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We consider a linearized kinetic BGK equation and the associated acoustic system on a network.
Coupling conditions for the macroscopic equations are derived from the kinetic conditions via an asymptotic analysis near the nodes of the network.
This analysis leads to the consideration of a fixpoint problem involving the solutions of kinetic half-space problems.
This work extends the procedure developed in [13], where coupling conditions for a simplified BGK model have been derived.
Numerical comparisons between different coupling conditions
confirm the accuracy of the proposed approximation.
Simulating the flow of water in district heating networks requires numerical methods which are independent of the CFL condition. We develop a high order scheme for networks of advection equations allowing large time steps. With the MOOD technique unphysical oscillations of non smooth solutions are avoided. In numerical tests the applicability to real networks is shown.
Im Zuge der Bologna-Reform besteht der Anspruch die universitäre Lehre kompetenzorien-tiert zu gestalten. Es werden gemäß der KMK-Rahmenvorgaben in den universitären Mo-dulplänen Kompetenzen formuliert, jedoch realisiert sich die Umsetzung in nur wenigen Fällen und es bleibt oftmals bei der formalen Angabe von Qualifikationszielen. Im Sinne einer adä-quaten Berufsvorbereitung der Studierenden ist eine kompetenzorientiere Lehre aber als ele-mentar anzusehen.
An der Technischen Universität Kaiserslautern wird den Lehramtsstudierenden im Rahmen des Sportstudiums eine breit gefächerte Schneesportausbildung angeboten. Eine praxisorien-tierte Schneesportausbildung bietet eine besondere Form des Erlebens und Erfahrens, wel-che Studierenden in rein theoretischen Veranstaltungen nicht geboten werden kann. Jedes Erleben und Erfahren bewirkt Emotionen; Kompetenzen lassen sich nur in emotionsaktivie-renden Lernarrangements aneignen.
Das Ziel dieses Beitrags besteht darin, die Schneesportausbildung der TU Kaiserslautern un-ter dem Aspekt einer Kompetenzermöglichung vorzustellen. Hierfür wurde zunächst das Ausbildungskonzept erhoben, und untersucht, inwiefern den Studierenden im Rahmen der Schneesportausbildung eine Kompetenzentwicklung ermöglicht wird. Als Grundlage dient hier der Kompetenzatlas nach Heyse und Erpenbeck. Die sich ergebenden Resultate zu Inhalten und Methoden der Schneesportausbildung werden zusammenfassend in einem Kompetenz-profil dargestellt. Darüber hinaus werden die Ausbildungsmaßnahmen beurteilt, Möglichkeiten und Potentiale zur Kompetenzförderung aufgezeigt und beispielhaft im Sinne eines Best Practice Beispiels in einem Wochenplan zusammengefasst.
Spatial regression models provide the opportunity to analyse spatial data and spatial processes. Yet, several model specifications can be used, all assuming different types of spatial dependence. This study summarises the most commonly used spatial regression models and offers a comparison of their performance by using Monte Carlo experiments. In contrast to previous simulations, this study evaluates the bias of the impacts rather than the regression coefficients and additionally provides results for situations with a non-spatial omitted variable bias. Results reveal that the most commonly used spatial autoregressive (SAR) and spatial error (SEM) specifications yield severe drawbacks. In contrast, spatial Durbin specifications (SDM and SDEM) as well as the simple SLX provide accurate estimates of direct impacts even in the case of misspecification. Regarding the indirect `spillover' effects, several - quite realistic - situations exist in which the SLX outperforms the more complex SDM and SDEM specifications.
A distributional solution framework is developed for systems consisting of linear hyperbolic partial differential equations (PDEs) and switched differential algebraic equations (DAEs) which are coupled via boundary conditions. The unique solvability is then characterize in terms of a switched delay DAE. The theory is illustrated with an example of electric power lines modeled by the telegraph equations which are coupled via a switching transformer where simulations confirm the predicted impulsive solutions.
In this article a new numerical solver for simulations of district heating networks is presented. The numerical method applies the local time stepping introduced in [11] to networks of linear advection equations. In combination with the high order approach of [4] an accurate and very efficient scheme is developed. In several numerical test cases the advantages for simulations of district heating networks are shown.
Multifacility location problems arise in many real world applications. Often, the facilities can only be placed in feasible regions such as development or industrial areas. In this paper we show the existence of a finite dominating set (FDS) for the planar multifacility location problem with polyhedral gauges as distance functions, and polyhedral feasible regions, if the interacting facilities form a tree. As application we show how to solve the planar 2-hub location problem in polynomial time. This approach will yield an ε-approximation for the euclidean norm case polynomial in the input data and 1/ε.
SDE-driven modeling of phenotypically heterogeneous tumors: The influence of cancer cell stemness
(2018)
We deduce cell population models describing the evolution of a tumor (possibly interacting with its
environment of healthy cells) with the aid of differential equations. Thereby, different subpopulations
of cancer cells allow accounting for the tumor heterogeneity. In our settings these include cancer
stem cells known to be less sensitive to treatment and differentiated cancer cells having a higher
sensitivity towards chemo- and radiotherapy. Our approach relies on stochastic differential equations
in order to account for randomness in the system, arising e.g., by the therapy-induced decreasing
number of clonogens, which renders a pure deterministic model arguable. The equations are deduced
relying on transition probabilities characterizing innovations of the two cancer cell subpopulations,
and similarly extended to also account for the evolution of normal tissue. Several therapy approaches
are introduced and compared by way of tumor control probability (TCP) and uncomplicated tumor
control probability (UTCP). A PDE approach allows to assess the evolution of tumor and normal
tissue with respect to time and to cell population densities which can vary continuously in a given set
of states. Analytical approximations of solutions to the obtained PDE system are provided as well.
This paper presents a case study of duty rostering for physicians at a department of orthopedics and trauma surgery. We provide a detailed description of the rostering problem faced and present an integer programming model that has been used in practice for creating duty rosters at the department for more than a year. Using real world data, we compare the model output to a manually generated roster as used previously by the department and analyze the quality of the rosters generated by the model over a longer time span. Moreover, we demonstrate how unforeseen events such as absences of scheduled physicians are handled.
We continue in this paper the study of k-adaptable robust solutions for combinatorial optimization problems with bounded uncertainty sets. In this concept not a single solution needs to be chosen to hedge against the uncertainty. Instead one is allowed to choose a set of k different solutions from which one can be chosen after the uncertain scenario has been revealed. We first show how the problem can be decomposed into polynomially many subproblems if k is fixed. In the remaining part of the paper we consider the special case where k=2, i.e., one is allowed to choose two different solutions to hedge against the uncertainty. We decompose this problem into so called coordination problems. The study of these coordination problems turns out to be interesting on its own. We prove positive results for the unconstrained combinatorial optimization problem, the matroid maximization problem, the selection problem, and the shortest path problem on series parallel graphs. The shortest path problem on general graphs turns out to be NP-complete. Further, we present for minimization problems how to transform approximation algorithms for the coordination problem to approximation algorithms for the original problem. We study the knapsack problem to show that this relation does not hold for maximization problems in general. We present a PTAS for the corresponding coordination problem and prove that the 2-adaptable knapsack problem is not at all approximable.