Related papers: Numerical Study of the Higher-Order Maxwell-Stefan…
Diffusion models have shown remarkable empirical success in sampling from rich multi-modal distributions. Their inference relies on numerically solving a certain differential equation. This differential equation cannot be solved in closed…
In this article we deduce a mathematical model of Maxwell-Stefan type for a reactive mixture of polyatomic gases with a continuous structure of internal energy. The equations of the model are derived in the diffusive limit of a kinetic…
Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial…
The formulation of combinatorial differential forms, proposed by Forman for analysis of topological properties of discrete complexes, is extended by defining the operators required for analysis of physical processes dependent on scalar…
The analysis of wave propagation problems in linear damped media must take into account both propagation features and attenuation process. To perform accurate numerical investigations by the finite differences or finite element method, one…
Implementing multicomponent diffusion models in numerical combustion studies is computationally expensive; to reduce cost, numerical simulations commonly use mixture-averaged diffusion treatments or simpler models. However, the accuracy and…
Due to the high complexity and technical requirements of industrial production processes, surface defects will inevitably appear, which seriously affects the quality of products. Although existing lightweight detection networks are highly…
In this paper, we propose high order numerical methods to solve a 2D advection diffusion equation, in the highly oscillatory regime. We use an integrator strategy that allows the construction of arbitrary high-order schemes {leading} to an…
Maxwell-Stefan systems describing the dynamics of the molar concentrations of a gas mixture with an arbitrary number of components are analyzed in a bounded domain under isobaric, isothermal conditions. The systems consist of mass balance…
Curse of Dimensionality is an unavoidable challenge in statistical probability models, yet diffusion models seem to overcome this limitation, achieving impressive results in high-dimensional data generation. Diffusion models assume that…
We present a new third-order, semi-discrete, central method for approximating solutions to multi-dimensional systems of hyperbolic conservation laws, convection-diffusion equations, and related problems. Our method is a high-order extension…
In this study we apply the maximum entropy principle to derive the properly scaled velocity distribution function of Boltzmann equations for mixtures, which leads to a non-isothermal Maxwell-Stefan diffusion model. We also analyze the…
Particle diffusion in rotating drums is studied via computer simulations using a full 3-D model which does not involve any arbitrary input parameters. The diffusion coefficient for single-component systems agree qualitatively with previous…
Nonequilibrium behaviors of positional order are discussed based on diffusion processes in particle systems. With the cumulant expansion method up to the second order, we obtain a relation between the positional order parameter $\Psi$ and…
The crossover among two or more types of diffusive processes represents a vibrant theme in nonequilibrium statistical physics. In this work we propose two models to generate crossovers among different L\'evy processes: in the first model we…
A particle with internal unobserved states diffusing in a force field will generally display effective advection-diffusion. The drift velocity is proportional to the mobility averaged over the internal states, or effective mobility, while…
We propose a new statistical observation scheme of diffusion processes named convolutional observation, where it is possible to deal with smoother observation than ordinary diffusion processes by considering convolution of diffusion…
Diffusion models have emerged from various theoretical and methodological perspectives, each offering unique insights into their underlying principles. In this work, we provide an overview of the most prominent approaches, drawing attention…
We derive and analyze a broad class of finite element methods for numerically simulating the stationary, low Reynolds number flow of concentrated mixtures of several distinct chemical species in a common thermodynamic phase. The underlying…
We explore the effects of mesh skewness on the accuracy of standard Hybrid High-Order (HHO) schemes for anisotropic diffusion equations. After defining a notion of regular skewed mesh sequences, which allows, e.g., for elements that become…