Towards understanding the dynamics of a Braess paradox model

This work studies a recently proposed model of the Braess paradox, which has four parameters and is defined piecewise continuous on three regions. The Braess paradox describes the fact that the introduction of a new choice into a system of rational agents may not improve the situation but can make it even worse. To investigate the system and its undergoing border collision bifurcations, we are going to fix some parameters and thereby get new results on the overall dynamics. Also part of the coexistence and the period adding scenario between the cycles are analyzed

Erfassung von Innenraummodellen mittels Smartphones

Unter Verwendung von aufgezeichneten Bewegungsspuren eines Inertialsensors ist es möglich, ein Innenraummodell eines Gebäudes zu generieren. Das Innenraummodell unterscheidet hierbei Räume und Korridore. Die Bewegungsspuren werden durch auf dem Fuß platzierte Inertialsensoren per ZUPT erfasst. Es wird von einer Vielzahl an Benutzern ausgegangen, welche sich in alltäglichen Situationen durch Gebäude bewegen und mit den Sensoren ihres Smartphones opportunistisch Daten erfassen. Bewegungsspuren werden in gerade Segmente unterteilt. Durch eine Äquivalenzrelation wird festgestellt, ob sich der Benutzer beim Erfassen der Spuren auf demselben Korridor befunden hatte. Die Geometrie von Korridoren wird durch Quantile und die empirische Verteilungsfunktion bestimmt. Durch die Ausrichtung der Spuren anhand der Geometrie der Korridore, können überstehende Abschnitte durch geeignete Kriterien als Räume erkannt werden. Für die Evaluation wurden von vier Testpersonen über 200 Spuren in alltäglichen Szenarien aufgenommen. Wählt man aus diesen Spuren 90 aus, so werden im Durchschnitt über 90% aller Korridore des Stockwerks erkannt. In 65% der so generierten Innenraummodelle war die durchschnittliche Verschiebung der Korridore kleiner als 1,5m.It is possible to generate indoor models by using traces recorded by inertial measurement units. The generated indoor model distinguishes between rooms and corridors. Traces will be collected by foot-mounted inertial measurement units via ZUPT. The data will be collected in a crowd based approach via Smartphones and sensor units carried by users. Users will walk inside the building in all-day situations, collecting data opportunistically. The collected traces will be segmented into parts where the user walked straight. Using a equivalence relation, segments collected from the same corridor can be combined. Reconstructing the geometry of corridors will use quantiles and the empirical distribution function. Using a method to correct traces via the constructed corridor geometry, rooms can be found by protruding parts of traces. To evaluate the system, four volunteers collected over 200 traces in everyday scenarios. Choosing 90 out of them, in average 90% of all corridors will be found. In 65% of this constructed indoor models, the average shift of corridors was less than 1.5 m

Diffusion-influenced reaction rates in the presence of pair interactions

The kinetics of bimolecular reactions in solution depends, among other factors, on intermolecular forces such as steric repulsion or electrostatic interaction. Microscopically, a pair of molecules first has to meet by diffusion before the reaction can take place. In this work, we establish an extension of Doi's volume reaction model to molecules interacting via pair potentials, which is a key ingredient for interacting-particle-based reaction-diffusion (iPRD) simulations. As a central result, we relate model parameters and macroscopic reaction rate constants in this situation. We solve the corresponding reaction-diffusion equation in the steady state and derive semi-analytical expressions for the reaction rate constant and the local concentration profiles. Our results apply to the full spectrum from well-mixed to diffusion--limited kinetics. For limiting cases, we give explicit formulas, and we provide a computationally inexpensive numerical scheme for the general case, including the intermediate, diffusion-influenced regime. The obtained rate constants decompose uniquely into encounter and formation rates, and we discuss the effect of the potential on both subprocesses, exemplified for a soft harmonic repulsion and a Lennard-Jones potential. The analysis is complemented by extensive stochastic iPRD simulations, and we find excellent agreement with the theoretical predictions

Utilizing networked mobile devices for scientific simulations

Numerical simulations on mobile devices create new applications supporting engineers and scientists in the field. Boosted by novel augmented reality devices, in-field analysis of complex systems allow engineers to make better decisions and predict the behavior of such systems by assuming different parameters before making risky and costly decisions. Mobile simulations are challenging as battery-powered mobile devices are only equipped with slow processors and are limited in energy resources. At the same time, mobile devices are only connected via wireless communication subjected to environmental conditions that might cause slow bandwidths or even disconnections to remote computing resources. Nevertheless, concepts presented in this thesis assume a distributed computation between mobile device and a powerful remote server. This thesis covers three major areas of the research field of mobile simulations. First, it provides concepts for distributed execution between server and mobile device in case of frequent disconnections. Second, it provides concepts using computationally less complex surrogate models for faster computation on the mobile device while still utilizing remote resources. Third, it provides concepts utilizing model order reduction for fast execution on mobile devices by pre-computing and adaptation of reduced models on a connected server. Evaluations show that concepts presented in this thesis significantly increase the performance of mobile simulations. In the case of disconnections, the number of deadline misses is reduced by 61 % while reducing the energy consumption by more than 74 % compared to a simplified approach. Concepts utilizing surrogate models speed-up the computation of the simulation by a factor of 6.5. Lastly, concepts utilizing model order reduction reduce the time for the computation of simulation results by a factor of 131 while using 73 times less energy for the specific test application