Stabilizing stochastically-forced oscillation generators with hard excitement: A confidence-domain control approach

In this paper, noise-induced destruction of self-sustained oscillations is studied for a stochastically-forced generator with hard excitement. The problem is to design a feedback regulator that can stabilize a limit cycle of the closed-loop system and to provide a required dispersion of the generated oscillations. The approach is based on the stochastic sensitivity function (SSF) technique and confidence domain method. A theory about the synthesis of assigned SSF is developed. For the case when this control problem is ill-posed, a regularization method is constructed. The effectiveness of the new method of confidence domain is demonstrated by stabilizing auto-oscillations in a randomly-forced generator with hard excitement.© EDP Sciences Società Italiana di Fisica Springer-Verlag 2013

Surface response of spherical core-shell structured nanoparticle by optically induced elastic oscillations of soft shell against hard core

The optically induced oscillatory response of a spherical two-component, shell-core structured, nanoparticle by nodeless elastic vibrations of soft peripheral shell against hard and dynamically immobile inner core is considered. The eigenfrequencies of the even-parity, spheroidal and odd-parity torsional vibrational modes trapped in the finite-depth shell are obtained which are of practical interest for modal specification of individual resonances in spectra of resonant scattering of long wavelength electromagnetic waves by ultrafine particles.Comment: Surface Review and Letters (World Scientific) Year: 2009 Vol: 16 Issue: 1 (February 2009) Page: 5 - 1

Limit-cycle oscillations in unsteady flows dominated by intermittent leading-edge vortex shedding

High-frequency limit-cycle oscillations of an airfoil at low Reynolds number are studied numerically. This regime is characterized by large apparent-mass effects and intermittent shedding of leading-edge vortices. Under these conditions, leading-edge vortex shedding has been shown to result in favourable consequences such as high lift and efficiencies in propulsion/power extraction, thus motivating this study. The aerodynamic model used in the aeroelastic framework is a potential-flow-based discrete-vortex method, augmented with intermittent leading-edge vortex shedding based on a leading-edge suction parameter reaching a critical value. This model has been validated extensively in the regime under consideration and is computationally cheap in comparison with Navier-Stokes solvers. The structural model used has degrees of freedom in pitch and plunge, and allows for large amplitudes and cubic stiffening. The aeroelastic framework developed in this paper is employed to undertake parametric studies which evaluate the impact of different types of nonlinearity. Structural configurations with pitch-to-plunge frequency ratios close to unity are considered, where the flutter speeds are lowest (ideal for power generation) and reduced frequencies are highest. The range of reduced frequencies studied is two to three times higher than most airfoil studies, a virtually unexplored regime. Aerodynamic nonlinearity resulting from intermittent leading-edge vortex shedding always causes a supercritical Hopf bifurcation, where limit-cycle oscillations occur at freestream velocities greater than the linear flutter speed. The variations in amplitude and frequency of limit-cycle oscillations as functions of aerodynamic and structural parameters are presented through the parametric studies. The excellent accuracy/cost balance offered by the methodology presented in this paper suggests that it could be successfully employed to investigate optimum setups for power harvesting in the low-Reynolds-number regime

Floquet theory of microwave absorption by an impurity in two dimensional electron gas

We investigate the dynamics of a two-dimensional electron gas (2DEG) under circular polarized microwave radiation in presence of dilute localized impurities. Inspired by recent developments on Floquet topological insulators we obtain the Floquet wavefunctions of this system which allow us to predict the microwave absorption and charge density responses of the electron gas, we demonstrate how these properties can be understood from the underlying semiclassical dynamics even for impurities with a size of around a magnetic length. The charge density response takes the form of a rotating charge density vortex around the impurity that can lead to a significant renormalization of the external microwave field which becomes strongly inhomogeneous on the scale of a cyclotron radius around the impurity. We show that this in-homogeneity can suppress the circular polarization dependence which is theoretically expected for MIRO but which was not observed in MIRO experiments on semiconducting 2DEGs. Our explanation, for this so far unexplained polarization independence, has close similarities with the Azbel'-Kaner effect in metals where the interaction length between the microwave field and conduction electrons is much smaller than the cyclotron radius due to skin effect generating harmonics of the cyclotron resonance

Inter-species Tunneling in One-dimensional Bose Mixtures

We study the ground-state properties and quantum dynamics of few-boson mixtures with strong inter-species repulsion in one-dimensional traps. If one species localizes at the center, e.g., due to a very large mass compared to the other component, it represents an effective barrier for the latter and the system can be mapped onto identical bosons in a double well. For weaker localization, the barrier atoms begin to respond to the light component, leading to an induced attraction between the mobile atoms that may even outweigh their bare intra-species repulsion. To explain the resulting effects, we derive an effective Hubbard model for the lighter species accounting for the backaction of the barrier in correction terms to the lattice parameters. Also the tunneling is drastically affected: Varying the degree of localization of the "barrier" atoms, the dynamics of intrinsically noninteracting bosons can change from Rabi oscillations to effective pair tunneling. For identical fermions (or fermionized bosons) this leads to the tunneling of attractively bound pairs.Comment: 13 pages, 11 figures; v2 reflects major revisio

Spatially structured oscillations in a two-dimensional excitatory neuronal network with synaptic depression

We study the spatiotemporal dynamics of a two-dimensional excitatory neuronal network with synaptic depression. Coupling between populations of neurons is taken to be nonlocal, while depression is taken to be local and presynaptic. We show that the network supports a wide range of spatially structured oscillations, which are suggestive of phenomena seen in cortical slice experiments and in vivo. The particular form of the oscillations depends on initial conditions and the level of background noise. Given an initial, spatially localized stimulus, activity evolves to a spatially localized oscillating core that periodically emits target waves. Low levels of noise can spontaneously generate several pockets of oscillatory activity that interact via their target patterns. Periodic activity in space can also organize into spiral waves, provided that there is some source of rotational symmetry breaking due to external stimuli or noise. In the high gain limit, no oscillatory behavior exists, but a transient stimulus can lead to a single, outward propagating target wave

Charge Oscillations in Debye-Hueckel Theory

The recent generalized Debye-Hueckel (GDH) theory is applied to the calculation of the charge-charge correlation function G_{ZZ}(r). The resulting expression satisfies both (i) the charge neutrality condition and (ii) the Stillinger-Lovett second-moment condition for all T and rho_N, the overall ion density, and (iii) exhibits charge oscillations for densities above a "Kirkwood line" in the (rho_N,T) plane. This corrects the normally assumed DH correlations, and, when combined with the GDH analysis of the density correlations, leaves the GDH theory as the only complete description of ionic correlation functions, as judged by (i)-(iii), (iv) exact low-density (rho_N,T) variation, and (v) reasonable behavior near criticality.Comment: 6 pages, EuroPhys.sty (now available on archive), 1 eps figur