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The increasing complexity of energy systems due to sector coupling and decarbonization calls for unified modeling frameworks that capture the physical and structural interactions between electricity, gas, and heat networks. This paper…
A generalized multibaker map with periodic boundary conditions is shown to model boundary-driven transport, when the driving is applied by a ``perturbation'' of the dynamics localised in a macroscopically small region. In this case there…
Integrating external heat into electrolysers can reduce the electrical power demand for carbon-neutral hydrogen production. Efficient operation requires detailed models that incorporate heat availability and its effect on startup costs.…
We prove an existence result for the steady state flow of gas mixtures on networks. The basis of the model are the physical principles of the isothermal Euler equation, coupling conditions for the flow and pressure, and the mixing of…
In this paper, we study hydrogen-natural gas mixtures transported through pipeline networks. The flow is modeled by the isothermal Euler equations with a pressure law involving a non-constant, composition-dependent compressibility factor.…
We develop a hydrodynamic description of self-generated electrolyte flow in capillaries whose bounding walls feature both non-uniform distributions of charge and non-uniform active ionic fluxes. The hydrodynamic velocity arising in such a…
The hydrogen production curve of the electrolyzer describes the non-linear and non-convex relationship between its power consumption and hydrogen production. An accurate representation of this curve is essential for the optimal scheduling…
In this paper, we introduce a model for a buoyancy-driven, air-to-air heat exchanger. This model, derived from first principles, features a conservative boundary condition at inflow based on the compressible Bernoulli equation, and a…
A consistent description of simultaneous heat and particle transport, including cross effects, and the associated entropy balance is given in the framework of a deterministic dynamical system. This is achieved by a multibaker map where,…
We examine the modeling, simulation, and optimization of district heating systems, which are widely used for thermal transport using steam or hot water as a carrier. We propose a generalizable framework to specify network models and…
This paper addresses the challenge of pressure constraint violations in water electrolysis systems operating under dynamic power conditions, a problem common to both Proton Exchange Membrane and alkaline technologies. To investigate this…
Modern energy systems in vehicles and built infrastructure are governed by high-dimensional dynamics spanning multiple physical domains (e.g., electrical, thermal, mechanical) and timescales. This tutorial paper presents a graph-based…
In this paper, a mathematical framework for the coupling of gas networks to electric grids is presented to describe in particular the transition from gas to power. The dynamics of the gas flow are given by the isentropic Euler equations,…
Graphene has generated a lot of research interest due to its special properties, which include a hydrodynamic regime. It is not yet clear however which boundary condition such a hydrodynamic current flow satisfies. The aim of this paper is…
We study systems containing electrons and nuclei. Based on the fact that the thermodynamic limit exists for systems with Dirichlet boundary conditions, we prove that the same limit is obtained if one imposes other boundary conditions such…
A two-dimensional free boundary transmission problem arising in the modeling of an electrostatically actuated plate is considered and a representation formula for the derivative of the associated electrostatic energy with respect to the…
In this paper we dwell over the study of the boundary layer problem in a hydrodynamical description of the electrons in gated graphene. It has been verified experimentally that this fluid can display non-Poiseuille like flow as reproduced…
This paper presents a thermodynamically consistent model for multicomponent electrolyte solutions. The first part of this paper derives the general governing equations for nonequilibrium systems within the theory of nonequilibrium…
Power-to-Hydrogen is crucial for the renewable energy transition, yet existing literature lacks business models for the significant excess heat it generates. This study addresses this by evaluating three models for selling…
In this paper, a new nonlinear heat equation is studied that arises as a model of the collective behavior of automated vehicles. The properties of the solutions of this equation are studied by introducing the appropriate notion of a weak…