In this work, we investigate resonance and antiresonance behaviour in forced coupled Duffing oscillators with nonlinear damping. Further, we will analyse the parameter dependence of the frequency response and stability. In the course of all the analysis, emphasis shall be on how different damping mechanisms contrast against each other.
A class of piecewise $C^2$ Lozi-like maps in three-dimensional Euclidean spaces is introduced, and the existence of Sinai-Ruelle-Bowen measures is studied, where the dimension of the instability is equal to two. Further, an example with computer simulations is provided to illustrate the theoretical results.
Numerical experiments with the standard map at high values of the stochasticity parameter reveal the existence of simple analytical relations connecting the volume and the dynamical temperature of the chaotic component of the phase space.
The Kompaneets theory of photon kinetic evolution due to the Compton effect is extended to the case of the Vlasov plasma wave oscillations. Taking into account Zel'dovich-Levich's approximation we study interaction of accumulating photons with plasma in the long wavelength limit.
The two‐stage clonal expansion model is a popular model for carcinogenesis data. One common form of this model is based on the approximate hazard function. In certain situations, this formulation is not appropriate, and the exact hazard should be applied. However, the difficulty of implementing the model based on the exact hazard has deterred many from using it. This paper presents a program implementing the exact hazard model for piecewise constant dosing using SAS, a package that is readily available to most that are interested in this type of analysis. Also, an analysis of the ED01 data is presented using this program, and comparisons are made to an earlier analysis based on the approximate hazard. By allowing for an independent background tumor mechanism, an excellent fit to the bladder tumor incidence data was obtained.
By viewing the covers of a fractal as a statistical mechanical system, the exact capacity of a multifractal is computed. The procedure can be extended to any multifractal described by a scaling function to show why the capacity and Hausdorff dimension are expected to be equal.
In an early work, Bernoulli shift dynamics of submanifolds was established in a neighborhood of a homoclinic tube. In this article, we will present a concrete example: sine-Gordon equation under a quasi-periodic perturbation.
It is shown that, under suitable conditions, involving in particular the existence of analytic constants of motion, the presence of Lie point symmetries can ensure the convergence of the transformation taking a vector field (or dynamical system) into normal form.
Using EDQNM approximation, it is shown that the magnetic stretching term is responsible for turning the small-scale turbulent structures into the large coherent magnetic structures in the 2-D MHD turbulence.
Resorting to classical techniques of Riemannian geometry we develop a geometrical method suitable to investigate the nonintegrability of geodesic flows and of natural Hamiltonian systems. Then we apply such method to the Anisotropic Kepler Problem (AKP) and we prove that it is not analytically integrable.
This material was presented in a series of lectures at the Santa Fe Institute, the Los Alamos National Laboratory, and the University of New Mexico, during a one-month visit to the Santa Fe Institute, April 1995.
A quantum system is described, whose wave function has a complexity which increases exponentially with time. Namely, for any fixed orthonormal basis, the number of components required for an accurate representation of the wave function increases exponentially.
We consider the transport of passive admixture in locally homogeneous isotropic reflectionally noninvariant turbulence of incompressible fluid. It is shown that anomalous convective flow appears which direction does not coincide with that of a mean flow.
Asymptotic behaviour of a tippe top, under the action of gliding friction. Liapunov stability analysis of the asymptotics of states with arbitrary initial conditions.