Related papers: Crystallization Kinetics in the Swift--Hohenberg M…
Gravity currents descending a slope in a linearly stratified environment can be frequently encountered in nature. However, few studies have quantitatively investigated the evolution process of lock-exchange gravity currents in such…
We consider pattern-forming fronts in the complex Ginzburg-Landau equation with a traveling spatial heterogeneity which destabilizes, or quenches, the trivial ground state while progressing through the domain. We consider the regime where…
We propose a minimal nonlinear model of brittle crack propagation by considering only the motion of the crack-tip atom. The model captures many essential features of steady-state crack velocity and is in excellent quantitative agreement…
We introduce a speed selection mechanism for front propagation in reaction-diffusion systems with multiple fields. This mechanism applies to pulled and pushed fronts alike, and operates by restricting the fields to large "finite" intervals…
The kinetics and microstructure of solid-phase crystallization under continuous heating conditions and random distribution of nuclei are analyzed. An Arrhenius temperature dependence is assumed for both nucleation and growth rates. Under…
The growth of striped order resulting from a quench of the two-dimensional Swift-Hohenberg model is studied in the regime of a small control parameter and quenches to zero temperature. We introduce an algorithm for finding and identifying…
The thermonuclear explosion of a massive white dwarf in a Type Ia supernova explosion is characterized by vastly disparate spatial and temporal scales. The extreme dynamic range inherent to the problem prevents the use of direct numerical…
In this paper, we carry out numerical bifurcation analysis of depinning of fronts near the homoclinic snaking region, involving a spatial stripe cellular pattern embedded in a quiescent state, in the two-dimensional Swift-Hohenberg equation…
We study a Fisher-KPP equation with spatially periodic diffusion and reaction terms. We identify a class of periodic media for which the equation admits an explicit, closed-form solution. Through a nonlinear change of variables, the problem…
Pattern-forming fronts are often controlled by an external stimulus which progresses through a stable medium at a fixed speed, rendering it unstable in its wake. By controlling the speed of excitation, such stimuli, or "triggers," can…
The (1+1)-dimensional kinetic model of crystal growth with simulated self-attraction and random sequential or parallel dynamics is introduced and studied via Monte-Carlo simulations. To imitate the attraction of absorbing atoms the…
We consider a one-dimensional Swift-Hohenberg equation coupled to a conservation law, where both equations contain additional dispersive terms breaking the reflection symmetry $x \mapsto -x$. This system exhibits a Turing instability and we…
We study the asymptotics of front speeds of the reaction-diffusion equations with Kolmogorov-Petrovsky-Piskunov (KPP) nonlinearity and zero mean stationary ergodic Gaussian shear advection on the entire plane. By exploiting connections of…
The theory of stationary spatially localized patterns in dissipative systems driven by time-independent forcing is well developed. With time-periodic forcing related but time-dependent structures may result. These may consist of breathing…
We aim to classify the long-time behavior of the solution to a free boundary problem with monostable reaction term in space-time periodic media. Such a model may be used to describe the spreading of a new or invasive species, with the free…
The rupture of dry frictional interfaces occurs through the propagation of fronts breaking the contacts at the interface. Recent experiments have shown that the velocities of these rupture fronts range from quasi-static velocities…
We review how phase-field models contributed to the understanding of various aspects of crystal nucleation including homogeneous and heterogeneous processes, and their role in microstructure evolution. We recall results obtained both by the…
The nonlocal-to-local asymptotics investigation for evolutionary problems is a central topic both in the theory of PDEs and in functional analysis. More recently, it became the main core of the mathematical analysis of phase-separation…
The freeze-out process in heavy ion collisions is driven by the competition between the scattering rate and the expansion rate of the matter. We analyse the expansion rate $\Theta$ (often called Hubble flow) in relativistic heavy ion…
Signal propagation in the non equilibirum evolution after quantum quenches has recently attracted much experimental and theoretical interest. A key question arising in this context is what principles, and which of the properties of the…