Noise-induced stability of the oscillatory mode of a system of magnetic dipoles

On the basis of numerical analysis, the dynamics of the magnetic moment of a ring system of ball-shaped bodies is studied under its excitation by a harmonic magnetic field and an additional noise signal. A stochastic effect is discovered, in which the system passes, under the action of noise, to unstable (in the absence of an additional excitation) oscillatory mode of the total magnetic moment with a frequency differing from the harmonic field frequency. The possibility of controlling the noise signal intensity, which is necessary for the realization of this effect, is demonstrated.     

Dynamic orientation transitions in a system of magnetic dipoles

Bistable states induced by a varying magnetic field in a system of two, three, and four coupled spherical bodies possessing dipole magnetic moments are studied numerically. Dynamic transitions between low-amplitude regimes differing in the direction of vibrational axis are considered. Possibilities of controlling bistable states by varying magnetic field parameters are indicated.     

Dynamic multistable states in a system of magnetic dipoles

Bistable and multistable states induced by a fluctuating magnetic field in a system of four magnetic dipoles were studied numerically. The possibility of performing switchings and cyclic transitions between the different oscillatory regimes by changing field parameters is examined, along with the possibility of creating conditions under which the system is sensitive to noise signals.     

Equilibrium values and dynamics of the net magnetic moment of a system of magnetic dipoles

Equilibrium states of different systems formed by coupled spherical bodies with dipole magnetic moments have been investigated using a numerical analysis. The bistable states and the corresponding values of the net magnetic moment are determined for a number of planar and three-dimensional systems of dipoles, and the conditions providing the existence of orientational configurations of coupled dipoles involved in the bistability are analyzed. The disturbances of the magnetic moment due to the quasi-static passage of an additional dipole and the dynamic modes excited by a homogeneous alternating magnetic field and represented by periodic, quasi-periodic, and chaotic oscillations of the magnetic moment of the system are considered for several types of systems. The bifurcation diagrams of the dynamic modes are constructed, and the specific features typical of the systems under consideration are revealed.     

Noise-induced mixed-mode oscillations in a relaxation oscillator near the onset of a limit cycle

A detailed asymptotic study of the effect of small Gaussian white noise on a relaxation oscillator undergoing a supercritical Hopf bifurcation is presented. The analysis reveals an intricate stochastic bifurcation leading to several kinds of noise-driven mixed-mode oscillations at different levels of amplitude of the noise. In the limit of strong time-scale separation, five different scaling regimes for the noise amplitude are identified. As the noise amplitude is decreased, the dynamics of the system goes from the limit cycle due to self-induced stochastic resonance to the coherence resonance limit cycle, then to bursting relaxation oscillations, followed by rare clusters of several relaxation cycles (spikes), and finally to small-amplitude oscillations (or stable fixed point) with sporadic single spikes. These scenarios are corroborated by numerical simulations.     

Mutual synchronization in a system of two bistable oscillators executing regular and chaotic oscillations

A numerical analysis of a new model describing two coupled modified Chua??s oscillators is conducted. Equations of a partial oscillator differ from classical equations in that the former contain additional delayed feedback in another writing of dimensionless time. Changeover from regular oscillations in the absence of additional feedback to additional-feedback-induced (switchable) chaotic oscillations is studied. It is shown that, when normal regular oscillations, as well as additional-feedback-induced chaotic oscillations, are synchronized, difference oscillations are left. They are absent only when the control parameters of partial oscillators are identical. The application of a harmonic signal allows one to control the oscillations of a chaotic system of coupled modified bistable oscillators.     

Noise-induced enhancement of chemical reactions in nonlinear flows

Motivated by the problem of ozone production in atmospheres of urban areas, we consider chemical reactions of the general type: A+B-->2C, in idealized two-dimensional nonlinear flows that can generate Lagrangian chaos. Our aims differ from those in the existing work in that we address the role of transient chaos versus sustained chaos and, more importantly, we investigate the influence of noise. We find that noise can significantly enhance the chemical reaction in a resonancelike manner where the product of the reaction becomes maximum at some optimal noise level. We also argue that chaos may not be a necessary condition for the observed resonances. A physical theory is formulated to understand the resonant behavior. (c) 2002 American Institute of Physics.     

Noise-induced synchronous stochastic oscillations small scale cultured heart-cell networks

This paper reports that the synchronous integer multiple oscillations of heart-cell networks or clusters are observed in the biology experiment. The behaviour of the integer multiple rhythm is a transition between super- and sub- threshold oscillations, the stochastic mechanism of the transition is identified. The similar synchronized oscillations are theoretically reproduced in the stochastic network composed of heterogeneous cells whose behaviours are chosen as excitable or oscillatory states near a Hopf bifurcation point. The parameter regions of coupling strength and noise density that the complex oscillatory rhythms can be simulated are identified. The results show that the rhythm results from a simple stochastic alternating process between super- and sub-threshold oscillations. Studies on single heart cells forming these clusters reveal excitable or oscillatory state nearby a Hopf bifurcation point underpinning the stochastic alternation. In discussion, the results are related to some abnormal heartbeat rhythms such as the sinus arrest.     

Noise-induced front propagation in a bistable system

A bistable system satisfying a generalized Maxwell condition exhibits an interface solution deterministically at rest. It is shown that state-dependent (multiplicative) noise induces an average motion of this interface into the region of higher noise intensity.     

