相关论文: Riemannian Geometrical Optics: Surface Waves in Di…

This paper is concerned with the problem of scattering of time-harmonic acoustic waves from an impenetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is established, employing the integral equation…

Simulation of conditioned diffusion processes is an essential tool in inference for stochastic processes, data imputation, generative modelling, and geometric statistics. Whilst simulating diffusion bridge processes is already difficult on…

Motivated by the use of degenerate Jacobi metrics for the study of brake orbits and homoclinics, we develop a Morse theory for geodesics in conformal metrics having conformal factors vanishing on a regular hypersurface of a Riemannian…

Diffusion models are recent state-of-the-art methods for image generation and likelihood estimation. In this work, we generalize continuous-time diffusion models to arbitrary Riemannian manifolds and derive a variational framework for…

Imaging systems are represented as linear operators, and their singular value spectra describe the structure recoverable at the operator level. Building on an operator-based information-theoretic framework, this paper introduces a minimal…

Accurate and efficient prediction of three-dimensional (3D) fields in wave interactions with large, complex-shaped objects is essential for applications in electromagnetic computation, computer graphics, optical metrology, and freeform…

Conventional X-ray methods use incoming plane waves and result in discrete diffraction patterns when scattered at crystals. Here we find, by a systematic method, incoming waveforms which exhibit discrete diffraction patterns when scattered…

A "genuinely" paraxial version of Miyamoto-Wolf's theory aimed at dealing with sharp-edge diffraction under Gaussian beam illumination is presented. The theoretical analysis is carried out in such a way the well known Young-Maggi-Rubinowicz…

The scattering of light observed through the turbid underwater channel is often regarded as the leading challenge when designing underwater electro-optical imaging systems. There have been many approaches to address the effects of…

Fluctuation geometry was recently proposed as a counterpart approach of Riemannian geometry of inference theory. This theory describes the geometric features of the statistical manifold $\mathcal{M}$ of random events that are described by a…

We consider the inverse problem of recovering a potential from the Dirichlet to Neumann map at a large fixed frequency on certain Riemannian manifolds. We extend the earlier result of [G. Uhlmann and Y. Wang, arXiv:2104.03477] to the case…

In this paper, we are concerned with the asymptotic behavior of solutions to the Cauchy problem (or initial-boundary value problem) of one-dimensional Keller-Segel model. For the Cauchy problem, we prove that the solutions…

We show that certain right-invariant metrics endow the infinite-dimensional Lie group of all smooth orientation-preserving diffeomorphisms of the circle with a Riemannian structure. The study of the Riemannian exponential map allows us to…

In this paper, we address several interconnected problems in the theory of harmonic maps between Riemannian manifolds. First, we present necessary background and establish one of the main results of the paper: a criterion characterizing…

We define and study isoparametric submanifolds of general ambient spaces and of arbitrary codimension. In particular we study their behaviour with respect to Riemannian submersions and their lift into a Hilbert space. These results are used…

Understanding feature-outcome associations in high-dimensional data remains challenging when relationships vary across subpopulations, yet standard methods assuming global associations miss context-dependent patterns, reducing statistical…

We extend a modal theory of diffraction by a set of parallel fibers to deal with the case of a hard boundary: that is a structure made for instance of air-holes inside a dielectric matrix. Numerical examples are given concerning some…

Tomography is the three-dimensional reconstruction of an object from images taken at different angles. The term classical tomography is used, when the imaging beam travels in straight lines through the object. This assumption is valid for…

Light diffraction at an aperture is a basic problem that has generated a tremendous amount of interest in optics. Some of the most significant diffraction results are the Fresnel-Kirchhoff and Rayleigh-Sommerfeld formulas. These theories…

We study wave scattering by a finite transversal strip in a discrete square-lattice waveguide with Dirichlet boundary conditions imposed on the strip and the waveguide walls. The setting is motivated as a discrete analogue of the classical…