相关论文: Categorical distribution theory; heat equation
In this work, a thermal energy transfer problem in a one-dimensional multilayer body is theoretically analyzed, considering diffusion, advection, internal heat generation or loss linearly dependent on temperature in each layer, as well as…
The mesosocpic concept is applied to the theory of mixtures. The aim is to investigate the diffusion phenomenon from a mesoscopic point of view. The domain of the field quantities is extended by the set of mesoscopic variables, here the…
Diffusion models have been widely used in time series and spatio-temporal data, enhancing generative, inferential, and downstream capabilities. These models are applied across diverse fields such as healthcare, recommendation, climate,…
Scattering is an important phenomenon which is observed in systems ranging from the micro- to macroscale. In the context of nuclear reaction theory the Heidelberg approach was proposed and later demonstrated to be applicable to many chaotic…
Heat diffusion describes the process by which heat flows from areas with higher temperatures to ones with lower temperatures. This concept was previously adapted to graph structures, whereby heat flows between nodes of a graph depending on…
A detailed description of the statistical distribution of thermal vacancies near the melting point is presented, using copper as an example. As the temperature is increased, the average number of thermal vacancies generated by atoms…
To optimally utilize all the exciting cosmological data coming in we need to sharpen also the theoretical tools available to cosmologists. One such indispensible tool to understand hot big bang cosmology is finite temperature field theory.…
An approach for solving scattering problems, based on two quantum field theory methods, the heat kernel method and the scattering spectral method, is constructed. This approach converts a method of calculating heat kernels into a method of…
The main aim of the present work is to arrive at a mathematical theory close to the historically original conception of generalized functions, i.e. set theoretical functions defined on, and with values in, a suitable ring of scalars and…
In Lipschitz domains, we study a Darcy-Forchheimer problem coupled with a singular heat equation by a nonlinear forcing term depending on the temperature. By singular we mean that the heat source corresponds to a Dirac measure. We establish…
We propose a thermodynamically consistent general-purpose model describing diffusion of a solute or a fluid in a solid undergoing possible phase transformations and damage, beside possible visco-inelastic processes. Also heat…
Graph is a prevalent discrete data structure, whose generation has wide applications such as drug discovery and circuit design. Diffusion generative models, as an emerging research focus, have been applied to graph generation tasks.…
This article presents a convenient approach to Fourier analysis for the investigation of functions and distributions defined in $\mathbb{T}^m \times \mathbb{R}^n$. Our approach involves the utilization of a mixed Fourier transform,…
The current paper is devoted to the study of spreading speeds and transition fronts of lattice KPP equations in time heterogeneous media. We first prove the existence, uniqueness, and stability of spatially homogeneous entire positive…
Since the turn of the century, there has been increased interest in the application of heavy-tailed distributions, particularly stable distributions, to problems in physics and finance. Although, the tails of stable distributions provide a…
The theory of commutative monads on cartesian closed categories provides a framework where aspects of the theory of distributions and other extensive quantities can be formulated and some results proved. We make explicit a link between our…
We introduce a novel explicit and stable numerical algorithm to solve the spatially discretized heat or diffusion equation. We compare the performance of the new method with analytical and numerical solutions. We show that the method is…
In this paper, we study large-time asymptotics for heat and fractional heat equations in two discrete settings: the full lattice \(\mathbb Z^d\) and finite connected subgraphs with Dirichlet boundary condition. These results provide a…
A thermodynamically consistent mathematical model for hydrogen adsorption in metal hydrides is proposed. Beside hydrogen diffusion, the model accounts for phase transformation accompanied by hysteresis, swelling, temperature and heat…
Generalizing an idea of Davie and Gaines (2001), we present a method for the simulation of fully discrete samples of the solution to the stochastic heat equation on an interval. We provide a condition for the validity of the approximation,…