相关论文: Motives from Diffraction

We analyze the tt-geometry of derived Artin motives, via modular representation theory of profinite groups. To illustrate our methods, we discuss Artin motives over a finite field, in which case we also prove stratification.

Bipartite graphs model the relationship between two disjoint sets of objects. They have a wide range of applications and are often visualized as a 2-layered drawing, where each set of objects is visualized as a set of vertices (points) on…

A description of an algorithm for a rather general modal grating calculation is presented. Arbitrary profiles, depth, and permittivity are allowed. Gratings built up from sub-gratings are allowed, as are coatings on the sidewalls of lines,…

A high-accuracy solution of the diffraction problem has become necessary for the treatment of certain special questions of statistical physics. This article reports the creation of a computer program that serves as an instrumental method of…

We consider the inverse problem of denoising an image where each point (pixel) is an element of a target set, which we refer to as a target-valued image. The target sets considered are either (i) a closed convex set of Euclidean space or…

Given a complex smooth algebraic variety X, we compute the generating function of the stringy motives of its symmetric powers as a function of motive of X. In dimension two we recover the Goettsche formulas for Hilbert schemes. We use the…

An electron beam traversing a structured plasmonic field is shown to undergo diffraction with characteristic angular patterns of both elastic and inelastic outgoing electron components. In particular, a plasmonic {\it grating} (e.g., a…

We study direct and inverse scattering problem for systems of interacting particles, having web-like structure. Such systems consist of a finite number of semi-infinite chains attached to the central part formed by a finite number of…

Dissipative phenomena manifest in multiple mechanical systems. In this dissertation, different geometric frameworks for modelling non-conservative dynamics are considered. The objective is to generalize several results from conservative…

Simple algebraic rules can produce complex networks with rich structures. These graphs are obtained when looking at a monoid operating on a ring. There are relations to dynamical systems theory and number theory. This document illustrates…

We develop random graph models where graphs are generated by connecting not only pairs of vertices by edges but also larger subsets of vertices by copies of small atomic subgraphs of arbitrary topology. This allows the for the generation of…

The general method to obtain solutions of the Maxwellian equations from scalar representatives is developed and applied to the diffraction of electromagnetic waves. Kirchhoff's integral is modified to provide explicit expressions for these…

Theoretical study of arrays of graphene ribbons is currently of high interest due to its potential application in beam splitters, absorbers, and polarizers. In this paper, an analytical method is presented for diffraction analysis of…

Stochastic point processes relevant to the theory of long-range aperiodic order are considered that display diffraction spectra of mixed type, with special emphasis on explicitly computable cases together with a unified approach of…

Frequent and structurally related subgraphs, also known as network motifs, are valuable features of many graph datasets. However, the high computational complexity of identifying motif sets in arbitrary datasets (motif mining) has limited…

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…

The Dirac equation in $\mathbb{R}^{1,3}$ with potential Z/r is a relativistic field equation modeling the hydrogen atom. We analyze the singularity structure of the propagator for this equation, showing that the singularities of the…

We apply the Hilbert transform to the physics of internal waves in two-dimensional fluids. Using this demodulation technique, we can discriminate internal waves propagating in different directions: this is very helpful in answering several…

Diffuse intensities in the electron diffraction patterns of concentrated face-centered cubic solid solutions have been widely attributed to chemical short-range order, although this connection has been recently questioned. This article…

We examine a number of results of infinite combinatorics using the techniques of reverse mathematics. Our results are inspired by similar results in recursive combinatorics. Theorems included concern colorings of graphs and bounded graphs,…