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Convergence of a finite volume scheme and dissipative measure-valued--strong stability for a hyperbolic-parabolic cross-diffusion system
Get PDFThis article is concerned with the approximation of hyperbolic-parabolic cross-diffusion systems modeling segregation phenomena for populations by a fully discrete finite-volume scheme. It is proved that the numerical scheme converges to a dissipative measure-valued solution of the PDE system and that, whenever the latter possesses a strong solution, the convergence holds in the strong sense. Furthermore, the ``parabolic density part'' of the limiting measure-valued solution is atomic and converges to its constant state for long times. The results are based on Young measure theory and a weak-strong stability estimate combining Shannon and Rao entropies. The convergence of the numerical scheme is achieved by means of discrete entropy dissipation inequalities and an artificial diffusion, which vanishes in the continuum limit
Spurious Four-Wave Mixing Processes in Generalized Nonlinear Schrödinger Equations
No full textNumerical solutions of a nonlinear Schrödinger equation may suffer from the spurious four-wave mixing processes. We study how these nonphysical resonances appear in solutions of a much more stiff generalized nonlinear Schrödinger equation with an arbitrary dispersion operator and determine the necessary restrictions on temporal and spatial resolution of a numerical scheme. The restrictions are especially important to meet when an envelope equation has to be applied in a wide spectral window, e.g., because of the spectral broadening
A Posteriori Optimization of Parameters in Stabilized Methods for Convection-Diffusion Problems - Part II
No full textExtensions of algorithms for computing optimal stabilization parameters in finite element methods for convection–diffusion equations are presented. These extensions reduce the dimension of the control space, in comparison to available methods, and thus address the long computing times of these methods. One method is proposed that considers only relevant mesh cells, another method that uses groups of mesh cells, and the combination of both methods is also studied. The incorporation of these methods within a gradient-based optimization procedure, via solving an adjoint problem, is explained. Numerical studies provide impressions on the gain of efficiency as well as on the loss of accuracy if control spaces with reduced dimensions are utilized
On two coupled degenerate parabolic equations motivated by thermodynamics
No full textWe discuss a system of two coupled parabolic equations that have degenerate diffusion constants depending on the energy-like variable. The dissipation of the velocity-like variable is fed as a source term into the energy equation leading to conservation of the total energy. The motivation of studying this system comes from Prandtl's and Kolmogorov's one and two-equation models for turbulence, where the energy-like variable is the mean turbulent kinetic energy. Because of the degeneracies there are solutions with time-dependent support like in the porous medium equation, which is contained in our system as a special case. The motion of the free boundary may be driven by either self-diffusion of the energy-like variable or by dissipation of the velocity-like variable. The cross-over of these two phenomena is exemplified for the associated planar traveling fronts. We provide existence of suitably defined weak and very weak solutions. After providing a thermodynamically motivated gradient structure we also establish convergence into steady state for bounded domains and provide a conjecture on the asymptotically self-similar behavior of the solutions in Rd for large times
Spin-Qubit Shuttles for Scalable Semiconductor QuantumComputers: Modeling, Simulation and Optimal Control
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Partial and Complete Wetting of Thin Films with Dynamic Contact Angle
No full textThe wetting of thin films depends critically on the sign of the spreading coefficient S. We discuss the cases S0 for transient models with contact line dissipation and find that the use of a dynamic contact angle solves problems for S>0 that models might otherwise have. For initial data with a non-zero slope and S>0, we show that there exists a finite time at which the contact angle of the thin film goes to zero. Then, a molecular precursor emerges from the thin film and moves outward at a constant velocity
MTSR 2023
No full textThis book constitutes the refereed post proceedings of the 17th Research Conference on Metadata and Semantic Research, MTSR 2023, held in Milan, Italy, during October 25–27, 2023. The 27 papers included in this book were carefully reviewed and selected from 75 submissions. These papers are compiled from the following eight tracks of the conference: Digital Libraries, Information Retrieval, Big, Linked, Social, and Open Data; Agriculture, Food, and Environment; Open Repositories, Research Information Systems, and Data Infrastructures; Digital Humanities and Digital Curation; Cultural Collections and Applications; European and National Projects; Knowledge IT Artifacts in Professional Communities and Aggregations; and Metadata, Identifiers, and Semantics in Decentralized Applications, Blockchains, and P2P Systems
CSNDD 2023
No full textThis book highlights recent advances in nonlinear dynamics and control with applications in mechanics and physics. The book includes selected articles from the 5th Conference on Structural Nonlinear Dynamics and Diagnosis (CSNDD 2023) and presents recent theoretical, experimental and numerical findings covering various topics in nonlinear structural dynamics and diagnosis. The main topics includes multiple scales dynamics, energy harvesting, dynamics of MEMS, NEMS and AFM, systems with time delay, quasi-periodic oscillations and synchronization, stochastic dynamics, analytical and semi-analytical methods, time series analysis, control and analysis of switching systems, structural health monitoring, nonlinear vibrations of structures, nonsmouth dynamics, nonlinear phenomena in discrete and continuum systems, dynamic modeling and fault diagnosis, constrained multi-catenary systems, conservative chaotic system, hysteretic structures, and nonlinear PDEs and their dynamics
Atomistic Study of Urbach Tail Energies in (Al,Ga)N Guantum Well Systems
No full textAluminium gallium nitride is a system of interest for developing ultraviolet (UV) optoelectronic devices. Here Urbach tails induced by carrier localization effects play a key role in determining device behaviour. We study the electronic structure of AlxGa1−xN/AlyGa1−yN single quantum wells using an atomistic framework. Results show that the density of states exhibits a tail at low energies due to disorder in the alloy microstructure. Our analysis allows for insight into the orbital character of the states forming the Urbach tails, which can affect light polarization characteristics, and important quantity for deep UV light emitters