1
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Shcherbinin SA, Kazakov AM, Bebikhov YV, Kudreyko AA, Dmitriev SV. Delocalized nonlinear vibrational modes and discrete breathers in β-FPUT simple cubic lattice. Phys Rev E 2024; 109:014215. [PMID: 38366423 DOI: 10.1103/physreve.109.014215] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2023] [Accepted: 12/12/2023] [Indexed: 02/18/2024]
Abstract
The problem of finding various discrete breathers (DBs) in the β-Fermi-Pasta-Ulam-Tsingou simple cubic lattice is addressed. DBs are obtained by imposing localizing functions on delocalized nonlinear vibrational modes (DNVMs) having frequencies above the phonon spectrum of the lattice. Among 27 DNVMs with the wave vector at the boundary of the first Brillouin zone there are three satisfying this condition. Seven robust DBs of different symmetries are found using this approach.
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Affiliation(s)
- S A Shcherbinin
- Peter the Great St. Petersburg Polytechnic University, Polytechnicheskaya St. 29, 195251, St. Petersburg, Russia
- Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, V. O., Bolshoj Ave. 61, 199178, St. Petersburg, Russia
| | - A M Kazakov
- Research Laboratory Metals and Alloys under Extreme Impacts, Ufa University of Science and Technology, Zaki Validi St. 32, Ufa 450076, Russia
| | - Yu V Bebikhov
- Polytechnic Institute (Branch) in Mirny, North-Eastern Federal University, Tikhonova St. 5/1, 678170 Mirny, Sakha Republic (Yakutia), Russia
| | - A A Kudreyko
- Bashkir State Medical University, Lenina St. 3, 450008 Ufa, Russia
| | - S V Dmitriev
- Institute of Molecule and Crystal Physics, UFRC of Russian Academy of Sciences, Oktyabrya Ave. 151, Ufa 450075, Russia
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2
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Naumov EK, Bebikhov YV, Ekomasov EG, Soboleva EG, Dmitriev SV. Discrete breathers in square lattices from delocalized nonlinear vibrational modes. Phys Rev E 2023; 107:034214. [PMID: 37072991 DOI: 10.1103/physreve.107.034214] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2023] [Accepted: 03/15/2023] [Indexed: 04/20/2023]
Abstract
Standing and moving discrete breathers (or equally, intrinsic localized modes) in a square β-Fermi-Pasta-Ulam-Tsingou lattice are obtained by applying localizing functions to the delocalized nonlinear vibrational modes (DNVMs) found earlier by Ryabov and Chechin. The initial conditions used in our study do not correspond to exact spatially localized solutions, but make it possible to obtain long-lived quasibreathers. The approach employed in this work can easily be used to search for quasibreathers in three-dimensional crystal lattices, for which DNVMs with frequencies outside the phonon spectrum are known.
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Affiliation(s)
- E K Naumov
- Institute of Molecule and Crystal Physics, UFRC of Russian Academy of Sciences, Ufa 450075, Russia
- Institute for Metals Superplasticity Problems of Russian Academy of Sciences, Khalturin Street 39, Ufa 450001, Russia
| | - Yu V Bebikhov
- Polytechnic Institute (Branch) in Mirny, North-Eastern Federal University, Tikhonova Street 5/1, 678170 Mirny, Sakha Republic (Yakutia), Russia
| | - E G Ekomasov
- Ufa University of Science and Technology, Zaki Validi 32, Ufa 450076, Russia
| | - E G Soboleva
- National Research Tomsk Polytechnic University, Tomsk 634050, Russia
| | - S V Dmitriev
- Institute of Molecule and Crystal Physics, UFRC of Russian Academy of Sciences, Ufa 450075, Russia
- Institute for Metals Superplasticity Problems of Russian Academy of Sciences, Khalturin Street 39, Ufa 450001, Russia
- Institute of Mathematics with Computing Centre, UFRC of Russian Academy of Sciences, Ufa 450000, Russia
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3
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Xiong D, Wang J. Subdiffusive energy transport and antipersistent correlations due to the scattering of phonons and discrete breathers. Phys Rev E 2022; 106:L032201. [PMID: 36266887 DOI: 10.1103/physreve.106.l032201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2021] [Accepted: 08/22/2022] [Indexed: 06/16/2023]
Abstract
While there are many physical processes showing subdiffusion and some useful particle models for understanding the underlying mechanisms have been established, a systematic study of subdiffusive energy transport is still lacking. Here we present convincing evidence that, in the range of system size investigated, the energy subdiffusion can take place in a Hamiltonian lattice system with both harmonic nearest-neighbor and anharmonic long-range interactions. In particular, we show that the interaction range dependence of antipersistent energy-current correlations are relevant to this special type of energy subdiffusion. The underlying mechanisms are related to the various scattering processes of phonons and discrete breathers. Our results shed light on understanding the extremely slow energy transport.
