Related papers: Darning and gluing of diffusions
We develop a versatile theoretical approach to the study of cold-atom diffractive scattering from light-field gratings by combining calculations of the optical near-field, generated by evanescent waves close to the surface of periodic…
A simple construction of Euclidean invariant and reflection positive measures on the cylindrical compactification is performed under a weaker hypothesis than has recently been obtained. Moreover, the results are extended to the case when…
Regular model sets, describing the point positions of ideal quasicrystallographic tilings, are mathematical models of quasicrystals. An important result in mathematical diffraction theory of regular model sets, which are defined on locally…
The properties of the compactness of interpolation sets of algebras of generalized analytic functions are investigated and convenient sufficient conditions for interpolation are given.
The gradient discretisation method (GDM) is a generic framework for designing and analysing numerical schemes for diffusion models. In this paper, we study the GDM for the porous medium equation, including fast diffusion and slow diffusion…
We survey the distributional properties of progressively dilating sets under projection by covering maps, focusing on manifolds of constant sectional curvature. In the Euclidean case, we review previously known results and formulate some…
A new mechanism of Bragg reflection is identified, one that, remarkably, occurs in a uniform medium and relies on resonant tuning of the medium's parameters. Due to uniformity, reflection ensues over a broad wavelength range, much like a…
A new type of metal-dielectric composites has been proposed that is characterised by a resonance-like behaviour of the effective permeability in the infrared and visible spectral ranges. This material can be referred to as optomagnetic…
The question of decoupling and freeze-out is reinvestigated and analysed in terms of transparent semi-classical decoupling formulae, which provide a smooth decoupling in time both, for single and two particle inclusive spectra. They…
Relocation of compact sets in an $n$-dimensional manifold by self-diffeomorphism is of its own interest as well as significant potential applications to data classification in data science. This paper presents a theory for relocating a…
Originally, tangles were invented as an abstract tool in mathematical graph theory to prove the famous graph minor theorem. In this paper, we showcase the practical potential of tangles in machine learning applications. Given a collection…
We give a necessary and sufficient condition for gluings of hyperconvex metric spaces along weakly externally hyperconvex subsets in order that the resulting space be hyperconvex. This leads to a full characterization of gluings of two…
We review both theoretical and experimental advances in the recently emerged physics of modulated photonic lattices. Artificial periodic dielectric media, such as photonic crystals and photonic lattices, provide a powerful tool for the…
Magnification of total image fluxes is typically considered a defining feature of gravitational microlensing. In contrast, I will show that nonminimal couplings to gravity can generate regions of negative gravitational potential curvature,…
Diffuse scattering of light from disordered assemblies is traditionally viewed as an uncontrollable broadband scattering background resulting in whitish hues. Here, we demonstrate that correlated disorder enables precise engineering of…
In a previous paper, we showed how certain orientations of the edges of a graph G embedded in a closed oriented surface S can be understood as discrete spin structures on S. We then used this correspondence to give a geometric proof of the…
We study the deformation of a fluctuating crystalline sheet confined between two flat rigid walls as a simple model for layered solids where bonds among atoms {\it within} the same layer are much stronger than those {\it between} layers.…
We describe our recent results concerning the rigidity/unlockability properties of clusters of rigid bodies sliding over the unit sphere.
We begin by reviewing some probabilistic results about the Dirichlet Process and its close relatives, focussing on their implications for statistical modelling and analysis. We then introduce a class of simple mixture models in which…
We study the convergence of the new family of mimetic finite difference schemes for linear diffusion problems recently proposed in [38]. In contrast to the conventional approach, the diffusion coefficient enters both the primary mimetic…