Related papers: Finite Resolution Dynamics
We study the theory of systems with constraints from the point of view of the formal theory of partial differential equations. For finite-dimensional systems we show that the Dirac algorithm completes the equations of motion to an…
The concept of random dynamical system is a comparatively recent development combining ideas and methods from the well developed areas of probability theory and dynamical systems. Due to our inaccurate knowledge of the particular physical…
We present Finite Volume methods for diffusion equations on generic meshes, that received important coverage in the last decade or so. After introducing the main ideas and construction principles of the methods, we review some literature…
We study the cosmological dynamics of a class of symmetric teleparallel gravity theories known as ``newer general relativity'' using the methods of dynamical systems, restricted to the case of vacuum solutions with a spatially flat…
A fully adaptive methodology is developed for reducing the complexity of large dissipative systems. This represents a significant step towards extracting essential physical knowledge from complex systems, by addressing the challenging…
We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous…
This survey paper is aimed to describe a relatively new branch of symbolic dynamics which we call Arithmetic Dynamics. It deals with explicit arithmetic expansions of reals and vectors that have a "dynamical" sense. This means precisely…
A general sufficient condition for the convergence of subsequences of solutions of non-autonomous, nonlinear difference equations and systems is obtained. For higher order equations the delay sizes and patterns play essential roles in…
The paper presents a method by which the mean field dynamics of a population of dynamical systems with parameter diversity and global coupling can be described in terms of a few macroscopic degrees of freedom. The method applies to…
Quantum resonances, i.e., metastable states with a finite lifetime, play an important role in nuclear physics and other domains. Describing this phenomenon theoretically is generally a challenging task. In this work, we combine two…
Directional motion towards a specified destination is a common occurrence in physical processes and human societal activities. Utilizing this prior information can significantly improve the control and predictive performance of system…
Developments in dynamical systems theory provides new support for the discretisation of \pde{}s and other microscale systems. By systematically resolving subgrid microscale dynamics the new approach constructs asymptotically accurate,…
We study the convex geometry of the forward reach sets for integrator dynamics in finite dimensions with bounded control. We derive closed-form expressions for the volume and the diameter (i.e., maximal width) of these sets in terms of the…
We develop a folding approach to study two-dimensional symmetry-enriched topological (SET) phases with the mirror reflection symmetry. Our folding approach significantly transforms the mirror SETs, such that their properties can be…
We conceive finite automata as dynamical systems on discontinuum and investigate their factors. Factors of finite automata include many well-known simple dynamical systems, e.g. hyperbolic systems and systems with finite attractors. In the…
In a complete metric space that is equipped with a doubling measure and supports a Poincar\'e inequality, we study strict subsets, i.e. sets whose variational capacity with respect to a larger reference set is finite, in the case $p=1$.…
We study a two-phase modified Stefan problem modeling solid combustion and nonequilibrium phase transition. The problem is known to exhibit a variety of non-trivial dynamical scenarios. We develop a priori estimates and establish…
We analyze the dynamics of a two-level system subject to driving by large-amplitude external fields, focusing on the resonance properties in the case of driving around the region of avoided level crossing. In particular, we consider three…
Convexity, though extremely important in mathematical programming, has not drawn enough attention in the field of dynamic programming. This paper gives conditions for verifying convexity of the cost-to-go functions, and introduces an…
-Molecular simulations allow the study of properties and interactions of molecular systems. This article presents an improved version of the Adaptive Resolution Scheme that links two systems having atomistic (also called fine-grained) and…