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At least 1,297 records · Page 72Linked to original sources
PubMed2006

Localized gap-edge fields of one-dimensional photonic crystals with an epsilon-negative and a mu-negative defect.

We study the properties of one-dimensional photonic crystals with an epsilon-negative and a mu-negative defect. With suitable parameters, the pair defect is equivalent to a transparent material with zero effective refractive index. This special pair defect has no influence on the spectral gap formed by the interference of propagating waves in positive-refractive-index materials. However, the field distribution is modified noticeably by the decaying wave in the pair defect. Particularly, the gap-edge field can be a highly localized wave instead of the usual standing wave as the size of the pair defect increases. The localized gap-edge field can reduce the switching thresholds for bistability greatly when Kerr-type nonlinear mu-negative material is involved. A nonideal model when the epsilon-negative and mu-negative materials are dispersive and lossy is used to verify the unusual properties.

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PubMed2006

Complex behavior in driven unidirectionally coupled overdamped Duffing elements.

It is well known that overdamped unforced dynamical systems do not oscillate. However, well-designed coupling schemes, together with the appropriate choice of initial conditions, can induce oscillations (corresponding to transitions between the stable steady states of each nonlinear element) when a control parameter exceeds a threshold value. In recent publications [A. Bulsara, Phys. Rev. E 70, 036103 (2004); V. In, ibid. 72, 045104 (2005)], we demonstrated this behavior in a specific prototype system, a soft-potential mean-field description of the dynamics in a hysteretic "single-domain" ferromagnetic sample. These oscillations are now finding utility in the detection of very weak "target" magnetic signals, via their effect on the oscillation characteristics--e.g., the frequency and asymmetry of the oscillation wave forms. We explore the underlying dynamics of a related system, coupled bistable "standard quartic" dynamic elements; the system shows similarities to, but also significant differences from, our earlier work. dc as well as time-periodic target signals are considered; the latter are shown to induce complex oscillatory behavior in different regimes of the parameter space. In turn, this behavior can be harnessed to quantify the target signal.

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PubMed2006

Stochastic resonance due to internal noise in reaction kinetics.

We study a reaction model that presents stochastic resonance purely due to internal noise. This means that the only source of fluctuations comes from the discrete character of the reactants, and no more noises enter into the system. Our analysis reveals that the phenomenon is highly complex, and that is generated by the interplay of different stochasticity at the three fixed points of a bistable system.

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PubMed2006

Fractional translational diffusion of a Brownian particle in a double well potential.

The fractional translational diffusion of a particle in a double-well potential (excluding inertial effects) is considered. The position correlation function and its spectrum are evaluated using a fractional probability density diffusion equation (based on the diffusion limit of a fractal time random walk). Exact and approximate solutions for the dynamic susceptibility describing the position response to a small external field are obtained. The exact solution is given by matrix continued fractions while the approximate solution relies on the exponential separation of the time scales of the fast "intrawell" and low overbarrier relaxation processes associated with the bistable potential. It is shown that knowledge of the characteristic relaxation times for normal diffusion allows one to predict accurately the anomalous relaxation behavior of the system for all relevant time scales.

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PubMed2006

Relaxation of a one-dimensional gravitational system.

We study the relaxation towards thermodynamical equilibrium of a one-dimensional gravitational system. This model shows a series of critical energies E(cn) where different equilibria appear and we focus on the homogeneous (n=0), one-peak (n = +/-1), and two-peak (n=2) states. Using numerical simulations we investigate the relaxation to the stable equilibrium n = +/-1 of this N-body system starting from initial conditions defined by equilibria n=0 and n=2. We find that in a fashion similar to other long-range systems the relaxation involves a fast violent relaxation phase followed by a slow collisional phase as the system goes through a series of quasistationary states. Moreover, in cases where this slow second stage leads to a dynamically unstable configuration (two peaks with a high mass ratio) it is followed by a different sequence, "violent relaxation-slow collisional relaxation." We obtain an analytical estimate of the relaxation time t(2--> +/- 1)through the mean escape time of a particle from its potential well in a bistable system. We find that the diffusion and dissipation coefficients satisfy Einstein's relation and that the relaxation time scales as Ne(1/T) at low temperature, in agreement with numerical simulations.