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Affiliation(s)
- Daxing Xiong
- MinJiang Collaborative Center for Theoretical Physics, College of Physics and Electronic Information Engineering, Minjiang University, Fuzhou 350108, China
| | - Jianjin Wang
- Department of Physics, Jiangxi Science and Technology Normal University, Nanchang 330013, Jiangxi, China
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4
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Romero-Bastida M, Amaya-Durán JI. Thermal rectification in oscillator lattices with a ballistic spacer and next nearest-neighbor interactions. Phys Rev E 2021; 103:032103. [PMID: 33862683 DOI: 10.1103/physreve.103.032103] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/26/2020] [Accepted: 02/11/2021] [Indexed: 11/07/2022]
Abstract
In this work we study the asymmetric heat flow, i.e., thermal rectification, of a one-dimensional, mass-graded system consisting of a coupled harmonic oscillator lattice (ballistic spacer) and two diffusive leads attached to the boundaries of the former with both nearest-neighbor and next nearest-neighbor (NNN) interactions. The latter enhance the rectification properties of the system and specially its independence on system size. The system presents a maximum rectification efficiency for a very precise value of the parameter that controls the coupling strength of the NNN interactions that depend on the temperature range wherein the device operates. The origin of this maximum value is the asymmetric local heat flow response corresponding to the NNN contribution at both sides of the lighter mass-loaded diffusive lead as quantified by the spectral properties. Upon variation of the system's parameters the performance of the device is always enhanced in the presence of NNN interactions.
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Affiliation(s)
- M Romero-Bastida
- SEPI ESIME-Culhuacán, Instituto Politécnico Nacional, Av. Santa Ana No. 1000, Col. San Francisco Culhuacán, Delegación Coyoacan, Distrito Federal 04430, Mexico
| | - Jeanette-Ivonne Amaya-Durán
- SEPI ESIME-Culhuacán, Instituto Politécnico Nacional, Av. Santa Ana No. 1000, Col. San Francisco Culhuacán, Delegación Coyoacan, Distrito Federal 04430, Mexico
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5
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Wang J, Chen J. Suppressed-to-enhanced thermal transport in a Fermi-Pasta-Ulam superlattice: Mediation roles of solitons and phonons. Phys Rev E 2020; 101:042207. [PMID: 32422702 DOI: 10.1103/physreve.101.042207] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2019] [Accepted: 03/16/2020] [Indexed: 11/07/2022]
Abstract
Managing thermal transport in nanostructured materials possesses both theoretical and application value in thermoelectric and microelectronics design. Though a suppressed thermal conductivity could be easily achieved through disorder-induced phonon scattering in a superlattice, it is challenging to enhance thermal transport in a periodically designed lattice. In this paper, we show the possibility of mediating thermal conductivity from a suppressed to an enhanced value in a Fermi-Pasta-Ulam β superlattice with periodic cells of arithmetically increased nonlinearity. When the cell length is increased, thermal conductivity in the superlattice crosses over a suppressed region into an enhanced one and it is even higher than in a homogeneous lattice with the same nonlinearity strength. The mediation originates from the long-lived nonlinear wave packets as solitons across the disorder-induced interface between cells of the superlattice, while at the same time the normal vibrational modes as phonons are suppressed. Our result shows a promising strategy to manipulate thermal transport over a wide range in a superlattice with strong nonlinearity.
