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Defaveri L, Almeida AAA, Anteneodo C. Approaching the perfect diode limit through a nonlinear interface. Phys Rev E 2023; 108:044126. [PMID: 37978639 DOI: 10.1103/physreve.108.044126] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/12/2022] [Accepted: 09/15/2023] [Indexed: 11/19/2023]
Abstract
We consider a system formed by two different segments of particles, coupled to thermal baths, one at each end, modeled by Langevin thermostats. The particles in each segment interact harmonically and are subject to an on-site potential for which three different types are considered, namely, harmonic, ϕ^{4}, and Frenkel-Kontorova. The two segments are nonlinearly coupled, between interfacial particles, by means of a power-law potential with exponent μ, which we vary, scanning from subharmonic to superharmonic potentials, up to the infinite-square-well limit (μ→∞). Thermal rectification is investigated by integrating the equations of motion and computing the heat fluxes. As a measure of rectification, we use the difference of the currents, resulting from the interchange of the baths, divided by their average (all quantities taken in absolute value). We find that rectification can be optimized by a given value of μ that depends on the bath temperatures and details of the chains. But, regardless of the type of on-site potential considered, the interfacial potential that produces maximal rectification approaches the infinite square well (μ→∞) when reducing the average temperature of the baths. Our analysis of thermal rectification focuses on this regime, for which we complement numerical results with heuristic considerations.
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Affiliation(s)
| | | | - Celia Anteneodo
- Department of Physics, PUC-Rio, Rio de Janeiro, 22453-900 RJ, Brazil
- Institute of Science and Technology for Complex Systems, INCT-CS, Rio de Janeiro, Brazil
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Alexander TJ. High-heat-flux rectification due to a localized thermal diode. Phys Rev E 2020; 101:062122. [PMID: 32688508 DOI: 10.1103/physreve.101.062122] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/17/2020] [Accepted: 04/14/2020] [Indexed: 06/11/2023]
Abstract
A theoretical implementation of a localized thermal diode with a rectification factor greater than 10^{6} is demonstrated. In reverse thermal bias, extremely low thermal conductivity is achieved through phononic Rayleigh scattering from a finite-depth defect. In forward bias, the diode oscillator escapes the defect and thermal conductivity becomes up to four orders of magnitude higher. The setup provides a minimal model of a localized thermal diode between two identical oscillator chains and opens up a pathway for thermal diode implementations.
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Affiliation(s)
- Tristram J Alexander
- School of Physics, University of Sydney, Sydney, New South Wales 2006, Australia
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Wang X, Kaviany M, Huang B. Phonon coupling and transport in individual polyethylene chains: a comparison study with the bulk crystal. NANOSCALE 2017; 9:18022-18031. [PMID: 29131229 DOI: 10.1039/c7nr06216h] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/16/2023]
Abstract
Using the first-principles-based anharmonic lattice dynamics, we calculate the thermal conductivities (κ) of both bulk and single-chain polyethylene (PE) and characterize the mode-wise phonon transport and scattering channels. A significantly higher room-temperature axial thermal conductivity in single-chain PE (1400 W m-1 K-1) is observed compared to bulk PE crystals (237 W m-1 K-1). The reduction of scattering phase space caused by the diminished inter-chain van der Waals interactions explains the much larger κ in single-chain PE. Different from many previous studies, the thermal conductivity of single-chain PE is predicted to converge at a chain length of ∼1 mm at 300 K. The convergence is explained by the indirect thermal resistance from momentum-conserving scatterings of long-wavelength phonons. It is also found that longitudinal phonon modes dominate the thermal transport in PE chains, while transverse phonon branches with quadratic dispersions contribute little to κ due to their vanishing group velocities and limited lifetimes in the long wavelength limit. The predicted high κ of bulk crystalline and single-chain PE show great potential for use of polymers in thermal management, and the unveiled phonon transport mechanisms offer guides for their molecule-level design.
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Affiliation(s)
- Xinjiang Wang
- Department of Mechanical and Aerospace Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong.
