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The problem of heat conduction on networks of multiply connected rods is solved by providing an explicit solution of the one-dimensional heat equation in each domain. The size and connectivity of the rods is known, but neither temperature…
We establish dispersion engineering rules that allow us to control the thermalization process and the thermal state of an initial beam propagating in a multimode nonlinear photonic circuit. To this end, we have implemented a kinetic…
Like any fluid heated from below, the atmosphere is subject to vertical instability which triggers convection. Convection occurs on small time and space scales, which makes it a challenging feature to include in climate models. Usually…
In the present paper a detailed mathematical model is derived for district heating networks. After semidiscretization of the convective heat equation and introducing coupling conditions at the nodes of the network one gets a…
Nonintegrable systems thermalize, leading to the emergence of fluctuating hydrodynamics. Typically, this hydrodynamics is diffusive. We use the effective field theory (EFT) of diffusion to compute higher-point functions of conserved…
This paper considers one-dimensional heat transfer in a media with temperature-dependent thermal conductivity. To model the transient behavior of the system, we solve numerically the one-dimensional unsteady heat conduction equation with…
We consider a diffusion problem on a network on whose nodes we impose Dirichlet and generalized, non-local Kirchhoff-type conditions. We prove well-posedness of the associated initial value problem, and we exploit the theory of…
Heat transfer in fractured media is governed by the interplay between advective transport along rough-walled fractures and conductive transport, both within the fractures and in the surrounding low-permeability matrix. Flow localization…
Grid independent is associated with the accuracy or even rationality of numerical results. This paper takes two-dimensional steady heat transfer for example to reveal the effect of grid resolution on numerical results. The law of grid…
This work is the second in a series focused on ferrofluid bend channel flows. Here, ferrofluid flows in bend channels are modeled using machine learning methods, based on data generated from the CFD simulation discussed in the first work in…
We present a scheme to extract information about plumes, a prominent coherent structure in turbulent thermal convection, from simultaneous local velocity and temperature measurements. Using this scheme, we study the temperature dependence…
We investigate the radiative heat transfer and spatial distributions of stationary temperatures in periodic many-body systems composed of alternating slabs of two different materials. We show that temperature distributions exhibit an…
Systems of reaction-diffusion equations are commonly used in biological models of food chains. The populations and their complicated interactions present numerous challenges in theory and in numerical approximation. In particular,…
In the present paper we propose a reduced temperature non-equilibrium model for simulating multicomponent flows with inter-phase heat transfer, diffusion processes (including the viscosity and the heat conduction) and external energy…
Thermionic emission has been exploited to give rise to the theory of thermionic cooling also known as electron transpiration cooling, which can potentially serve as a powerful and engineerable cooling mode for hypersonic leading edges that…
This work focuses on exploring the potential benefits of introducing a nonlinear Laplacian in Sheaf Neural Networks for graph-related tasks. The primary aim is to understand the impact of such nonlinearity on diffusion dynamics, signal…
In the last decade, wildfires have become wider and more destructive. The climate change and the growth of urban areas may further increase the probability of incidence of large-scale fires. The risk of fire can be lowered with preventive…
A theoretical study is presented in this paper to investigate the conjugate heat transfer across a vertical finite wall separating two forced and free convection flows at different temperatures. The heat conduction in the wall is in the…
We investigated the effective influence of grain structures on the heat transfer between a fluid and solid domain using mathematical homogenization. The presented model consists of heat equations inside the different domains, coupled…
Measurements of the energy relaxation in the integer quantum hall edge at filling factor $\nu=2$ suggest the breakdown of heat current quantization [H. le Sueur et al., Phys. Rev. Lett. 105, 056803]. It was shown, in a hydrodynamic model,…