3,857 research outputs found
Stability of a chain of phase oscillators
We study a chain of N + 1 phase oscillators with asymmetric but uniform coupling. This type of chain possesses 2 N ways to synchronize in so-called traveling wave states, i.e., states where the phases of the single oscillators are in relative equilibrium. We show that the number of unstable dimensions of a traveling wave equals the number of oscillators with relative phase close to π . This implies that only the relative equilibrium corresponding to approximate in-phase synchronization is locally stable. Despite the presence of a Lyapunov-type functional, periodic or chaotic phase slipping occurs. For chains of lengths 3 and 4 we locate the region in parameter space where rotations (corresponding to phase slipping) are present
Self-organized escape of oscillator chains in nonlinear potentials
We present the noise free escape of a chain of linearly interacting units
from a metastable state over a cubic on-site potential barrier. The underlying
dynamics is conservative and purely deterministic. The mutual interplay between
nonlinearity and harmonic interactions causes an initially uniform lattice
state to become unstable, leading to an energy redistribution with strong
localization. As a result a spontaneously emerging localized mode grows into a
critical nucleus. By surpassing this transition state, the nonlinear chain
manages a self-organized, deterministic barrier crossing. Most strikingly,
these noise-free, collective nonlinear escape events proceed generally by far
faster than transitions assisted by thermal noise when the ratio between the
average energy supplied per unit in the chain and the potential barrier energy
assumes small values
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Design of coupled Andronov-Hopf oscillators with desired strange attractors
Statistical Mechanics of Recurrent Neural Networks I. Statics
A lecture notes style review of the equilibrium statistical mechanics of
recurrent neural networks with discrete and continuous neurons (e.g. Ising,
coupled-oscillators). To be published in the Handbook of Biological Physics
(North-Holland). Accompanied by a similar review (part II) dealing with the
dynamics.Comment: 49 pages, LaTe
Symmetry-broken dissipative exchange flows in thin-film ferromagnets with in-plane anisotropy
Planar ferromagnetic channels have been shown to theoretically support a
long-range ordered and coherently precessing state where the balance between
local spin injection at one edge and damping along the channel establishes a
dissipative exchange flow, sometimes referred to as a spin superfluid. However,
realistic materials exhibit in-plane anisotropy, which breaks the axial
symmetry assumed in current theoretical models. Here, we study dissipative
exchange flows in a ferromagnet with in-plane anisotropy from a dispersive
hydrodynamic perspective. Through the analysis of a boundary value problem for
a damped sine-Gordon equation, dissipative exchange flows in a ferromagnetic
channel can be excited above a spin current threshold that depends on material
parameters and the length of the channel. Symmetry-broken dissipative exchange
flows display harmonic overtones that redshift the fundamental precessional
frequency and lead to a reduced spin pumping efficiency when compared to their
symmetric counterpart. Micromagnetic simulations are used to verify that the
analytical results are qualitatively accurate, even in the presence of nonlocal
dipole fields. Simulations also confirm that dissipative exchange flows can be
driven by spin transfer torque in a finite-sized region. These results
delineate the important material parameters that must be optimized for the
excitation of dissipative exchange flows in realistic systems.Comment: 20 pages, 5 figure
Hamiltonian formalism of fractional systems
In this paper we consider a generalized classical mechanics with fractional
derivatives. The generalization is based on the time-clock randomization of
momenta and coordinates taken from the conventional phase space. The fractional
equations of motion are derived using the Hamiltonian formalism. The approach
is illustrated with a simple-fractional oscillator in a free state and under an
external force. Besides the behavior of the coupled fractional oscillators is
analyzed. The natural extension of this approach to continuous systems is
stated. The interpretation of the mechanics is discussed.Comment: 16 pages, 5 figure
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