Related papers: Crossover between parabolic and hyperbolic scaling…
Two-frequency Wigner distribution is introduced to capture the asymptotic behavior of the space-frequency correlation of paraxial waves in the radiative transfer limits. The scaling limits give rises to deterministic transport-like…
Chemical, physical and ecological systems passing through a saddle-node bifurcation will, momentarily, find themselves balanced at a semi-stable steady state. If perturbed by noise, such systems will escape from the zero-steady state, with…
A class of parabolic cross-diffusion systems modeling the interaction of an arbitrary number of population species is analyzed in a bounded domain with no-flux boundary conditions. The equations are formally derived from a random-walk…
We present a systematic approach to regularity theory of the multi-dimensional Euler alignment systems with topological diffusion introduced in \cite{STtopo}. While these systems exhibit flocking behavior emerging from purely local…
Bistability generated via a pure noise-induced phase transition is reexamined from the view of bifurcations in macroscopic cumulant dynamics. It allows an analytical study of the phase diagram in more general cases than previous methods. In…
The apparent stability of population oscillations in ecological systems is a long-standing puzzle. A generic solution for this problem is suggested here. The stabilizing mechanism involves the combined effect of spatial migration,…
In this paper, we study a continuous ocking Cucker-Smale model with noise, which has isotropic and polarized stationary solutions depending on the intensity of the noise. The first result establishes the threshold value of the noise…
Several classes of physical systems exhibit ultraslow diffusion for which the mean squared displacement at long times grows as a power of the logarithm of time ("strong anomaly") and share the interesting property that the probability…
The behaviour of solutions to the Einstein equations with a causal viscous fluid source is investigated. In this model we consider a spatially flat Robertson-Walker metric, the bulk viscosity coefficient is related to the energy density as…
Vicsek Model is widely used in simulations of dry active matter. We re-examined two typical phase transitions in the original Vicsek model by using the velocity correlation length. One is the noise-driven disordered-to-ordered phase…
The dynamics of an infinite system of point particles in $\mathbb{R}^d$, which hop and interact with each other, is described at both micro- and mesoscopic levels. The states of the system are probability measures on the space of…
The effect of thermally generated bulk stochastic forces on the statistical growth dynamics of forwards bifurcating propagating macroscopic patterns is compared with the influence of fluctuations at the boundary of a semiinfinite system,…
The Ohta-Kawasaki model for diblock copolymers exhibits a rich equilibrium bifurcation structure. Even on one-dimensional base domains the bifurcation set is characterized by high levels of multi-stability and numerous secondary bifurcation…
Living many-body systems often exhibit scale-free collective behavior reminiscent of thermal critical phenomena. But their mutual interactions are inevitably retarded due to information processing and delayed actuation. We numerically…
We study the large time behavior of Lipschitz continuous, possibly unbounded, viscosity solutions of Hamilton-Jacobi Equations in the whole space $\R^N$. The associated ergodic problem has Lipschitz continuous solutions if the analogue of…
A new type of instability - electrokinetic instability - and an unusual transition to chaotic motion near a charge-selective surface was studied by numerical integration of the Nernst-Planck-Poisson-Stokes system and a weakly nonlinear…
We are concerned with large-time behaviors of solutions for Vlasov--Navier--Stokes equations in two dimensions and Vlasov-Stokes system in three dimensions including the effect of velocity alignment/misalignment. We first revisit the…
In this paper, we present a two-species Vicsek model, that describes alignment interactions of self-propelled particles which can either move or not. The model consists in two populations with distinct Vicsek dynamics that interact only via…
In this note, we study the hydrodynamic limit, in the hyperbolic space-time scaling, for a one-dimensional unpinned chain of quantum harmonic oscillators with random masses. To the best of our knowledge, this is among the first examples,…
We consider fluid flows, governed by the Navier-Stokes equations, subject to a steady symmetry-breaking bifurcation and forced by a weak noise acting on a slow time scale. By generalizing the multiple-scale weakly nonlinear expansion…