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Affiliation(s)
- Jianjin Wang
- Department of Physics, Jiangxi Science & Technology Normal University, Nanchang 330013, China.,Zhangjiang Laboratory, Shanghai Advanced Research Institute, Chinese Academy of Sciences, Shanghai 201210, China
| | - Jige Chen
- Zhangjiang Laboratory, Shanghai Advanced Research Institute, Chinese Academy of Sciences, Shanghai 201210, China.,Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, China
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6
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Raj A, Eapen J. Exact diagonal representation of normal mode energy, occupation number, and heat current for phonon-dominated thermal transport. J Chem Phys 2019; 151:104110. [DOI: 10.1063/1.5099936] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Anant Raj
- Department of Nuclear Engineering, North Carolina State University, Raleigh, North Carolina 27695, USA
| | - Jacob Eapen
- Department of Nuclear Engineering, North Carolina State University, Raleigh, North Carolina 27695, USA
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7
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Ming Y, Ye L, Chen HS, Mao SF, Li HM, Ding ZJ. Solitons as candidates for energy carriers in Fermi-Pasta-Ulam lattices. Phys Rev E 2018; 97:012221. [PMID: 29448422 DOI: 10.1103/physreve.97.012221] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/25/2017] [Indexed: 11/07/2022]
Abstract
Currently, effective phonons (renormalized or interacting phonons) rather than solitary waves (for short, solitons) are regarded as the energy carriers in nonlinear lattices. In this work, by using the approximate soliton solutions of the corresponding equations of motion and adopting the Boltzmann distribution for these solitons, the average velocities of solitons are obtained and are compared with the sound velocities of energy transfer. Excellent agreements with the numerical results and the predictions of other existing theories are shown in both the symmetric Fermi-Pasta-Ulam-β lattices and the asymmetric Fermi-Pasta-Ulam-αβ lattices. These clearly indicate that solitons are suitable candidates for energy carriers in Fermi-Pasta-Ulam lattices. In addition, the root-mean-square velocity of solitons can be obtained from the effective phonons theory.
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Affiliation(s)
- Yi Ming
- School of Physics and Material Science, Anhui University, Hefei, Anhui 230601, China
| | - Liu Ye
- School of Physics and Material Science, Anhui University, Hefei, Anhui 230601, China
| | - Han-Shuang Chen
- School of Physics and Material Science, Anhui University, Hefei, Anhui 230601, China
| | - Shi-Feng Mao
- School of Nuclear Science and Technology, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Hui-Min Li
- Supercomputing Center, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Ze-Jun Ding
- Department of Physics and Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China.,Key Laboratory of Strongly-coupled Quantum Matter Physics, Chinese Academy of Sciences, Hefei, Anhui 230026, China
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8
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Xiong D. Observing golden-mean universality class in the scaling of thermal transport. Phys Rev E 2018; 97:022116. [PMID: 29548205 DOI: 10.1103/physreve.97.022116] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2017] [Indexed: 11/07/2022]
Abstract
We address the issue of whether the golden-mean [ψ=(sqrt[5]+1)/2≃1.618] universality class, as predicted by several theoretical models, can be observed in the dynamical scaling of thermal transport. Remarkably, we show strong evidence that ψ appears to be the scaling exponent of heat mode correlation in a purely quartic anharmonic chain. This observation seems to somewhat deviate from the previous expectation and we explain it by the unusual slow decay of the cross correlation between heat and sound modes. Whenever the cubic anharmonicity is included, this cross correlation gradually dies out and another universality class with scaling exponent γ=5/3, as commonly predicted by theories, seems recovered. However, this recovery is accompanied by two interesting phase transition processes characterized by a change of symmetry of the potential and a clear variation of the dynamic structure factor, respectively. Due to these transitions, an additional exponent close to γ≃1.580 emerges. All this evidence suggests that, to gain a full prediction of the scaling of thermal transport, more ingredients should be taken into account.
