriummolecular dynamics simulations, hydrodynamic and kinetic approaches and thesolution of stochastic models.The second part(Chapters 7-10) deals with applications to nano and microscale heat transfer,as for instance phononic transport in carbon-based nanomaterials, inc

luding theprominent case of nanotubes and graphene. Possible future developments onheat flow control and thermoelectric energy conversion will be outlined.This volume aims atbeing the first step for graduate students and researchers entering the fieldas well as a reference for the community of scientists that, from differentbackgrounds (theoretical physics, mathematics, material sciences andengineering), has grown in the recent years around those themes.

Heat transport in low dimensions:introduction and phenomenology.- Heat transport in harmonic systems.-Fluctuating hydrodynamics approach to equilibrium time correlations foranharmonic chains.- Kinetic theory of phonons in weakly anharmonic particlechains.- Thermal conductivity in harmonic lattices with random collisions.-Simulation of heat transport in low-dimensional oscillator lattices.-Simulation of dimensionality effects in thermal transport.- ExperimentalProbing of Non_Fourier ThermalConductors.- Thermal Transport in Graphene, Few-Layer Graphene and GrapheneNanoribbons.- From thermal rectifiers to thermoelectric devices.
1 Heat Transport in Low Dimensions: Introduction and Phenomenology
1(38)
Stefano Lepri
Roberto Livi
Antonio Politi
1.1 Introduction
1(2)
1.2 Models
3(3)
1.3 Signatures of Anomalous Transport
6(11)
1.3.1 Diverging Finite-Size Conductivity
7(1)
1.3.2 Long-Time Tails
8(2)
1.3.3 Diffusion of Perturbations
10(2)
1.3.4 Relaxation of Spontaneous Fluctuations
12(1)
1.3.5 Temperature Profiles
13(4)
1.4 Universality and Theoretical Approaches
17(6)
1.4.1 Methods
17(2)
1.4.2 Connection with the Interface Problem
19(1)
1.4.3 Other Universality Classes
20(2)
1.4.4 Comparison with Simulations and Experiments
22(1)
1.5 The Coupled Rotors Model
23(1)
1.6 Two-Dimensional Lattices
24(1)
1.7 Integrable Nonlinear Systems
25(1)
1.8 Coupled Transport
26(7)
1.8.1 Coupled Rotors
26(3)
1.8.2 The Discrete Nonlinear Schrodinger Equation
29(4)
1.9 Conclusions and Open Problems
33(6)
References
34(5)
2 Heat Transport in Harmonic Systems
39(68)
Abhishek Dhar
Keiji Saito
2.1 Introduction
39(3)
2.2 Steady State Current from Langevin Equations and Green's Function Formalism
42(8)
2.2.1 Derivation of the Langevin Equation and It's Steady-State Solution
42(4)
2.2.2 Steady State Properties
46(4)
2.3 Steady State Current Fluctuations
50(15)
2.3.1 General Theory
50(4)
2.3.2 Cumulant Generating Function for Harmonic Lattices
54(11)
2.4 Explicit Results for Steady State Properties in Ordered and Disordered Harmonic Crystal
65(34)
2.4.1 Current
66(22)
2.4.2 Temperature Profiles
88(3)
2.4.3 Fluctuation
91(8)
2.5 Summary
99(8)
Appendix
100(1)
References
101(6)
3 Fluctuating Hydrodynamics Approach to Equilibrium Time Correlations for Anharmonic Chains
107(52)
Herbert Spohn
3.1 Introduction, Long Time Tails for Simple Fluids
107(6)
3.2 Anharmonic Chains
113(8)
3.3 Nonlinear Fluctuating Hydrodynamics
121(9)
3.4 Mode-Coupling Theory
130(8)
3.5 Molecular Dynamics Simulations
138(7)
3.6 Total Current Correlations
145(3)
3.7 Other ID Hamiltonian Systems
148(11)
References
155(4)
4 Kinetic Theory of Phonons in Weakly Anharmonic Particle Chains
159(56)
Jani Lukkarinen
4.1 Kinetic Scaling Limit for Weakly Anharmonic Chains
159(22)
4.1.1 Introduction
159(3)
4.1.2 Free Motion of Phonons
162(3)
4.1.3 Particle Chains with Anharmonic Perturbations
165(5)
4.1.4 Choice of Initial Data
170(5)
4.1.5 Green-Kubo Formula
175(6)
4.2 Phonon Boltzmann Equation of Spatially Homogeneous Anharmonic Chains
181(17)
4.2.1 Identifying the Collision Operator
181(7)
4.2.2 Solution of the Collisional Constraints
188(10)
4.3 Energy Transport in the Kinetic Theory of Phonons
198(14)
4.3.1 Entropy and H-Theorem of the Phonon Boltzmann Equations
198(2)
4.3.2 Steady States
200(1)
4.3.3 Green-Kubo Formula and the Linearized Boltzmann Equation
201(2)
4.3.4 Kinetic Theory Prediction for Thermal Conductivity in Chains with Anharmonic Pinning
203(5)
4.3.5 Anomalous Energy Conduction in the Kinetic Theory of FPU Chains
