Bifurcations and Chaos in Time Delayed Piecewise Linear Dynamical Systems

We reinvestigate the dynamical behavior of a first order scalar nonlinear delay differential equation with piecewise linearity and identify several interesting features in the nature of bifurcations and chaos associated with it as a function of the delay time and external forcing parameters. In particular, we point out that the fixed point solution exhibits a stability island in the two parameter space of time delay and strength of nonlinearity. Significant role played by transients in attaining steady state solutions is pointed out. Various routes to chaos and existence of hyperchaos even for low values of time delay which is evidenced by multiple positive Lyapunov exponents are brought out. The study is extended to the case of two coupled systems, one with delay and the other one without delay.Comment: 34 Pages, 14 Figure

Multistability in nonlinear left-handed transmission lines

Employing a nonlinear left-handed transmission line as a model system, we demonstrate experimentally the multi-stability phenomena predicted theoretically for microstructured left-handed metamaterials with a nonlinear response. We show that the bistability is associated with the period doubling which at higher power may result in chaotic dynamics of the transmission line

Triggering up states in all-to-all coupled neurons

Slow-wave sleep in mammalians is characterized by a change of large-scale cortical activity currently paraphrased as cortical Up/Down states. A recent experiment demonstrated a bistable collective behaviour in ferret slices, with the remarkable property that the Up states can be switched on and off with pulses, or excitations, of same polarity; whereby the effect of the second pulse significantly depends on the time interval between the pulses. Here we present a simple time discrete model of a neural network that exhibits this type of behaviour, as well as quantitatively reproduces the time-dependence found in the experiments.Comment: epl Europhysics Letters, accepted (2010

Do columnar defects produce bulk pinning?

From magneto-optical imaging performed on heavy-ion irradiated YBaCuO single crystals, it is found that at fields and temperatures where strong single vortex pinning by individual irradiation-induced amorphous columnar defects is to be expected, vortex motion is limited by the nucleation of vortex kinks at the specimen surface rather than by half-loop nucleation in the bulk. In the material bulk, vortex motion occurs through (easy) kink sliding. Depinning in the bulk determines the screening current only at fields comparable to or larger than the matching field, at which the majority of moving vortices is not trapped by an ion track.Comment: 5 pages, 5 figures, submitted to Physical Review Letter

Stellar Populations in the Phoenix Dwarf (dIrr/dSph) Galaxy as Observed by HST/WFPC2

We present HST/WFPC2 photometry of the central regions of the Phoenix dwarf. Accurate photometry allows us to: 1) confirm the existence of the horizontal branch previously detected by ground-based observations, and use it to determine a distance to Phoenix, 2) clearly detect the existence of multiple ages in the stellar population of Phoenix, 3) determine a mean metallicity of the old red giant branch stars in Phoenix, and suggest that Phoenix has evolved chemically over its lifetime, 4) extract a rough star formation history for the central regions which suggests that Phoenix has been forming stars roughly continuously over its entire lifetime.Comment: Accepted by AJ, 22 pages including 6 figures + 1 figure in JPEG forma

Separation of suspended particles in microfluidic systems by directional-locking in periodic fields

We investigate the transport and separation of overdamped particles under the action of a uniform external force in a two-dimensional periodic energy landscape. Exact results are obtained for the deterministic transport in a square lattice of parabolic, repulsive centers that correspond to a piecewise-continuous linear-force model. The trajectories are periodic and commensurate with the obstacle lattice and exhibit phase-locking behavior in that the particle moves at the same average migration angle for a range of orientation of the external force. The migration angle as a function of the orientation of the external force has a Devil's staircase structure. The first transition in the migration angle was analyzed in terms of a Poincare map, showing that it corresponds to a tangent bifurcation. Numerical results show that the limiting behavior for impenetrable obstacles is equivalent to the high Peclet number limit in the case of transport of particles in a periodic pattern of solid obstacles. Finally, we show how separation occurs in these systems depending on the properties of the particles

Non-monotonic pseudo-gap in high-Tc cuprates

The mechanism of high temperature superconductivity is not resolved for so long because the normal state of cuprates is not yet understood. Here we show that the normal state pseudo-gap exhibits an unexpected non-monotonic temperature dependence, which rules out the possibility to describe it by a single mechanism such as superconducting phase fluctuations. Moreover, this behaviour, being remarkably similar to the behaviour of the charge ordering gap in the transition-metal dichalcogenides, completes the correspondence between these two classes of compounds: the cuprates in the PG state and the dichalcogenides in the incommensurate charge ordering state reveal virtually identical spectra of one-particle excitations as function of energy, momentum and temperature. These results suggest that the normal state pseudo-gap, which was considered to be very peculiar to cuprates, seems to be a general complex phenomenon for 2D metals. This may not only help to clarify the normal state electronic structure of 2D metals but also provide new insight into electronic properties of 2D solids where the metal-insulator and metal-superconductor transitions are considered on similar basis as instabilities of particle-hole and particle-particle interaction, respectively

Renormalization group theory for finite-size scaling in extreme statistics

We present a renormalization group (RG) approach to explain universal features of extreme statistics, applied here to independent, identically distributed variables. The outlines of the theory have been described in a previous Letter, the main result being that finite-size shape corrections to the limit distribution can be obtained from a linearization of the RG transformation near a fixed point, leading to the computation of stable perturbations as eigenfunctions. Here we show details of the RG theory which exhibit remarkable similarities to the RG known in statistical physics. Besides the fixed points explaining universality, and the least stable eigendirections accounting for convergence rates and shape corrections, the similarities include marginally stable perturbations which turn out to be generic for the Fisher-Tippett-Gumbel class. Distribution functions containing unstable perturbations are also considered. We find that, after a transitory divergence, they return to the universal fixed line at the same or at a different point depending on the type of perturbation.Comment: 15 pages, 8 figures, to appear in Phys. Rev.

Stochastic gain in population dynamics

We introduce an extension of the usual replicator dynamics to adaptive learning rates. We show that a population with a dynamic learning rate can gain an increased average payoff in transient phases and can also exploit external noise, leading the system away from the Nash equilibrium, in a reasonance-like fashion. The payoff versus noise curve resembles the signal to noise ratio curve in stochastic resonance. Seen in this broad context, we introduce another mechanism that exploits fluctuations in order to improve properties of the system. Such a mechanism could be of particular interest in economic systems.Comment: accepted for publication in Phys. Rev. Let

Superconductor strip with transport current: Magneto-optical study of current distribution and its relaxation

The dynamics of magnetic flux distributions across a YBaCuO strip carrying transport current is measured using magneto-optical imaging at 20 K. The current is applied in pulses of 40-5000 ms duration and magnitude close to the critical one, 5.5 A. During the pulse some extra flux usually penetrates the strip, so the local field increases in magnitude. When the strip is initially penetrated by flux, the local field either increases or decreases depending both on the spatial coordinate and the current magnitude. Meanwhile, the current density always tends to redistribute more uniformly. Despite the relaxation, all distributions remain qualitatively similar to the Bean model predictions.Comment: RevTeX, 9 pages, 9 figures, submitted to Supercond. Sci. Technol. Revision: MO image and more refs are adde