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The radiative transfer equation (RTE) arises in many different areas of science and engineering. In this paper, we propose and investigate a discrete-ordinate discontinuous-streamline diffusion (DODSD) method for solving the RTE, which is a…
In this article we consider the approximation of a variable coefficient (two-sided) fractional diffusion equation (FDE), having unknown $u$. By introducing an intermediate unknown, $q$, the variable coefficient FDE is rewritten as a lower…
Recent diffusion distillation methods have achieved remarkable progress, enabling high-quality ${\sim}4$-step sampling for large-scale text-conditional image and video diffusion models. However, further reducing the number of sampling steps…
We propose a long-distance continuous-variable measurement-device-independent quantum key distribution (CV-MDI-QKD) protocol with discrete modulation. This kind of discrete-modulated schemes have good compatibility with efficient error…
Quantum Key Distribution (QKD) is a cutting-edge communication method that enables secure communication between two parties. Continuous-variable QKD (CV-QKD) is a promising approach to QKD that has several advantages over traditional…
In this work, we propose a nonlinear stabilization technique for scalar conservation laws with implicit time stepping. The method relies on an artificial diffusion method, based on a graph-Laplacian operator. It is nonlinear, since it…
Divergence and vorticity damping, which operate upon horizontal divergence and relative vorticity, are explicit diffusion mechanisms used in dynamical cores to ensure stability. To avoid numerical blow-up from excessively strong diffusion,…
Discrete diffusion models have recently shown great promise for modeling complex discrete data, with masked diffusion models (MDMs) offering a compelling trade-off between quality and generation speed. MDMs denoise by progressively…
We present a novel hyperviscosity formulation for stabilizing RBF-FD discretizations of the advection-diffusion equation. The amount of hyperviscosity is determined quasi-analytically for commonly-used explicit, implicit, and…
The secret key rate of a continuous-variable quantum key distribution (CV-QKD) system is limited by excess noise. A key issue typical to all modern CV-QKD systems implemented with a reference or pilot signal and an independent local…
The four-state continuous-variable quantum key distribution (CVQKD) protocol has a long practical secure distance \cite{Leverrier_PRL_2009}, while it has the difficulty of parameter estimation. We propose an improved four-state protocol,…
This paper continues our research devoted to an accurate nonlinear Bayesian filters' design. Our solution implies numerical methods for solving ordinary differential equations (ODE) when propagating the mean and error covariance of the…
We report the results of experimental studies of the short time-long wavelength behavior of collective particle displacements in quasi-one-dimensional and quasi-two-dimensional colloid suspensions. Our results are represented by the…
Continuous-variable quantum key distribution (CVQKD) offers the specific advantage of sharing keys remotely by the use of standard telecom components, thereby promoting cost-effective and high-performance metropolitan applications.…
Quasi-periodic solutions with multiple base frequencies exhibit the feature of $2\pi$-periodicity with respect to each of the hyper-time variables. However, it remains a challenge work, due to the lack of effective solution methods, to…
We consider a general McKean-Vlasov stochastic differential equation driven by a rotationally invariant $\alpha$-stable process on $\mathbb{R}^d$ with $\alpha \in (1,2)$. We assume that the diffusion coefficient is the identity matrix and…
Quantum Key Distribution (QKD) is a technology that allows secure key exchange between two distant users. A widespread adoption of QKD requires the development of simple, low-cost, and stable systems. However, implementation of the current…
In this paper, we aim to study the diffusion approximation for multi-scale McKean-Vlasov stochastic differential equations. More precisely, we prove the weak convergence of slow process $X^\varepsilon$ in $C([0,T];\mathbb{R}^n)$ towards the…
This paper explores the innovative application of Stable Video Diffusion (SVD), a diffusion model that revolutionizes the creation of dynamic video content from static images. As digital media and design industries accelerate, SVD emerges…
A module for the ZEUS-2D code is described which may be used to solve the equations of radiation hydrodynamics to order unity in v/c, in the flux-limited diffusion (FLD) approximation. In this approximation, the tensor Eddington factor f…