We consider the following Helmholtz problem which models the propagation of a wave of frequency ω > 0 and velocity of propagation c > 0 in an unbounded homogeneous medium:  ∆u + k2u = 0 in ΩE, u = g on Γ, lim r→∞ √ r ( ∂u ∂r − iku ) = 0, where k := ω/c is the wave number, ΩE := R\ΩI, with ΩI ⊂ R2 being a simply connected bounded domain with regular boundary Γ, and g ∈ H 1 2 (Γ) is a given...

Electromechanical resonators and filters, such as quartz, ceramic, and surface-acoustic wave devices, are important signal-processing elements in communication systems. Over the past decade, there has been substantial progress in developing new types of miniaturized electromechanical resonators using microfabrication processes. For these micro-resonators to be viable they must have high and pre...

Radiative cooling is a natural and effective method of phase-space cooling for stored electron beams. In electron storage rings the average effects of synchrotron radiation from the bending magnets cause the beam emittances in all three degrees of freedom to damp towards equilibria, determined by the fluctuating nature of quantum emissions. In this paper, we show that the radiation damping in a...

The analogues of r-modes in superfluid neutron stars are studied here. These modes, which are governed primarily by the Coriolis force, are identical to their ordinary-fluid counterparts at the lowest order in the small angular-velocity expansion used here. The equations that determine the next order terms are derived and solved numerically for fairly realistic superfluid neutron-star models. T...

Wave self-focusing in molecular systems subject to thermal effects, such as thin molecular films and long biomolecules, can be modeled by stochastic versions of the Discrete Self-Trapping equation of Eilbeck, Lomdahl and Scott, and this can be approximated by continuum limits in the form of stochastic nonlinear Schrödinger equations. Previous studies directed at the SNLS approximations have ind...

The two beams of the 2 GeV Stanford electron-positron storage ring can exhibit, under certain modes of operation, coherent oscillations which have a rate of growth proportional to the beam current. Since this rate is much slower than the machine revolution tiequency, it is possible to produce damping by means of negative feedback, the beam itself being part of the feedback loop. Three systems h...

An efficient formalism is elaborated to analytically describe dynamics of the Ablowitz-Ladik soliton in the presence of perturbations. This formalism is based on using the Riemann-Hilbert problem and provides the means of calculating evolution of the discrete soliton parameters, as well as shape distortion and perturbation-induced radiation effects. As an example, soliton characteristics are ca...