Related papers: Shape-preserving diffusion of a high-order mode
Rendering highly scattering participating media using brute force path tracing is a challenge. The diffusion approximation reduces the problem to solving a simple linear partial differential equation. Flux-limited diffusion introduces…
In this paper, we develop a family of high order asymptotic preserving schemes for some discrete-velocity kinetic equations under a diffusive scaling, that in the asymptotic limit lead to macroscopic models such as the heat equation, the…
State-of-the-art diffusion models can generate highly realistic images based on various conditioning like text, segmentation, and depth. However, an essential aspect often overlooked is the specific camera geometry used during image…
We study diffusion in systems of classical particles whose dynamics conserves the total center of mass. This conservation law leads to several interesting consequences. In finite systems, it allows for equilibrium distributions that are…
This study addresses the challenge of, without training or fine-tuning, controlling the global color aspect of images generated with a diffusion model. We rewrite the guidance equations to ensure that the outputs are closer to a known color…
In coherent X-ray diffraction microscopy the diffraction pattern generated by a sample illuminated with coherent x-rays is recorded, and a computer algorithm recovers the unmeasured phases to synthesize an image. By avoiding the use of a…
We have experimentally investigated the formation of off-diagonal long-range order in a gas of ultracold atoms. A magnetically trapped atomic cloud prepared in a highly nonequilibrium state thermalizes and thereby crosses the Bose-Einstein…
We investigate which jump-diffusion models are convexity preserving. The study of convexity preserving models is motivated by monotonicity results for such models in the volatility and in the jump parameters. We give a necessary condition…
An electron beam traversing a structured plasmonic field is shown to undergo diffraction with characteristic angular patterns of both elastic and inelastic outgoing electron components. In particular, a plasmonic {\it grating} (e.g., a…
Diffraction of a high-frequency large-number whispering gallery mode is studied, which runs along a concave curve turning to a straight line. At the point of straitening, the curvature of the boundary suffers a jump. The parabolic equation…
We present high-order variational Lagrangian finite element methods for compressible fluids using a discrete energetic variational approach. Our spatial discretization is mass/momentum/energy conserving and entropy stable. Fully implicit…
Diffusion models are a powerful class of generative models capable of producing high-quality images from pure noise using a simple text prompt. While most methods which introduce additional spatial constraints into the generated images…
The numerical approximation of an inverse problem subject to the convection--diffusion equation when diffusion dominates is studied. We derive Carleman estimates that are on a form suitable for use in numerical analysis and with explicit…
We study the quantitative homogenization of linear second order elliptic equations in non-divergence form with highly oscillating periodic diffusion coefficients and with large drifts, in the so-called ``centered'' setting where…
Atoms in high-finesse optical resonators interact via the photons they multiply scatter into the cavity modes. The dynamics is characterized by dispersive and dissipative optomechanical long-range forces, which are mediated by the cavity…
In this article, the possibility of generating non-classical light due to Planck-scale effects is considered. For this purpose, a widely studied model of deformation of the Heisenberg uncertainty relation is applied to single-mode and…
L\'{e}vy flight models whose jumps have infinite moments are mathematically used to describe the superdiffusion in complex systems. Exponentially tempering the Levy measure of L\'{e}vy flights leads to the tempered stable L\'{e}vy processes…
We are interested in the high-order approximation of anisotropic, potential-driven advection-diffusion models on general polytopal partitions. We study two hybrid schemes, both built upon the Hybrid High-Order technology. The first one…
Using an exactly soluble one-dimensional atomic model we explore the idea that the recently observed high-order nonlinearity in optical filaments is due to virtual transitions involving the continuum states. We show that the model's…
Typical diffusion models are trained to accept a particular form of conditioning, most commonly text, and cannot be conditioned on other modalities without retraining. In this work, we propose a universal guidance algorithm that enables…