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We study the effect of varying sound speed on clustering dark energy in the Dirac-Born-Infeld (DBI) scenario. The DBI action is included in the class of $k$-essence models, and it has an important role in describing the effective degrees of…
We consider stochastic 2D Euler equations with $L^2$-initial vorticity and driven by L\'evy transport noise in the Marcus sense. Under a suitable scaling limit of the noises, we prove that the weak solutions converge weakly to the unique…
The Rouse-Zimm equation for the position vectors of beads mapping the polymer is generalized by taking into account the viscous aftereffect and the hydrodynamic noise. For the noise, the random fluctuations of the hydrodynamic tensor of…
The shock wave structure in a one-dimensional lattice (e.g. granular chain) with a power law dependence of force on displacement between particles with viscous dissipation is considered and compared to the corresponding long wave…
We study general aspects of active motion with fluctuations in the speed and the direction of motion in two dimensions. We consider the case in which fluctuations in the speed are not correlated to fluctuations in the direction of motion,…
Supercooled liquids are characterized by relaxation times that increase dramatically by cooling or compression. Many liquids have been shown to obey power-law density scaling, according to which the relaxation time is a function of density…
The behavior of a dynamical system can exhibit abrupt changes when it crosses a tipping point. To prevent catastrophic events, it is useful to analyze indicators of the incoming bifurcation, as the divergence of the relaxation time of the…
We study the spontaneously broken phase of the $XY$ model in three dimensions, with boundary conditions enforcing the presence of a vortex line. Comparing Monte Carlo and field theoretic determinations of the magnetization and energy…
Young pulsars deviate from a perfectly regular spin-down by two non-deterministic phenomena: impulsive glitches and timing noise. Both phenomena are interesting per se, and may provide insights into the superfluid properties of neutron…
The dynamics of a tracer particle in a glassy matrix of obstacles displays slow complex transport as the free volume approaches a critical value and the void space falls apart. We investigate the emerging subdiffusive motion of the test…
It is well known that the optical Kerr effect can be a source of highly squeezed light, however the analytical limit of the noise suppression has not been found yet. The process is reconsidered and an analytical estimation of the optimal…
Let $A\in\mathbb{R}^{m\times n}$ be a matrix of rank $r$ with singular value decomposition (SVD) $A=\sum_{k=1}^r\sigma_k (u_k\otimes v_k),$ where $\{\sigma_k, k=1,\ldots,r\}$ are singular values of $A$ (arranged in a non-increasing order)…
We explore the velocity distributions in a vibrated binary granular gas system, focusing on how these distributions are influenced by the coefficient of restitution (CoR) and the inelasticity of particle collisions. Through molecular…
We show that that the stochastic 3D primitive equations with either the physical boundary conditions or Neumann boundary conditions on the top and bottom and Dirichlet boundary condition on the sides driven by multiplicative…
We study a two-dimensional granular system where external driving force is applied to each particle in the system in such a way that the system is driven into a steady state by balancing the energy input and the dissipation due to inelastic…
We study the autocorrelation time of the size of the cluster at the origin in discrete-time dynamical percolation. We focus on binary trees and high-dimensional tori, and show in both cases that this autocorrelation time is linear in the…
An equation for the evolution of the energy of a dynamical system (Keldysh model with one degree of freedom), which contains a white noise source, is constructed. It is shown that self-oscillations (flutter) are suppressed if the intensity…
Theoretical models that describe oscillations in biological systems are often either a limit cycle oscillator, where the deterministic nonlinear dynamics gives sustained periodic oscillations, or a noise-induced oscillator, where a fixed…
This paper concerns the McKean-Vlasov stochastic differential equation (SDE) with common noise. An appropriate definition of a weak solution to such an equation is developed. The importance of the notion of compatibility in this definition…
Based on the dielectric formalism in the generalised random phase approximation, we generalise the description of a Bose condensed gas to allow for a relative velocity between the superfluid and normal fluid. In this model, we determine the…