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Yoshimura K, Doi Y, Kitamura T. Heat transport in nonlinear lattices free from the umklapp process. Phys Rev E 2022; 105:024140. [PMID: 35291156 DOI: 10.1103/physreve.105.024140] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/05/2021] [Accepted: 12/16/2021] [Indexed: 06/14/2023]
Abstract
We construct one-dimensional nonlinear lattices having the special property such that the umklapp process vanishes and only the normal processes are included in the potential functions. These lattices have long-range quartic nonlinear and nearest-neighbor harmonic interactions with/without harmonic onsite potential. We study heat transport in two cases of the lattices with and without harmonic onsite potential by nonequilibrium molecular dynamics simulation. It is shown that the ballistic heat transport occurs in both cases, i.e., the scaling law κ∝N holds between the thermal conductivity κ and the lattice size N. This result directly validates Peierls's hypothesis that only the umklapp processes can cause the thermal resistance while the normal ones do not.
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Affiliation(s)
- Kazuyuki Yoshimura
- Faculty of Engineering, Tottori University, 4-101 Koyama-Minami, Tottori 680-8552, Japan
| | - Yusuke Doi
- Division of Mechanical Engineering, Graduate School of Engineering, Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-0871, Japan
| | - Tomoya Kitamura
- Department of Engineering, Graduate School of Sustainability Science, Tottori University 4-101 Koyama-Minami, Tottori 680-8552, Japan
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Lee-Dadswell GR, Barrett N, Power M. Cluster sizes in a classical Lennard-Jones chain. Phys Rev E 2018; 96:032144. [PMID: 29346925 DOI: 10.1103/physreve.96.032144] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2017] [Indexed: 11/07/2022]
Abstract
The definitions of breaks and clusters in a one-dimensional chain in equilibrium are discussed. Analytical expressions are obtained for the expected cluster length, 〈K〉, as a function of temperature and pressure in a one-dimensional Lennard-Jones chain. These expressions are compared with results from molecular dynamics simulations. It is found that 〈K〉 increases exponentially with β=1/k_{B}T and with pressure, P in agreement with previous results in the literature. A method is illustrated for using 〈K〉(β,P) to generate a "phase diagram" for the Lennard-Jones chain. Some implications for the study of heat transport in Lennard-Jones chains are discussed.
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Affiliation(s)
- G R Lee-Dadswell
- Math, Physics and Geology Department, Cape Breton University, Sydney, Nova Scotia, Canada
| | - Nicholas Barrett
- Math, Physics and Geology Department, Cape Breton University, Sydney, Nova Scotia, Canada
| | - Michael Power
- Math, Physics and Geology Department, Cape Breton University, Sydney, Nova Scotia, Canada
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Xiong D, Saadatmand D, Dmitriev SV. Crossover from ballistic to normal heat transport in the ϕ^{4} lattice: If nonconservation of momentum is the reason, what is the mechanism? Phys Rev E 2017; 96:042109. [PMID: 29347584 DOI: 10.1103/physreve.96.042109] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2017] [Indexed: 11/07/2022]
Abstract
Anomalous (non-Fourier) heat transport is no longer just a theoretical issue since it has been observed experimentally in a number of low-dimensional nanomaterials, such as SiGe nanowires, carbon nanotubes, and others. To understand these anomalous behaviors, exploring the microscopic origin of normal (Fourier) heat transport is a fascinating theoretical topic. However, this issue has not yet been fully understood even for one-dimensional (1D) model chains, in spite of a great amount of thorough studies done to date. From those studies, it has been widely accepted that the conservation of momentum is a key ingredient to induce anomalous heat transport, while momentum-nonconserving systems usually support normal heat transport where Fourier's law is valid. But if the nonconservation of momentum is the reason, what is the underlying microscopic mechanism for the observed normal heat transport? Here we carefully revisit a typical 1D momentum-nonconserving ϕ^{4} model, and we present evidence that the mobile discrete breathers, or, in other words, the moving intrinsic localized modes with frequency components above the linear phonon band, can be responsible for that.
