Related papers: Stochastic Flips on Dimer Tilings

We study a few problems related to Markov processes of flipping triangulations of the sphere. We show that these processes are ergodic and mixing, but find a natural example which does not satisfy detailed balance. In this example, the…

A stochastic hierarchical model for the evolution of low grade gliomas is proposed. Starting with the description of cell motion using piecewise diffusion Markov processes (PDifMPs) at the cellular level, we derive an equation for the…

In this paper, we propose a general mechanism for the existence of quasicrystals in spatially extended systems (partial differential equations with Euclidean symmetry). We argue that the existence of quasicrystals with higher order…

Stochastic approximation is a foundation for many algorithms found in machine learning and optimization. It is in general slow to converge: the mean square error vanishes as $O(n^{-1})$. A deterministic counterpart known as quasi-stochastic…

In a recent Letter we proposed a means to realize a quasicrystal with eight-fold symmetry by trapping particles in an optical potential created by four lasers. The quasicrystals obtained in this way, which are closely related to the…

A family of exponential martingales of a stochastic Laplacian growth problem is proposed. Stochastic Laplacian growth describes a regularized interface dynamics in a two-fluid system, where the viscous fluid is incompressible at a large…

Stochastic models of surface growth are usually based on randomly choosing a substrate site to perform iterative steps, as in the etching model [1]. In this paper I modify the etching model to perform sequential, instead of random,…

Semiflexible slender filaments are ubiquitous in nature and cell biology, including in the cytoskeleton, where reorganization of actin filaments allows the cell to move and divide. Most methods for simulating semiflexible inextensible…

We consider the stochastic evolution of a 1+1-dimensional interface (or polymer) in presence of a substrate. This stochastic process is a dynamical version of the homogeneous pinning model. We start from a configuration far from…

Random tilings of very large domains will typically lead to a solid, a liquid, and a gas phase. In the two-phase case, the solid-liquid boundary (arctic curve) is smooth, possibly with singularities. At the point of tangency of the arctic…

We study the behaviour at tipping points close to (smoothed) non-smooth fold bifurcations in one-dimensional oscillatory forced systems. The focus is the Stommel-Box, and related climate models, which are piecewise-smooth continuous…

Amorphous solids are known to fail catastrophically via fracture, wherein cavitation at nano-metric scales is known to play a significant role. Micro-alloying via inclusions is often used as a means to increase the fracture toughness of…

We present limit theorems for a sequence of Piecewise Deterministic Markov Processes (PDMPs) taking values in a separable Hilbert space. This class of processes provides a rigorous framework for stochastic spatial models in which discrete…

We investigate a two-dimensional tiling model. Even though the degrees of freedom in this model are discrete, it has a hidden continuous global symmetry in the infinite lattice limit, whose corresponding Goldstone modes are the…

The selfconsistent cranking approach is extended to the case of rotation about an axis which is tilted with respect to the principal axes of the deformed potential (Tilted Axis Cranking). Expressions for the energies and the intra bands…

We introduce the notion of a random relaxed asymptotic contraction in the setting of random normed modules. The contraction condition employs two quasi-metrics that are built directly from the random operator: a lower quasi-metric which…

This paper deals with the problem of measurable lifting modification for stochastic processes in its most general form and with the 'product lifting problem'. Solutions to the positive are reduced to the existence of marginals with respect…

Commensurability is of paramount importance in numerous strongly interacting electronic systems. In the Fractional Quantum Hall effect, a rich cascade of increasingly narrow plateaux appear at larger denominator filling fractions. Rich…

Delaunay flip is an elegant, simple tool to convert a triangulation of a point set to its Delaunay triangulation. The technique has been researched extensively for full dimensional triangulations of point sets. However, an important case of…

To understand an aperiodic tiling (or a quasicrystal modeled on an aperiodic tiling), we construct a space of similar tilings, on which the group of translations acts naturally. This space is then an (abstract) dynamical system. Dynamical…