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In recent years, there has been a mounting interest in better methods of measuring nanoscale objects, especially in fields such as nanotechnology, biomedicine, cleantech, and microelectronics. Conventional methods have proved insufficient,…

We describe a self calibrating optical technique that allows to perform absolute measurements of scattering cross sections for the light scattered at extremely small angles. Very good performances are obtained by using a very simple optical…

We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…

Peculiar velocities introduce correlations between supernova magnitudes, which implies that the supernova Hubble diagram residual carries information on both the matter power spectrum at the present time and its growth rate. By a…

In this paper we study the inverse conductivity problem with partial data. Moreover, we show that, in dimension $n\geq 3$ the uniqueness of the Calder\'{o}n problem holds for the $C^{1}\bigcap H^{3/2, 2}$ conductivities.

One challenge impeding the analysis of terabyte scale x-ray scattering data from the Linac Coherent Light Source LCLS, is determining the number of clusters required for the execution of traditional clustering algorithms. Here we…

This paper is concerned with analysis of electromagnetic wave scattering by an obstacle which is embedded in a two-layered lossy medium separated by an unbounded rough surface. Given a dipole point source, the direct problem is to determine…

High precision asteroseismic data provide a unique opportunity to test input microphysics such as stellar opacities, chemical composition or equation of state. These tests are possible because pulsational frequencies as well as amplitudes…

We compute the scattering angle for a scalar neutral probe undergoing unbound motion around a Topological Star, including self-force effects. Moreover we identify the `electro-magnetic' source of the background as Papapetrou Field…

An exact trace formula for the perturbation of the Laplacian by a Dirac delta potential on a compact hyperbolic Riemann surface is derived. The formula can be considered an analogue of the Selberg trace formula. The difference of perturbed…

Two methodological troubles of the quantum theory of collisions are considered. The first is the undesirable interference of the incident and scattered waves in the stationary approach to scattering. The second concerns the nonstationary…

In many situations, the statistical properties of wave systems with chaotic classical limits are well-described by random matrix theory. However, applications of random matrix theory to scattering problems require introduction of system…

We consider the classical obstacle problem on bounded, connected Lipschitz domains $D \subset \mathbb{R}^n$. We derive quantitative bounds on the changes to contact sets under general perturbations to both the right hand side and the…

Phase singularities are universal features found across diverse wave systems. Their ensembles exhibit distance correlations governing exotic material phases. However, the full correlations in phase-space have remained unexplored and…

We consider a gas of bosons in a bichromatic optical lattice at finite temperatures. As the amplitude of the secondary lattice grows, the single-particles eigenstates become localized. We calculate the canonical partition function using…

A simple experiment is described for the direct determination of the wavelength dependence of the Rayleigh scattering cross section using the classical example of the blue sky.

We consider an inverse problem for the linear one-dimensional wave equation with variable coefficients consisting in determining an unknown source term from a boundary observation. A method to obtain approximations of this inverse problem…

Every field of Science is undergoing unprecedented changes in the discovery process, and Astronomy has been a main player in this transition since the beginning. The ongoing and future large and complex multi-messenger sky surveys impose a…

Consider a spherically symmetric spacelike slice through a spherically symmetric spacetime. One can derive a universal bound for the optical scalars on any such slice. The only requirement is that the matter sources satisfy the dominant…

With the upcoming plethora of astronomical time-domain datasets and surveys, anomaly detection as a way to discover new types of variable stars and transients has inspired a new wave of research. Yet, the fundamental definition of what…