Related papers: Chain Paradoxes
It is revealed that distribution functions of practical gases relate to singularities and such singularities can, with molecular motion, spread to the entire region of interest. It is also shown that even common continuous distribution…
Discovery of causal relations is fundamental for understanding the dynamics of complex systems. While causal interactions are well defined for acyclic systems that can be separated into causally effective subsystems, a mathematical…
In this work, we study the dynamical systems analysis of phantom dark energy models considering a general potential. The stability analysis of the system shows that there is only one fixed point which could be the beginning of the universe…
One dimensional systems are under intense investigation, both from theoretical and experimental points of view, since they have rather peculiar characteristics which are of both conceptual and technological interest. We analyze the…
Contraction theory is a mathematical framework for studying the convergence, robustness, and modularity properties of dynamical systems and algorithms. In this opinion paper, we provide five main opinions on the virtues of contraction…
Model transformations operate on models conforming to precisely defined metamodels. Consequently, it often seems relatively easy to chain them: the output of a transformation may be given as input to a second one if metamodels match.…
The central problem of fully developed turbulence is the energy cascading process. It has revisited all attempts at a full physical understanding or mathematical formulation. The main reason for this failure are related to the large…
In this article, we consider transport networks with uncertain demands. Network dynamics are given by linear hyperbolic partial differential equations and suitable coupling conditions, while demands are incorporated as solutions to…
We consider a one dimensional infinite chain of har- monic oscillators whose dynamics is perturbed by a stochastic term conserving energy and momentum. We prove that in the unpinned case the macroscopic evolution of the energy converges to…
Bayesian networks are directed acyclic graphs representing independence relationships among a set of random variables. A random variable can be regarded as a set of exhaustive and mutually exclusive propositions. We argue that there are…
We give a survey on classical and recent applications of dynamical systems to number theoretic problems. In particular, we focus on normal numbers, also including computational aspects. The main result is a sufficient condition for…
We introduce a notion of $\varepsilon$-chains for continuous-time semiflows inspired by the shadow-orbit property. Although this definition differs from the $(\varepsilon,T)$-chains introduced by Conley, we prove that, for semiflows with…
We consider a many-parametric piecewise mapping with discontinuity. That is a one dimensional model of singular dynamic system. The stability boundary are calculated analytically and numerically. New typical features of stable cycle…
Chaotic systems arise naturally in Statistical Mechanics and in Fluid Dynamics. A paradigm for their modelization are smooth hyperbolic systems. Are there consequences that can be drawn simply by assuming that a system is hyperbolic? here…
We introduce a field theoretic formalism enabling the direct study of dislocation and interstitial dynamics. Explicit expressions for the energies of such defects are given. We provide links to earlier numerical, discrete elastic, time…
The reversibility and recurrence paradoxes are key issues that have been left unsolved in researches on the foundation of thermodynamics since the 19th century. This article shows that (1) the reversibility paradox can be overcome if we pay…
In this paper we present an approach in which synchronization of chaos is used to address identification problems. In particular, we are able to identify: (i) the discontinuity points of systems described by piecewise dynamical equations…
Percolation has long served as a model for diverse phenomena and systems. The percolation transition, that is, the formation of a giant cluster on a macroscopic scale, is known as one of the most robust continuous transitions. Recently,…
We develop a dynamical systems theory for the compressible Navier-Stokes equations based on global in time weak solutions. The following questions will be addressed: Global existence and critical values of the adiabatic constant;…
We prove that for every discrete-time linear switching system in two complex variables and with finitely many switching states, either the system is Lyapunov stable or there exists a trajectory which escapes to infinity with at least linear…