Related papers: Stable localized moving patterns in the 2-D Gray-S…
Stability is a key aspect of data analysis. In many applications, the natural notion of stability is geometric, as illustrated for example in computer vision. Scattering transforms construct deep convolutional representations which are…
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…
We consider ultracold atoms in 2D-disordered optical potentials and calculate microscopic quantities characterizing matter wave quantum transport in the non-interacting regime. We derive the diffusion constant as function of all relevant…
The process of pattern formation in the two dimensional Swift-Hohenberg equation is examined through numerical and analytic methods. Dynamic scaling relationships are developed for the collective ordering of convective rolls in the limit of…
We study diffusion-driven pattern-formation in networks of networks, a class of multilayer systems, where different layers have the same topology, but different internal dynamics. Agents are assumed to disperse within a layer by undergoing…
A core capability for robot manipulation is reasoning over where and how to stably place objects in cluttered environments. Traditionally, robots have relied on object-specific, hand-crafted heuristics in order to perform such reasoning,…
Understanding how patterns and travelling waves form in chemical and biological reaction-diffusion models is an area which has been widely researched, yet is still experiencing fast development. Surprisingly enough, we still do not have a…
We investigate the evaporation of a two-dimensional droplet on a solid surface. The solid is flat but with smooth chemical variations that lead to a space-dependent local contact angle. We perform a detailed bifurcation analysis of the…
We study the formation of steady waves in two-dimensional fluids under a current with mean velocity $c$ flowing over a periodic bottom. Using a formulation based on the Dirichlet-Neumann operator, we establish the unique continuation of a…
Cooperative behaviors arising from bacterial cell-to-cell communication can be modeled by reaction-diffusion equations having only a single diffusible component. This paper presents the following three contributions for the systematic…
We define a simple model of conformal field theory in random space-time environments, which we refer to as stochastic conformal field theory. This model accounts for the effects of dilute random impurities in strongly interacting critical…
This paper treats the solvability of a semilinear reaction-diffusion system, which incorporates transport (diffusion) and reaction effects emerging from two separated spatial scales: $x$ - macro and $y$ - micro. The system's origin connects…
This work investigates experimentally and numerically the dynamics of rigid particles settling under gravity in a highly viscous fluid. We demonstrate that certain shapes: cones, crescent moons, arrowheads, and open flat rings reorient and…
The paper is concerned with a scalar conservation law with discontinuous gradient-dependent flux. Namely, the flux is described by two different functions $f(u)$ or $g(u)$, when the gradient $u_x$ of the solution is positive or negative,…
There is a growing interest, inspired by advances in technology, in the low temperature physics of thin films. These quasi-2D systems show a wide range of ordering effects including formation of striped states, reorientation transitions,…
This work is concerned with the stability properties of linear stochastic differential equations with random (drift and diffusion) coefficient matrices, and the stability of a corresponding random transition matrix (or exponential…
We consider active Brownian particles that intermittently switch between active and inactive states. Such behavior is ubiquitous at all scales, from bacteria to animals and in artificial active systems. We derive exact expressions for key…
We consider a thin droplet that spreads over a flat, horizontal and chemically heterogeneous surface. The droplet is subjected to changes in its volume though a prescribed, arbitrary spatiotemporal function, which varies slowly and vanishes…
We compare spot patterns generated by Turing mechanisms with those generated by replication cascades, in a model one-dimensional reaction-diffusion system. We determine the stability region of spot solutions in parameter space as a function…
We address the dynamics of damped collective modes in terms of first and second moments. The modes are introduced in a self-consistent fashion with the help of a suitable application of linear response theory. Quantum effects in the…