Related papers: Hysteresis and Stabillity
We prove stability for a class of heterogeneous catalysis models in the $L_p$-setting. We consider a setting in a finite three-dimensional pore of cylinder-like geometry, with the lateral walls acting as a catalytic surface. Under a…
We consider nonequilibrium systems with complex dynamics in stationary states with large fluctuations of intensive quantities (e.g. the temperature, chemical potential, or energy dissipation) on long time scales. Depending on the…
We study the dynamics of a one-dimensional fluid of orientable hard rectangles with a non-coarse-grained microscopic mechanism of facilitation. The length occupied by a rectangle depends on its orientation, which is coupled to an external…
Hysteresis dispersion under a varying external field Hex is investigated through numerical simulations based on the Landau-Lifshitz-Gilbert (LLG) equation, indicating the energy dissipation can be determined by W({\eta}) = A (f, H0). A…
The paper discusses the fundamental characteristics distinguishing the natural and social systems from each other. It considers in detail the basic approaches, prospects, and possibilities of constructing mathematical description for social…
Entropy is a very useful concept from physics that tries to explain how a system behaves from a point of view of the thermodynamics. However, there are two ways to explain entropy, and it depends on if we are studying a microsystem or a…
Various formulations of counterfactual general equilibrium in economies -- systems of actors manipulating economic goods -- are logically and mathematically analyzed. Evenly-rotating economies are systems whose evolution is stable, steady,…
In [1] we present an extension of Prime Event Structures by a mechanism to express dynamicity in the causal relation. More precisely we add the possibility that the occurrence of an event can add or remove causal dependencies between events…
We propose a combination of cluster analysis and stochastic process analysis to characterize high-dimensional complex dynamical systems by few dominating variables. As an example, stock market data are analyzed for which the dynamical…
The problem of proper symmetry definition for constraint dynamical systems with Hamiltonians is considered. Finally, we choose a definition of symmetry which agrees with the analogous definition used for the non-constraint dynamical systems…
We discuss the possibility of making the {\it initial} definitions of mutually different (possibly interacting, or even entangled) systems in the context of decoherence theory. We point out relativity of the concept of elementary physical…
The concept of hypocoercivity for linear evolution equations with dissipation is discussed and equivalent characterizations that were developed for the finite-dimensional case are extended to separable Hilbert spaces. Using the concept of a…
The paper considers some class of dynamical systems that called density systems. For such systems the derivative of quadratic function depends on so-called density function. The density function is used to set the properties of phase space,…
This note discusses dynamical systems-systems that evolve through time. We start with two contemporary examples illustrating the qualitative and the quantitative behavior of dynamical systems. These are two broad categories, usually called…
Hybrid dynamical systems have proven to be a powerful modeling abstraction, yet fundamental questions regarding the dynamical properties of these systems remain. In this paper, we develop a novel class of relaxations which we use to recover…
We consider the systematic force on a heavy probe induced by interaction with an overdamped diffusive medium where particles undergo a rotating force around a fixed center. The stiffness matrix summarizes the stability of the probe around…
During motion from deep to shallow water, multiple equilibria may emerge, each with identical drag - a phenomenon that can be explained by a localised amplification of the wave drag near the shallow wave speed. The implication of this is…
Hysteresis can be found in driven many-body systems such as magnets and superfluids. Rate-dependent hysteresis arises when a system is driven periodically while relaxing towards equilibrium. A two-state paramagnet driven by an oscillating…
Centering theory posits a discourse center, a distinguished discourse entity that is the topic of a discourse. A simplified version of this theory is developed in a Dynamic Semantics framework. In the resulting system, the mechanism of…
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…