For the Generalized Plane Stress (GPS) problem in linear elasticity, we obtain an optimal stability estimate of logarithmic type for inverse determining smooth cavities inside a thin isotropic cylinder from single boundary measurement traction and displacement. The result is obtained by reformulating GPS as Kirchhoff–Love plate-like terms Airy function, using strong unique continuation at plate...

We demonstrate both experimentally and theoretically controlled acceleration of one- and two-dimensional Airy beams in optically induced refractive-index potentials. Enhancement as well as reduction of beam acceleration are realized by changing the index gradient, while the beam shape is maintained during propagation through the linear optical potential. Our results of active acceleration manip...

Procedures are described for the high-precision calculation of the modiied Bessel function K(x), 0 < < 1, and the Airy function Ai(x), for positive arguments x, as prerequisites for generating Gaussian quadrature rules having these functions as weight function.

One-dimensional system of Brownian motions called Dyson’s model is the particle system with long-range repulsive forces acting between any pair of particles, where the strength of force is β/2 times the inverse of particle distance. When β = 2, it is realized as the Brownian motions in one dimension conditioned never to collide with each other. For any initial configuration, it is proved that D...

Sliding-frequency filter systems are known to admit two families of accelerating solitons: high-amplitude and low-amplitude families. Such equilibrium solutions are computed here, for a wide range of filter strengths, as self-similar solutions having Airy function asymptotics. In a limited parameter region, the profile possesses a secondary small hump. The high-amplitude solitons are found to b...

We investigate the spatially optical solitons shedding from Airy beams and anomalous interactions of Airy beams in nonlocal nonlinear media by means of direct numerical simulations. Numerical results show that nonlocality has profound effects on the propagation dynamics of the solitons shedding from the Airy beam. It is also shown that the strong nonlocality can support periodic intensity distr...

Deconvolution of phased microphone array source maps is a commonly applied technique in order to improve the dynamic range and resolution of beamforming. Most deconvolution algorithms require a point spread function (PSF). In this work, it is shown that the conventional definition of the PSF, based on steering vectors, is changed when the source is rotating. The effect of rotation results in an...

We use the Airy stress function to derive exact solutions for plane strain deformations of a functionally graded (FG) hollow cylinder with the inner and the outer surfaces subjected to different boundary conditions, and the cylinder composed of an isotropic and incompressible linear elastic material. For the shear modulus given by either a power law or an exponential function of the radius r, w...

In this Letter we propose the concept of the evanescent Airy beam. We analyze the structure of the ideal evanescent Airy beam, which initial profile has the Airy form, while the spectral decomposition consists of only evanescent partial waves. Also, we discuss the refraction of the Airy beam through the interface and investigate the field of the transmitted evanescent Airy beam. c © 2009 Optica...