Anomalous dynamical scaling in anharmonic chains and plasma models with multiparticle collisions

Cintio, Pierfrancesco Di; Livi, Roberto; Bufferand, Hugo; Ciraolo, Guido; Lepri, Stefano; Straka, Mika J.

doi:10.1103/physreve.92.062108

Cited by 20 publications

(30 citation statements)

References 74 publications

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“…Anyway, a good deal of numerical studies have paved the path of most of these achievements and still allow us to obtain inference about many still open problems, like the way anomalous behaviors depend on the kind of nonlinearity [12,13,14], dimension (e.g. 1 or 2D) [15], disorder and the kind of the interaction (e.g., short-or long-range; deterministic or stochastic) [16,17].…”

Section: Introductionmentioning

confidence: 99%

Transport in perturbed classical integrable systems: The pinned Toda chain

Cintio

Iubini

Lepri

et al. 2018

Chaos, Solitons & Fractals

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Nonequilibrium and thermal transport properties of the Toda chain, a prototype of classically integrable system, subject to additional (nonintegrable) terms are considered. In particular, we study via equilibrium and nonequilibrium simulations, the Toda lattice with a power-law pinning potential, recently analyzed by Lebowitz and Scaramazza [arXiv:1801.07153]. We show that, according to general expectations, even the case with quadratic pinning is genuinely non-integrable, as demonstrated by computing the Lyapunov exponents, and displays normal (diffusive) conductivity for very long chains. However, the model has unexpected dynamical features and displays strong finite-size effects and slow decay of correlations to be traced back to the propagation of soliton-like excitations, weakly affected by the harmonic pinning potential. Some novel results on current correlations for the standard integrable Toda model are also reported.

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Section: Introductionmentioning

confidence: 99%

Transport in perturbed classical integrable systems: The pinned Toda chain

Cintio

Iubini

Lepri

et al. 2018

Chaos, Solitons & Fractals

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“…In the case of the one-dimensional fluid we are interested in, the above steps can be carried on as follows [21]. Let us denote by m j and v j the mass and velocity of the j-th particle and by N i and the instantaneous number of particles inside each cell i on which the system is coarse grained.…”

Section: Multi-particle-collision Methodsmentioning

confidence: 99%

Collisional Relaxation and Dynamical Scaling in Multiparticle Collisions Dynamics

Lepri¹,

Bufferand²,

Ciraolo³

et al. 2019

Springer Proceedings in Mathematics &Amp; Statistics

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We present the Multi-Particle-Collision (MPC) dynamics approach to simulate properties of low-dimensional systems. In particular, we illustrate the method for a simple model: a one-dimensional gas of point particles interacting through stochastic collisions and admitting three conservation laws (density, momentum and energy). Motivated from problems in fusion plasma physics, we consider an energy-dependent collision rate that accounts for the lower collisionality of high-energy particles. We study two problems: (i) the collisional relaxation to equilibrium starting from an off-equilibrium state and (ii) the anomalous dynamical scaling of equilibrium time-dependent correlation functions. For problem (i), we demonstrate the existence of long-lived population of suprathermal particles that propagate ballistically over a quasi-thermalized background. For (ii) we compare simulations with the predictions of nonlinear fluctuating hydrodynamics for the structure factors of density fluctuations. Scaling analysis confirms the prediction that such model belong to the Kardar-Parisi-Zhang universality class.

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“…In one dimension, the multi-particle collision instead involves a velocity sign inversion with a momentum shift (see also Ref. 24), and the two conserved quantities are the linear momentum P i and the kinetic energy K i . During the collision step, the stochastic momentum shifts w j are extracted for each particle from a normal distribution depending on the cell temperature so that the conservation of P i and K i now reads…”

Section: Multi-particle Collision Methodsmentioning

confidence: 99%

“…In one dimension, the multi‐particle collision instead involves a velocity sign inversion with a momentum shift (see also Ref. ), and the two conserved quantities are the linear momentum P i and the kinetic energy K i . During the collision step, the stochastic momentum shifts w j are extracted for each particle from a normal distribution depending on the cell temperature so that the conservation of P i and K i now reads

\begin{matrix} lefttrue \\ right P_{i} & center = & left {false\sum}_{j = 1}^{N_{i}} m_{j} v_{j} = {false\sum}_{j = 1}^{N_{i}} m_{j} v_{j}^{'} = {false\sum}_{j = 1}^{N_{i}} (c_{i} w_{j} + d_{i} m_{j}); \\ right K_{i} & center = & left \frac{1}{2} {false\sum}_{j = 1}^{N_{i}} m_{j} v_{j}^{2} = \frac{1}{2} {false\sum}_{j = 1}^{N_{i}} m_{j} v_{j}^{' 2} = \frac{1}{2} {false\sum}_{j = 1}^{N_{i}} m_{j} {((), c_{i} w_{j} false/ m_{j} + d_{i})}^{2}, \end{matrix}

where N i is the number of particles in cell i ; m j and v j are the j ‐th particles mass and velocity, respectively; and c i and d i are unknown cell‐dependent quantities, respectively.…”

Section: Kinetic Modelling Of Heat Transfermentioning

confidence: 99%

“…In a series of papers on the anomalous diffusion and heat transfer in 1D one‐component plasmas, we have applied a hybrid PIC‐MPC technique where velocity exchange inside the cells is conditioned to an interaction probability

P_{i}

dependent on the local plasma parameters in order to account for Coulomb collisions in a more physical way and also to treat spatially and thermally inhomogeneous systems.…”

Section: Kinetic Modelling Of Heat Transfermentioning

confidence: 99%

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Fluid and kinetic modelling for non‐local heat transport in magnetic fusion devices

Ciraolo

Bufferand

Cintio

et al. 2018

Contributions to Plasma Physics

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In order to improve the presently used ad hoc flux limiter treatment of parallel heat flux transport in edge plasma fluid codes, here, we consider a generalized version of the Fourier law implementing a non‐local kernel for the heat flux computation. The Bohm boundary condition at the wall is recovered, introducing a volumetric loss term representing the contribution of suprathermal particles to the energy out flux. As expected, this contribution is negligible in the strongly collisional regime, while it becomes more and more dominant for marginally and low‐collisional regimes. In the second part of the paper, we consider a kinetic approach where collisions are considered using the multi‐particle collision algorithm. Kinetic simulation results at medium and low collisionality are also reported.

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Anomalous dynamical scaling in anharmonic chains and plasma models with multiparticle collisions

Cited by 20 publications

References 74 publications

Transport in perturbed classical integrable systems: The pinned Toda chain

Transport in perturbed classical integrable systems: The pinned Toda chain

Collisional Relaxation and Dynamical Scaling in Multiparticle Collisions Dynamics

Fluid and kinetic modelling for non‐local heat transport in magnetic fusion devices

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