139,099 research outputs found
Qualitative analysis of the dynamics of the time delayed Chua's circuit
IEEE TRANS. CIRCUITS SYST.
Scaling of Chaos in Strongly Nonlinear Lattices
Although it is now understood that chaos in complex classical systems is the
foundation of thermodynamic behavior, the detailed relations between the
microscopic properties of the chaotic dynamics and the macroscopic
thermodynamic observations still remain mostly in the dark. In this work, we
numerically analyze the probability of chaos in strongly nonlinear Hamiltonian
systems and find different scaling properties depending on the nonlinear
structure of the model. We argue that these different scaling laws of chaos
have definite consequences for the macroscopic diffusive behavior, as chaos is
the microscopic mechanism of diffusion. This is compared with previous results
on chaotic diffusion [New J.\ Phys.\ 15, 053015 (2013)], and a relation between
microscopic chaos and macroscopic diffusion is established.Comment: 6 pages, 4 figure
Theory of weakly nonlinear self sustained detonations
We propose a theory of weakly nonlinear multi-dimensional self sustained
detonations based on asymptotic analysis of the reactive compressible
Navier-Stokes equations. We show that these equations can be reduced to a model
consisting of a forced, unsteady, small disturbance, transonic equation and a
rate equation for the heat release. In one spatial dimension, the model
simplifies to a forced Burgers equation. Through analysis, numerical
calculations and comparison with the reactive Euler equations, the model is
demonstrated to capture such essential dynamical characteristics of detonations
as the steady-state structure, the linear stability spectrum, the
period-doubling sequence of bifurcations and chaos in one-dimensional
detonations and cellular structures in multi- dimensional detonations
The effects of kinematic condensation on internally resonant forced vibrations of shallow horizontal cables
This study aims at comparing non-linear modal interactions in shallow horizontal cables with kinematically non-condensed vs. condensed modeling, under simultaneous primary external and internal resonances. Planar 1:1 or 2:1 internal resonance is considered. The governing partial-differential equations of motion of non-condensed model account for spatio-temporal modification of dynamic tension, and explicitly capture non-linear coupling of longitudinal/ vertical displacements. On the contrary, in the condensed model, a single integro-differential equation is obtained by eliminating the longitudinal inertia according to a quasi-static cable stretching assumption, which entails spatially uniform dynamic tension. This model is largely considered in the literature. Based on a multi-modal discretization and a second-order multiple scales solution accounting for higher-order quadratic effects of a infinite number of modes, coupled/uncoupled dynamic responses and the associated stability are evaluated by means of frequency- and force-response diagrams. Direct numerical integrations confirm the occurrence of amplitude-steady or -modulated responses. Non-linear dynamic configurations and tensions are also examined. Depending on internal resonance condition, system elasto-geometric and control parameters, the condensed model may lead to significant quantitative and/or qualitative discrepancies, against the non-condensed model, in the evaluation of resonant dynamic responses, bifurcations and maximal/minimal stresses. Results of even shallow cables reveal meaningful drawbacks of the kinematic condensation and allow us to detect cases where the more accurate non-condensed model has to be used
Quantum Mechanical Hysteresis and the Electron Transfer Problem
We study a simple quantum mechanical symmetric donor-acceptor model for
electron transfer (ET) with coupling to internal deformations. The model
contains several basic properties found in biological ET in enzymes and
photosynthetic centers; it produces tunnelling with hysteresis thus providing a
simple explanation for the slowness of the reversed rate and the near 100%
efficiency of ET in many biological systems. The model also provides a
conceptual framework for the development of molecular electronics memory
elements based on electrostatic architectures.Comment: Accepted Physica
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