相关论文: Computing the Sound of the Sea in a Seashell

The problem of scattering of harmonic plane acoustic waves by fluid spheroids (prolate and oblate) is addressed from an analytical approach. Mathematically, it consists in solving the Helmholtz equation in an unbounded domain with…

In this paper, we present algorithms for computing approximate hulls and centerpoints for collections of matrices in positive definite space. There are many applications where the data under consideration, rather than being points in a…

Physical design problems, such as photonic inverse design, are typically solved using local optimization methods. These methods often produce what appear to be good or very good designs when compared to classical design methods, but it is…

The complex-scaling method can be used to calculate molecular resonances within the Born-Oppenheimer approximation, assuming the electronic coordinates are dilated independently of the nuclear coordinates. With this method, one will…

We present a novel multipole formulation for computing the band structures of two-dimensional arrays of cylindrical Helmholtz resonators. This formulation is derived by combining existing multipole methods for arrays of ideal cylinders with…

We derive the weak limit of a linear viscoacoustic model in an acoustic liner that is a chamber connected to a periodic repetition of elongated chambers -- the Helmholtz resonators. As model we consider the time-harmonic and linearized…

We derive formulas for Whispering Gallery Mode resonances and bending losses in infinite cylindrical dielectric shells and sets of concentric cylindrical shells. The formulas also apply to spherical shells and to sections of bent…

An analysis is developed linking the form of the sound field from a circular source to the radial structure of the source, without recourse to far-field or other approximations. It is found that the information radiated into the field is…

Using a combination of multipole methods and the method of matched asymptotics, we present a solution procedure for acoustic plane wave scattering by a single Helmholtz resonator in two dimensions. Closed-form representations for the…

We survey functional analytic methods for studying subwavelength resonator systems. In particular, rigorous discrete approximations of Helmholtz scattering problems are derived in an asymptotic subwavelength regime. This is achieved by…

Numerical solutions are given for a parabolic approximation of the acoustic wave equation at 200 and 250 Hz in two and three spatial dimensions to determine if azimuthal coupling in the cross-range coordinate significantly affects…

We consider the scattering of acoustic perturbations in a presence of a flow. We suppose that the space can be split into a zone where the flow is uniform and a zone where the flow is potential. In the first zone, we apply a Prandtl-Glauert…

The spectrum of a quantum system has in general bound, scattering and resonant parts. The Hilbert space includes only the bound and scattering spectra, and discards the resonances. One must therefore enlarge the Hilbert space to a rigged…

The coherent stochastic resonance is observed and studied with multi-step periodic signal in continuous medium having two absorbing boundaries. The general features of this process are exihibited. The universal features at the resonance…

In this work we discuss the problem of identifying sound sources from pressure measurements with a Bayesian approach. The acoustics are modelled by the Helmholtz equation and the goal is to get information about the number, strength and…

We prove lower bounds on the error incurred when approximating any oscillating function using piecewise polynomial spaces. The estimates are explicit in the polynomial degree and have optimal dependence on the meshwidth and frequency when…

For a nonrelativistic atom, which is minimally coupled to the quantized radiation field, resonances emerging from excited atomic eigenstates are constructed by an iteration scheme inspired by \cite{Pizzo2003} and…

We prove an optimal exponential lower bound on the width of the resonance associated to the first eigenvalue of the cavity for a general Helmholtz resonator with straight neck, in any dimension.

We consider a two-dimensional analogue of Helmholtz resonator with walls of finite thickness in the critical case when there exists an eigenfrequency equalling to the limit of poles generated by both the bounded component of the resonator…

The design of starshades, i.e. external occulters for stellar coronography, relies on the fast and precise computation of their associated diffraction patterns of incoming plane waves in the telescope aperture plane. We present here a…