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Zhang Z, Tang C, Tong P. Dynamical thermalization of Frenkel-Kontorova model in the thermodynamic limit. Phys Rev E 2016; 93:022216. [PMID: 26986340 DOI: 10.1103/physreve.93.022216] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/25/2015] [Indexed: 06/05/2023]
Abstract
We study numerically the process of dynamical thermalization in the Frenkel-Kontorova (FK) model with weak nonlinearity. The total energy has initially equidistributed among some of the lowest frequency linear modes. It is found that the energy transfers continuously to the high-frequency modes and finally evolves towards energy equipartition in the FK model. However, the metastable state, which was found in Fermi-Pasta-Ulam (FPU) model and φ(4) model in a relatively short time scale, is not found in the FK model. We further perform a very accurate systematic study of the equipartition time T(eq) as functions of the particle number N, the nonlinear parameter β, and the energy density ɛ. In the thermodynamic limit, the dependence of T(eq) on β and ɛ is found to display a power law behavior: T(eq)∝β(a)ɛ(b). The exponents a and b are numerically found to be approximately -2.0 and 1.43. This scaling law is also quite different from those of the FPU-β model and φ(4) model.
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Affiliation(s)
- Zhenjun Zhang
- College of Science, Hohai University, Nanjing, Jiangsu 210098, People's Republic of China
| | - Chunmei Tang
- College of Science, Hohai University, Nanjing, Jiangsu 210098, People's Republic of China
| | - Peiqing Tong
- School of Physics Science and Technology, Nanjing Normal University, Nanjing, Jiangsu 210023, People's Republic of China
- Jiangsu Provincial Key Laboratory for Numerical Simulation of Large Scale Complex Systems, Nanjing Normal University, Nanjing, Jiangsu 210023, People's Republic of China
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Iubini S, Lepri S, Livi R, Politi A. Boundary-induced instabilities in coupled oscillators. PHYSICAL REVIEW LETTERS 2014; 112:134101. [PMID: 24745424 DOI: 10.1103/physrevlett.112.134101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/13/2014] [Indexed: 06/03/2023]
Abstract
A novel class of nonequilibrium phase transitions at zero temperature is found in chains of nonlinear oscillators. For two paradigmatic systems, the Hamiltonian XY model and the discrete nonlinear Schrödinger equation, we find that the application of boundary forces induces two synchronized phases, separated by a nontrivial interfacial region where the kinetic temperature is finite. Dynamics in such a supercritical state displays anomalous chaotic properties whereby some observables are nonextensive and transport is superdiffusive. At finite temperatures, the transition is smoothed, but the temperature profile is still nonmonotonic.
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Affiliation(s)
- Stefano Iubini
- Dipartimento di Fisica e Astronomia and CSDC, Università di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino, Italy and Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino, Italy and Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy
| | - Stefano Lepri
- Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino, Italy and Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy
| | - Roberto Livi
- Dipartimento di Fisica e Astronomia and CSDC, Università di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino, Italy and Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino, Italy
| | - Antonio Politi
- Institute for Complex Systems and Mathematical Biology & SUPA, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom
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Iubini S, Lepri S, Politi A. Nonequilibrium discrete nonlinear Schrödinger equation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:011108. [PMID: 23005369 DOI: 10.1103/physreve.86.011108] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/11/2012] [Indexed: 06/01/2023]
Abstract
We study nonequilibrium steady states of the one-dimensional discrete nonlinear Schrödinger equation. This system can be regarded as a minimal model for the stationary transport of bosonic particles such as photons in layered media or cold atoms in deep optical traps. Due to the presence of two conserved quantities, namely, energy and norm (or number of particles), the model displays coupled transport in the sense of linear irreversible thermodynamics. Monte Carlo thermostats are implemented to impose a given temperature and chemical potential at the chain ends. As a result, we find that the Onsager coefficients are finite in the thermodynamic limit, i.e., transport is normal. Depending on the position in the parameter space, the "Seebeck coefficient" may be either positive or negative. For large differences between the thermostat parameters, density and temperature profiles may display an unusual nonmonotonic shape. This is due to the strong dependence of the Onsager coefficients on the state variables.
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Affiliation(s)
- Stefano Iubini
- Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy.
