Related papers: Shadowing effects for continuum and discrete depos…
Deformable objects present a formidable challenge for robotic manipulation due to the lack of canonical low-dimensional representations and the difficulty of capturing, predicting, and controlling such objects. We construct compact…
The relaxation process of one dimensional surface modulations is re-examined. Surface evolution is described in terms of a standard step flow model. Numerical evidence that the surface slope, D(x,t), obeys the scaling ansatz…
Causal representation learning promises to extend causal models to hidden causal variables from raw entangled measurements. However, most progress has focused on proving identifiability results in different settings, and we are not aware of…
An investigation of the effect of surface diffusion in random deposition model is made by analytical methods and reasoning. For any given site, the extent to which a particle can diffuse is decided by the morphology in the immediate…
We introduce a deep appearance model for rendering the human face. Inspired by Active Appearance Models, we develop a data-driven rendering pipeline that learns a joint representation of facial geometry and appearance from a multiview…
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…
Video prediction is a crucial task for intelligent agents such as robots and autonomous vehicles, since it enables them to anticipate and act early on time-critical incidents. State-of-the-art video prediction methods typically model the…
In recent years there has been a growing interest in the statistical properties of surfaces growing under deposition of material. Yet it is clear that a theory describing the evolution of a surface should at the same time describe the…
A gradient dynamics model based on an extended interface Hamiltonian is presented that is able to describe the dynamics of structuring processes in thin films of liquid mixtures, solutions and suspensions on solid substrates including…
We use the dynamical analysis to study the evolution of the universe at late time for the model in which the interaction between dark energy and dark matter is inspired by disformal transformation. We extend the analysis in the existing…
We discuss whether classical examples of dynamical systems satisfying the shadowing property also satisfy the shadowing property for the induced map on the hyperspace of continua, obtaining both positive and negative results. We prove that…
We show how permutability of transforms of smooth surfaces with particular characteristics leads to discrete surfaces with discrete analogues of the same characteristics.
A limited mobility nonequilibrium solid-on-solid dynamical model for kinetic surface growth is introduced as a simple description for the morphological evolution of a growing interface under random vapor deposition and surface diffusion…
We study the dynamical properties of a large body of varying vacuum cosmologies for which dark matter interacts with vacuum. In particular, performing the critical point analysis we investigate the existence and the stability of…
In two papers we proposed a continuum model for the dynamics of systems of self propelling particles with kinematic constraints on the velocities and discussed some of its properties. The model aims to be analogous to a discrete algorithm…
The continuum mechanics of line defects representing singularities due to terminating discontinuities of the elastic displacement and its gradient field is developed. The development is intended for application to coupled phase…
We introduce a theoretical framework for differentiable surface evolution that allows discrete topology changes through the use of topological derivatives for variational optimization of image functionals. While prior methods for inverse…
We study the effect of an explicit interaction between two scalar fields components describing dark matter in the context of a recent proposal framework for interaction. We find that, even assuming a very small coupling, it is sufficient to…
We develop categorical foundations of discrete dynamical systems, aimed at understanding how the structure of the system affects its dynamics. The key technical innovation is the notion of a cycle set, which provides a formal language in…
The focus is on discrete defects that can be modeled by continuum mechanics, but where the discreteness of the carriers of plastic deformation plays a significant role. The formulations are restricted to small deformation kinematics and the…