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Sun Y, Wang L. Heat transport in an angular-momentum-conserving lattice. Phys Rev E 2024; 109:034118. [PMID: 38632744 DOI: 10.1103/physreve.109.034118] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/04/2024] [Accepted: 02/23/2024] [Indexed: 04/19/2024]
Abstract
It is expected that the energy-diffusion propagator in a one-dimensional nonlinear lattice with three conserved quantities: energy, momentum, and stretch, consists of a central heat mode and two sound modes. The heat mode follows a Lévy distribution. Consequently, the heat diffusion is super, i.e., the second moment of the diffusion propagator diverges as t^{β} with β>1; and the heat conduction is anomalous, i.e., the heat conductivity is size dependent and diverges with size N by N^{α}, with α>0. In this paper, we study a one-dimensional lattice with two-dimensional transverse motions, in which the total angular momentum also conserves. More importantly, the diffusion of this conserved quantity is ballistic. Surprisingly, the above pictures and the values of the mentioned power exponents keep unchanged. The universality of the scalings is then further extended. On the other hand, the detailed strengths of heat transports are largely enhanced. Such a counterintuitive finding can be explained by the change of the phonon mean-free path of the lattices.
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Affiliation(s)
- Yachao Sun
- Department of Physics, Beijing Key Laboratory of Opto-electronic Functional Materials and Micro-nano Devices, and Key Laboratory of Quantum State Construction and Manipulation (Ministry of Education), Renmin University of China, Beijing 100872, People's Republic of China
| | - Lei Wang
- Department of Physics, Beijing Key Laboratory of Opto-electronic Functional Materials and Micro-nano Devices, and Key Laboratory of Quantum State Construction and Manipulation (Ministry of Education), Renmin University of China, Beijing 100872, People's Republic of China
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Dmitriev SV, Kuzkin VA, Krivtsov AM. Nonequilibrium thermal rectification at the junction of harmonic chains. Phys Rev E 2023; 108:054221. [PMID: 38115418 DOI: 10.1103/physreve.108.054221] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2023] [Accepted: 11/03/2023] [Indexed: 12/21/2023]
Abstract
A thermal diode or rectifier is a system that transmits heat or energy in one direction better than in the opposite direction. We investigate the influence of the distribution of energy among wave numbers on the diode effect for the junction of two dissimilar harmonic chains. An analytical expression for the diode coefficient, characterizing the difference between heat fluxes through the junction in two directions, is derived. It is shown that the diode coefficient depends on the distribution of energy among wave numbers. For an equilibrium energy distribution, the diode effect is absent, while for non-equilibrium energy distributions the diode effect is observed even though the system is harmonic. We show that the diode effect can be maximized by varying the energy distribution and relative position of spectra of the two harmonic chains. Conditions are formulated under which the system acts as an ideal thermal rectifier, i.e., transmits heat only in one direction. The results obtained are important for understanding the heat transfer in heterogeneous low-dimensional nanomaterials.
