In this paper, we obtain sufficient conditions so that every solution of neutral functional difference equation ∆(yn − pnyτ(n)) + qnG(yσ(n)) = fn oscillates or tends to zero as n → ∞. Here ∆ is the forward difference operator given by ∆xn = xn+1−xn, and pn, qn, fn are the terms of oscillating infinite sequences; {τn} and {σn} are non-decreasing sequences, which are less than n and approaches ∞ ...

The formation of spatially localized patterns in a system with subcritical instability under feedback control with delay is investigated within the framework of globally controlled Ginzburg-Landau equation. It is shown that feedback control can stabilize spatially localized solutions. With the increase of delay, these solutions undergo oscillatory instability that, for large enough control stre...

Numerical homogenization tries to approximate solutions of elliptic partial differential equations with strongly oscillating coefficients by the solution of localized problems over small subregions. We develop and analyze a rapidly convergent iterative method for numerical homogenization that shares this feature with existing approaches and is modeled after the Schwarz method. The method is hig...

We investigate an optimal velocity model which includes the reflex time of drivers. After an analytical study of the stability and local bifurcations of the steady-state solution, we apply numerical continuation techniques to investigate the global behavior of the system. Specifically, we find branches of oscillating solutions connecting Hopf bifurcation points, which may be super- or subcritic...

In this paper we study the minimax control of systems governed by a nonlinear evolution inclusion of the subdifferential type. Using some continuity and lower semicontinuity results for the solution map and the cost functional respectively, we are able to establish the existence of an optimal control. The abstract results are then applied to obstacle problems, semilinear systems with weakly var...

We present a class of BPS solutions of the IIB Matrix Theory which preserve 1/4 supersymmetry. The solutions desrcibe D-string configurations with left-moving oscillations. We demonstrate that the one-loop quantum effective action of Matrix Theory vanishes for this solution, confirming its BPS nature. We also study the world-volume gauge theory of oscillating strings and show its connection wit...

The GKZ system for the Hesse pencil of elliptic curves has more solutions than the period integrals. In this work we give different realizations and interpretations of the extra solution, in terms of oscillating integral, Eichler integral, chain integral on the elliptic curve, limit of a period of a certain compact Calabi–Yau threefold geometry, etc. We also highlight the role played by the orb...

The currents at the terminals of a mesoscopic conductor are evaluated in the presence of slowly oscillating potentials applied to the contacts of the sample. The need to find a charge and current conserving solution to this dynamic current partition problem is emphasized. We present results for the electro-chemical admittance describing the long range Coulomb interaction in a Hartree approach. ...

We i n vestigate the cosmological perturbation of two-scalar eld model during the reheating phase after innation. Using the exact solution of the perturbation in long-wavelength limit, which is expressed in terms of the background quantities, we analyze the behavior of the metric perturbation. The oscillating innaton eld gives rise to the parametric resonance of the massless scalar eld and this...

Submitted for the DFD09 Meeting of The American Physical Society Dynamics of pinned-contact oscillating gas/liquid lenses AMIR HIRSA, BERNARD MALOUIN, JOSEPH OLLES, Rensselaer Polytechnic Institute, CARLOS LOPEZ, Intel Corp., MICHAEL VOGEL, Cornell University — Liquid lenses are a natural solution for applications in adaptive optics requiring a fast response. Existing liquid lenses use large di...