Properties of spacetimes with magnetic dipoles

The properties of an asymptotically flat spacetime with a mass and a magnetic dipole are studied. We focus on the breaking of spherical symmetry by the magnetic dipole. We investigate the geometry of the spacetime through the trajectories of null geodesics and the embedding diagrams of various hypersurfaces, included constant t and r surfaces and the infinite red shift surface. We find that the effects of the magnetic dipole on the spacetime are larger at the poles than on the equator.     

Noise-induced synchronous stochastic oscillations in small scale cultured heart-cell networks

This paper reports that the synchronous integer multiple oscillations of heart-cell networks or clusters are observed in the biology experiment.The behaviour of the integer multiple rhythm is a transition between super-and subthreshold oscillations,the stochastic mechanism of the transition is identified.The similar synchronized oscillations are theoretically reproduced in the stochastic network composed of heterogeneous cells whose behaviours are chosen as excitable or oscillatory states near a Hopf bifurcation point.The parameter regions of coupling strength and noise density that the complex oscillatory rhythms can be simulated are identified.The results show that the rhythm results from a simple stochastic alternating process between super-and sub-threshold oscillations.Studies on single heart cells forming these clusters reveal excitable or oscillatory state nearby a Hopf bifurcation point underpinning the stochastic alternation.In discussion,the results are related to some abnormal heartbeat rhythms such as the sinus arrest.     

Numerical analysis of noise-induced regular oscillations

Constructive sufficient conditions for regular oscillations in systems with stochastic resonance are given. Using these conditions, a numerical procedure for indicating domains of parameters corresponding to the regular oscillations are proposed. The regular oscillations in systems with additive and multiplicative noise are considered. Results of numerical experiments are presented.     

Acceleration of magnetic dipoles by a sequence of current-carrying turns

Magnetic dipoles are accelerated by a running gradient of the magnetic field that is produced by sequentially energizing current-carrying turns. Magnetic dipoles d _sh = 60 mm in diameter and l _tot = 1 m in length are gasdynamically preaccelerated to velocity V _in = 1 km/s, with which they are injected into the main accelerator. The turnover of the dipoles in the field of an accelerating pulse is prevented and focusing of dipoles is provided by directing the dipoles into a titanium tube. The weight of the dipoles is m = 2 kg, and they acquire final velocity V _fin = 5 km/s over acceleration length L _acc = 300 m.     

Thermodynamics of a continuous medium with electric and magnetic dipoles

The thermodynamics of an electrically charged, multicomponent fluid with spontaneous electric and magnetic dipoles is analysed in the presence of electromagnetic fields. Taking into account the chemical composition of the current densities and stress tensors leads to three types of irreversible terms: scalars, vectors and pseudo-vectors. The scalar terms account for chemical reactivities, the vectorial terms account for transport and the pseudo-vectorial terms account for relaxation. The linear phenomenological relations, derived from the irreversible evolution, describe notably the Lehmann and electric Lehmann effects, the Debye relaxation of polar molecules and the Landau-Lifshitz relaxation of the magnetisation. This formalism accounts for the thermal and electric magnetisation accumulations and magnetisation waves. It also predicts that a temperature gradient affects the dynamics of magnetic vortices and drives magnetisation waves.     

Ground-state properties of a one-dimensional system of dipoles

A one-dimensional (1D) Bose system with dipole-dipole repulsion is studied at zero temperature by means of a quantum Monte Carlo method. It is shown that, in the limit of small linear density, the bosonic system of dipole moments acquires many properties of a system of noninteracting fermions. At larger linear densities, a variational Monte Carlo calculation suggests a crossover from a liquidlike to a solidlike state. The system is superfluid on the liquidlike side of the crossover and is normal deep on the solidlike side. Energy and structural functions are presented for a wide range of densities. Possible realizations of the model are 1D Bose atomic systems, with permanent dipoles or dipoles induced by static field or resonance radiation; or indirect excitons in coupled quantum wires; etc. We propose parameters of a possible experiment and discuss manifestations of the zero-temperature quantum crossover.     

Strong enhancement of magnetic dipole emission in a multilevel electronic system

The Purcell effect is commonly used to increase light emission by enhancing the radiative decay of electric dipole transitions. In this Letter, we demonstrate that the opposite effect, namely, the inhibition of electric dipole transitions, can be used to strongly enhance light emission via magnetic dipole transitions. Specifically, by exploiting the differing symmetries of competitive electric and magnetic dipole transitions in trivalent europium, we demonstrate a fourfold enhancement of the far-field emission from the (5)D(0)→(7)F(1) magnetic dipole transition in trivalent europium. We show that this strong enhancement is well predicted by a three-level model that couples the individual Purcell enhancement factors of competitive transitions from the same excited state.     

Phase transitions in lattices of magnetic dipoles

Hexagonal magnetic-dipole lattices containing three to six rows are investigated. Conditions of the excitation of phase transitions that change the orientation configuration of the system are revealed on the basis of a numerical analysis. The changes in the magnetic moment of the system and in the energy of dipole-dipole interaction upon the emergence of phase transitions are found. Both symmetric phase transitions propagating identically on the two sides of the lattice away from the excitation region and asymmetric phase transitions such in which the configurations of the system to the left and to the right of the excitation region are different are considered. Conditions under which there occur unidirectional phase transitions in which either the left-or the right-hand front of the phase transition propagates along the lattice are found.