Related papers: Numerical analysis of grasshopper escapement
The main purpose of this paper is to study both the underdamped and the overdamped dynamics of the nonlinear Helmholtz oscillator with a fractional order damping. For that purpose, we use the Grunwald-Letnikov fractional derivative…
One or more small holes provide non-destructive windows to observe corresponding closed systems, for example by measuring long time escape rates of particles as a function of hole sizes and positions. To leading order the escape rate of…
We identify a fundamental phenomenon of heterogeneous one dimensional random walks: the escape (traversal) time is maximized when the heterogeneity in transition probabilities forms a pyramid-like potential barrier. This barrier corresponds…
This paper investigates the dynamics and integrability of the double spring pendulum, which has great importance in studying nonlinear dynamics, chaos, and bifurcations. Being a Hamiltonian system with three degrees of freedom, its analysis…
We present a comprehensive investigation of $\epsilon$-entropy, $h(\epsilon)$, in dynamical systems, stochastic processes and turbulence. Particular emphasis is devoted on a recently proposed approach to the calculation of the…
We explore the escape dynamics in open Hamiltonian systems with multiple channels of escape continuing the work initiated in Part I. A thorough numerical investigation is conducted distinguishing between trapped (ordered and chaotic) and…
We compare the performance of several discretizations of the simple pendulum equation in a series of numerical experiments. The stress is put on the long-time behaviour. We choose for the comparison numerical schemes which preserve the…
We study deterministic escape dynamics in the framework of the discrete Klein-Gordon modelwith a repulsive quartic on-site potential. Using a combination of analytical techniques, based on differential and algebraic inequalities and…
When placed in parallel magnetic and electric fields, the electron trajectories of a classical hydrogen atom are chaotic. The classical escape rate of such a system can be computed with classical trajectory Monte Carlo techniques, but these…
We have studied the nature of classical work ($W_{c}$) and thermodynamic work ($W$) fluctuations in systems driven out of equilibrium both in transient and time periodic steady state. As the observation time of trajectory increases, we show…
We introduce a new methodology for the analysis of the phenomenon of chaotic itinerancy in a dynamical system using the notion of entropy and a clustering algorithm. We determine systems likely to experience chaotic itinerancy by means of…
Analytical solutions to the chaotic and ergodic motion of a certain class of one-dimensional dissipative and discrete dynamical systems are derived. This allows us to obtain exact expressions for physical properties like the time…
We investigate the classical scattering dynamics of the driven elliptical billiard. Two fundamental scattering mechanisms are identified and employed to understand the rich behavior of the escape rate. A long-time algebraic decay which can…
This paper considers the chattering problem of sliding mode control while delay in robot manipulator caused chaos in such electromechanical systems. Fractional calculus as a powerful theorem to produce a novel sliding mode; which has a…
We consider a system-reservoir model where the reservoir is modulated by an external noise. Both the internal noise of the reservoir and the external noise are stationary, Gaussian and are characterized by arbitrary decaying correlation…
Using the damped pendulum system we introduce the averaging method to study the periodic solutions of a dynamical system with small perturbation. We provide sufficient conditions for the existence of periodic solutions with small amplitude…
Inspired by the experimental results of Cuevas et al. (Physical Review Letters 102, 224101 (2009)), we consider theoretically the behavior of a chain of planar rigid pendulums suspended in a uniform gravitational field and subjected to a…
A set of algorithms is presented for efficient numerical calculation of the time evolution of classical dynamical systems. Starting with a first approximation for solving the differential equations that has a "reversible" character, we show…
We investigate an optomechanical system as a model of an autonomous mechanical pendulum clock in the quantum regime, whose operation relies only on incoherent (thermal) resources. The escapement of the clock, the mechanism that translates…
The dynamics of the tip of the falling chain is analyzed. Results of laboratory experiments are presented and compared with results of numerical simulations. Time dependences of the velocity and the acceleration of the chain tip for a…