Understanding the transport of particles immersed in a carrier fluid (bedload transport) is still an exciting challenge. Among the different types of gas-solid flows, when the dynamics of solid particles is essentially dominated by collisions between them, kinetic theory can be considered as a reliable tool to derive continuum approaches from a fundamental point of view. In a recent paper, Chassagne et al. [J. Fluid Mech. 964, A27, (2023)] have proposed a two-fluid model based on modifications to a classical kinetic theory model. First, in contrast to the classical model, the model proposed by Chassagne et al. (2023) takes into account the interparticle friction not only in the radial distribution function but also through an effective restitution coefficient in the rate of dissipation term of granular temperature. As a second modification, at the top of the bed where the volume fraction is quite small, the model accounts for the saltation regime in the continuum framework. The theoretical results derived from the model agree with discrete simulations for moderate and high densities and they are also consistent with experiments. Thus, the model proposed by Chassagne et al. (2023) helps to a better understanding on the combined impact of friction and inelasticity on the macroscopic properties of granular flows.
Abstract We explain the ‘phases’ of a Frenkel–Kontorova chain of atoms in a different way to the commented article. We reject the decision of states of the chain into commensurate and incommensurate states introduced by Aubry.
Abstract We introduce a minimalist dynamical model of wealth evolution and wealth sharing among N agents as a platform to compare the relative merits of altruism and individualism. In our model, the wealth of each agent independently evolves by diffusion. For a population of altruists, whenever any agent reaches zero wealth (that is, the agent goes bankrupt), the remaining wealth of the other N − 1 agents is equally shared among all. The population is collectively defined to be bankrupt when its total wealth falls below a specified small threshold value. For individualists, each time an agent goes bankrupt (s)he is considered to be ‘dead’ and no wealth redistribution occurs. We determine the evolution of wealth in these two societies. Altruism leads to more global median wealth at early times; eventually, however, the longest-lived individualists accumulate most of the wealth and are richer and more long lived than the altruists.
We determine the asymptotic forms of work distributions at arbitrary times $T$, in a class of driven stochastic systems using a theory developed by Engel and Nickelsen (EN theory) (arXiv:1102.4505v1 [cond-mat.stat-mech]), which is based on the contraction principle of large deviation theory. In this paper, we extend the theory, previously applied in the context of deterministically driven systems, to a model in which the driving is stochastic. The models we study are described by overdamped Langevin equations and the work distributions in the path integral form, are characterised by having quadratic actions. We first illustrate EN theory, for a deterministically driven system - the breathing parabola model, and show that within its framework, the Crooks flucutation theorem manifests itself as a reflection symmetry property of a certain characteristic polynomial function. We then extend our analysis to a stochastically driven system, studied in ( arXiv:1212.0704v2 [cond-mat.stat-mech], arXiv:1402.5777v1 [cond-mat.stat-mech]) using a moment-generating-function method, for both equilibrium and non - equilibrium steady state initial distributions. In both cases we obtain new analytic solutions for the asymptotic forms of (dissipated) work distributions at arbitrary $T$. For dissipated work in the steady state, we compare the large $T$ asymptotic behaviour of our solution to that already obtained in ( arXiv:1402.5777v1 [cond-mat.stat-mech]). In all cases, special emphasis is placed on the computation of the pre-exponential factor and the results show excellent agreement with the numerical simulations. Our solutions are exact in the low noise limit.