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Affiliation(s)
- Sergey V Dmitriev
- Institute of Molecule and Crystal Physics, Ufa Federal Research Centre of RAS, Ufa 450054, Russia
- Ufa State Petroleum Technological University, Ufa 450062, Russia
| | - Vitaly A Kuzkin
- Institute for Problems in Mechanical Engineering RAS, Saint Petersburg 199178, Russia
- Peter the Great Saint Petersburg Polytechnic University, Saint Petersburg 195251, Russia
| | - Anton M Krivtsov
- Institute for Problems in Mechanical Engineering RAS, Saint Petersburg 199178, Russia
- Peter the Great Saint Petersburg Polytechnic University, Saint Petersburg 195251, Russia
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Guo Y, Sun Y, Wang L. Energy diffusion in two-dimensional momentum-conserving nonlinear lattices: Lévy walk and renormalized phonon. Phys Rev E 2023; 107:014109. [PMID: 36797934 DOI: 10.1103/physreve.107.014109] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/28/2022] [Accepted: 12/21/2022] [Indexed: 01/12/2023]
Abstract
The energy diffusion process in a few two-dimensional Fermi-Pasta-Ulam-type lattices is numerically simulated via the equilibrium local energy spatiotemporal correlation. Just as the nonlinear fluctuating hydrodynamic theory suggested, the diffusion propagator consists of a bell-shaped central heat mode and a sound mode extending with a constant speed. The profiles of the heat and sound modes satisfy the scaling properties from a random-walk-with-velocity-fluctuation process very well. An effective phonon approach is proposed, which expects the frequencies of renormalized phonons as well as the sound speed with quite good accuracy. Since many existing analytical and numerical studies indicate that heat conduction in such two-dimensional momentum-conserving lattices is divergent and the thermal conductivity κ increases logarithmically with lattice length, it is expected that the mean-square displacement of energy diffusion grows as tlnt. Discrepancies, however, are noticeably observed.
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Affiliation(s)
- Yanjiang Guo
- Department of Physics and Beijing Key Laboratory of Opto-electronic Functional Materials and Micro-nano Devices, Renmin University of China, Beijing 100872, People's Republic of China
| | - Yachao Sun
- Department of Physics and Beijing Key Laboratory of Opto-electronic Functional Materials and Micro-nano Devices, Renmin University of China, Beijing 100872, People's Republic of China
| | - Lei Wang
- Department of Physics and Beijing Key Laboratory of Opto-electronic Functional Materials and Micro-nano Devices, Renmin University of China, Beijing 100872, People's Republic of China
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Luo R, Huang L, Lepri S. Heat conduction in a three-dimensional momentum-conserving fluid. Phys Rev E 2021; 103:L050102. [PMID: 34134304 DOI: 10.1103/physreve.103.l050102] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2021] [Accepted: 04/28/2021] [Indexed: 11/07/2022]
Abstract
Size dependence of energy transport and the effects of reduced dimensionality on transport coefficients are of key importance for understanding nonequilibrium properties of matter on the nanoscale. Here, we perform nonequilibrium and equilibrium simulations of heat conduction in a three-dimensional (3D) fluid with the multiparticle collision dynamics, interacting with two thermal walls. We find that the bulk 3D momentum-conserving fluid has a finite nondiverging thermal conductivity. However, for large aspect ratios of the simulation box, a crossover from 3D to one-dimensional (1D) abnormal behavior of the thermal conductivity occurs. In this case, we demonstrate a transition from normal to abnormal transport by a suitable decomposition of the energy current. These results not only provide a direct verification of Fourier's law, but also further confirm the validity of existing theories for 3D fluids. Moreover, they indicate that abnormal heat transport persists also for almost 1D fluids over a large range of sizes.
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Affiliation(s)
- Rongxiang Luo
- Department of Physics, Fuzhou University, Fuzhou 350108, Fujian, China.,Fujian Science and Technology Innovation Laboratory for Optoelectronic Information of China, Fuzhou 350108, Fujian, China
| | - Lisheng Huang
- Department of Physics, Fuzhou University, Fuzhou 350108, Fujian, China.,Fujian Science and Technology Innovation Laboratory for Optoelectronic Information of China, Fuzhou 350108, Fujian, China
| | - Stefano Lepri
- Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy.,Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino, Italy
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Korznikova EA, Kuzkin VA, Krivtsov AM, Xiong D, Gani VA, Kudreyko AA, Dmitriev SV. Equilibration of sinusoidal modulation of temperature in linear and nonlinear chains. Phys Rev E 2020; 102:062148. [PMID: 33465976 DOI: 10.1103/physreve.102.062148] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/13/2020] [Accepted: 12/01/2020] [Indexed: 06/12/2023]
Abstract
The equilibration of sinusoidally modulated distribution of the kinetic temperature is analyzed in the β-Fermi-Pasta-Ulam-Tsingou chain with different degrees of nonlinearity and for different wavelengths of temperature modulation. Two different types of initial conditions are used to show that either one gives the same result as the number of realizations increases and that the initial conditions that are closer to the state of thermal equilibrium give faster convergence. The kinetics of temperature equilibration is monitored and compared to the analytical solution available for the linear chain in the continuum limit. The transition from ballistic to diffusive thermal conductivity with an increase in the degree of anharmonicity is shown. In the ballistic case, the energy equilibration has an oscillatory character with an amplitude decreasing in time, and in the diffusive case, it is monotonous in time. For smaller wavelength of temperature modulation, the oscillatory character of temperature equilibration remains for a larger degree of anharmonicity. For a given wavelength of temperature modulation, there is such a value of the anharmonicity parameter at which the temperature equilibration occurs most rapidly.
