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A steady state of a granular gas with homogeneous granular temperature, no mass flow, and nonzero heat flux is studied. The state is created by applying an external position--dependent force or by enclosing the grains inside a curved…
We analyze the asymptotic behavior corresponding to the arbitrary high conductivity of the heat in the thermoelectric devices. This work deals with a steady-state multidimensional thermistor problem, considering the Joule effect and both…
In this article we survey recent progress on mathematical results on gas flow in pipe networks with a special focus on questions of control and stabilization. We briefly present the modeling of gas flow and coupling conditions for flow…
Analyzing complex fluid flow problems that involve multiple coupled domains, each with their respective set of governing equations, is not a trivial undertaking. Even more complicated is the elaborate and tedious task of specifying the…
We extend the canonical problems of simulation and optimization of steady-state gas flows in pipeline networks with compressors to the transport of mixtures of highly heterogeneous gases injected throughout a network. Our study is motivated…
A one-dimensional multi-phase flow model for thermomagnetically pumped ferrofluid with heat transfer is proposed. The thermodynamic model is a combination of a simplified particle model and thermodynamic equations of state for the base…
Choice models for populations of agents on graphs are studied in terms of statistical thermodynamics. Equations of state are derived and discussed for different connectivity schemes, utility approximations, and temperature and volume…
We consider the problem of heat diffusion in branched systems and networks on the basis of a model described in terms of heat equation on metric graphs. Using the explicit analytical solutions of the latter, evolution of the temperature…
High-temperature electrolysis (HTE) is a promising technology for achieving high-efficiency power-to-gas, which mitigates the renewable curtailment by transforming wind or solar energy into fuels. Different from low-temperature…
We introduce a simple model, a binary mixture of patchy particles, which has been designed to form a gel upon heating. Due to the specific nature of the particle interactions, notably the number and geometry of the patches as well as their…
Fluid polyamorphism, the existence of multiple amorphous fluid states in a single-component system, has been observed or predicted in a variety of substances. A remarkable example of this phenomenon is the fluid-fluid phase transition in…
A brief derivation of a specific regularization for the magnetic gas dynamic system of equations is given in the case of general equations of gas state (in presence of a body force and a heat source). The entropy balance equation in two…
We propose a model to directly predict the steady-state flow field for a given geometry setup. The setup is an Eulerian representation of the fluid flow as a meshed domain. We introduce a graph network architecture to process the mesh-space…
We propose and investigate an exactly solvable model of non-equilibrium Luttinger liquid on a star graph, modeling a multi-terminal quantum wire junction. The boundary condition at the junction is fixed by an orthogonal matrix S, which…
In this paper we propose new boundary conditions at the hot walls with thermionic electron emission for two-temperature thermal arc models. In the derived boundary conditions the walls are assumed to be made from refractory metals and that…
We study steady-state properties of inelastic gases in two-dimensions in the presence of an energy source. We generalize previous hydrodynamic treatments to situations where high and low density regions coexist. The theoretical predictions…
Exergy, or availability, is a thermodynamic concept representing the useful work that can be extracted from a system evolving from a given state to a reference state. It is also a system metric, formulated from the first and the second law…
We show that a reformulation of the governing equations for incompressible multi-phase flow in the volume of fluid setting leads to a well defined energy rate. Weak nonlinear inflow-outflow and solid wall boundary conditions complement the…
We introduce an algorithmic model of heat conduction, the thermodynamic graph. The thermodynamic graph is analogous to meshes in the finite difference method in the sense that the calculation of temperature is carried out at the vertices of…
We consider convection in an internally heated layer of fluid that is bounded below by a perfect insulator and above by a poor conductor. The poorly conducting boundary is modelled by a fixed heat flux. Using solely analytical methods, we…