Eliminating the Cuspidal Temperature Profile of a Non-equilibrium Chain

Cândido, Michael M.; Morgado, Welles A. M.; Queirós, Sı́lvio M. Duarte

doi:10.1007/s13538-017-0494-z

Cited by 6 publications

(5 citation statements)

References 36 publications

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“…These boundary jumps represent the resistance offered to the heat transport due to the scattering of energy at the boundaries [21] and are not merely simulation effects. For F P U C chains, the boundary resistance is smaller because the collisions between the end thermostatted particles and the fixed boundary particles create an extra "pinning" effect [22]. Note that such reductions have been observed in collid-ing Φ 4 chains as well [8].…”

Section: Boundary Jumpsmentioning

confidence: 98%

Thermal transport characteristics of Fermi-Pasta-Ulam chains undergoing soft-sphere type collisions

Bhattacharyya¹,

Patra²

2020

Preprint

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We show numerically that including soft-sphere type collisions in the celebrated Fermi-Pasta-Ulam (F P U ) chain completely alters the thermal transport characteristics. The resulting F P U C chains, while being momentum preserving, satisfy the Fourier's law and do not show anomalous thermal transport behavior. Collisions play a significant role in reducing the boundary jumps typically observed in F P U chains. The thermal conductivity of the F P U C chains is significantly smaller than the F P U chains at low temperatures due to the fast redistribution of energy from the lowest mode of vibrations to the higher modes. At high temperatures, however, the F P U C chains have larger thermal conductivity than the F P U chains due to the large contributions to the heat flux because of the large-magnitude short-ranged anharmonic collision force.

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Section: Boundary Jumpsmentioning

confidence: 98%

Thermal transport characteristics of Fermi-Pasta-Ulam chains undergoing soft-sphere type collisions

Bhattacharyya¹,

Patra²

2020

Preprint

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“…They showed that the temperature is approximately flat in the bulk of the chain (with deviations at the extremities [17]), with value (T L + T R )/2, instead of the linear temperature profile we would expect from Fourier's law (see figure 1.5). They also proved that the heat current in the chain is proportional to the temperature difference between both heat baths J ∝ (T L − T R ), instead of the temperature gradient, as in section 1.1, and hence κ ∝ N (diverging in the thermodynamic limit N → ∞).…”

Section: Thermal Conductivity Of Solidsmentioning

confidence: 98%

A Study on Thermal Conduction and Rectification

ALMEIDA¹

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It is a known result in the literature that a one-dimensional chain of particles that interact harmonically with its first neighbors does not conduct heat, and nonlinear forces are needed to reproduce Fourier's law of heat conduction. When asymmetries are introduced in such a conducting system, a rectifying effect is obtained where the thermal current shows different magnitudes depending on which side of the chain has higher temperature, such devices being called thermal diodes. In this work we study both phenomena, heat conduction and thermal rectification, in a onedimensional chain of particles, with fixed boundary conditions, coupled to two thermal baths, one at each end, modeled as Langevin thermostats.The particles interact with their first neighbors harmonically and have a nonlinear on-site potential, for which we study two types, Frenkel-Kontorova and φ 4 potentials. We verify that, for both cases, Fourier's law is observed, where the temperature profile and the thermal conductivity are dependent on the relation between the harmonic and anharmonic amplitudes, and the system's average temperature. Next, to create an asymmetry in the chain, we coupled two different segments of equal lengths. We observed a rectifying effect, where the preferential direction differs for each of the two on-site potentials studied. How the heat-bath temperatures changes the magnitude of rectification was also observed. We also investigated the effect of interfacial nonlinearities through a power-law potential, coupling φ 4 segments. By changing the power-law exponent, we looked for the conditions under which optimal rectification is achieved.

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“…Adotando esta mudança, nota-se que as cúspides próximasàs extremidades vão se tornando mais suaves conforme o parâmetro de ancoragem de volume aumenta. As cúspides são eliminadas do perfil de temperaturas quando os acoplamentos atingem o limiar [62]: Capítulo 3. O papel das correlações entre as velocidades nos perfis de temperatura do sistema 39…”

Section: Figura 22unclassified

“…O papel das correlações entre as velocidades nos perfis de temperatura do sistema 41 k 1 ą k 1 crit 1 as cúspides voltam a surgir no sistema, mostrando que a presença da ancoragem de volumeé um fator necessário mas não suficiente para que o sistema não exiba tal característica em seu perfil de temperatura. O perfil semelhante ao modelo RLLé apresentado para todos os valores de k 1 inferiores a[62] de temperaturas bem suave próximoàs extremidades, marcando assim mais uma mudança de comportamento das partículas medianteà mudança de k 1 . A partir de então, para um crescimento contínuo do acoplamento das extremidades, nota-se que tal mudança tende a isolar as partículas 1 e N do restante da cadeia, de forma que o volume do sistema passa a interagir praticamente com si próprio, criando assim a caixa de fônons já descrita anteriormente.…”

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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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Eliminating the Cuspidal Temperature Profile of a Non-equilibrium Chain

Cited by 6 publications

References 36 publications

Thermal transport characteristics of Fermi-Pasta-Ulam chains undergoing soft-sphere type collisions

Thermal transport characteristics of Fermi-Pasta-Ulam chains undergoing soft-sphere type collisions

A Study on Thermal Conduction and Rectification

Problemas Em Condutividade Térmica Em Cadeias Harmônicas E Anarmônicas

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