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We review evolutionary models on quantum graphs expressed by linear and nonlinear partial differential equations. Existence and stability of the standing waves trapped on quantum graphs are studied by using methods of the variational…
Granular flows in a narrow pipe are studied numerically by the model taking account of hydrodynamic effects of fluid surrounding particles. In the simulations density waves are observed over the wide range of the Stokes number, which…
Understanding how statistical equilibrium can occur in out-of-equilibrium systems is of paramount interest, as it would enable the use of statistical mechanics tools to these systems. Here, we report the first experimental evidence of…
The thermodynamic stability of the hard-sphere gas has been examined, using the formalism of scaled particle theory [SPT], and by applying explicitly the conditions of stability required by both the second and third laws of thermodynamics.…
We prove limit theorems for systems of interacting diffusions on sparse graphs. For example, we deduce a hydrodynamic limit and the propagation of chaos property for the stochastic Kuramoto model with interactions determined by…
For a gas confined in a container, particle-wall interactions produce modifications to the partition function involving the average surface density of gas particles. While such correlations have a vanishing effect in the thermodynamic…
We derive linear fluctuating hydrodynamics as the low density limit of a deterministic system of particles at equilibrium. The proof builds upon previous results of the authors where the asymptotics of the covariance of the fluctuation…
We present a graph theory-based method to characterise flow defects and structural shifts in condensed matter. We explore the connection between dynamical properties, particularly the recently introduced concept of ''softness'', and…
The problem of interest in this article are waves on a layer of finite depth governed by the Euler equations in the presence of gravity, surface tension, and vertical electric fields. Perturbation theory is used to identify canonical…
For interacting particle systems that satisfies the gradient condition, the hydrodynamic limit and the equilibrium fluctuations are well known. We prove that under the presence of a symmetric random environment, these scaling limits also…
We derive the hydrodynamic limit of a kinetic equation with a stochastic, short range perturbation of the velocity operator. Under some mixing hypotheses on the stochastic perturbation, we establish a diffusion-approximation result: the…
We present a method for two-scale model derivation of the periodic homogenization of the one-dimensional wave equation in a bounded domain. It allows for analyzing the oscillations occurring on both microscopic and macroscopic scales. The…
Hydrodynamic forces acting on a neutrally-buoyant spherical particle immersed in a wall-bounded axisymmetric stagnation point flow (Hiemenz-Homann flow) are predicted, based on a suitable form of the reciprocal theorem. An approximate…
The velocity of a passive particle in a one-dimensional wave field is shown to converge in law to a Wiener process, in the limit of a dense wave spectrum with independent complex amplitudes, where the random phases distribution is invariant…
Expectation value of dynamical variables in thermodynamically equilibrium state can be typically provided through well-known canonical average. The average includes tremendous number of possible states considered far beyond practically…
Exact expressions for all the steady-state fields (E, H, D, B) in uniaxial linear media composed of an arbitrary number of layers having arbitrary thicknesses subjected to normal incidence are derived. Generic boundary condition relations…
We study an interacting particle system in $\mathbf{R}^d$ motivated by Stein variational gradient descent [Q. Liu and D. Wang, NIPS 2016], a deterministic algorithm for sampling from a given probability density with unknown normalization.…
The fractional diffusion equation is rigorously derived as a scaling limit from a deterministic Rayleigh gas, where particles interact via short range potentials with support of size $\varepsilon$ and the background is distributed in space…
Here we present the entropic dynamics formalism for networks. That is, a framework for the dynamics of graphs meant to represent a network derived from the principle of maximum entropy and the rate of transition is obtained taking into…
A new variational method for studying the equilibrium states of an interacting particles system has been proposed. The statistical description of the system is realized by means of a density matrix. This method is used for description of…