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Affiliation(s)
- Daxing Xiong
- Department of Physics, Fuzhou University, Fuzhou 350108, Fujian, China
| | - Danial Saadatmand
- Department of Physics, University of Sistan and Baluchestan, Zahedan, Iran
| | - Sergey V Dmitriev
- Institute for Metals Superplasticity Problems of RAS, Khalturin St. 39, 450001 Ufa, Russia.,National Research Tomsk State University, Lenin Avenue 36, 634050 Tomsk, Russia
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Gao Z, Li N, Li B. Heat conduction and energy diffusion in momentum-conserving one-dimensional full-lattice ding-a-ling model. Phys Rev E 2016; 93:022102. [PMID: 26986283 DOI: 10.1103/physreve.93.022102] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/13/2015] [Indexed: 06/05/2023]
Abstract
The ding-a-ling model is a kind of half lattice and half hard-point-gas (HPG) model. The original ding-a-ling model proposed by Casati et al. does not conserve total momentum and has been found to exhibit normal heat conduction behavior. Recently, a modified ding-a-ling model which conserves total momentum has been studied and normal heat conduction has also been claimed. In this work, we propose a full-lattice ding-a-ling model without hard point collisions where total momentum is also conserved. We investigate the heat conduction and energy diffusion of this full-lattice ding-a-ling model with three different nonlinear inter-particle potential forms. For symmetrical potential lattices, the thermal conductivities diverges with lattice length and their energy diffusions are superdiffusive signaturing anomalous heat conduction. For asymmetrical potential lattices, although the thermal conductivity seems to converge as the length increases, the energy diffusion is definitely deviating from normal diffusion behavior indicating anomalous heat conduction as well. No normal heat conduction behavior can be found for the full-lattice ding-a-ling model.
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Affiliation(s)
- Zhibin Gao
- Center for Phononics and Thermal Energy Science, School of Physics Science and Engineering, Tongji University, 200092 Shanghai, People's Republic of China
| | - Nianbei Li
- Center for Phononics and Thermal Energy Science, School of Physics Science and Engineering, Tongji University, 200092 Shanghai, People's Republic of China
| | - Baowen Li
- Department of Mechanical Engineering, University of Colorado Boulder, Colorado 80309, USA
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Lee-Dadswell GR. Universality classes for thermal transport in one-dimensional oscillator systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:032102. [PMID: 25871049 DOI: 10.1103/physreve.91.032102] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/03/2014] [Indexed: 06/04/2023]
Abstract
Two universality classes for thermal transport in one-dimensional oscillator systems are proposed. In class A the asymptotic behavior of the frequency dependent thermal conductivity is κ(ω)∼ω-1/2, whereas the bulk viscosity is finite. In class B the asymptotic behavior of the thermal conductivity is κ∼ω-α, where α<0.4, and the frequency dependent bulk viscosity has the same asymptotic behavior as the thermal conductivity. It is further proposed that the criterion for membership in class A is that the ratio of specific heat capacities γ≡cP/cV=1. A one-dimensional cubic-plus-quartic coupled oscillator is examined at conditions for which γ=1 but P≠0. It is found that the system belongs to class A, in agreement with the proposed criterion. Additionally, it is proposed that examination of whether a system has a well-defined bulk Prandtl number is a more reliable way of determining whether a system is in class A or class B.
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Affiliation(s)
- G R Lee-Dadswell
- Math, Physics and Geology Department, Cape Breton University, Sydney, Nova Scotia, Canada, B1P 6L2
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Lee-Dadswell GR. Predicting and identifying finite-size effects in current spectra of one-dimensional oscillator chains. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:012138. [PMID: 25679601 DOI: 10.1103/physreve.91.012138] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/30/2014] [Indexed: 06/04/2023]
Abstract
The existence of a finite-size effect in one-dimensional oscillator systems causing the energy current power spectrum to saturate to a constant value at low frequencies is discussed. It is shown that a mode-coupling theory presented in earlier papers can be used to predict the frequency of onset of this finite-size effect. This can be used by researchers to plan simulations with large enough numbers of particles to avoid the presence of this finite-size effect.
