Length dependence of heat conduction in (an)harmonic chains with asymmetries or long range interparticle interactions

Ávila, Ricardo; Pereira, Emmanuel; Teixeira, Daniel

doi:10.1016/j.physa.2014.12.018

Cited by 18 publications

(22 citation statements)

References 34 publications

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“…Heat transport in long-range models exhibits quite interesting and peculiar features, that depend on the nature of the interaction potential. The comparison between the rotor chain and the FPU-β chain confirms this scenario, that was already outlined in some recent pubblications [5][6][7]. In this paper we have shown that in the non-additive regime corresponding to 0 < α < 1 the mechanism of heat transport is dominated by the direct, mean-field like contribution, irrespectively of the kind of the interaction potential.…”

Section: Discussionsupporting

confidence: 86%

“…What should we expect when two or more external reservoirs drive a long-range interacting system in out-ofequilibrium conditions? Some peculiar features, pointed out in a recent paper by Avila et al [5] have been confirmed and more systematically investigated in a longrange coupled rotor chain [6]. This model is quite interesting, because for nearest-neighbor (i.e.…”

Section: Introductionsupporting

confidence: 54%

“…In the inset of Fig. 6 we can observe that for model (5) with α = 2 the temperature profile deviates more from flatness the larger the system size N . On the basis of this observation, we can just argue that finite size effects are playing a dominant role in this case.…”

Section: The Fpu Chainmentioning

confidence: 90%

“…Here we extend our study of heat transport in longrange models to the FPU-β chain, whose interaction potential is given in Eq. (5). We report just the main results, without going through a detailed description as for the rotor chain.…”

Section: The Fpu Chainmentioning

confidence: 99%

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Heat transport in oscillator chains with long-range interactions coupled to thermal reservoirs

et al. 2018

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We investigate thermal conduction in arrays of long-range interacting rotors and Fermi-Pasta-Ulam (FPU) oscillators coupled to two reservoirs at different temperatures. The strength of the interaction between two lattice sites decays as a power α of the inverse of their distance. We point out the necessity of distinguishing between energy flows towards or from the reservoirs and those within the system. We show that energy flow between the reservoirs occurs via a direct transfer induced by long-range couplings and a diffusive process through the chain. To this aim, we introduce a decomposition of the steady-state heat current that explicitly accounts for such direct transfer of energy between the reservoir. For 0≤α<1, the direct transfer term dominates, meaning that the system can be effectively described as a set of oscillators each interacting with the thermal baths. Also, the heat current exchanged with the reservoirs depends on the size of the thermalized regions: In the case in which such size is proportional to the system size N, the stationary current is independent on N. For α>1, heat transport mostly occurs through diffusion along the chain: For the rotors transport is normal, while for FPU the data are compatible with an anomalous diffusion, possibly with an α-dependent characteristic exponent.

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Section: Discussionsupporting

confidence: 86%

Section: Introductionsupporting

confidence: 54%

Section: The Fpu Chainmentioning

confidence: 90%

Section: The Fpu Chainmentioning

confidence: 99%

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Heat transport in oscillator chains with long-range interactions coupled to thermal reservoirs

et al. 2018

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“…A discussão sobre algumas propriedades do Capítulo 3. O papel das correlações entre as velocidades nos perfis de temperatura do sistema 49 fluxo de calor em cadeias não lineares possui uma vasta literatura associada a resultados obtidos via simulação numérica [25,26,[66][67][68], enquanto o tratamento analítico para este tipo de modeloé abordado por poucos autores [69][70][71]. Para ilustrar um dos impactos das não linearidades sobre o sistema original, mostra-se na figura 3.8 o que ocorre com as correlações entre as velocidades quando introduz-se um termo cúbico de interação entre as partículas.…”

Section: Figura 22unclassified

Problemas Em Condutividade Térmica Em Cadeias Harmônicas E Anarmônicas

CANDIDO¹

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AgradecimentosGostaria de fazer uma homenagem em primeiro lugarà minha avó, Maria de Lourdes, que me ensinou sobre a importância do estudo na vida de uma pessoa. Nada do que fiz até hoje noâmbito acadêmico seria possível se não fosse o apoio de minha avó.Ao meu orientador Welles Morgado, por todos os conselhos e ensinamentos passados ao longo dos anos de doutorado. Obrigado também pela confiança depositada no meu trabalho e paciência demonstrada nas inúmeras conversas onde eu aparecia com uma enxurrada de dúvidas em sua sala.Ao meu co-orientador Sílvio Queirós, pela extrema dedicação em nosso projeto. Reuniões no CBPF seguidas por fatias de cheesecake, discussões via Skype, troca de emails durante madrugadas, enfim, só me resta agradecer por todo o suporte que me foi dado.Aos meus amigos do IF-UFRJ, de Melo, que me acompanham na minha trajetória na física desde o princípio. Muito obrigado pela amizade de vocês! Aos meus amigos da PUC-Rio Carlos Olivares, Eduardo Colombo, Júlio Nicolini e Lucianno Defaveri, que me acompanharam durante esta jornada sempre me dando o apoio necessário.A minha noiva e futura esposa, Karen, por todas as ocasiões que tivemos que nos privar de momentos de diversão para que eu pudesse trabalhar. Obrigado pela sua compreensão, seu amor e companheirismo incondicionais :).Gostaria de agradecer as minhas tias Carla e Mariana, e a minha irmã Esther, minhas amigas de toda vida, que sempre estiveram ao meu lado me dando apoio.Aos meus pais, Paula e Márcio, por tudo que fizeram por mim ao longo da minha vida. Obrigado por sempre acreditarem em mim e pela motivação que vocês me dão em qualquer circunstância.Ao CNPq pelos auxílios concedidos, sem os quais este trabalho não poderia ter sido realizado. AbstractCândido, Michael Moraes; Martinez Morgado, Welles Antonio (advisor); Duarte Queirós, Sílvio Manuel. Problems in thermal conductivity for harmonic and anharmonic chains. Rio de Janeiro, 2017. 109p. Tese de Doutorado -Departamento de Física, Pontifícia Universidade Católica do Rio de Janeiro.In the present work I make an analysis about statistical quantities for linear and nonlinear chains in the stationary state. We start the discussion from a general linear model, with arbitrary couplings and connected to Gaussian reservoirs. A detailed analysis for quantities like heat flow and site temperatures is obtained, where all analytical expressions respective to those quantities are derived and a compared with numerical results. Then I study the quantitative and qualitative changes presented by the aforementioned quantities when the pinnings related to the reservoirs are modified. The changes in temperature profiles are related with the extrema of heat flux cumulants, motivating the investigation of whether phase transitions in the chain might occur. In order to investigate possible critical behaviors, I define velocity correlation functions between pair particles and squared velocities correlation functions. From where, one is able to estabilish a correlation length respective to these quantities. Th...

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Nonequilibrium Phenomena in Nonlinear Lattices: From Slow Relaxation to Anomalous Transport

Iubini¹,

Lepri²,

Livi³

et al. 2020

Nonlinear Systems and Complexity

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Length dependence of heat conduction in (an)harmonic chains with asymmetries or long range interparticle interactions

Cited by 18 publications

References 34 publications

Heat transport in oscillator chains with long-range interactions coupled to thermal reservoirs

Heat transport in oscillator chains with long-range interactions coupled to thermal reservoirs

Problemas Em Condutividade Térmica Em Cadeias Harmônicas E Anarmônicas

Nonequilibrium Phenomena in Nonlinear Lattices: From Slow Relaxation to Anomalous Transport

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