Dynamical Heat Channels

Денисов, С. В.; Klafter, J.; Urbakh, Michael

doi:10.1103/physrevlett.91.194301

Cited by 103 publications

(120 citation statements)

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“…As a consequence, (3) should be replaced by equations like (21), meaning that hydrodynamic fluctuations must be described by generalized Langevin equation with power-law memory [32,33]. This provides a sound basis for the connection between anomalous transport and kinetics (superdiffusion in this case) [34].…”

Section: Discussionmentioning

confidence: 99%

Anomalous kinetics and transport from 1D self-consistent mode-coupling theory

et al. 2007

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Abstract. We study the dynamics of long-wavelength fluctuations in onedimensional (1D) many-particle systems as described by self-consistent modecoupling theory. The corresponding nonlinear integro-differential equations for the relevant correlators are solved analytically and checked numerically. In particular, we find that the memory functions exhibit a power-law decay accompanied by relatively fast oscillations. Furthermore, the scaling behaviour and, correspondingly, the universality class depends on the order of the leading nonlinear term. In the cubic case, both viscosity and thermal conductivity diverge in the thermodynamic limit. In the quartic case, a faster decay of the memory functions leads to a finite viscosity, while thermal conductivity exhibits an even faster divergence. Finally, our analysis puts on a more firm basis the previously conjectured connection between anomalous heat conductivity and anomalous diffusion.

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Section: Discussionmentioning

confidence: 99%

Anomalous kinetics and transport from 1D self-consistent mode-coupling theory

et al. 2007

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“…Just to give an idea of the possible applications, we explicitly mention only some important results, e.g. the subdiffusive charge transport in amorphous semiconductors (Scher, Montroll 1975), the anomalous diffusion properties of heat channels (Denisov et al 2003), the chemical reaction processes in high-k dielectric films (de Almeida, Baumvol 2003), the motion of DNA-binding proteins along the DNA structure (Slutsky et al 2003), the waiting time between two financial transactions (Mainardi et al 2000), the contaminant transport in geological formations (Kosakowski 2004). Here we focus on this last subject: the underground migration of contaminants driven by the subsurface water flow, where the medium heterogeneities over many scales and the trapping of the contaminant particles in the solid environment support the occurrence of subdiffusion phenomena.…”

Section: Introductionmentioning

confidence: 99%

The Monte Carlo and fractional kinetics approaches to the underground anomalous subdiffusion of contaminants

Marseguerra¹,

Zoia²

2006

Annals of Nuclear Energy

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It is nowadays recognized that the experimental evidences of many transport phenomena must be interpreted in the framework of the so-called anomalous diffusion: this is the case e.g. of the spread of contaminant particles in porous media, whose mean squared displacement (MSD) has been experimentally reported to grow in time as t α (with 0<α<2). This is in deep contrast with the linear increase which characterizes the standard Fickian diffusive processes. Anomalous transport is currently tackled within the Fractional Diffusion Equation (FDE) analytical model, which has blown new life into the concept of fractional derivatives, dormant since Leibniz's first discovery, about 300 years ago.In this paper we focus on subdiffusion, i.e. the case α<1, which provides a suitable explanation of the observed nonFickian persistence of the contaminant particles near the source in various transport experiences in heterogeneous media. Unfortunately, the FDE approach requires several approximations to overcome its analytical complexities. To evaluate the relevance of these approximations, we propound the use of the Monte Carlo simulation as a suitable reference for the analytical FDE results. This comparison shows that the FDE results are less and less reliable as α becomes closer to 1. The approach herein proposed can be easily applied to various fields of science where anomalous diffusion phenomena may occur, from physics and chemistry to biology and finance.

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“…The absence of interactions simplifies the task of understanding heat conductivity and allows, in particular, tracing back heat conductivity properties to the diffusion of single particles at equilibrium. Assuming that the mean square displacement x 2 (t) scales as t β (β = 1 corresponds to normal diffusion), it can be shown that α = β − 1 [11], under the assumption that each particle exchanges energy only at the channel borders, where thermal reservoirs operate. The limit of this approach is, on the one hand, that the relationship between the diffusion exponent β and the microscopic dynamics remains to be established [12] and, on the other hand, that particles do not mutually interact.…”

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confidence: 99%

From Anomalous Energy Diffusion to Levy Walks and Heat Conductivity in One-Dimensional Systems

Cipriani¹,

2005

Self Cite

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The evolution of infinitesimal, localized perturbations is investigated in a one-dimensional diatomic gas of hard-point particles (HPG) and thereby connected to energy diffusion. As a result, a Levy walk description, which was so far invoked to explain anomalous heat conductivity in the context of non-interacting particles is here shown to extend to the general case of truly many-body systems. Our approach does not only provide a firm evidence that energy diffusion is anomalous in the HPG, but proves definitely superior to direct methods for estimating the divergence rate of heat conductivity which turns out to be 0.333 ± 0.004, in perfect agreement with the dynamical renormalization-group prediction (1/3).PACS numbers: 44.10.+i,05.45.Jn, 05.70.Ln After the discovery of anomalous heat conductivity in classical one-dimensional lattice systems [1], in the last years a renewed attention has been devoted to the old problem of identifying the minimal ingredients required for the Fourier law to be ensured. As summarized in a recent review article [2], many different models have been numerically investigated to identify the physical conditions under which the thermal conductivity κ diverges with the system size L and, having assessed that κ ≈ L α , to determine the possibly different universality classes for the divergence rate α. Simultaneously, several attempts have been made to estimate analytically the scaling behaviour of κ: self-consistent mode-coupling theory [2] and the Boltzmann equation [3] suggest that α = 2/5, while dynamical renormalization group indicates α = 1/3 [4]. Both predictions are compatible with numerical simulations which are, however, often affected by relatively strong finite-size corrections. The only system where convincing results have been obtained is the Fermi, Pasta Ulam β-model in the infinite temperature limit. Its behaviour is consistent with α = 2/5 [5], but the simmetry of the potential casts doubts about the generality of this model [6]. A further simple system that can be effectively simulated on a computer is the diatomic hard-point gas: there, interactions are provided by elastic collisions of point-like particles [7]. Unfortunately, the most detailed numerical simulations reported in the literature show a slow growth of the divergence rate with L, so that some authors claim that α = 1/3 [8], while others state that the conservative guess α = 0.25 is more realistic [9]. Settling this issue is not only conceptually important, but it is a necessary requisite to later quantify finite-size corrections, a crucial issue in applications to, e.g., carbon nanotubes, where one needs to know the prefactor as well.Although the problem involves intrinsically many degrees of freedom, some researchers have tried to shed some light with reference to the simpler setup of noninteracting particles moving along a periodic array of convex scatterers (billiard gas channels) [10]. The absence of interactions simplifies the task of understanding heat conductivity and allows, in particular, tracing b...

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Dynamical Heat Channels

Cited by 103 publications

References 15 publications

Anomalous kinetics and transport from 1D self-consistent mode-coupling theory

Anomalous kinetics and transport from 1D self-consistent mode-coupling theory

The Monte Carlo and fractional kinetics approaches to the underground anomalous subdiffusion of contaminants

From Anomalous Energy Diffusion to Levy Walks and Heat Conductivity in One-Dimensional Systems

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