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In this work, we propose an adaptive learning approach based on temporal normalizing flows for solving time-dependent Fokker-Planck (TFP) equations. It is well known that solutions of such equations are probability density functions, and…
In Hamiltonian systems subjected to periodic perturbations the stable and unstable manifolds of the unstable periodic orbits provide the dynamical "skeleton" that drives the mixing process and bounds the chaotic regions of the phase space.…
Given a connected compact Riemannian manifold $(M,g)$ without boundary, $\dim M\ge 2$, we consider a space--time fractional diffusion equation with an interior source that is supported on an open subset $V$ of the manifold. The…
We consider an inverse problem of determining the time-dependent lowest order coefficient of two-dimensional (2D) heat equation with Ionkin boundary and total energy integral overdetermination condition. The well-posedness of the problem is…
In this research, a novel method to investigation the transient heat transfer coefficient in a channel is suggested experimentally, in which the water flow, itself, is considered both just liquid phase and liquid-vapor phase. The…
Algorithms based on the particle flow approach are becoming increasingly utilized in collider experiments due to their superior jet energy and missing energy resolution compared to the traditional calorimeter-based measurements. Such…
This work proposes an extension of phase change and latent heat models for the simulation of metal powder bed fusion additive manufacturing processes on the macroscale and compares different models with respect to accuracy and numerical…
We study the regularity of the bounded self-similar solution to the one-phase Stefan problem with fractional diffusion posed on the whole line. In terms of the enthalpy $h(x,t)$, the evolution problem reads \[ \begin{cases} \partial_t h +…
We consider a new Stefan-type problem for the classical heat equation with a latent heat and phase-change temperature depending of the variable time. We prove the equivalence of this Stefan problem with a class of boundary value problems…
We study the dynamical and statistical behavior of the Hamiltonian Mean Field (HMF) model in order to investigate the relation between microscopic chaos and phase transitions. HMF is a simple toy model of $N$ fully-coupled rotators which…
In this paper, we regularize the nonlinear inverse time heat problem in the unbounded region by Fourier method. Some new convergence rates are obtained. Meanwhile, some quite sharp error estimates between the approximate solution and exact…
We present a novel Hybrid High-Order (HHO) discretization of fourth-order elliptic problems arising from the mechanical modeling of the bending behavior of Kirchhoff-Love plates, including the biharmonic equation as a particular case. The…
The direct simulation Monte Carlo (DSMC) method is widely used to describe rarefied gas flows. The DSMC method accounts for the transport and collisions of computational particles, resulting in higher computational costs in the continuum…
We study the recovery of a spatially dependent source in a one-dimensional space-time fractional wave equation using boundary measurement data collected at a single endpoint. The main challenge arises from the fact that the eigenfunctions…
A generalized Neumann solution for the two-phase fractional Lam\'e--Clapeyron--Stefan problem for a semi--infinite material with constant initial temperature and a particular heat flux condition at the fixed face is obtained, when a…
The Hamiltonian coupled-mode theory (HCMT), recently derived by Athanassoulis and Papoutsellis [1], provides an efficient new approach for solving fully nonlinear water-wave problems over arbitrary bathymetry. In HCMT, heavy use is made of…
We present a simple, analytic point source model for both static and time-varying point-like heat sources and the resulting temperature profile that solves the heat equation in dimension three. Simple algorithms to detect the location and…
We present an interpolation method for the specific heat $c_v(T)$, when there is a phase transition with a logarithmic singularity in $c_v$ at a critical temperature $T=T_c$. The method uses the fact that $c_v$ is constrained both by its…
This paper deals with the numerical approximation of the biharmonic inverse source problem in an abstract setting in which the measurement data is finite-dimensional. This unified framework in particular covers the conforming and…
Motivated by the modeling of temperature regulation in some mediums, we consider the non-classical heat conduction equation in the domain $D=\mathbb{R}^{n-1}\times\br^{+}$ for which the internal energy supply depends on an average in the…