Related papers: Fractional calculus within the optical model used …
We extend the concept of optical flow to a dynamic non-Euclidean setting. Optical flow is traditionally computed from a sequence of flat images. It is the purpose of this paper to introduce variational motion estimation for images that are…
Many biological processes and objects can be described by fractals. The paper uses a new type of objects - blinking fractals - that are not covered by traditional theories considering dynamics of self-similarity processes. It is shown that…
The properties of excited nuclear matter and the quest for a phase transition which is expected to exist in this system are the subject of intensive investigations. High energy nuclear collisions between finite nuclei which lead to matter…
We use the fractional integrals in order to describe dynamical processes in the fractal media. We consider the "fractional" continuous medium model for the fractal media and derive the fractional generalization of the equations of balance…
A recapitulatory analysis of total nuclear cross sections of various nuclei is presented, which yields detailed knowledge on the different physical processes such as potential/resonance scatter and nuclear reactions. The physical base for…
Factorial moments are convenient tools in particle physics to characterize the multiplicity distributions when phase-space resolution ($\Delta$) becomes small. They include all correlations within the system of particles and represent…
A finite element-based modal formulation of diffraction of a plane wave by an absorbing photonic crystal slab of arbitrary geometry is developed for photovoltaic applications. The semi-analytic approach allows efficient and accurate…
Fractals are geometric shapes that can display complex and self-similar patterns found in nature (e.g., clouds and plants). Recent works in visual recognition have leveraged this property to create random fractal images for model…
We compare the properties of transmission across one-dimensional finite samples which are associated with two types of "quantum diffusion", one related to a classical chaotic dynamics, the other to a multifractal energy spectrum. We…
The knowledge of the exact structure of the optical system PSF enables a high-quality image reconstruction in fluorescence microscopy. Accurate PSF models account for the vector nature of light and the phase and amplitude modifications.…
Optical trapping is a widely used technique, with many important applications in biology and metrology. Complete modelling of trapping requires calculation of optical forces, primarily a scattering problem, and non-optical forces. The…
In this work we present a model reduction procedure to derive a hybrid-dimensional framework for the mathematical modeling of reactive transport in fractured porous media. Fractures are essential pathways in the underground which allow fast…
Conventional scattering theory is incomplete in that it does not adequately describe the behaviour of the wave function at macroscopic distances from the scattering reaction volume. In scattering experiments particles are incident from…
The optical theorem is an important tool for scattering analysis in acoustics, electromagnetism, and quantum mechanics. We derive an extended version of the optical theorem for the scattering of elastic waves by a spherical inclusion…
Formulas to describe the photoabsorption and the photon scattering by a plasma or a liquid metal are derived in a unified manner with each other. It is shown how the nuclear motion, the free-electron motion and the core-electron behaviour…
The theory of fractional calculus is attracting a lot of attention from mathematicians as well as physicists. The fractional generalisation of the well-known ordinary calculus is being used extensively in many fields, particularly in…
Typically one expects that when a heavy particle collides with a surface, the scattered angular distribution will follow classical mechanics. The heavy mass assures that the de Broglie wavelength of the incident particle in the direction of…
The light scattering experiment establishes a relationship between refractive index fluctuations and fractal dimension in weakly scattering tissue-like media. Based on the box-counting approach, an analytical model is developed and shows…
The decay of $\alpha$ particle from a nucleus is viewed as a quantum resonance state of a two-body scattering process of the $\alpha$+daughter nucleus pair governed by a novel nucleus-nucleus potential in squared Woods-Saxon form. By the…
In this paper, we study the mathematical imaging problem of optical diffraction tomography (ODT) for the scenario of a microscopic rigid particle rotating in a trap created, for instance, by acoustic or optical forces. Under the influence…