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We present our deep learning framework to solve and accelerate the Time-Dependent partial differential equation's solution of one and two spatial dimensions. We demonstrate DiffusionNet solver by solving the 2D transient heat conduction…
The present research proposes a new memory-efficient method using diffusion models to inject turbulent inflow conditions into Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS) for various flow problems. A guided diffusion…
Gradient ascent methods are developed to compute incompressible flows that maximize heat transport between two isothermal no-slip parallel walls. Parameterizing the magnitude of velocity fields by a P\'eclet number $\text{Pe}$ proportional…
In this paper we present a systematic and rigorous method for calculating the diffusion tensor for a Brownian particle moving in a periodic potential which is valid in arbitrary dimensions and for all values of the dissipation. We use this…
In this paper, we study the diffusive limit of the steady state radiative heat transfer system for non-homogeneous Dirichlet boundary conditions in a bounded domain with flat boundaries. A composite approximate solution is constructed using…
Using information entropy formalism, we consider a one-dimensional system with heat flux and extend the meaning of equilibrium variables to non equilibrium scenarios when classical local equilibrium approach is not applicable; this is…
We study diffusion properties of an inertial Brownian motor moving on a ratchet substrate, i.e. a periodic structure with broken reflection symmetry. The motor is driven by an unbiased time-periodic symmetric force which takes the system…
The fidelity of a model relies both on its accuracy to predict the physical phenomena and its capability to estimate unknown parameters using observations. This article focuses on this second aspect by analyzing the reliability of two…
We present a new stochastic analysis for steady and transient one-dimensional heat conduction problem based on the homogenization approach. Thermal conductivity is assumed to be a random field K consisting of random variables of a total…
In this paper, we study an insulation problem that seeks to determine the optimal distribution of a given amount $m>0$ of insulating material coating an insulated boundary part $\Gamma_I\subseteq \partial\Omega$ of a thermally conducting…
The local heat transfer coefficient measurement with temperature oscillation induced by periodic thermal perturbation - usually via a Gaussian laser beam, was investigated for the impact of the spikiness (i.e., the standard deviation)…
An equation based reduced order model applicable to generalized heat equation and thermal simulations of power electronics systems developed in commercial CFD tools, is presented in this work. The model considers the physics of heat…
In this paper, a thermal-dynamical consistent model for mass transfer across permeable moving interfaces is proposed by using the energy variation method. We consider a restricted diffusion problem where the flux across the interface…
Thermal wave packets are used to analyze transmission probabilities and characteristic times through a parabolic repeller within the dissipative Bohmian mechanics. Thermal arrival, dwelling, transmission and reflection times are defined and…
We employ matrix product state simulations to study energy transport within the non-integrable regime of the one-dimensional $\mathbb{Z}_3$ chiral clock model. To induce a non-equilibrium steady state throughout the system, we consider open…
In this paper we study the harmonic map heat flow problem for a radially symmetric case. The corresponding partial dfferential equation plays a key role in many analyses of harmonic map heat flow problems. We consider a basic discretization…
A quantitative theory is developed, which accounts for heating artifacts in three-pulse photon echo (3PE) experiments. The heat diffusion equation is solved and the average value of the temperature in the focal volume of the laser is…
We consider the problem of frequency estimation by observations of the periodic diffusion process possesing ergodic properties in two different situations. The first one corresponds to continuously differentiable with respect to parameter…
Calibration of the uncertain Arrhenius diffusion parameters for quantifying mixing rates in Zr-Al nanolaminate foils was performed in a Bayesian setting [Vohra et al., 2014]. The parameters were inferred in a low temperature regime…
Inverse problems of recovering heat transfer coefficient from integral measurements are considered. The heat transfer coefficient occurs in the transmission conditions of imperfect contact type or the Robin type boundary conditions. It is…