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Generalized gradient flow structure of internal energy driven phase field systems
In this paper we introduce a general abstract formulation of a variational thermomechanical model, by means of a unified derivation via a generalization of the principle of virtual powers for all the variables of the system, including the thermal one. In particular, choosing as thermal variable the entropy of the system, and as driving functional the internal energy, we get a gradient flow structure (in a suitable abstract setting) for the whole nonlinear PDE system. We prove a global in time existence of (weak) solutions result for the Cauchy problem associated to the abstract PDE system as well as uniqueness in case of suitable smoothness assumptions on the functionals.
Drift-diffusion modeling, analysis and simulation of organic semiconductor devices
We discuss drift-diffusion models for charge-carrier transport in organic semiconductor devices. The crucial feature in organic materials is the energetic disorder due to random alignment of molecules and the hopping transport of carriers between adjacent energetic sites. The former leads to so-called Gauss-Fermi statistics, which describe the occupation of energy levels by electrons and holes. The latter gives rise to complicated mobility models with a strongly nonlinear dependence on temperature, density of carriers, and electric field strength. We present the state-of-the-art modeling of the transport processes and provide a first existence result for the stationary drift-diffusion model taking all of the peculiarities of organic materials into account. The existence proof is based on Schauders fixed-point theorem. Finally, we discuss the numerical discretization of the model using finite-volume methods and a generalized Scharfetter-Gummel scheme for the Gauss-Fermi statistics.
An existence result for a class of electrothermal drift-diffusion models with Gauss--Fermi statistics for organic semiconductors
This work is concerned with the analysis of a drift-diffusion model for the electrothermal behavior of organic semiconductor devices. A "generalized Van Roosbroeck'' system coupled to the heat equation is employed, where the former consists of continuity equations for electrons and holes and a Poisson equation for the electrostatic potential, and the latter features source terms containing Joule heat contributions and recombination heat. Special features of organic semiconductors like Gauss--Fermi statistics and mobilities functions depending on the electric field strength are taken into account. We prove the existence of solutions for the stationary problem by an iteration scheme and Schauder's fixed point theorem. The underlying solution concept is related to weak solutions of the Van Roosbroeck system and entropy solutions of the heat equation. Additionally, for data compatible with thermodynamic equilibrium, the uniqueness of the solution is verified. It was recently shown that self-heating significantly influences the electronic properties of organic semiconductor devices. Therefore, modeling the coupled electric and thermal responses of organic semiconductors is essential for predicting the effects of temperature on the overall behavior of the device. This work puts the electrothermal drift-diffusion model for organic semiconductors on a sound analytical basis.
Analysis of a diffuse interface model of multispecies tumor growth
We consider a diffuse interface model for tumor growth recently proposed in [3]. In this new approach sharp interfaces are replaced by narrow transition layers arising due to adhesive forces among the cell species. Hence, a continuum thermodynamically consistent model is introduced. The resulting PDE system couples four different types of equations: a Cahn-Hilliard type equation for the tumor cells (which include proliferating and dead cells), a Darcy law for the tissue velocity field, whose divergence may be different from 0 and depend on the other variables, a transport equation for the proliferating (viable) tumor cells, and a quasi-static reaction diffusion equation for the nutrient concentration. We establish existence of weak solutions for the PDE system coupled with suitable initial and boundary conditions. In particular, the proliferation function at the boundary is supposed to be nonnegative on the set where the velocity u satisfies u ypsilon 0, where ypsilon is the outer normal to the boundary of the domain. We also study a singular limit as the diffuse interface coefficient tends to zero.
An effective bulk-surface thermistor model for large-area organic light-emitting diodes
The existence of a weak solution for an effective system of partial differential equations describing the electrothermal behavior of large-area organic light-emitting diodes (OLEDs) is proved. The effective system consists of the heat equation in the three-dimensional bulk glass substrate and two semi-linear equations for the current flow through the electrodes coupled to algebraic equations for the continuity of the electrical fluxes through the organic layers. The electrical problem is formulated on the (curvilinear) surface of the glass substrate where the OLED is mounted. The source terms in the heat equation are due to Joule heating and are hence concentrated on the part of the boundary where the current-flow equation is posed. The existence of weak solutions to the effective system is proved via Schauder's fixed-point theorem. Moreover, since the heat sources are a priori only in $L^1$, the concept of entropy solutions is used.