相关论文: Universal wavenumber selection laws in apical grow…

We propose conditions for the emergence of Turing patterns in a domain that changes in size by homogeneous growth/shrinkage. These conditions to determine the bifurcation are based on considering the geometric change of a potential function…

We revisit previously developed analytic models for defect evolution and adapt them appropriately for the study of semilocal string networks. We thus confirm the expectation (based on numerical simulations) that linear scaling evolution is…

We consider a collection of weakly interacting diffusion processes moving in a two-scale locally periodic environment. We study the large deviations principle of the empirical distribution of the particles' positions in the combined limit…

We study the onset of the propagation failure of wave fronts in systems of coupled cells. We introduce a new method to analyze the scaling of the critical external field at which fronts cease to propagate, as a function of intercellular…

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…

We derive a general upper bound on the spreading rate of wavepackets in the framework of Schr\"odinger time evolution. Our result consists of showing that a portion of the wavepacket cannot escape outside a ball whose size grows dynamically…

Scaling laws illuminate Nature's fundamental biological principles and guide bioinspired materials and structural designs. In simple cases they are based on the fundamental principle that all laws of nature remain unchanged (i.e.,…

Phenomenological scaling arguments suggest the existence of universal amplitudes in the finite-size scaling of certain correlation lengths in strongly anisotropic or dynamical phase transitions. For equilibrium systems, provided that…

We present scaling laws that dictate both local and global connectivity properties of bounded wireless networks. These laws are defined with respect to the key system parameters of per-node transmit power and the number of antennas…

In this paper we study the macroscopic conduction properties of large but finite binary networks with conducting bonds. By taking a combination of a spectral and an averaging based approach we derive asymptotic formulae for the conduction…

We consider spatially coupled systems governed by a set of scalar density evolution equations. Such equations track the behavior of message-passing algorithms used, for example, in coding, sparse sensing, or constraint-satisfaction…

In this paper we introduce a model of spatial network growth in which nodes are placed at randomly selected locations on a unit square in $\mathbb{R}^2$, forming new connections to old nodes subject to the constraint that edges do not…

A semi-continuum model is introduced to study the dynamics of the formation of granular heaplets in tapped granular layers. By taking into account the energy dissipation of collisions and screening effects due to avalanches, this model is…

We consider growing spheres seeded by random injection in time and space. Growth stops when two spheres meet leading eventually to a jammed state. We study the statistics of growth limited by packing theoretically in d dimensions and via…

The dynamics of complex systems in nature often occurs in terms of punctuations, or avalanches, rather than following a smooth, gradual path. A comprehensive theory of avalanche dynamics in models of growth, interface depinning, and…

Pattern formation often occurs in confined systems, yet how boundaries shape patterning dynamics is unclear. We develop techniques to analyze confinement effects in nonlocal advection-diffusion equations, which generically capture the…

We have studied the AC response of a hopping model in the variable range hopping regime by dynamical Monte Carlo simulations. We find that the conductivity as function of frequency follows a universal scaling law. We also compare the…

We review various methods for the analysis of initial-value problems for integrable dispersive equations in the weak-dispersion or semiclassical regime. Some methods are sufficiently powerful to rigorously explain the generation of…

We develop fractional buffer layers (FBLs) to absorb propagating waves without reflection in bounded domains. Our formulation is based on variable-order spatial fractional derivatives. We select a proper variable-order function so that…

We expand upon a new theoretical framework for Diffusion Limited Aggregation and associated Dielectric Breakdown Models in two dimensions [R. C. Ball and E. Somfai, Phys. Rev. Lett. 89, 135503 (2002)]. Key steps are understanding how these…