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A solution of the scattering problem is obtained for the Schr\"odinger equation with the potential of induced dipole interaction, which decreases as the inverse square of the distance. Such a potential arises in the collision of an incident…
General formulas describing the multiple scattering of electron by polyatomic molecules have been derived within the framework of the model of non-overlapping atomic potentials. These formulas are applied to different carbon molecules, both…
Hard sphere suspensions are well recognized model systems of statistical physics and soft condensed matter. We here investigate the temporal evolution of the immediate environment of nucleating and growing crystals and/or their global scale…
The behaviour of solitons in integrable theories is strongly constrained by the integrability of the theory; i.e. by the existence of an infinite number of conserved quantities which these theories are known to possess. One usually expects…
We revisit the scattering of surface plasmons by shallow surface defects for both protrusions and indentations of various lengths, which are deemed infinite in one-dimension parallel to the surface. Subwavelength protrusions and…
We describe experimental investigations of the structure of two-dimensional spherical crystals. The crystals, formed by beads self-assembled on water droplets in oil, serve as model systems for exploring very general theories about the…
In this paper, the approach for considering fast charged particles scattering on targets of complex structure, which contain some isolated substructures, is introduced. Based on this approach, the differential cross section for scattering…
Formation of monodispersed colloidal particles is a complex process: nuclei, produced rapidly in a supersaturated solution, grow to nanosize primary particles, which then aggregate (coagulate) to form much larger final colloids. This paper…
Using a single-scattering theory, we derive the expression of the degree of polarization of the light scattered from a layer exhibiting both surface and volume scattering. The expression puts forward the intimate connection between the…
The article discusses the correctness of the assumption about the similarity of molecular continuum electron functions with wave functions in electron-atom scattering. The elastic scattering of slow particles by pair of non-overlapping…
One usually expects localized solitons in integrable systems to interact trivially. There is an integrable (2+1)-dimensional chiral equation which admits multi-soliton solutions with trivial dynamics. This paper describes how to generate…
We study the weak solvability of a quasilinear reaction-diffusion system nonlinearly coupled with an linear elliptic system posed in a domain with distributed microscopic balls in $2D$. The size of these balls are governed by an ODE with…
A film-like or a thread-like system is a system such that one of its constituting homogeneous phases has a constant thickness $\delta$ or a constant normal section of largest diameter $\delta$. The stick probability function of this phase,…
We investigate the formation of cluster crystals with multiply occupied lattice sites on a spherical surface in systems of ultra-soft particles interacting via repulsive, bounded pair potentials. Not all interactions of this kind lead to…
Scattering transforms are a new type of summary statistics recently developed for the study of highly non-Gaussian processes, which have been shown to be very promising for astrophysical studies. In particular, they allow one to build…
We present a stochastic description of multiple scattering of polarized waves in the regime of forward scattering. In this regime, if the source is polarized, polarization survives along a few transport mean free paths, making it possible…
We consider the elastic scattering in deformed space with minimal length. We give the basic relation for the elastic scattering in deformed space. We also investigate the partial wave method in deformed space. It is shown that the relations…
A method is given for calculation of a distribution of small particles, embedded in a medium, so that the resulting medium would have a desired radiation pattern for the plane wave scattering by this medium.
We propose a generic mechanism for the formation of narrow rings in rotating systems. For this purpose we use a system of discs rotating about a common center lying well outside the discs. A discussion of this system shows that narrow rings…
In this work the polarizability of a subwavelength core-shell sphere is considered, where the shell exhibits a radially inhomogeneous permittivity profile. A mathematical treatment of the elec- trostatic polarizability is formulated in…