Using numerical simulations we investigate the space-time properties of a system in which spirals emerge within coarsening domains, thus giving rise to nontrivial internal dynamics. Initially proposed in the context of population dynamics, the studied six-species model exhibits growing domains composed of three species in a rock-paper-scissors relationship. Through the investigation of differen...

The coarsening process in a class of driven systems exhibiting striped structures is studied. The dynamics is governed by the motion of the driven interfaces between the stripes. When two interfaces meet they coalesce thus giving rise to a coarsening process in which l(t), the average width of a stripe, grows with time. This is a generalization of the reaction-diffusion process A+A-->A to the c...

In this paper, an adaptive wavelet method for solving linear operator equations is constructed that is a modification of the method from [Math. Comp, 70 (2001), pp.27–75] by Cohen, Dahmen and DeVore, in the sense that there is no recurrent coarsening of the approximate solutions. Despite of this, it will be shown that the method has optimal computational complexity. Numerical results in a simpl...

Yagasaki et al. [Phys. Rev. E 89, 020301 (2014)] present results from a molecular dynamics trajectory illustrating coarsening of ice, which they interpret as evidence of transient coexistence between two distinct supercooled phases of liquid water. We point out that neither two distinct liquids nor criticality are demonstrated in this simulation study. Instead, the illustrated trajectory is con...

In order to quantitatively study the accuracy of the unconditionally stable coarsening algorithms, we calculate the Fourier space multi step error on the order parameter field by explicitly distinguishing the analytic time τ and the algorithmic time t. The calculation determines the error in the order parameter and the scaled correlations. This error contributes a correction term in the analyti...

A nite element method with optimal convergence on non-smooth three dimensional domains requires anisotropic mesh reenement towards the edges. Multigrid methods for anisotropic tensor product meshes are available and are based either on line (or plane) smoothers or on semi-coarsening strategies. In this paper we suggest and analyze a new multigrid scheme combining semi-coarsening and line smooth...

Title of dissertation: UNIVERSAL BOUNDS ON COARSENING RATES FOR SOME MODELS OF PHASE TRANSITIONS Shibin Dai, Doctor of Philosophy, 2005 Dissertation directed by: Professor Robert L. Pego Department of Mathematics In this thesis, we prove one-sided, universal bounds on coarsening rates for three models of phase transitions by following a strategy developed by Kohn and Otto (Comm. Math. Phys. 229...

If quenched to zero temperature, the one-dimensional Ising spin chain undergoes coarsening, whereby the density of domain walls decays algebraically in time. We show that this coarsening process can be interrupted by exerting a rapidly oscillating periodic field with enough strength to compete with the spin-spin interaction. By analyzing correlation functions and the distribution of domain leng...

Fast multigrid solvers are considered for the linear systems arising from the bilinear finite element discretizations of second order elliptic equations with anisotropic diffusion. Optimal convergence of Vcycle multigrid method in the semi-coarsening case and nearly optimal convergence of V-cycle multigrid method with line smoothing in the uniformly coarsening case are established using the XZ ...

We study slowly moving solutions of the real Ginzburg-Landau equation on the line, by a method due to J. Carr and R.L. Pego. These are functions taking alternately positive or negative values on large intervals. A consequence of our approach is that we can propose a rigorous derivation of a stochastic model of coarsening by successive elimination of the smallest interval, which was described in...