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Affiliation(s)
- Elena A Korznikova
- Institute of Molecule and Crystal Physics, Ufa Federal Research Centre of the Russian Academy of Sciences, Ufa 450054, Russia
- Ufa State Aviation Technical University, Ufa 450008, Russia
| | - Vitaly A Kuzkin
- Peter the Great Saint Petersburg Polytechnical University, Saint Petersburg 195251, Russia
- Institute for Problems in Mechanical Engineering, RAS, Saint Petersburg 199178, Russia
| | - Anton M Krivtsov
- Peter the Great Saint Petersburg Polytechnical University, Saint Petersburg 195251, Russia
- Institute for Problems in Mechanical Engineering, RAS, Saint Petersburg 199178, Russia
| | - Daxing Xiong
- MinJiang Collaborative Center for Theoretical Physics, Department of Physics and Electronic Information Engineering, Minjiang University, Fuzhou, Fujian 350108, China
| | - Vakhid A Gani
- National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Moscow 115409, Russia
- Institute for Theoretical and Experimental Physics of National Research Centre "Kurchatov Institute," Moscow 117218, Russia
| | - Aleksey A Kudreyko
- Department of Medical Physics and Informatics, Bashkir State Medical University, Ufa 450008, Russia
| | - Sergey V Dmitriev
- Institute of Molecule and Crystal Physics, Ufa Federal Research Centre of the Russian Academy of Sciences, Ufa 450054, Russia
- Institute of Mathematics with Computing Centre, Ufa Federal Research Centre of RAS, Ufa 450008, Russia
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Luo R. Heat conduction in two-dimensional momentum-conserving and -nonconserving gases. Phys Rev E 2020; 102:052104. [PMID: 33327068 DOI: 10.1103/physreve.102.052104] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2020] [Accepted: 10/18/2020] [Indexed: 06/12/2023]
Abstract
Compared to that for two-dimensional (2D) lattices, our understanding of heat conduction in 2D gases is still limited. Here we study heat conduction behavior of 2D gas systems with momentum-conserving and -nonconserving interparticle interactions by using the nonequilibrium and equilibrium molecular dynamics methods. For the momentum-conserving system, we find that when the dimensionality of the system is changed from 2D to quasi-one-dimensional (quasi-1D), the heat conductivity κ diverges with the system size L as κ∼lnL (the theoretical prediction for 2D systems) for a short L and shows, in the thermodynamic limit, a tendency to κ∼L^{1/3} like that predicted in 1D fluids. This suggests that the dimensional-crossover effect of heat conduction exists in 2D systems with conserved momentum. In contrast, for the momentum-nonconserving system, as L increases, finite heat conductivity independent of L is observed. These findings are in agreement with the predictions given by hydrodynamic theory and thus further confirm the validity of the theory in 2D gases.
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Affiliation(s)
- Rongxiang Luo
- Department of Physics, Fuzhou University, Fuzhou 350108, Fujian, China and Fujian Science and Technology Innovation Laboratory for Optoelectronic Information of China, Fuzhou 350108, Fujian, China
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