Related papers: Doubly Degenerate Diffuse Interface Models of Anis…
The mathematical analysis of diffuse-interface models for multiphase flows has attracted significant attention due to their ability to capture complex interfacial dynamics, including curvature effects, within a unified, energetically…
With the rapid advancement of diffusion-based generative models, Stable Diffusion (SD) has emerged as a state-of-the-art framework for high-fidelity im-age synthesis. However, existing SD models suffer from suboptimal feature aggregation,…
This work presents a comprehensive framework for enhanced diffusion modeling in fluid-structure interactions by combining the Immersed Boundary Method (IBM) with stochastic trajectories and high-order spectral boundary conditions. Using…
Phase retrieval refers to the problem of recovering an image from the magnitudes of its complex-valued linear measurements. Since the problem is ill-posed, the recovery requires prior knowledge on the unknown image. We present DOLPH as a…
Incomplete data are common in real-world tabular applications, where numerical, categorical, and discrete attributes coexist within a single dataset. This heterogeneous structure presents significant challenges for existing diffusion-based…
The "double diffusivity" model was proposed in the late 1970s, and reworked in the early 1980s, as a continuum counterpart to existing discrete models of diffusion corresponding to high diffusivity paths, such as grain boundaries and…
In this work, the author developed a multiple scattering model for heterogeneous elastic continua with strong property fluctuation and obtained the exact solution to the dispersion equation derived from the Dyson equation under the…
In this paper we study the Cauchy problem for doubly dissipative elastic waves in two space dimensions, where the damping terms consist of two different friction or structural damping. We derive energy estimates and diffusion phenomena with…
We propose an alternative method for one-dimensional continuum diffusion models with spatially variable (heterogeneous) diffusivity. Our method, which extends recent work on stochastic diffusion, assumes the constant-coefficient homogenized…
We study a nonlinear, degenerate cross-diffusion model which involves two densities with two different drift velocities. A general framework is introduced based on its gradient flow structure in Wasserstein space to derive a notion of…
In this paper, we introduce an interfacial profile-preserving approach for phase field modeling for simulating incompressible two-phase flows. While the advective Cahn-Hilliard equation effectively captures the topological evolution of…
This paper considers the iterative solution of linear systems arising from discretization of the anisotropic radiative transfer equation with discontinuous elements on the sphere. In order to achieve robust convergence behavior in the…
Diffusion-based generative models are machine learning models that use diffusion processes to learn the probability distribution of high-dimensional data. In recent years, they have become extremely successful in generating multimedia…
The multi-phase-field approach is generalized to treat capillarity-driven diffusion parallel to the surfaces and phase-boundaries, i.e. the boundaries between a condensed phase and its vapor and the boundaries between two or multiple…
Biomembranes and vesicles consisting of multiple phases can attain a multitude of shapes, undergoing complex shape transitions. We study a Cahn--Hilliard model on an evolving hypersurface coupled to Navier--Stokes equations on the surface…
We report an experimental assessment of surface kinetic roughening properties that are anisotropic in space. Working for two specific instances of silicon surfaces irradiated by ion-beam sputtering under diverse conditions (with and without…
Diffusion models have shown remarkable capabilities in generating high-fidelity data across modalities such as images, audio, and video. However, their computational intensity makes deployment on edge devices a significant challenge. This…
Nonlinear, i.e., multi-photon microscopy is a powerful technique for imaging deep into biological tissues. Its penetration depth can be increased further using adaptive optics. In this work, we present a fast, feedback-based adaptive-optics…
The subject matter of this paper concerns anisotropic diffusion equations: we consider heat equations whose diffusion matrix have disparate eigenvalues. We determine first and second order approximations, we study the well-posedness of them…
Coherency misfit stresses and their related anisotropies are known to influence the equilibrium shapes of precipitates. Additionally, mechanical properties of the alloys are also dependent on the shapes of the precipitates. Therefore, in…