Related papers: Recent progress in mathematical diffraction
This paper is based on the opening lecture given at the 2017 edition of the Evry Schatzman school on high-angular resolution imaging of stars and their direct environment. Two relevant observing techniques: long baseline interferometry and…
A few years ago, diffraction of atoms by double slits and gratings was achieved for the first time, and standard optical wave-theory provided an excellent description of the experiments. More recently, diffraction of weakly bound molecules…
This paper is devoted to the mathematical analysis of a time-domain electromagnetic scattering by periodic structures which are known as diffraction gratings. The scattering problem is reduced equivalently into an initial-boundary value…
This article gives an overview of the developments in controlled diffusion processes, emphasizing key results regarding existence of optimal controls and their characterization via dynamic programming for a variety of cost criteria and…
We generalize the notion of the Franhoufer diffraction from a single slit and a circular aperture to the case of partially temporal coherent and quasimonochromatic light. The problem is studied analytically and the effect of coherence…
There has been considerable recent study in "sub-diffusion" models that replace the standard parabolic equation model by a one with a fractional derivative in the time variable. There are many ways to look at this newer approach and one…
In this work we derive important properties regarding matrix invariants which occur in the theory of differential equations with reflection.
A brief review of theoretical progress in hadron spectroscopy and nonperturbative QCD is presented. Attention is focussed on recent lattice gauge theory, the Dyson-Schwinger formalism, effective field theory, unquenching constituent models,…
We study a second order scheme for spatial fractional differential equations with variable coefficients. Previous results mainly concentrate on equations with diffusion coefficients that are proportional to each other. In this paper, by…
Novel optical elements containing semitransparent wavelike films embedded into the bulk of transparent material, which form a reflection image without transmitted light distortion, are studied. The dynamic theory of light diffraction by a…
Recent progress in Lattice QCD is highlighted. After a brief introduction to the methodology of lattice computations the presentation focuses on three main topics: Hadron Spectroscopy, Hadron Structure and Lattice Flavor Physics. In each…
We describe the mathematical theory of diffusion and heat transport with a view to including some of the main directions of recent research. The linear heat equation is the basic mathematical model that has been thoroughly studied in the…
In coherent X-ray diffraction microscopy the diffraction pattern generated by a sample illuminated with coherent x-rays is recorded, and a computer algorithm recovers the unmeasured phases to synthesize an image. By avoiding the use of a…
The advantages of convergent beam electron diffraction for symmetry determination at the scale of a few nm are well known. In practice, the approach is often limited due to the restriction on the angular range of the electron beam imposed…
It has been recently pointed out that dynamical systems depending on future values of the unknowns may be useful in different areas of knowledge. We explore in this context the extension of the concept of order reduction that has been…
We survey recent developments on the Restriction conjecture.
Transmission electron diffraction is a powerful and versatile structural probe for the characterization of a broad range of materials, from nanocrystalline thin films to single crystals. With recent developments in fast electron detectors…
Using diffusion priors to solve inverse problems in imaging have significantly matured over the years. In this chapter, we review the various different approaches that were proposed over the years. We categorize the approaches into the more…
This article provides a survey on some main results and recent developments in the mathematical theory of water waves. More precisely, we briefly discuss the mathematical modeling of water waves and then we give an overview of local and…
We review several recent developments in the theory and phenomenology of deep-inelastic scattering, with particular emphasis on precision tests of QCD and progress in the detailed perturbative treatment of structure functions and parton…