Related papers: Mixing in an anharmonic potential well

We propose a mechanism by which the efficiency of mixing in chaotic flows can be enhanced. Our mechanism consists of introducing small changes in the system parameters in regions of phase space where the local Lyapunov exponent falls…

Physical systems with non-reciprocal or dissipative forces evolve according to a generalization of Liouville's equation that accounts for the expansion and contraction of phase space volume. Here, we connect geometric descriptions of these…

In a recent paper, Melbourne and Terhesiu [Operator renewal theory and mixing rates for dynamical systems with infinite measure, Invent. Math. 189 (2012), 61-110] obtained results on mixing and mixing rates for a large class of…

The Liouville theorem is a fundamental concept in understanding the properties of systems that adhere to Hamilton's equations. However, the traditional notion of the theorem may not always apply. Specifically, when the entropy gradient in…

A condition for the synchronizability of a pair of PDE systems, coupled through a finite set of variables, is commonly the existence of internal synchronization or internal coherence in each system separately. The condition was previously…

Fluid mixing usually involves the interplay between advection and diffusion, which together cause any initial distribution of passive scalar to homogenize and ultimately reach a uniform state. However, this scenario only holds when the…

This article is devoted to the study of the dynamical behavior of a collisionless kinetic gas in d=1,2,3 space dimensions which is trapped in a rotationally symmetric potential well. Although at the microscopic level the trajectories of…

We study metastability and mixing time for a non-reversible probabilistic cellular automaton. With a suitable choice of the parameters, we first show that the stationary distribution is close in total variation to a low temperature Ising…

Providing efficient nonlinear optical frequency conversion is essential for numerous applications. Fundamentally, dispersion limits the efficiency of such processes through mismatch of the phase velocities and the group velocities of the…

This paper summarises a numerical investigation of phase mixing in time-independent Hamiltonian systems that admit a coexistence of regular and chaotic phase space regions, allowing also for low amplitude perturbations idealised as periodic…

We present a phase condition under which there is no suitable multiplier for a given continuous-time plant. The condition can be derived from either the duality approach or from the frequency interval approach. The condition has a simple…

We consider the pipeline flow of blended gas. The flow is governed by a coupled system where for each component we have the isothermal Euler equations with an additional velocity coupling term that couples the velocities of the different…

In its continuous version, the entropy functional measuring the information content of a given probability density may be plagued by a "measure" problem that results from improper weighting of phase space. This issue is addressed…

We describe a simple mechanism to transform bunches with matched longitudinal phase-space distributions from one RF system to a matched distribution of a second RF system operating on a different harmonic and with a different accelerating…

We study the propagation of energy in one-dimensional anharmonic chains subject to a periodic, localized forcing. For the purely harmonic case, forcing frequencies outside the linear spectrum produce exponentially localized responses,…

We consider the game-theoretic approach to time-inconsistent stopping of a one-dimensional diffusion where the time-inconsistency is due to the presence of a non-exponential (weighted) discount function. In particular, we study (weak)…

We study the mixing time of the unit-rate zero-range process on the complete graph, in the regime where the number $n$ of sites tends to infinity while the density of particles per site stabilizes to some limit $\rho>0$. We prove that the…

We derive a general WKB energy splitting formula in a double-well potential by incorporating both phase loss and anharmonicity effect in the usual WKB approximation. A bare application of the phase loss approach to the usual WKB method…

In this paper we consider several families of potential non-isochronous systems and study their associated period functions. Firstly, we prove some properties of these functions, like their local behavior near the critical point or…

The chaotic diffusion for particles moving in a time dependent potential well is described by using two different procedures: (i) via direct evolution of the mapping describing the dynamics and ; (ii) by the solution of the diffusion…