In this paper, we introduce a methodology applicable to a wide range of localized two-dimensional sources of stress. This methodology is based on a geometric formulation of elasticity. Localized sources of stress are viewed as singular defects-point charges of the curvature associated with a reference metric. The stress field in the presence of defects can be solved using a scalar stress functi...

We point out a simple criterion for convergence of polynomials to concrete entire function in the Laguerre-Pólya ( LP ) class (of all functions arising as uniform limits with only real roots). then use this show that any random can be obtained limit rescaled characteristic principal submatrices an infinite unitarily invariant Hermitian matrix. Conversely, matrix converge uniformly function. Thi...

Purpose To demonstrate the viability of improving transverse image resolution in reflectance scanning adaptive optics ophthalmoscopy using sub-Airy disk confocal detection. Methods The foveal cone mosaic was imaged in five human subjects free of known eye disease using two custom adaptive optics scanning light ophthalmoscopes (AOSLOs) in reflectance with 7.75 and 4.30 mm pupil diameters. Conf...

Fabry-Perot (FP) etalons are used as filters and sensors in a range of optical systems. The reflected transmitted fields associated with an FP etalon have traditionally been predicted by the Airy function, which assumes plane wave illumination. are, however, often illuminated non-collimated beams, rendering function invalid. To address this limitation, we describe angular calculates for arbitra...

We demonstrate how the complex integral formula for the Airy functions arises from Penrose’s twistor contour integral formula. We then use the Lax formulation of the isomonodromy problem with one irregular singularity of order four to show that the Airy equation arises from the anti-self-duality equations for conformal structures of neutral signature invariant under the isometric action of the ...

We consider several aspects of the scaling limit of percolation on random planar triangulations, both finite and infinite. The equivalents for random maps of Cardy’s formula for the limit under scaling of various crossing probabilities are given. The limit probabilities are expressed in terms of simple events regarding Airy-Lévy processes. Some explicit formulas for limit probabilities follow f...

Nonlinear vibrations of thin rectangular plates are considered, using the von Kármán equations in order to take into account the effect of geometric nonlinearities. Solutions are derived through an expansion over the linear eigenmodes of the system for both the transverse displacement and the Airy stress function, resulting in a series of coupled oscillators with cubic nonlinearities, where the...

A 30-year-old man presented with headache, vomiting, altered sensorium and seizures. There was no history of trauma or surgery. On examination, he was unconscious with signs of meningeal irritation and asymmetrical pupils. Computed tomography (CT) scan of brain revealed pneumocephalus. He died immediately after the CT scan. He was later found to be immunocompetent. Computed tomography scan (fig...

We demonstrate both theoretically and experimentally the generation of a tunable two-dimensional superoscillating optical field through the interference of multiple Airy beams. The resulting pattern exhibits self-healing properties for a set of sub-Fourier diffraction spots with decreasing dimensions. Such spatial optical fields might find applications in microscopy, particle manipulation, and ...