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Fractional calculus provides a rigorous mathematical framework to describe anomalous stochastic processes by generalizing the notion of classical differential equations to their fractional-order counterparts. By introducing the fractional…
Development of experimental techniques for characterization of magnetic properties at high spatial resolution is essential for progress in miniaturization of magnetic devices, for example, in data storage media. Inelastic scattering of…
Uncertainty in physical parameters can make the solution of forward or inverse light scattering problems in astrophysical, biological, and atmospheric sensing applications, cost prohibitive for real-time applications. For example, given a…
This paper presents a novel machine-learning framework for reconstructing low-order gust-encounter flow field and lift coefficients from sparse, noisy surface pressure measurements. Our study thoroughly investigates the time-varying…
We develop fast and memory efficient numerical methods for learning functions of many variables that admit sparse representations in terms of general bounded orthonormal tensor product bases. Such functions appear in many applications…
We here present the first analytic effective fly-by (EFB) waveforms designed to accurately capture the burst of gravitational radiation from the closest approach of highly eccentric compact binaries. The waveforms are constructed by…
We study imaging with an array of sensors that probes a medium with single frequency electromagnetic waves and records the scattered electric field. The medium is known and homogenous except for some small and penetrable inclusions. The…
For problems of time-harmonic scattering by polygonal obstacles, embedding formulae provide a useful means of computing the far-field coefficient induced by any incident plane wave, given the far-field coefficient of a relatively small set…
For the scattering of plane electromagnetic waves by a general possibly anisotropic stationary linear medium in three dimensions, we give a condition on the permittivity and permeability tensors of the medium under which the first Born…
We consider the problem of fixed frequency acoustic scattering from a sound-soft flat screen. More precisely the obstacle is restricted to a two-dimensional plane and interacting with a arbitrary incident wave, it scatters acoustic waves to…
Approximated numerical techniques, for the solution of the elastic wave scattering problem over semi-infinite domains are reviewed. The approximations involve the representation of the half-space by a boundary condition described in terms…
Electromagnetic scattering on a sphere is one of the most fundamental problems, which has a closed form analytical solution in the form of Mie series. Being initially formulated for a plane incident wave, the formalism can be extended to…
We apply boundary integral equations for the first time to the two-dimensional scattering of time-harmonic waves from a smooth obstacle embedded in a continuously-graded unbounded medium. In the case we solve the square of the wavenumber…
We consider frequency-domain acoustic scattering at a homogeneous star-shaped penetrable obstacle, whose shape is uncertain and modelled via a radial spectral parameterization with random coefficients. Using recent results on the stability…
Posterior distributions on parameters computed from experimental data using Bayesian techniques are only as accurate as the models used to construct them. In many applications these models are incomplete, which both reduces the prospects of…
Modulating macroscopic parameters of materials in time offers innovative avenues for manipulating electromagnetic waves. Due to such enticing prospects, the general research subject of time-varying systems is expanding today in different…
Coherent control of ultrafast quantum phenomena benefits from pulse-shaping capabilities allowing to modulate the envelope and instantaneous phase of optical fields on femtosecond time scales. While such control is available for optical…
We study matter wave scattering from an ultracold, many body atomic system trapped in an optical lattice. We determine the angular cross section that a matter wave probe sees and show that it is strongly affected by the many body phase,…
We present concise, computationally efficient formulas for several quantities of interest -- including absorbed and scattered power, optical force (radiation pressure), and torque -- in scattering calculations performed using the…
We are concerned with the reconstruction of a sound-soft obstacle using far field measurements of the scattered waves associated with incident plane waves sent from one direction but at multiple frequencies. We define, for each frequency,…