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Affiliation(s)
- Daxing Xiong
- Department of Physics, Fuzhou University, Fuzhou 350108, Fujian, China
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9
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Schütz GM, Wehefritz-Kaufmann B. Kardar-Parisi-Zhang modes in d-dimensional directed polymers. Phys Rev E 2018; 96:032119. [PMID: 29346934 DOI: 10.1103/physreve.96.032119] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/19/2017] [Indexed: 11/07/2022]
Abstract
We define a stochastic lattice model for a fluctuating directed polymer in d≥2 dimensions. This model can be alternatively interpreted as a fluctuating random path in two dimensions, or a one-dimensional asymmetric simple exclusion process with d-1 conserved species of particles. The deterministic large dynamics of the directed polymer are shown to be given by a system of coupled Kardar-Parisi-Zhang (KPZ) equations and diffusion equations. Using nonlinear fluctuating hydrodynamics and mode coupling theory we argue that stationary fluctuations in any dimension d can only be of KPZ type or diffusive. The modes are pure in the sense that there are only subleading couplings to other modes, thus excluding the occurrence of modified KPZ-fluctuations or Lévy-type fluctuations, which are common for more than one conservation law. The mode-coupling matrices are shown to satisfy the so-called trilinear condition.
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Affiliation(s)
- G M Schütz
- Institute of Complex Systems II, Forschungszentrum Jülich, 52425 Jülich, Germany
| | - B Wehefritz-Kaufmann
- Department of Mathematics and Department of Physics and Astronomy, Purdue University, 150 North University Street, West Lafayette, Indiana 47906, USA
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10
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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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11
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Xiong D, Thiel F, Barkai E. Using Hilbert transform and classical chains to simulate quantum walks. Phys Rev E 2017; 96:022114. [PMID: 28950452 DOI: 10.1103/physreve.96.022114] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2017] [Indexed: 06/07/2023]
Abstract
We propose a simulation strategy which uses a classical device of linearly coupled chain of springs to simulate quantum dynamics, in particular quantum walks. Through this strategy, we obtain the quantum wave function from the classical evolution. Specially, this goal is achieved with the classical momenta of the particles on the chain and their Hilbert transform, from which we construct the many-body momentum and Hilbert transformed momentum pair correlation functions yielding the real and imaginary parts of the wave function, respectively. With such a wave function, we show that the classical chain's energy and heat spreading densities can be related to the wave function's modulus square. This relation provides a new perspective to understand ballistic heat transport. The results here may give a definite answer to Feynman's idea of using a classical device to simulate quantum physics.
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Affiliation(s)
- Daxing Xiong
- Department of Physics, Fuzhou University, Fuzhou 350108, Fujian, China
- Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan, 52900, Israel
| | - Felix Thiel
- Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan, 52900, Israel
| | - Eli Barkai
- Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan, 52900, Israel
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12
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Xiong D. Heat perturbation spreading in the Fermi-Pasta-Ulam-β system with next-nearest-neighbor coupling: Competition between phonon dispersion and nonlinearity. Phys Rev E 2017; 95:062140. [PMID: 28709315 DOI: 10.1103/physreve.95.062140] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/25/2017] [Indexed: 06/07/2023]
Abstract
We employ the heat perturbation correlation function to study thermal transport in the one-dimensional Fermi-Pasta-Ulam-β lattice with both nearest-neighbor and next-nearest-neighbor couplings. We find that such a system bears a peculiar phonon dispersion relation, and thus there exists a competition between phonon dispersion and nonlinearity that can strongly affect the heat correlation function's shape and scaling property. Specifically, for small and large anharmoncities, the scaling laws are ballistic and superdiffusive types, respectively, which are in good agreement with the recent theoretical predictions; whereas in the intermediate range of the nonlinearity, we observe an unusual multiscaling property characterized by a nonmonotonic delocalization process of the central peak of the heat correlation function. To understand these multiscaling laws, we also examine the momentum perturbation correlation function and find a transition process with the same turning point of the anharmonicity as that shown in the heat correlation function. This suggests coupling between the momentum transport and the heat transport, in agreement with the theoretical arguments of mode cascade theory.
