Related papers: A simplified model for coupling Darrieus-Landau an…
In this paper, we establish the large time asymptotic behavior of solutions to the linearized Vlasov-Poisson system near general spatially homogenous equilibria $\mu(\frac12|v|^2)$ with connected support on the torus $\mathbb{T}^3_x \times…
We study the existence and long-time asymptotics of weak solutions to a system of two nonlinear drift-diffusion equations that has a gradient flow structure in the Wasserstein distance. The two equations are coupled through a…
In the context of mathematical modeling, it is sometimes convenient to integrate models of different nature. These types of combinations, however, might entail difficulties even when individual models are well-understood, particularly in…
We investigate a boundary-driven Ginzburg-Landau dynamics with long-range interactions. In the hydrodynamic limit, the macroscopic evolution is governed by a fractional heat equation with Dirichlet boundary conditions, while the…
A novel probabilistic framework for modelling anomalous diffusion is presented. The resulting process is Markovian, non-homogeneous, non-stationary, non-ergodic, and state-dependent. The fundamental law governing this process is driven by…
A powerful mathematical method for front instability analysis that was recently developed in the field of nonlinear dynamics is applied to the 1+1 (spatial and time) dimensional Landau-Lifshitz-Gilbert (LLG) equation. From the essential…
In this paper, uniformly unconditionally stable first and second order finite difference schemes are developed for kinetic transport equations in the diffusive scaling. We first derive an approximate evolution equation for the macroscopic…
The linear and non-linear dynamics of centrifugal instability in Taylor-Couette flow are investigated when fluids are stably stratified and highly diffusive. One-dimensional local linear stability analysis (LSA) on cylindrical Couette flow…
Several new families of nonlinear three-dimensional travelling wave solutions to the Navier-Stokes equation, also known as exact coherent states, are computed for Newtonian plane Poiseuille flow. The symmetries and streak/vortex structures…
We investigate diffusion-driven instabilities in a FitzHugh-Nagumo reaction-diffusion system with superdiffusive transport, modeled by fractional Laplacian operators with different diffusion orders for the activator and the inhibitor. A…
Origin of hydrodynamical instability and turbulence in the Keplerian accretion disc as well as similar laboratory shear flows, e.g. plane Couette flow, is a long standing puzzle. These flows are linearly stable. Here we explore the…
Thermoacoustic instabilities observed in turbulent combustion systems have disastrous consequences and are notoriously challenging to model, predict and control. Here, we introduce a mean-field model of thermoacoustic transitions, where the…
This paper investigates the long time dynamics of interacting particle systems subject to singular interactions. We consider a microscopic system of $N$ interacting point particles, where the time evolution of the joint distribution…
In this paper we investigate the dynamic properties of the minimal Bell-Lavis (BL) water model and their relation to the thermodynamic anomalies. The Bell-Lavis model is defined on a triangular lattice in which water molecules are…
Thermodynamic nonequilibrium effects play a central role in momentum and energy transport in compressible flows. In conventional BGK kinetic models, the relaxation time $\tau$ is taken as a constant, which neglects the dependence of the…
In this note we provide some precise estimates explaining the diffusive structure of partially dissipative systems with time-dependent coefficients satisfying a uniform Kalman rank condition. Precisely, we show that under certain (natural)…
Three-dimensional CP-DNS of reacting iron particle dust clouds in a turbulent mixing layer are conducted. The simulation approach considers the Eulerian transport equations for the reacting gas phase and resolves all scales of turbulence,…
We have studied the conductance distribution function of two-dimensional disordered noninteracting systems in the crossover regime between the diffusive and the localized phases. The distribution is entirely determined by the mean…
The coupled Stuart-Landau equation serves as a fundamental model for exploring synchronization and emergent behavior in complex dynamical systems. However, understanding its dynamics from a comprehensive nonlinear perspective remains…
Study of Langevin dynamics and the fluctuation-dissipation relation (FDR) for a generic probe system (represented by a mass $M$), bilinearly coupled to a bath of harmonic oscillators, has been a standard paradigm for a microscopic theory of…