208(4)
4.4 Concluding Remarks
212(3)
References
213(2)
5 Thermal Conductivity in Harmonic Lattices with Random Collisions
215(24)
Giada Basile
Cedric Bernardin
Milton Jara
Tomasz Komorowski
Stefano Olla
5.1 Introduction
215(4)
5.1.1 Unpinned Chains
216(1)
5.1.2 Pinned Chains
217(1)
5.1.3 Dynamics with Stochastic Collisions
217(1)
5.1.4 Equilibrium Stationary Measures
218(1)
5.1.5 Macroscopic Space-Time Scales
218(1)
5.2 Hyperbolic Scaling: The Linear Wave Equation
219(1)
5.3 Superdiffusive Evolution of the Temperature Profile
220(1)
5.4 The Diffusive Behavior of the Phonon-Modes
221(1)
5.5 Equilibrium Fluctuations
222(1)
5.6 The Phonon Boltzmann Equation
223(4)
5.7 Non-acoustic Chains: Beam Dynamics
227(1)
5.8 A Simpler Model with Two Conserved Quantities
228(2)
5.8.1 The Extension Problem for the Skew-Fractional Laplacian
229(1)
5.9 The Dynamics in Higher Dimension
230(1)
5.10 Thermal Boundary Conditions and the Non-equilibrium Stationary States
231(2)
5.11 The Non-linear Chain
233(1)
5.12 The Disordered Chain
234(5)
References
236(3)
6 Simulation of Heat Transport in Low-Dimensional Oscillator Lattices
239(36)
Lei Wang
Nianbei Li
Peter Hanggi
6.1 Simulation of Heat Transport with Non-equilibrium Heat Bath Method and Equilibrium Green-Kubo Method
240(18)
6.1.1 Power-Law Divergent Thermal Conductivity in 1D Momentum-Conserving Nonlinear Lattices
240(8)
6.1.2 Logarithmic Divergent Thermal Conductivity in 2D Momentum-Conserving Nonlinear Lattices
248(5)
6.1.3 Normal Heat Conduction in a 3D Momentum-Conserving Nonlinear Lattice
253(5)
6.2 Simulation of Heat Transport with the Diffusion Method
258(17)
6.2.1 Energy Diffusion
260(8)
6.2.2 Momentum Diffusion
268(5)
References
273(2)
7 Simulation of Dimensionality Effects in Thermal Transport
275(30)
Davide Donadio
7.1 Introduction
275(2)
7.2 Simulation Tools
277(6)
7.2.1 Anharmonic Lattice Dynamics
277(3)
7.2.2 Equilibrium Molecular Dynamics
280(1)
7.2.3 Non-equilibrium Molecular Dynamics
281(1)
7.2.4 Empirical Interatomic Potentials
282(1)
7.3 Carbon Based Nanostructures
283(7)
7.3.1 Graphene
283(4)
7.3.2 Carbon Nanotubes
287(3)
7.4 Nanostructured Silicon
290(10)
7.4.1 Silicon Nanowires
291(6)
7.4.2 Ultra-Thin Silicon Membranes
297(3)
7.5 Conclusions
300(5)
References
301(4)
8 Experimental Probing of Non-Fourier Thermal Conductors
305(34)
Chih-Wei Chang
8.1 Introduction
305(2)
8.2 Experimental Methods for Probing Non-Fourier Thermal Conduction
307(5)
8.3 Non-Fourier (Ballistic) Thermal Conduction in SiGe Nanowires
312(7)
8.4 Non-Fourier (Ballistic) Thermal Conduction in Si-Ge interfaces
319(5)
8.5 Non-Fourier (Ballistic) Thermal Conduction in Multiwall Nanotubes
324(5)
8.6 Non-Fourier (Anomalous) Thermal Conduction in Ultralong Carbon Nanotubes
329(5)
8.7 Conclusion
334(5)
References
335(4)
9 Thermal Transport in Graphene, Few-Layer Graphene and Graphene Nanoribbons
339(26)
Denis L. Nika
Alexander A. Balandin
9.1 Introduction
339(1)
9.2 Basics of Phonon Transport and Thermal Conductivity
340(2)
9.3 Experimental Data for Thermal Conductivity of Graphene and Few-Layer Graphene
342(4)
9.4 Theories of Phonon Thermal Conductivity in Graphene, Few-Layer Graphene and Graphene Nanoribbons
346(12)
9.4.1 Specifics of Two-Dimensional Phonon Transport
353(5)
9.5 Conclusions
358(7)
References
358(7)
10 From Thermal Rectifiers to Thermoelectric Devices
365(44)
Giuliano Benenti
Giulio Casati
Carlos Mejia-Monasterio
Michel Peyrard
10.1 Dynamical Foundations of Fourier Law
365(3)
10.2 Fourier Law in Quantum Mechanics
368(7)
10.2.1 Fourier Law and the Onset of Quantum Chaos
370(5)
10.3 Controlling the Heat Flow: Thermal Rectifiers
375(10)
10.3.1 The Fourier Law and the Design of a Thermal Rectifier
375(2)
10.3.2 A One-Dimensional Model for a Thermal Rectifier
377(5)
10.3.3 Model in Higher Dimension
382(2)
10.3.4 Building an Actual Thermal Rectifier
384(1)
10.4 Thermoelectric Efficiency
385(18)
10.4.1 The Thermoelectric Figure of Merit ZT
386(2)
10.4.2 The Onsager Matrix
388(1)
10.4.3 Non-interacting Systems
389(3)
10.4.4 Interacting Systems
392(5)
10.4.5 Breaking Time-Reversibility
397(3)
10.4.6 Inelastic Scattering and Probe Terminals
400(3)
10.5 Concluding Remarks
403(6)
References
404(5)
Index 409