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Affiliation(s)
- Daxing Xiong
- Department of Physics, Fuzhou University, Fuzhou, 350108 Fujian, China
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13
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Xiong D. Anomalous temperature-dependent heat transport in one-dimensional momentum-conserving systems with soft-type interparticle interaction. Phys Rev E 2017; 95:042127. [PMID: 28505818 DOI: 10.1103/physreve.95.042127] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/12/2016] [Indexed: 06/07/2023]
Abstract
We numerically investigate the heat transport problem in a one-dimensional momentum-conserving lattice with a soft-type (ST) anharmonic interparticle interaction. It is found that with the increase of the system's temperature, while the introduction of ST anharmonicity softens phonons and decreases their velocities, this type of nonlinearity like its hard type (HT) counterpart, can still not be able to fully damp the longest wavelength phonons. Therefore, a usual anomalous temperature dependence of heat transport with certain scaling properties similarly to those shown in the Fermi-Pasta-Ulam-β-like systems with HT interactions can be seen. Our detailed examination from simulations verifies this temperature-dependent behavior well.
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Affiliation(s)
- Daxing Xiong
- Department of Physics, Fuzhou University, Fuzhou 350108, Fujian, China
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14
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Romero-Bastida M, Miranda-Peña JO, López JM. Thermal rectification in mass-graded next-nearest-neighbor Fermi-Pasta-Ulam lattices. Phys Rev E 2017; 95:032146. [PMID: 28415322 DOI: 10.1103/physreve.95.032146] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/12/2016] [Indexed: 06/07/2023]
Abstract
We study the thermal rectification efficiency, i.e., quantification of asymmetric heat flow, of a one-dimensional mass-graded anharmonic oscillator Fermi-Pasta-Ulam lattice both with nearest-neighbor (NN) and next-nearest-neighbor (NNN) interactions. The system presents a maximum rectification efficiency for a very precise value of the parameter that controls the coupling strength of the NNN interactions, which also optimizes the rectification figure when its dependence on mass asymmetry and temperature differences is considered. The origin of the enhanced rectification is the asymmetric local heat flow response as the heat reservoirs are swapped when a finely tuned NNN contribution is taken into account. A simple theoretical analysis gives an estimate of the optimal NNN coupling in excellent agreement with our simulation results.
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Affiliation(s)
- M Romero-Bastida
- SEPI ESIME-Culhuacán, Instituto Politécnico Nacional, Av. Santa Ana No. 1000, Col. San Francisco Culhuacán, Delegación Coyoacan, Distrito Federal 04430, Mexico
| | - Jorge-Orlando Miranda-Peña
- SEPI ESIME-Culhuacán, Instituto Politécnico Nacional, Av. Santa Ana No. 1000, Col. San Francisco Culhuacán, Delegación Coyoacan, Distrito Federal 04430, Mexico
| | - Juan M López
- Instituto de Física de Cantabria (IFCA), CSIC-Universidad de Cantabria, E-39005 Santander, Spain
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15
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Zhou H, Zhang G, Wang JS, Zhang YW. Phonon transport in a one-dimensional harmonic chain with long-range interaction and mass disorder. Phys Rev E 2016; 94:052123. [PMID: 27967065 DOI: 10.1103/physreve.94.052123] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/05/2016] [Indexed: 11/07/2022]
Abstract
Atomic mass and interatomic interaction are the two key quantities that significantly affect the heat conduction carried by phonons. Here, we study the effects of long-range (LR) interatomic interaction and mass disorder on the phonon transport in a one-dimensional harmonic chain with up to 10^{5} atoms. We find that while LR interaction reduces the transmission of low-frequency phonons, it enhances the transmission of high-frequency phonons by suppressing the localization effects caused by mass disorder. Therefore, LR interaction is able to boost heat conductance in the high-temperature regime or in the large size regime, where the high-frequency modes are important.
