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We study singularity formation in two one-dimensional nonlinear wave models with quadratic time-derivative nonlinearities. The non-null model violates the null condition and typically develops finite-time blow-up; the null-form model is…
We derive the exact late-time asymptotics for small spherically symmetric solutions of nonlinear wave equations with a potential. The dominant tail is shown to result from the competition between linear and nonlinear effects.
We numerically investigate the athermal creep deformation of amorphous materials having a wide range of stability. The imposed shear stress serves as the control parameter, allowing us to examine the time-dependent transient response…
The structure of spiral galaxies is essential to understanding the dynamics and evolution of disk galaxies; however, the precise nature of spiral arms remains uncertain. Two challenges in understanding the mechanisms driving spirals are how…
It has been revealed by mean-field theories and computer simulations that the nature of the collapse transition of a polymer is influenced by its bending stiffness $\epsilon_{\rm b}$. In two dimensions, a recent analytical work demonstrated…
This paper investigates the properties of unstable single-spiral wave solutions arising in the Karma model of two-dimensional cardiac tissue. In particular, we discuss how such solutions can be computed numerically on domains of arbitrary…
We present experimental evidence and theoretical arguments showing that the time-evolution of freely decaying 2-d turbulence is governed by a {\it discrete} time scale invariance rather than a continuous time scale invariance. Physically,…
We investigate the spectrum of linearized excitations of global vortices in $2+1$ dimensions. After identifying the existence of localized excitation modes, we compute the decay time scale of the first two and compare the results to the…
Understanding the formation of binary and multiple stellar systems largely comes down to studying the circumstances for the fragmentation of a condensing core during the first stages of the collapse. However, the probability of…
The phase diagram of a driven two-dimensional vortex lattice in the presence of dense quasi-point pins is investigated. The transition from the crystal to the liquid is found continuous at intermediate inductions. The correlations in the…
The aim of this work is to analyze the dynamical behavior of relativistic infinite axial-symmetric shells with flat interior and a radiation filled curved exterior spacetimes. It will be proven, by the use of conservation equations of…
We consider a branching stable process with positive jumps, i.e. a continuous-time branching process in which the particles evolve independently as stable L{\'e}vy processes with positive jumps. Assuming the branching mechanism is critical…
We find computable criteria for stability of symplectic leaves of Poisson manifolds. Using Poisson geometry as an inspiration, we also give a general criterion for stability of leaves of Lie algebroids, including singular ones. This not…
We consider the formation and evolution of vortices in a hydrodynamic shearing-sheet model. The evolution is done numerically using a version of the ZEUS code. Consistent with earlier results, an injected vorticity field evolves into a set…
We derive a simple, accurate, non-linear, global equation governing spiral density waves in thin, non-self-gravitating, inviscid accretion discs. These discs may have any slowly varying surface density or temperature profile. For specific…
The temperature effect on the linear instability and the splitting process of a doubly quantized vortex is studied. Using the linear perturbation theory to calculate out the quasi-normal modes of the doubly quantized vortex, we find that…
We investigate the spatio-temporal quantity of coherence for turbulent velocity fluctuations at spatial distances of the order or larger than the integral length scale $l_{0}$. Using controlled laboratory experiments, an exponential decay…
The stability of transparent spherically symmetric thin shells (and wormholes) to linearized spherically symmetric perturbations about static equilibrium is examined. This work generalizes and systematizes previous studies and explores the…
The purpose of this article is to give a streamlined and self-contained treatment of the long-time asymptotics of the Toda lattice for decaying initial data in the soliton and in the similarity region via the method of nonlinear steepest…
We study the long-time behaviour of axisymmetric solutions without swirl for the threedimensional Navier-Stokes equations in the whole space. Assuming that the initial vorticity is sufficiently localised, we compute explicitly the leading…