Related papers: Chain Paradoxes
We consider a chain of one-dimensional dipole moments connected to two thermal baths with different temperatures. The system is in nonequilibrium steady state and heat flows through it. Assuming that fluctuation of the dipole moment is a…
Nowadays, chaos theory and nonlinear dynamics lack research focuses. Here we mention a few major open problems: 1. an effective description of chaos and turbulence, 2. rough dependence on initial data, 3. arrow of time, 4. the paradox of…
We analyze the coherent dynamics of excitons in three dimensional topologically disordered networks with traps. If the interactions between the nodes of the network are long ranged, i.e., algebraically decaying as a function of the distance…
A nonlinear cyclic system with delay and the overall negative feedback is considered. The characteristic equation of the linearized system is studied in detail. Sufficient conditions for the oscillation of all solutions and for the…
Limit theorems for a linear dynamical system with random interactions are established. These theorems enable us to characterize the dynamics of a large complex system in details and assess whether a large complex system is stable or…
This article deals with stabilizing discrete-time switched linear systems. Our contributions are threefold: Firstly, given a family of linear systems possibly containing unstable dynamics, we propose a large class of switching signals that…
Continuous and discrete time systems possessing strange non-chaotic attractors are under investigation. It is demonstrated that unpredictable trajectories exist in the dynamics. A recent numerical technique, the sequential test, is utilized…
The theory of substitution sequences and their higher-dimensional analogues is intimately connected with symbolic dynamics. By systematically studying the factors (in the sense of dynamical systems theory) of a substitution dynamical…
This paper studies the distribution of chain and maximal chain lengths in a causal set. We first provide a new derivation for these distributions for a causal set uniformly embedded in Minkowski space, for various dimensionalities, which…
Peculiar measurements can be obtained on systems that undergo both pre- and post-selection. We prove a conjecture from [1] on logical Pre- and Post-Selection (PPS) paradoxes for a restricted case. We prove that all of these paradoxes admit…
Following a brief historical introduction of the notions of chaos in dynamical systems, we will present recent developments that attempt to profit from the rich structure and complexity of the chaotic dynamics. In particular, we will…
Two paradoxical aspects of the prevailing kinetic equations are presented. One is related to the usual understanding of distribution function and the other to the usual understanding of the phase space. With help of simple counterexamples…
We consider the survival probability of a particle in the presence of a finite number of diffusing traps in one dimension. Since the general solution for this quantity is not known when the number of traps is greater than two, we devise a…
We review recent results on the metastable behavior of continuous-time Markov chains derived through the characterization of Markov chains as unique solutions of martingale problems.
This work deals with bifurcation and the chaotic behavior in one dimensional chains of small particles. We consider two distinct possibilities, one where the particles are modeled by a fourth-order potential which was already studied. We…
Understanding the structural evolution of granular systems is a long-standing problem. A recently proposed theory for such dynamics in two dimensions predicts that steady states of very dense systems satisfy detailed-balance. We analyse…
In order to investigate the evolutionary process of many deterministic Dynamical systems with unfixed parameter, a set of dynamical models with parameter changing continuously and the accumulation of this change might be large is introduced…
We prove the existence of fractal solutions to a class of linear ordinary differential equations.This reveals the possibility of chaos in the very short time limit of the evolution even of a linear one dimensional dynamical system.
A loop of chain can move along its own tangents, maintaining a steady shape. An open-ended chain undergoing a nontrivial motion must change its shape. One consequence is that chains pulled around objects will fail to follow the contours of…
The use of linear response theory for forced dissipative stochastic dynamical systems through the fluctuation dissipation theorem is an attractive way to study climate change systematically among other applications. Here, a mathematically…