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Affiliation(s)
- Hangbo Zhou
- Institute of High Performance Computing, A*STAR, 138632, Singapore
| | - Gang Zhang
- Institute of High Performance Computing, A*STAR, 138632, Singapore
| | - Jian-Sheng Wang
- Department of Physics, National University of Singapore, 117551, Singapore
| | - Yong-Wei Zhang
- Institute of High Performance Computing, A*STAR, 138632, Singapore
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16
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Hurtado PI, Garrido PL. A violation of universality in anomalous Fourier's law. Sci Rep 2016; 6:38823. [PMID: 27958318 PMCID: PMC5153844 DOI: 10.1038/srep38823] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2016] [Accepted: 11/15/2016] [Indexed: 12/04/2022] Open
Abstract
Since the discovery of long-time tails, it has been clear that Fourier's law in low dimensions is typically anomalous, with a size-dependent heat conductivity, though the nature of the anomaly remains puzzling. The conventional wisdom, supported by renormalization-group arguments and mode-coupling approximations within fluctuating hydrodynamics, is that the anomaly is universal in 1d momentum-conserving systems and belongs in the Lévy/Kardar-Parisi-Zhang universality class. Here we challenge this picture by using a novel scaling method to show unambiguously that universality breaks down in the paradigmatic 1d diatomic hard-point fluid. Hydrodynamic profiles for a broad set of gradients, densities and sizes all collapse onto an universal master curve, showing that (anomalous) Fourier's law holds even deep into the nonlinear regime. This allows to solve the macroscopic transport problem for this model, a solution which compares flawlessly with data and, interestingly, implies the existence of a bound on the heat current in terms of pressure. These results question the renormalization-group and mode-coupling universality predictions for anomalous Fourier's law in 1d, offering a new perspective on transport in low dimensions.
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Affiliation(s)
- Pablo I. Hurtado
- Institute Carlos I for Theoretical and Computational Physics and Departamento de Electromagnetismo y Física de la Materia, Universidad de Granada, 18071 Granada, Spain
| | - Pedro L. Garrido
- Institute Carlos I for Theoretical and Computational Physics and Departamento de Electromagnetismo y Física de la Materia, Universidad de Granada, 18071 Granada, Spain
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17
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Gao Z, Li N, Li B. Stretch diffusion and heat conduction in one-dimensional nonlinear lattices. Phys Rev E 2016; 93:032130. [PMID: 27078315 DOI: 10.1103/physreve.93.032130] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/23/2015] [Indexed: 06/05/2023]
Abstract
For heat conduction in one-dimensional (1D) nonlinear Hamiltonian lattices, it has been known that conserved quantities play an important role in determining the actual heat conduction behavior. In closed or microcanonical Hamiltonian systems, the total energy and stretch are always conserved. Depending on the existence of external on-site potential, the total momentum can be conserved or not. All the momentum-conserving lattices have anomalous heat conduction except the 1D coupled rotator lattice. It was recently claimed that "whenever stretch (momentum) is not conserved in a 1D model, the momentum (stretch) and energy fields exhibit normal diffusion." The stretch in a coupled rotator lattice was also argued to be nonconserved due to the requirement of a finite partition function, which enables the coupled rotator lattice to fulfill this claim. In this work, we will systematically investigate stretch diffusion and heat conduction in terms of energy diffusion for typical 1D nonlinear lattices. Contrary to what was claimed, no clear connection between conserved quantities and heat conduction can be established. The actual situation might be more complicated than what was proposed.
