相关论文: Front propagation in geometric and phase field mod…
We investigate the sharp interface limit of a diffuse interface system that couples the Allen--Cahn equation with the instationary Navier--Stokes system in a bounded domain in $\mathbb{R}^d$ with $d \in \{2,3\}$. This model is used to…
The morphology of flame fronts propagating in reactive systems comprised of randomly positioned, point-like sources is studied. The solution of the temperature field and the initiation of new sources is implemented using the superposition…
We show that for an observer in translational, rotational or gravitational motion, a linearly polarized plane wave has two modes of propagation in a stationary, homogeneous and isotropic medium according to Hertz's version of Maxwell's…
Space-time varying media enable unprecedented control over electromagnetic waves, yet most existing studies assume idealized, nondispersive materials and thus fail to capture the intrinsic frequency dispersion of realistic platforms. Here,…
A Hamiltonian reduction approach is defined, studied, and finally used to derive asymptotic models of internal wave propagation in density stratified fluids in two-dimensional domains. Beginning with the general Hamiltonian formalism of…
We consider solutions in frequency bands of dispersive equations on the line defined by Fourier multipliers, these solutions being considered as wave packets. In this paper, a refinement of an existing method permitting to expand…
The phase-field method is reviewed from the general perspective of converting a free boundary problem into a set of coupled partial differential equations. Its main advantage is that it avoids front tracking by using phase fields to locate…
The dynamics of transient patterns formed by front propagation in extended nonequilibrium systems is considered. Under certain circumstances, the state left behind a front propagating into an unstable homogeneous state can be an unstable…
We study acoustic wave propagation in a uniform stationary flow. We develop a method founded on the Lorentz transform and a hypothesis of irrotationality of the acoustic perturbation. After a transformation of the space-time and of the…
Recent theoretical work has shown that so-called pulled fronts propagating into an unstable state always converge very slowly to their asymptotic speed and shape. In the the light of these predictions, we reanalyze earlier experiments by…
We analyze the propagation of two-dimensional dispersive and relativistic wavepackets localized in the vicinity of the zero level set $\Gamma$ of a domain wall. The main applications we consider are a topologically non-trivial Dirac model…
We investigate the mean electromotive force in the kinematic framework, that is, ignoring the back-reaction of the magnetic field on the fluid velocity, under the assumption of axisymmetric turbulence determined by the presence of either…
It is demonstrated that the description of surface-diffusion controlled dynamics via the phase-field method is less trivial than it appears at first sight. A seemingly straightforward approach previously used in the literature is shown to…
Propagation of energetic particles across the mean field direction in turbulent magnetic fields is often described as spatial diffusion. Recently, it has been suggested that initially the particles propagate systematically along meandering…
We investigate the time evolution of waves in evanescent media generated by a source within this medium and observed at some distance away from the location of the source. The aim is to find a velocity which describes a causal process and…
The description of surface-diffusion controlled dynamics via the phase-field method is less trivial than it appears at first sight. A seemingly straightforward approach from the literature is shown to fail to produce the correct…
A numerical study of the role of anomalous diffusion in front propagation in reaction-diffusion systems is presented. Three models of anomalous diffusion are considered: fractional diffusion, tempered fractional diffusion, and a model that…
When a particle diffuses in a medium with spatially dependent friction coefficient $\alpha(r)$ at constant temperature $T$, it drifts toward the low friction end of the system even in the absence of any real physical force $f$. This…
An FFT-based algorithm is developed to simulate the propagation of elastic waves in heterogeneous $d$-dimensional rectangular shape domains. The method allows one to prescribe the displacement as a function of time in a subregion of the…
A planar crack generically segments into an array of "daughter cracks" shaped as tilted facets when loaded with both a tensile stress normal to the crack plane (mode I) and a shear stress parallel to the crack front (mode III). We…