Related papers: Darning and gluing of diffusions
This work focuses on the combinatorial properties of glued semigroups and provides its combinatorial characterization. Some classical results for affine glued semigroups are generalized and some methods to obtain glued semigroups are…
A synoptic view on the long-established theory of light propagation in crystalline dielectrics is presented, providing a new exact solution for the microscopic local electromagnetic field thus disclosing the role of the divergence-free…
We present recent theoretical investigations on the dynamics of metal clusters in contact with an environment, deposited of embedded. This concerns soft deposition as well as irradiation of the deposited/embedded clusters by intense laser…
Light propagating in an optically thick sample experiences multiple scattering. It is now known that interferences alter this propagation, leading to an enhanced backscattering, a manifestation of weak localization of light in such diffuse…
In the ELTs era, where the need for versatile and innovative solutions to produce very high spatial resolution images has become a major issue, the search of synergies with other science fields seems a logic step. One of the considered…
A multilayered particle is illuminated by plane acoustic or electromagnetic waves of one or several frequencies. We consider the inverse scattering problem for the identification of the layers and of the refraction coefficients of the…
The physics of electrons, photons, and their plasmonic interactions changes greatly when one or more dimensions are reduced down to the nanometer scale. For example, graphene shows unique electrical, optical, and plasmonic properties, which…
In recent years there has been a great interest in topological materials and in their fascinating properties. Topological band theory was initially developed for condensed matter systems, but it can be readily applied to arbitrary wave…
In this short note we survey theorems and provide conjectures on gluing constructions under lower curvature bounds in smooth and non-smooth context. Focusing on synthetic lower Ricci curvature bounds we consider Riemannian manifolds,…
To ensure the discrete maximum principle or solution positivity in finite volume schemes, diffusive flux is sometimes discretized as a conical combination of finite differences. Such a combination may be impossible to construct along…
Limited-diffraction beams are a class of waves that may be localized in space and time. Theoretically, these beams are propagation invariant and can propagate to an infinite distance without spreading. In practice, when these beams are…
A general theoretical framework is developed for interpreting spectropolarimetric observations of optically thin emission line scattering from small dust particles. Spatially integrated and spatially resolved line profiles of both scattered…
The formulation of combinatorial differential forms, proposed by Forman for analysis of topological properties of discrete complexes, is extended by defining the operators required for analysis of physical processes dependent on scalar…
This work discusses the homogenization analysis for diffusion processes on scale-free metric graphs, using weak variational formulations. The oscillations of the diffusion coefficient along the edges of a metric graph induce internal…
We study theoretically the concept of homogenization in optics using an ensemble of randomly distributed resonant stationary atoms with density $\rho$. The ensemble is dense enough for the usual condition for homogenization, viz.…
It gives some new forms of General Neron Desingularization and new applications.
We present a new multi-layer peeling technique to cluster points in a metric space. A well-known non-parametric objective is to embed the metric space into a simpler structured metric space such as a line (i.e., Linear Arrangement) or a…
The chapter contains a detailed presentation of the surface integral theory for modelling light diffraction by surface-relief diffraction gratings having a one-dimensional periodicity. Several different approaches are presented, leading…
The diffraction of stochastic point sets, both Bernoulli and Markov, and of random tilings with crystallographic symmetries is investigated in rigorous terms. In particular, we derive the diffraction spectrum of 1D random tilings, of…
We present a theory for the cloaking of arbitrarily-shaped objects and demonstrate electromagnetic scattering-cancellation through designed homogeneous coatings. First, in the small-particle limit, we expand the dipole moment of a coated…