Related papers: Transverse modulational dynamics of quenched patte…
Monitoring the dynamics processes in combustors is crucial for safe and efficient operations. However, in practice, only limited data can be obtained due to limitations in the measurable quantities, visualization window, and temporal…
We use the mapping between Burgers' equation and the problem of a directed polymer in a random medium in order to study the fully developped turbulence in the $N$ dimensional forced Burgers' equation. The stirring force corresponds to a…
In fluid dynamics governed by the one dimensional inviscid Burgers equation $\partial_t u+u\partial_x(u)=0$, the stirring is explained by the sticky particles model. A Markov process $([Z^1_t,Z^2_t],\,t\geq0)$ describes the motion of random…
We investigate the wrinkling dynamics of a thin elastic sheet that is indented or compressed while floating on a viscous liquid. We show that the deformation speed controls the dynamics, leading to a wrinkle wavelength significantly smaller…
We consider the model of a transverse vector (e.g. magnetic) field with the most general form of the nonlinearity, known as the ${\cal A}$ model, passively advected by a strongly compressible turbulent flow, governed by the randomly stirred…
We consider the equilibrium shapes of a thin, annular strip cut out in an elastic sheet. When a central fold is formed by creasing beyond the elastic limit, the strip has been observed to buckle out-of-plane. Starting from the theory of…
We consider pattern formation using reaction-diffusion equation on various non-uniformly curved surfaces. We explore how, in general, curvature and, in particular the domain shape would affect the pattern formation in these geometries. As…
The dynamics of sandpile models are mapped to discrete interface equations. We study in detail the Bak-Tang-Wiesenfeld model, a stochastic model with random thresholds, and the Manna model. These are, respectively, discretizations of the…
Membrane bending is an extensively studied problem from both modeling and experimental perspectives because of the wide implications of curvature generation in cell biology. Many of the curvature generating aspects in membranes can be…
Using dynamical density functional theory we calculate the speed of solidification fronts advancing into a quenched two-dimensional model fluid of soft-core particles. We find that solidification fronts can advance via two different…
The spontaneous symmetry breaking taking place in the direction perpendicular to the energy flux in a dilute vibrofluidized granular system is investigated, using both a hydrodynamic description and simulation methods. The latter include…
In many oscillatory or excitable systems, dynamical patterns emerge which are stationary or periodic up in a moving frame of reference. Examples include traveling waves or spiral waves in chemical systems or cardiac tissue. We present a…
The stability properties of line solitary wave solutions of the (2+1)-dimensional Boussinesq equation with respect to transverse perturbations and their consequences are considered. A geometric condition arising from a multi-symplectic…
Using molecular dynamics simulations, we determine the linear and nonlinear viscoelastic properties of a model polymer melt in the unentangled regime. Several approaches are compared for the computation of linear moduli, including…
We consider a one-dimensional fluid-solid interaction model governed by the Burgers equation with a time varying interface. We discuss on the inverse problem of determining the shape of the interface from Dirichlet and Neumann data at one…
Kinematic equations for the motion of slowly propagating, weakly curved fronts in bistable media are derived. The equations generalize earlier derivations where algebraic relations between the normal front velocity and its curvature are…
We use numerical simulations to explore biases that arise in dynamical estimates of the mean mass profile for a collection of galaxy clusters that have been stacked to make a composite. There are three types of bias. One arises from…
The flow behavior of granular matter is significantly influenced by the shape of constituent particles. This effect is particularly pronounced for very concave particles, which exhibit unique flow characteristics such as higher porosity and…
We rigorously prove the bifurcation of slow-moving pattern interfaces with general direction in a two-dimensional Swift-Hohenberg-type model close to a Turing instability for a large class of nonlinearities. These interfaces describe the…
Localized patterns are coherent structures embedded in a quiescent state and occur in both discrete and continuous media across a wide range of applications. While it is well-understood how domain covering patterns (for example stripes and…