相关论文: Constants of Motion for Conserved and Non-conserve…

We consider two linearly coupled masses, where one mass can have inelastic impacts with a fixed, rigid stop. This leads to the study of a two degree of freedom, piecewise linear, frictionless, unforced, constrained mechanical system. The…

In the present work we examine the dynamics of a model for oscillons in 1-dimensional spacetime field theories with a cubic nonlinearity. We utilize a reduction of the model to first and third harmonics, which leads to a reduced partial…

We investigate the stability properties of discrete and hybrid stochastic nonlinear dynamical systems. More precisely, we extend the stochastic contraction theorems (which were formulated for continuous systems) to the case of discrete and…

This paper considers discontinuous dynamical systems, i.e., systems whose associated vector field is a discontinuous function of the state. Discontinuous dynamical systems arise in a large number of applications, including optimal control,…

We provide the detailed asymptotic behavior for first-order aggregation models of heterogeneous oscillators. Due to the dissimilarity of natural frequencies, one could expect that all relative distances converge to definite positive value…

In this paper, the compressible quantum model with the given mass source and the external force of general form in three-dimensional whole space is considered. Based on the weighted $L^2$ method and $L^\infty$ estimates, the existence and…

The stability of dynamical systems with oscillatory behaviors and well-defined average vector fields has traditionally been studied using averaging theory. These tools have also been applied to hybrid dynamical systems, which combine…

Dipole-conserving fluids serve as examples of kinematically constrained systems that can be understood on the basis of symmetry. They are known to display various exotic features including glassylike dynamics, subdiffusive transport, and…

The coupled motion is investigated for a mechanical system consisting of water and a body freely floating in it. Water occupies either a half-space or a layer of constant depth into which an infinitely long surface-piercing cylinder is…

Nonlocal constants are functions that are constant along motion but whose value depends on the past history of the motion itself. They are a powerful tool to provide first integrals in classical mechanics and, in this respect, a new…

We give a recipe to generate "nonlocal" constants of motion for ODE Lagrangian systems and we apply the method to find useful constants of motion for dissipative system, for the Lane-Emden equation, and for the Maxwell-Bloch system with…

The dynamics of dislocations can be formulated in terms of the evolution of continuous variables representing dislocation densities ('continuum dislocation dynamics'). We show for various variants of this approach that the resulting models…

Oscillators have two main limitations: their synchronization properties are limited (i.e they have a finite synchronization region) and they have no memory of past interactions (i.e. they return to their intrinsic frequency whenever the…

It is argued that the world is a dissipative dynamic system, a phase flow of which is formed by conformally-symplectic mapping. The key assumption is that the concept of energy in microcosm makes sense only for the steady motions…

The goal of this paper is to investigate the stability of the Helmholtz equation in the high- frequency regime with non-smooth and rapidly oscillating coefficients on bounded domains. Existence and uniqueness of the problem can be proved…

Some mechanical systems, that are modeled to have inelastic collisions, nonetheless possess energy-conserving intermittent-contact solutions, known as collisionless solutions. Such a solution, representing a persistent hopping or walking…

We investigate the asymptotic behavior of probability measures associated with stochastic dynamical systems featuring either globally contracting or $B_{r}$-contracting drift terms. While classical results often assume constant diffusion…

We formulate a low-storage method for performing dynamic mode decomposition that can be updated inexpensively as new data become available; this formulation allows dynamical information to be extracted from large datasets and data streams.…

Evidence is presented of universal behavior in modulationally unstable media. An ensemble of nonlinear evolution equations, including three partial differential equations, an integro-differential equation, a nonlocal system and a…

Equations of motion are developed for the oscillatory rotation of a disk suspended between twisted strings kept under tension by a hanging mass, to which additional forces may be applied. In the absence of forcing, damped harmonic…