Related papers: Hyperuniformity and conservation laws in non-equil…
We study the condensation phenomenon for the invariant measures of the mean-field model of reversible coagulation-fragmentation processes conditioned to a supercritical density of particles. It is shown that when the parameters of the…
Self-sustained order can emerge in complex systems due to internal feedback between coupled subsystems. Here, we present our discovery of a non-monotonic emergence of order amidst chaos in a turbulent thermo-acoustic fluid system.…
Small thermodynamic systems exhibit peculiar behavior different from that observed in long-scale systems. Non-equilibrium processes taking place in those systems are strongly influenced by the presence of fluctuations which can be large.…
We study the evolution in equilibrium of the fluctuations for the conserved quantities of a chain of anharmonic oscillators in the hyperbolic space-time scaling. Boundary conditions are determined by applying a constant tension at one side,…
We derive hydrodynamics of a prototypical one dimensional model, having variable-range hopping, which mimics passive diffusion and ballistic motion of active, or self-propelled, particles. The model has two main ingredients - the hardcore…
The concept of hyperuniformity has been a useful tool in the study of large-scale density fluctuations in systems ranging across the natural and mathematical sciences. One can rank a large class of hyperuniform systems by their ability to…
This paper is concerned with the construction of high order schemes on irregular grids for balance laws, including a discussion of an a-posteriori error indicator based on the numerical entropy production. We also impose well-balancing on…
From the equations of conservation laws for energy, linear momentum, angular momentum and mass the evolutionary relation in differential forms follows. This relation connects the differential of entropy and the skew-symmetric form, whose…
The dynamics of an M-dimensional extended object whose M+1 dimensional world volume in M+2 dimensional space-time has vanishing mean curvature is formulated in term of geometrical variables (the first and second fundamental form of the…
These lecture notes give a short review of methods such as the matrix ansatz, the additivity principle or the macroscopic fluctuation theory, developed recently in the theory of non-equilibrium phenomena. They show how these methods allow…
We review some recent results on the anomalous diffusion of energy in systems of 1D coupled oscillators and we revisit the role of momentum conservation.
Random non-reciprocal interactions between a large number of conserved densities are shown to enhance the stability of the system towards pattern formation. The enhanced stability is an exact result when the number of species approaches…
Self-assembly is a ubiquitous process in synthetic and biological systems, broadly defined as the spontaneous organization of multiple subunits (e.g. macromolecules, particles) into ordered multi-unit structures. The vast majority of…
Consider a balance law where the flux depends explicitly on the space variable. At jump discontinuities, modeling considerations may impose the defect in the conservation of some quantities, thus leading to non conservative products. Below,…
Random organizing hyperuniform fluid induced by reciprocal activation is a non-equilibrium fluid with vanishing density fluctuations at large length scales like crystals. Here we extend this new state of matter to a closed manifold, namely…
We show that equilibrium systems in $d$ dimension that obey the inequality $d\nu> 2,$ known as Harris criterion, exhibit suppressed energy fluctuation in their critical state. Ashkin-Teller model is an example in $d=2$ where the correlation…
We discuss the non-equilibrium critical phenomena in liquids, and the models for these phenomena based on local equilibrium and extended scaling assumptions. Special situations are proposed for experimental tests of the theory.…
We introduce a schematic non-linear diffusion model where density fluctuations induce a rich out of equilibrium dynamics. The properties of the model are studied by numerical simulations and analytically in a mean field approximation. At…
Overdamped stochastic systems maintained far from equilibrium can display sustained oscillations with fluctuations that decrease with the system size. The correlation time of such noisy limit cycles expressed in units of the cycle period is…
For chaotic systems there is a theory for the decay of the survival probability, and for the parametric dependence of the local density of states. This theory leads to the distinction between "perturbative" and "non-perturbative" regimes,…