Related papers: Shape-preserving diffusion of a high-order mode
Self-similar solutions of the coherent diffusion equation are derived and measured. The set of real similarity solutions is generalized by the introduction of a nonuniform phase surface, based on the elegant Gaussian modes of optical…
An optical field will undergo coherent diffusion when it is mapped into thermal-motioned atoms, e.g., in a slow or storage light process. As was demonstrated before, such diffusion effect is equivalent to a spatial low-pass filter…
The aim of the study is to compare the standard Maxwell-Stefan model of diffusion with the higher-order one recently derived. This higher-order model takes into account the influence of the complete pressure tensor. A numerical scheme is…
Do contemporary diffusion models preserve the class geometry of hyperspherical data? Standard diffusion models rely on isotropic Gaussian noise in the forward process, inherently favoring Euclidean spaces. However, many real-world problems…
Let E be an unbounded open (or closed) domain in Euclidean space of dimension greater or equal to two. We present conservativeness criteria for (possibly reflected) diffusions with state space E that are associated to fairly general…
We theoretically investigate image propagation and storage in hot atomic vapor. A $4f$ system is adopted for imaging and an atomic vapor cell is placed over the transform plane. The Fraunhofer diffraction pattern of an object in the object…
Generative diffusion models have achieved remarkable success in producing high-quality images. However, these models typically operate in continuous intensity spaces, diffusing independently across pixels and color channels. As a result,…
The paper studies a higher-order diffusion model of Maxwell-Stefan kind. The model is based upon higher-order moment equations of kinetic theory of mixtures, which include viscous dissipation in the model. Governing equations are analyzed…
Classical diffusion models typically rely on isotropic Gaussian noise, treating all regions uniformly and overlooking structural information important for high-quality generation. We introduce an edge-preserving diffusion process that…
Quantum mechanics predicts that massive particles exhibit wave-like behavior. Matterwave interferometry has been able to validate such predictions through ground-breaking experiments involving microscopic systems like atoms and molecules.…
In this paper, we derive two bound-preserving and mass-conserving schemes based on the fractional-step method and high-order compact (HOC) finite difference method for nonlinear convection-dominated diffusion equations. We split the…
We construct high order symmetric volume-preserving methods for the relativistic dynamics of a charged particle by the splitting technique with processing. Via expanding the phase space to include time $t$, we give a more general…
General properties of linear propagation of discretized light in homogeneous and curved waveguide arrays are comprehensively investigated and compared to those of paraxial diffraction in continuous media. In particular, general laws…
A high-order finite element method is proposed to solve the nonlinear convection-diffusion equation on a time-varying domain whose boundary is implicitly driven by the solution of the equation. The method is semi-implicit in the sense that…
In this paper, we extend the paraxial conical refraction model to the case of the partially coherent light using the unified optical coherence theory. We demonstrate the decomposition of conical refraction correlation functions into…
We study the coherence properties of optical vortices stored in atomic ensembles. In the presence of thermal diffusion, the topological nature of stored optical vortices is found not to guarantee slow decoherence. Instead the stored vortex…
Partially coherent light is abundant in many physical systems, and its propagation properties are well understood. Here we extend current theory of propagation of partially coherent light beams to the field of coherent diffusion. Based on a…
In this paper diffusion processes with changing modes are studied involving the variable order partial differential equations. We prove the existence and uniqueness theorem of a solution of the Cauchy problem for fractional variable order…
Reflection and transmission of narrow beams at a dielectric interface is analysed. It is confirmed that for arbitrary incidence two types of beams - Elegant Hermite-Gaussians of linear polarization and Elegant Laguerre-Gaussians of circular…
A quantum optical model for the high-order harmonic generation is presented, in which both the exciting field and the high harmonic modes are quantized, while the target material appears via parameters only. As a consequence, the model is…