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Lee-Dadswell GR, Turner E, Ettinger J, Moy M. Momentum conserving one-dimensional system with a finite thermal conductivity. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:061118. [PMID: 21230655 DOI: 10.1103/physreve.82.061118] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/17/2009] [Revised: 09/16/2010] [Indexed: 05/30/2023]
Abstract
A one-dimensional system of particles is examined in which even numbered particles are bound to adjacent even particles by harmonic spring forces, while odd particles are free. Even and odd particles collide elastically. This is a momentum conserving modification of the famous "ding-a-ling" model. Molecular-dynamics simulations are carried out and the current power spectra are obtained. The energy current power spectrum has zero slope at low frequencies. This implies that the thermal conductivity κ is finite and independent of system length L , for L sufficiently large. Steady-state simulations provide further evidence that κ is independent of L at large values of L . The relevance of this result to the proof by Prosen and Campbell that momentum conservation with nonvanishing pressure implies an infinite thermal conductivity is discussed.
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Affiliation(s)
- G R Lee-Dadswell
- Mathematics, Physics and Geology Department, Cape Breton University, Sydney, Nova Scotia, Canada.
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Abstract
Heat conduction is an old yet important problem. Since Fourier introduced the law bearing his name almost 200 years ago, a first-principle derivation of this simple law from statistical mechanics is still lacking. Worse still, the validity of this law in low dimensions, and the necessary and sufficient conditions for its validity are far from clear. In this paper we will review recent works on heat conduction in a simple nonintegrable model called the Frenkel-Kontorova model. The thermal conductivity of this model has been found to be finite. We will study the dependence of the thermal conductivity on the temperature and other parameters of the model such as the strength and the periodicity of the external potential. We will also discuss other related problems such as phase transitions and finite-size effects. The study of heat conduction is not only of theoretical interest but also of practical interest. We will show various recent designs of thermal rectifiers and thermal diodes by coupling nonlinear chains together. The study of heat conduction in low dimensions is also important to the understanding of the thermal properties of carbon nanotubes.
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Affiliation(s)
- Bambi Hu
- Department of Physics, Centre for Nonlinear Studies, and The Beijing-Hong Kong-Singapore Joint Centre for Nonlinear and Complex Systems (Hong Kong), Hong Kong Baptist University, Kowloon Tong, Hong Kong, China
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Gendelman OV, Savin AV. Heat conduction in a one-dimensional chain of hard disks with substrate potential. PHYSICAL REVIEW LETTERS 2004; 92:074301. [PMID: 14995858 DOI: 10.1103/physrevlett.92.074301] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/2003] [Indexed: 05/24/2023]
Abstract
Heat conduction in a one-dimensional chain of equivalent rigid particles in the field of the external on-site potential is considered. The zero diameters of the particles correspond to the integrable case with the divergent heat conduction coefficient. By means of a simple analytical model it is demonstrated that for any nonzero particle size the integrability is violated and the heat conduction coefficient converges. The result of the analytical computation is verified by means of numerical simulation in a plausible diapason of parameters, and good agreement is observed.
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Affiliation(s)
- O V Gendelman
- Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel
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Pereverzev A. Fermi-Pasta-Ulam beta lattice: Peierls equation and anomalous heat conductivity. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 68:056124. [PMID: 14682863 DOI: 10.1103/physreve.68.056124] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2003] [Indexed: 05/24/2023]
Abstract
The Peierls equation is considered for the Fermi-Pasta-Ulam beta lattice. Explicit form of the linearized collision operator is obtained. Using this form the decay rate of the normal-mode energy as a function of wave vector k is estimated to be proportional to k(5/3). This leads to the t(-3/5) long-time behavior of the current correlation function, and, therefore, to the divergent coefficient of heat conductivity. These results are in good agreement with the results of recent computer simulations. Compared to the results obtained through the mode coupling theory our estimations give the same k dependence of the decay rate but a different temperature dependence. Using our estimations we argue that adding a harmonic on-site potential to the Fermi-Pasta-Ulam beta lattice may lead to finite heat conductivity in this model.
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Affiliation(s)
- Andrey Pereverzev
- Center for Studies in Statistical Mechanics and Complex Systems, University of Texas at Austin, Austin, TX 78712, USA.