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PubMed2006

One-way coupling enables noise-mediated spatiotemporal patterns in media of otherwise quiescent multistable elements.

Recent work has demonstrated that undriven and overdamped bistable systems, which are normally quiescent, can oscillate if unidirectionally coupled into arrays with cyclic boundary conditions. Here, we understand such oscillations as corresponding to the propagation of solitonlike waves. Further, in large arrays, we demonstrate how noise and coupling, together, mediate the resulting complex spatiotemporal dynamics.

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PubMed2006

Coexistence of tonic firing and bursting in cortical neurons.

Sustained neuronal activity can be broadly classified as either tonic firing or bursting. These two major patterns of neuronal oscillations are state dependent and may coexist. The dynamics and intracellular mechanisms of transitions between tonic firing and bursting in cortical networks remain poorly understood. Here we describe a detailed two-compartment conductance-based cortical neuron model which exhibits bistability with hysteresis between tonic firing and bursting for elevated extracellular potassium concentration. The study explains the ionic and dynamical mechanisms of burst generation and reveals the conditions underlying coexistence of two different oscillatory modes as a function of neuronal excitability.

Action Potentials↗
PubMed2006

Wave-front dynamics in systems with directional anomalous diffusion.

In this paper we study the solutions of a generalized reaction-diffusion system with a bistable reaction term, and considering directional anomalous diffusion. We use the well-known properties of fractional derivatives to model asymmetric anomalous diffusion, and obtain traveling wave solutions that propagate in a direction that depends on the metastability of the front, the fractional exponent and the asymmetry of the diffusion.

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PubMed2000

Presence of many stable nonhomogeneous states in an inertial car-following model

We present a single lane car- following model of traffic flow which is inertial and free of collisions. It demonstrates observed features of traffic flow such as existence of three regimes: free, nonhomogeneous congested (NHC) or synchronized, and homogeneous congested (HC) or jammed flow; bistability of free and NHC flow states in a range of densities, hysteresis in transitions between these states; jumps in the density-flux plane in the NHC regime; gradual spatial transition from synchronized to free flow; long survival time of jams in the HC regime. The model predicts that in the NHC regime there exist many stable states with different wavelengths, and noise can cause transitions between them.

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PubMed2000

Modulated optical lattice as an atomic fabry-perot interferometer

We propose to engineer the atomic band structure in optical lattices in order to design a Fabry-Perot interferometer with large mode spacing and strong nonlinear coupling to be employed in atom optics. The use of an optical lattice allows for a significant reduction of the atomic effective mass, while the slow modulation of its parameters spatially confines the matter waves on a length scale of a few dozen optical wavelengths. As a consequence, the mode spacing in such a cavity would be as high as one-tenth of the recoil energy, allowing for a very efficient filter action, while the nonlinear coupling due to interatomic interactions could lead to bistability and limiting effects in the transmission of the atomic beam.

Journal Article↗
PubMed2000

Dispersion gap and localized spiral waves in a model for intracellular Ca2+ dynamics.

The dispersion relation is the dependence of the velocity of periodic planar wave trains on their wavelength. We study the occurrence of a velocity gap in the dispersion relation in a bistable three component reaction-diffusion system modeling intracellular Ca2+ dynamics. In two spatial dimensions, localized pinned spirals are observed, if their wavelength falls into the dispersion gap. Destruction of free spirals occurs already for conditions where the asymptotic planar wave train exists and the dispersion gap is absent.

