4,585 research outputs found
A homoclinic tangle on the edge of shear turbulence
Experiments and simulations lend mounting evidence for the edge state
hypothesis on subcritical transition to turbulence, which asserts that simple
states of fluid motion mediate between laminar and turbulent shear flow as
their stable manifolds separate the two in state space. In this Letter we
describe a flow homoclinic to a time-periodic edge state. Its existence
explains turbulent bursting through the classical Smale-Birkhoff theorem.
During a burst, vortical structures and the associated energy dissipation are
highly localized near the wall, in contrast to the familiar regeneration cycle
Hyperbolic chaos in self-oscillating systems based on mechanical triple linkage: Testing absence of tangencies of stable and unstable manifolds for phase trajectories
Dynamical equations are formulated and a numerical study is provided for
self-oscillatory model systems based on the triple linkage hinge mechanism of
Thurston -- Weeks -- Hunt -- MacKay. We consider systems with holonomic
mechanical constraint of three rotators as well as systems, where three
rotators interact by potential forces. We present and discuss some quantitative
characteristics of the chaotic regimes (Lyapunov exponents, power spectrum).
Chaotic dynamics of the models we consider are associated with hyperbolic
attractors, at least, at relatively small supercriticality of the
self-oscillating modes; that follows from numerical analysis of the
distribution for angles of intersection of stable and unstable manifolds of
phase trajectories on the attractors. In systems based on rotators with
interacting potential the hyperbolicity is violated starting from a certain
level of excitation.Comment: 30 pages, 18 figure
Antiphase dynamics in a multimode semiconductor laser with optical injection
A detailed experimental study of antiphase dynamics in a two-mode
semiconductor laser with optical injection is presented. The device is a
specially designed Fabry-Perot laser that supports two primary modes with a THz
frequency spacing. Injection in one of the primary modes of the device leads to
a rich variety of single and two-mode dynamical scenarios, which are reproduced
with remarkable accuracy by a four dimensional rate equation model. Numerical
bifurcation analysis reveals the importance of torus bifurcations in mediating
transitions to antiphase dynamics and of saddle-node of limit cycle
bifurcations in switching of the dynamics between single and two-mode regimes.Comment: 7 pages, 9 figure
On the limited amplitude resolution of multipixel Geiger-mode APDs
The limited number of active pixels in a Geiger-mode Avalanche Photodiode
(G-APD) results not only in a non-linearity but also in an additional
fluctuation of its response. Both these effects are taken into account to
calculate the amplitude resolution of an ideal G-APD, which is shown to be
finite. As one of the consequences, the energy resolution of a scintillation
detector based on a G-APD is shown to be limited to some minimum value defined
by the number of pixels in the G-APD.Comment: 5 pages, 3 figure
Hopf Bifurcations in a Watt Governor With a Spring
This paper pursues the study carried out by the authors in "Stability and
Hopf bifurcation in a hexagonal governor system", focusing on the codimension
one Hopf bifurcations in the hexagonal Watt governor differential system. Here
are studied the codimension two, three and four Hopf bifurcations and the
pertinent Lyapunov stability coefficients and bifurcation diagrams, ilustrating
the number, types and positions of bifurcating small amplitude periodic orbits,
are determined. As a consequence it is found an open region in the parameter
space where two attracting periodic orbits coexist with an attracting
equilibrium point.Comment: 30 pages and 7 figure
Electron Mass Operator in a Strong Magnetic Field and Dynamical Chiral Symmetry Breaking
The electron mass operator in a strong magnetic field is calculated. The
contribution of higher Landau levels of virtual electrons, along with the
ground Landau level, is shown to be essential in the leading log approximation.
The effect of the electron dynamical mass generation by a magnetic field is
investigated. In a model with N charged fermions, it is shown that some
critical number N_{cr} exists for any value of the electromagnetic coupling
constant alpha, such that the fermion dynamical mass is generated with a
doublet splitting for N < N_{cr}, and the dynamical mass does not arise at all
for N > N_{cr}, thus leaving the chiral symmetry unbroken.Comment: 4 pages, REVTEX4, 3 figure
Universal behavior in populations composed of excitable and self-oscillatory elements
We study the robustness of self-sustained oscillatory activity in a globally
coupled ensemble of excitable and oscillatory units. The critical balance to
achieve collective self-sustained oscillations is analytically established. We
also report a universal scaling function for the ensemble's mean frequency. Our
results extend the framework of the `Aging Transition' [Phys. Rev. Lett. 93,
104101 (2004)] including a broad class of dynamical systems potentially
relevant in biology.Comment: 4 pages; Changed titl
Continuous and discontinuous phase transitions and partial synchronization in stochastic three-state oscillators
We investigate both continuous (second-order) and discontinuous (first-order)
transitions to macroscopic synchronization within a single class of discrete,
stochastic (globally) phase-coupled oscillators. We provide analytical and
numerical evidence that the continuity of the transition depends on the
coupling coefficients and, in some nonuniform populations, on the degree of
quenched disorder. Hence, in a relatively simple setting this class of models
exhibits the qualitative behaviors characteristic of a variety of considerably
more complicated models. In addition, we study the microscopic basis of
synchronization above threshold and detail the counterintuitive subtleties
relating measurements of time averaged frequencies and mean field oscillations.
Most notably, we observe a state of suprathreshold partial synchronization in
which time-averaged frequency measurements from individual oscillators do not
correspond to the frequency of macroscopic oscillations observed in the
population
Stability properties of periodically driven overdamped pendula and their implications to physics of semiconductor superlattices and Josephson junctions
We consider the first order differential equation with a sinusoidal
nonlinearity and periodic time dependence, that is, the periodically driven
overdamped pendulum. The problem is studied in the case that the explicit
time-dependence has symmetries common to pure ac-driven systems. The only
bifurcation that exists in the system is a degenerate pitchfork bifurcation,
which describes an exchange of stability between two symmetric nonlinear modes.
Using a type of Prufer transform to a pair of linear differential equations, we
derive an approximate condition of the bifurcation. This approximation is in
very good agreement with our numerical data. In particular, it works well in
the limit of large drive amplitudes and low external frequencies. We
demonstrate the usefulness of the theory applying it to the models of pure
ac-driven semiconductor superlattices and Josephson junctions. We show how the
knowledge of bifurcations in the overdamped pendulum model can be utilized to
describe effects of rectification and amplification of electric fields in these
microstructures.Comment: 15 pages, 7 figures, Revtex 4.1. Revised and expanded following
referee's report. Submitted to journal Chaos
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