Related papers: Scaling limit of a discrete prion dynamics model
The numerical solutions of the non-linear evolution equation are shown to display the ``geometric'' scaling recently discovered in the experimental data. The phenomena hold both for proton and nucleus targets for all $x$ below $10^{-2}$ and…
We consider an idealized network, formed by N neurons individually described by the FitzHugh-Nagumo equations and connected by electrical synapses. The limit for N to infinity of the resulting discrete model is thoroughly investigated, with…
In this Letter, the 2-dimensional dense flow of polygonal particles on an incline with a flat frictional inferior boundary is analyzed by means of contact dynamics discrete element simulations, in order to develop boundary conditions for…
The lilypond model on a point process in $d$-space is a growth-maximal system of non-overlapping balls centred at the points. We establish central limit theorems for the total volume and the number of components of the lilypond model on a…
The finite-size scaling function and the leading corrections for the single species 1D coagulation model $(A + A \rightarrow A)$ and the annihilation model $(A + A \rightarrow \emptyset)$ are calculated. The scaling functions are universal…
For interacting particle systems that satisfies the gradient condition, the hydrodynamic limit and the equilibrium fluctuations are well known. We prove that under the presence of a symmetric random environment, these scaling limits also…
Analysis of mathematical models in ecology and epidemiology often focuses on asymptotic dynamics, such as stable equilibria and periodic orbits. However, many systems exhibit long transient behaviors where certain aspects of the dynamics…
We study surface growth models exhibiting anomalous scaling of the local surface fluctuations. An analytical approach to determine the local scaling exponents of continuum growth models is proposed. The method allows to predict when a…
The scalability of massively parallel algorithms is a fundamental question in computer science. We study the scalability and the efficiency of a conservative massively parallel algorithm for discrete-event simulations where the discrete…
We present an analytical description of the large-amplitude stationary oscillations of the finite discrete system of harmonically-coupled pendulums without any restrictions to their amplitudes (excluding a vicinity of $\pi$). Although this…
We describe an explicitly discrete model of the process of DNA branch migration. The model matches the existing data well, but we find that branch migration along long strands of DNA ($N \simge 40$~bp) is also well modeled by continuum…
We describe the macroscopic behaviour of a particle system with long-range interactions. We describe conditions on the interaction strength in dependency of the distance of the particles, such that the scaling limit of the particle system…
We formulate a scaling theory for the long-time diffusive motion in a space occluded by a high density of moving obstacles in dimensions 1, 2 and 3. Our tracers diffuse anomalously over many decades in time, before reaching a diffusive…
We give a method for taking microscopic limits of normal matrix ensembles. We apply this method to study the behaviour near certain types of singular points on the boundary of the droplet. Our investigation includes ensembles without…
A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves…
In the context of mathematical modeling, it is sometimes convenient to integrate models of different nature. These types of combinations, however, might entail difficulties even when individual models are well-understood, particularly in…
We focus on an epidemiological model (the archetypical SIR system) defined on graphs and study the asymptotic behavior of the solutions as the number of vertices in the graph diverges. By relying on the theory of so called graphons we…
This chapter aims to inform a practitioner about current methods for predicting potential distributions of invasive species. It mostly addresses single species models, covering the conceptual bases, touching on mechanistic models, and then…
We study families of dependent site percolation models on the triangular lattice ${\mathbb T}$ and hexagonal lattice ${\mathbb H}$ that arise by applying certain cellular automata to independent percolation configurations. We analyze the…
We introduce a continuum percolation model defined on the points of a d-dimensional homogeneous Poisson process. Each Poisson point is connected to all points within its connection range, which depends on the distances to the other Poisson…