Calcium↗
PubMed2000

Structures of thermal double donors in silicon

Accurate total-energy calculations are used to study the structures and formation energies of oxygen chains as models for thermal double donors (TDD's) in Si. We find that the first three TDD's (TDD0-TDD2) consist of one four-member ring, with one or two adjacent interstitial O atoms. These metastable TDD's form bistable negative-U systems with the corresponding stable, electrically inactive staggered structures. The TDD3-TDD7 structures are found to consist of four-member rings with adjacent interstitial O atoms at both ends. The TDD's with a central "di-Y-lid" core are found to become energetically competitive with the four-member ring TDD's only for clusters larger than ten O atoms.

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PubMed2000

From low-dimensional synchronous chaos to high-dimensional desynchronous spatiotemporal chaos in coupled systems

The dynamic behavior of coupled chaotic oscillators is investigated. For small coupling, chaotic state undergoes a transition from a spatially disordered phase to an ordered phase with an orientation symmetry breaking. For large coupling, a transition from full synchronization to partial synchronization with translation symmetry breaking is observed. Two bifurcation branches, one in-phase branch starting from synchronous chaos and the other antiphase branch bifurcated from spatially random chaos, are identified by varying coupling strength epsilon. Hysteresis, bistability, and first-order transitions between these two branches are observed.

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PubMed2001

Uniting Bose-Einstein condensates in optical resonators.

The relative phase of two initially independent Bose-Einstein condensates can be laser cooled to unite the two condensates by putting them into a ring cavity and coupling them with an internal Josephson junction. First, we show that this phase cooling process already appears within a semiclassical model. We calculate the stationary states, find regions of bistable behavior, and suggest a Ramsey-type experiment to measure the buildup of phase coherence between the condensates. We also study quantum effects and imperfections of the system.

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PubMed2001

Nonlinear micromechanical Casimir oscillator.

The Casimir force between uncharged metallic surfaces originates from quantum-mechanical zero-point fluctuations of the electromagnetic field. We demonstrate that this quantum electrodynamical effect has a profound influence on the oscillatory behavior of microstructures when surfaces are in close proximity (< or =100 nm). Frequency shifts, hysteretic behavior, and bistability caused by the Casimir force are observed in the frequency response of a periodically driven micromachined torsional oscillator.

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PubMed2001

Energy dissipation in atomic force microscopy and atomic loss processes.

Atomic scale dissipation is of great interest in nanomechanics and atomic manipulation. We present dissipation measurements with a linearized, ultra-small amplitude atomic force microscope which is capable of measuring dissipation at chosen, fixed separations. We show that the dynamic dissipation in the noncontact regime is of the order of a few 10-100 meV per cycle. This dissipation is likely due to the motion of a bistable atomic defect in the tip-surface region. In the contact regime we observe dc hysteresis associated with nanoscale plasticity. We find the hysteretic energy loss to be 1 order of magnitude higher for a silicon surface than for copper.

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PubMed2001

Droplet nucleation and domain wall motion in a bounded interval.

We study a spatially extended model of noise-induced magnetization reversal: a classical Ginzburg-Landau model, restricted to a bounded interval and perturbed by weak spatiotemporal noise. By adapting the Coleman-Langer approach to false vacuum decay, we determine the dependence of the activation barrier and Kramers rate prefactor on the interval length. As it increases, a transition between activation regimes occurs, at which the prefactor diverges. Similar transitions between activation regimes should occur in many other bistable, spatially extended classical models.

Journal Article↗
PubMed2001

Noise induced propagation in monostable media.

We show that external fluctuations are able to induce propagation of harmonic signals through monostable media. This property is based on the phenomenon of doubly stochastic resonance, where the joint action of multiplicative noise and spatial coupling induces bistability in an otherwise monostable extended medium, and additive noise resonantly enhances the response of the system to a harmonic forcing. Under these conditions, propagation of the harmonic signal through the unforced medium is observed for optimal intensities of the two noises. This noise-induced propagation is studied and quantified in a simple model of coupled nonlinear electronic circuits.

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