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Savin AV, Gendelman OV. Heat conduction in one-dimensional lattices with on-site potential. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 67:041205. [PMID: 12786351 DOI: 10.1103/physreve.67.041205] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/30/2002] [Revised: 02/11/2003] [Indexed: 05/24/2023]
Abstract
The process of heat conduction in one-dimensional lattices with on-site potential is studied by means of numerical simulation. Using the discrete Frenkel-Kontorova, phi(4), and sinh-Gordon models we demonstrate that contrary to previously expressed opinions the sole anharmonicity of the on-site potential is insufficient to ensure the normal heat conductivity in these systems. The character of the heat conduction is determined by the spectrum of nonlinear excitations peculiar for every given model and therefore depends on the concrete potential shape and the temperature of the lattice. The reason is that the peculiarities of the nonlinear excitations and their interactions prescribe the energy scattering mechanism in each model. For sine-Gordon and phi(4) models, phonons are scattered at a dynamical lattice of topological solitons; for sinh-Gordon and for phi(4) in a different parameter regime the phonons are scattered at localized high-frequency breathers (in the case of phi(4) the scattering mechanism switches with the growth of the temperature).
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Affiliation(s)
- A V Savin
- Institute of Chemical Physics, RAS, Kosygin Street 4, Moscow, Russia.
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Aoki K, Kusnezov D. Fermi-Pasta-Ulam beta model: boundary jumps, Fourier's law, and scaling. PHYSICAL REVIEW LETTERS 2001; 86:4029-4032. [PMID: 11328087 DOI: 10.1103/physrevlett.86.4029] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/17/2001] [Indexed: 05/23/2023]
Abstract
We examine the interplay of surface and volume effects in systems undergoing heat flow. In particular, we compute the thermal conductivity in the Fermi-Pasta-Ulam beta model as a function of temperature and lattice size, and scaling arguments are used to provide analytic guidance. From this we show that boundary temperature jumps can be quantitatively understood, and that they play an important role in determining the dynamics of the system, relating soliton dynamics, kinetic theory, and Fourier transport.
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Affiliation(s)
- K Aoki
- Department of Physics, Keio University, 4-1-1 Hiyoshi, Kouhoku-ku, Yokohama 223-8521, Japan
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Gillan MJ. A simulation model for hydrogen in palladium. II. Mobility and thermotransport. ACTA ACUST UNITED AC 2000. [DOI: 10.1088/0022-3719/20/4/005] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Gendelman OV, Savin AV. Normal heat conductivity of the one-dimensional lattice with periodic potential of nearest-neighbor interaction. PHYSICAL REVIEW LETTERS 2000; 84:2381-2384. [PMID: 11018890 DOI: 10.1103/physrevlett.84.2381] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/16/1999] [Indexed: 05/23/2023]
Abstract
The process of heat conduction in a chain with a periodic potential of nearest-neighbor interaction is investigated by means of molecular dynamics simulation. It is demonstrated that the periodic potential of nearest-neighbor interaction allows one to obtain normal heat conductivity in an isolated one-dimensional chain with conserved momentum. The system exhibits a transition from infinite to normal heat conductivity with the growth of its temperature. The physical reason for normal heat conductivity is the excitation of high-frequency stationary localized rotational modes. These modes absorb the momentum and facilitate locking of the heat flux.
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Affiliation(s)
- OV Gendelman
- N. N. Semenov Institute of Chemical Physics, Russian Academy of Sciences, ul. Kosygina 4, 117977 Moscow, Russia
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Braun OM, Dauxois T, Paliy MV, Peyrard M. Mobility and diffusivity in a generalized Frenkel-Kontorova model. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:321-331. [PMID: 9984261 DOI: 10.1103/physrevb.54.321] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Braun OM, Kivshar YS. Concentration dependence of the conductivity and diffusivity in one-dimensional anharmonic lattices. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 50:13388-13400. [PMID: 9975531 DOI: 10.1103/physrevb.50.13388] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Bazhenov AM, Heyes DM. Dynamical properties and transport coefficients of one‐dimensional Lennard‐Jones fluids: A molecular dynamics study. J Chem Phys 1990. [DOI: 10.1063/1.458172] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Mareschal M, Amellal A. Thermal conductivity in a one-dimensional Lennard-Jones chain by molecular dynamics. PHYSICAL REVIEW. A, GENERAL PHYSICS 1988; 37:2189-2196. [PMID: 9899914 DOI: 10.1103/physreva.37.2189] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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