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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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18
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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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Yang L, Li N, Li B. Temperature-dependent thermal conductivities of one-dimensional nonlinear Klein-Gordon lattices with a soft on-site potential. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:062122. [PMID: 25615059 DOI: 10.1103/physreve.90.062122] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/19/2014] [Indexed: 06/04/2023]
Abstract
The temperature-dependent thermal conductivities of one-dimensional nonlinear Klein-Gordon lattices with soft on-site potential (soft-KG) are investigated systematically. Similarly to the previously studied hard-KG lattices, the existence of renormalized phonons is also confirmed in soft-KG lattices. In particular, the temperature dependence of the renormalized phonon frequency predicted by a classical field theory is verified by detailed numerical simulations. However, the thermal conductivities of soft-KG lattices exhibit the opposite trend in temperature dependence in comparison with those of hard-KG lattices. The interesting thing is that the temperature-dependent thermal conductivities of both soft- and hard-KG lattices can be interpreted in the same framework of effective phonon theory. According to the effective phonon theory, the exponents of the power-law dependence of the thermal conductivities as a function of temperature are only determined by the exponents of the soft or hard on-site potentials. These theoretical predictions are consistently verified very well by extensive numerical simulations.
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Affiliation(s)
- Linlin Yang
- 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
- Center for Phononics and Thermal Energy Science, School of Physics Science and Engineering, Tongji University, 200092 Shanghai, People's Republic of China and Department of Physics and Centre for Computational Science and Engineering, National University of Singapore, Singapore 117546, Republic of Singapore and NUS Graduate School for Integrative Sciences and Engineering, Singapore 117456, Republic of Singapore
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Xiong D, Zhang Y, Zhao H. Temperature dependence of heat conduction in the Fermi-Pasta-Ulam-β lattice with next-nearest-neighbor coupling. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:022117. [PMID: 25215699 DOI: 10.1103/physreve.90.022117] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2013] [Indexed: 06/03/2023]
Abstract
We show numerically that introducing the next-nearest-neighbor interactions (of appropriate strength) into the one-dimensional (1D) Fermi-Pasta-Ulam-β (FPU-β) lattice can result in an unusual, nonmonotonic temperature dependent divergence behavior in a wide temperature range, which is in clear contrast to the universal divergence manner independent of temperature as suggested previously in the conventional 1D FPU-β models with nearest-neighbor (NN) coupling only. We also discuss the underlying mechanism of this finding by analyzing the temperature variations of the properties of discrete breathers, especially that with frequencies having the intraband components. The results may provide useful information for establishing the connection between the macroscopic heat transport properties and the underlying dynamics in general 1D systems with interactions beyond NN couplings.
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Affiliation(s)
- Daxing Xiong
- Department of Physics, Fuzhou University, Fuzhou 350002, Fujian, China
| | - Yong Zhang
- Department of Physics and Institute of Theoretical Physics and Astrophysics, Xiamen University, Xiamen 361005, Fujian, China
| | - Hong Zhao
- Department of Physics and Institute of Theoretical Physics and Astrophysics, Xiamen University, Xiamen 361005, Fujian, China
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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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Xiong D, Zhang Y, Zhao H. Heat transport enhanced by optical phonons in one-dimensional anharmonic lattices with alternating bonds. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:052128. [PMID: 24329235 DOI: 10.1103/physreve.88.052128] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/20/2013] [Indexed: 06/03/2023]
Abstract
In lattice systems, the effects of optical phonons on heat transport are usually neglected due to their relatively small group velocities compared with acoustic phonons, or even assumed to be negative because introducing optical phonons may simultaneously reduce the group velocities of acoustic phonons. In order to well understand the role played by optical phonons, we propose a one-dimensional anharmonic lattice model with alternating interactions, where the optical phonons can be conveniently tuned. We find that in contrast to previous studies, the optical phonons (in coordination with the nonlinearities) can enhance heat transport in the thermodynamical limit, suggesting that optical phonons can also play an active role. The underlying mechanism is related to the effects of two kinds of nonlinear excitations, i.e., the optical and the gap discrete breathers (DBs). These DBs release energy and in turn facilitate heat transport.
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Affiliation(s)
- Daxing Xiong
- Department of Physics, Fuzhou University, Fuzhou 350002, Fujian, China
| | - Yong Zhang
- Department of Physics and Institute of Theoretical Physics and Astrophysics, Xiamen University, Xiamen 361005, Fujian, China
| | - Hong Zhao
- Department of Physics and Institute of Theoretical Physics and Astrophysics, Xiamen University, Xiamen 361005, Fujian, China
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