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The investigation into the scattering of plane waves by a periodic array of parallel cylinders utilizes the method of cylindrical wave decomposition, thereby reducing the problem complexity to a series of linear algebraic equations. This…

This work discusses the homogenization analysis for diffusion processes on scale-free metric graphs, using weak variational formulations. The oscillations of the diffusion coefficient along the edges of a metric graph induce internal…

In this paper, we generalize the usual notions of waves, fronts and propagation speeds in a very general setting. These new notions, which cover all classical situations, involve uniform limits, with respect to the geodesic distance, to a…

Accurate and efficient prediction of three-dimensional (3D) fields in wave interactions with large, complex-shaped objects is essential for applications in electromagnetic computation, computer graphics, optical metrology, and freeform…

We present a new methodology, based on the WKB approximation and Fast Fourier Transforms, for the evaluation of wave propagation through inhomogeneous media. This method can accurately resolve fields containing caustics, while still…

Wavefront aberrations can reflect the imaging quality of high-performance optical systems better than geometric aberrations. Although laser interferometers have emerged as the main tool for measurement of transmitted wavefronts, their…

All random wave fields possess a network of phase singularities. We show that while the phase statistics within speckle patterns is generic, the statistics of the motion of phase singularities differs substantially for diffusive and…

The increasing use of freeform optical surfaces raises the demand for optical design tools developed for generalized systems. In the design process surface-by-surface aberration contributions are of special interest. The expansion of the…

Propagation modeling is a crucial tool for successful wireless deployments and spectrum planning with the demand for high modeling accuracy continuing to grow. Recognizing that detailed knowledge of the physical environment (terrain and…

Disordered nanostructures are commonly encountered in many nanophotonic systems, from colloid dispersions for sensing, to heterostructured photocatalysts. Randomness, however, imposes severe challenges for nanophotonics modeling, often…

In this paper, we investigate the geometric propagation and diffraction of singularities of solutions to the wave equation on manifolds with edge singularities.

The tasks of identifying separation structures and clusters in flow data are fundamental to flow visualization. Significant work has been devoted to these tasks in flow represented by vector fields, but there are unique challenges in…

We study the propagation of surface waves across structured surfaces with random, localized inhomogeneities. A discrete analogue of Gurtin-Murdoch model is employed and surface elasticity, in contrast to bulk elasticity, is captured by…

A new method for numerical solving of boundary problem for ordinary differential equations with slowly varying coefficients which is aimed at better representation of solutions in the regions of their rapid oscillations or exponential…

Segmentation, a useful/powerful technique in pattern recognition, is the process of identifying object outlines within images. There are a number of efficient algorithms for segmentation in Euclidean space that depend on the variational…

In this paper, we empirically reveal an invariance over images-images share a set of one-way wave equations with latent speeds. Each image is uniquely associated with a solution to these wave equations, allowing for its reconstruction with…

We develop a theoretical model to investigate wave propagation in media with random time-varying properties, where temporal fluctuations lead to complex scattering dynamics. Focusing on the ensemble-averaged field, we derive an exact…

We present a technique for measuring the transverse spatial properties of an optical wavefront. Intensity and phase profiles are recovered by analysis of a series of interference patterns produced by the combination of a scanning X-shaped…

In a recent letter [Europhys. Lett. 97, 34002 (2012)], random matrix theory is introduced for long-range acoustic propagation in the ocean. The theory is expressed in terms of unitary propagation matrices that represent the scattering…

Pixel intensity is a widely used feature for clustering and segmentation algorithms, the resulting segmentation using only intensity values might suffer from noises and lack of spatial context information. Wavelet transform is often used…