Related papers: Shadowing effects for continuum and discrete depos…
We propose the first continuous model with long range screening (shadowing) that described columnar growth in one space dimension, as observed in plasma sputter deposition. It is based on a new continuous partial derivative equation with…
We look at the preservation of various notions of shadowing in discrete dynamical systems under inverse limits, products, factor maps and the induced maps for symmetric products and hyperspaces. The shadowing properties we consider are the…
There are three fundamental physical processes that gives rise to the morphology of a surface: deposition, surface diffusion and desorption. The characteristics of the interfaces generated by the combination of deposition and surface…
Shadow molecular dynamics provide an efficient and stable atomistic simulation framework for flexible charge models with long-range electrostatic interactions. While previous implementations have been limited to atomic monopole charge…
Accurately modeling the effects of illumination and shadows during head rotation is critical in computer vision for enhancing image realism and reducing artifacts. This study delves into the latent space of denoising diffusion models to…
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 consider the problem of shadowing for differential equations with grow-up. We introduce so-called nonuniform shadowing properties (in which size of the error depends on the point of the phase space) and prove for them analogs of…
In this paper we provide theoretical results that relate steady states of continuous and discrete models arising from biology.
A simple (2+1) dimensional discrete model is introduced to study the evolution of solid surface morphologies during ion-beam sputtering. The model is based on the same assumptions about the erosion process as the existing analytic theories.…
Inhomogeneities in deposition may lead to formation of rough surfaces, whose height fluctuations can be probed directly by scanning microscopy, or indirectly by scattering. Analytical or numerical treatments of simple growth models suggest…
Ordinary differential equation (ODE) models of gradient-based optimization methods can provide insights into the dynamics of learning and inspire the design of new algorithms. Unfortunately, this thought-provoking perspective is weakened by…
In this paper we examine the interplay between recurrence properties and the shadowing property in dynamical systems on compact metric spaces. In particular, we demonstrate that if the dynamical system $(X,f)$ has shadowing, then it is…
We formalize the intuitive idea of a labelled discrete surface which evolves in time, subject to two natural constraints: the evolution does not propagate information too fast; and it acts everywhere the same.
In this paper we consider a discrete or continuous landscape with correlations and we consider a source of light (a sun) at infinity emitting parallel rays of light making a slope l with the horizontal plane. Depending on the value of l…
We strengthen a result of two of us on the existence of effective interactions for discretised continuous-spin models. We also point out that such an interaction cannot exist at very low temperatures. Moreover, we compare two ways of…
Formally capturing the transition from a continuous model to a discrete model is investigated using model based refinement techniques. A very simple model for stopping (eg. of a train) is developed in both the continuous and discrete…
In this paper, we examine the notion of topological stability and its relation to the shadowing properties in zero-dimensional spaces. Several counter-examples on the topological stability and the shadowing properties are given. Also, we…
We study shadowing-type properties for set-valued dynamical systems. In particular, we investigate the periodic shadowing property and its relationship with expansivity and chain transitivity. We establish that for positively expansive…
Recent experiments of imbibition in columnar geometries show interfacial fluctuations whose dynamic scaling is not compatible with the usual non local model governed by surface tension that results from a macroscopic description. To explore…
Self-organisation of individuals within large collectives occurs throughout biology. Mathematical models can help elucidate the individual-level mechanisms behind these dynamics, but analytical tractability often comes at the cost of…