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Affiliation(s)
- G R Lee-Dadswell
- Math, Physics and Geology Department, Cape Breton University, Sydney, Nova Scotia, Canada
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Das SG, Dhar A, Saito K, Mendl CB, Spohn H. Numerical test of hydrodynamic fluctuation theory in the Fermi-Pasta-Ulam chain. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:012124. [PMID: 25122268 DOI: 10.1103/physreve.90.012124] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2014] [Indexed: 06/03/2023]
Abstract
Recent work has developed a nonlinear hydrodynamic fluctuation theory for a chain of coupled anharmonic oscillators governing the conserved fields, namely, stretch, momentum, and energy. The linear theory yields two propagating sound modes and one diffusing heat mode, all three with diffusive broadening. In contrast, the nonlinear theory predicts that, at long times, the sound mode correlations satisfy Kardar-Parisi-Zhang scaling, while the heat mode correlations have Lévy-walk scaling. In the present contribution we report on molecular dynamics simulations of Fermi-Pasta-Ulam chains to compute various spatiotemporal correlation functions and compare them with the predictions of the theory. We obtain very good agreement in many cases, but also some deviations.
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Affiliation(s)
- Suman G Das
- Raman Research Institute, CV Raman Avenue, Sadashivanagar, Bangalore 560080, India
| | - Abhishek Dhar
- International Center for Theoretical Sciences, TIFR, IISC Campus, Bangalore 560012, India
| | - Keiji Saito
- Department of Physics, Keio University, Yokohama 223-8522, Japan
| | - Christian B Mendl
- Zentrum Mathematik, TU München, Boltzmannstraße 3, 85747 Garching, Germany
| | - Herbert Spohn
- Institute for Advanced Study, Einstein Drive, Princeton, New Jersey 08540, USA
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Gill-Comeau M, Lewis LJ. Cross-correlations between phonon modes in anharmonic oscillator chains: role in heat transport. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:042114. [PMID: 24827200 DOI: 10.1103/physreve.89.042114] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/28/2014] [Indexed: 06/03/2023]
Abstract
We have computed current-current correlation functions in chains of anharmonic oscillators described by various models (FPU-β, FPU-αβ, ϕ4), considering both the total current and the currents associated with individual phonon modes, which are important in view of the Green-Kubo relation for heat conductivity. Our simulations show that, contrary to the common hypothesis, there are, under some circumstances, significant correlations between neighboring modes. These cross-mode correlations are the dominant contribution to the conductivity in the low anharmonicity regime. The inverse of the timescale over which they are significant, 1/τc, is related to the anharmonicity level in a way similar to the largest Lyapunov exponent, suggesting that the two quantities are related. Cross-mode correlations exist in both anomalous and regular heat-conducting systems although we are unable to observe a transition to the independent-mode regime in the latter case.
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Affiliation(s)
- Maxime Gill-Comeau
- Département de Physique et Regroupement Québécois sur les Matériaux de Pointe (RQMP), Université de Montréal, C.P. 6128, Succursale Centre-Ville, Montréal, Québec H3C 3J7, Canada
| | - Laurent J Lewis
- Département de Physique et Regroupement Québécois sur les Matériaux de Pointe (RQMP), Université de Montréal, C.P. 6128, Succursale Centre-Ville, Montréal, Québec H3C 3J7, Canada
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Zhong Y, Zhang Y, Wang J, Zhao H. Normal heat conduction in one-dimensional momentum conserving lattices with asymmetric interactions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:060102. [PMID: 23005043 DOI: 10.1103/physreve.85.060102] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/23/2011] [Indexed: 06/01/2023]
Abstract
We study heat conduction behavior of one-dimensional lattices with asymmetric, momentum conserving interparticle interactions. We find that with a certain degree of interaction asymmetry, the heat conductivity measured in nonequilibrium stationary states converges in the thermodynamical limit. Our analysis suggests that the mass gradient resulting from asymmetric interactions may provide a phonon scattering mechanism in addition to that caused by nonlinear interactions.
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Affiliation(s)
- Yi Zhong
- Department of Physics and Institute of Theoretical Physics and Astrophysics, Xiamen University, Xiamen 361005, People's Republic of China
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