A Critical Assessment of the Boltzmann Approach for Active Systems

Generic models of propelled particle systems posit that the emergence of polar order is driven by the competition between local alignment and noise. Although this notion has been confirmed employing the Boltzmann equation, the range of applicability of this equation remains elusive. We introduce a broad class of mesoscopic collision rules and analyze the prerequisites for the emergence of polar order in the framework of kinetic theory. Our findings suggest that a Boltzmann approach is appropriate for weakly aligning systems but is incompatible with experiments on cluster forming systems.Comment: 11 pages, 3 figure

Role of particle conservation in self-propelled particle systems

Actively propelled particles undergoing dissipative collisions are known to develop a state of spatially distributed coherently moving clusters. For densities larger than a characteristic value, clusters grow in time and form a stationary well-ordered state of coherent macroscopic motion. In this work we address two questions. (i) What is the role of the particles’ aspect ratio in the context of cluster formation, and does the particle shape affect the system’s behavior on hydrodynamic scales? (ii) To what extent does particle conservation influence pattern formation? To answer these questions we suggest a simple kinetic model permitting us to depict some of the interaction properties between freely moving particles and particles integrated in clusters. To this end, we introduce two particle species: single and cluster particles. Specifically, we account for coalescence of clusters from single particles, assembly of single particles on existing clusters, collisions between clusters and cluster disassembly. Coarse graining our kinetic model, (i) we demonstrate that particle shape (i.e. aspect ratio) shifts the scale of the transition density, but does not impact the instabilities at the ordering threshold and (ii) we show that the validity of particle conservation determines the existence of a longitudinal instability, which tends to amplify density heterogeneities locally, and in turn triggers a wave pattern with wave vectors parallel to the axis of macroscopic order. If the system is in contact with a particle reservoir, this instability vanishes due to a compensation of density heterogeneities

Modeling electricity spot prices - Combining mean-reversion, spikes and stochastic volatility

Starting with the liberalization of electricity trading, this market grew rapidly over the last decade. However, while spot and future markets are rather liquid nowadays, option trading is still limited. One of the potential reasons for this is that the spot price process of electricity is still puzzling researchers and practitioners. In this paper, we propose an approach to model spot prices that combines mean-reversion, spikes and stochastic volatility. Thereby we use different mean-reversion rates for 'normal' and 'extreme' (spike) periods. Another feature of the model is its ability to capture correlation structures of electricity price spikes. Furthermore, all model parameters can easily be estimated with help of historical data. Consequently, we argue that this model does not only extend academic literature on electricity spot price modeling, but is also suitable for practical purposes, e.g. as underlying price model for option pricing. --Electricity,Energy markets,Lévy processes,Mean-reversion,Spikes,Stochastic volatility,GARCH

Fully Convolutional Neural Networks for Dynamic Object Detection in Grid Maps

Grid maps are widely used in robotics to represent obstacles in the environment and differentiating dynamic objects from static infrastructure is essential for many practical applications. In this work, we present a methods that uses a deep convolutional neural network (CNN) to infer whether grid cells are covering a moving object or not. Compared to tracking approaches, that use e.g. a particle filter to estimate grid cell velocities and then make a decision for individual grid cells based on this estimate, our approach uses the entire grid map as input image for a CNN that inspects a larger area around each cell and thus takes the structural appearance in the grid map into account to make a decision. Compared to our reference method, our concept yields a performance increase from 83.9% to 97.2%. A runtime optimized version of our approach yields similar improvements with an execution time of just 10 milliseconds.Comment: This is a shorter version of the masters thesis of Florian Piewak and it was accapted at IV 201

Hybrid suburbia: New research perspectives in France and Southern California

Geographical research on French and US suburbia has concentrated in recent decades on urban sprawl and concomitant processes of devaluation and exclusion. In the case of the French banlieues, with their much-publicised urban riots, this particular analytic focus has become overwhelming, with resultant loss to other developments and perspectives. However, certain districts in the first (or inner) ring of both French and US suburbia are currently showing distinct urbanisation tendencies in planning and architecture, evident in the new usage of brownfield sites and the ongoing demolition, replacement, and rededication of the older building core. Such processes induce population changes, e.g. the displacement of lower in favour of higher income groups. Overall, they result in an architectonic, social and cultural heterogeneity that escapes the specificity of received categories and merits the term hybridisation. The article describes and compares these processes as exemplified in Greater Paris and San Diego (Southern California)

L'Université en temps de pandémie

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