Exakte Lösungen für getriebene Diffusionssysteme: Dynamische Defektbildung und Phasenübergänge

A totally asymmetric exclusion process on a ring is investigated in which particles can move one or two sites. Special attention is spent to the high-speed case where particles are not allowed to move a single site if they could move two sites. The stationary state is calculated exactly in the framework of the matrix-product ansatz. Independently of the update this process evolves into subspace of the configuration space and can lead to the formation of an excess hole. One observes two phases where its velocity takes different values which are calculated exactly from the normalization-generating function. Numerically computed density profiles show an interesting algebraic form as a limit of a shock profile. For continuous time the process turns out to be related to the ASEP with a single defect particle and for synchronous update it leads to a natural defect dynamics. For the general definition of the process with maximum velocity two, from an exact analysis of the two-particle sector we find that the distribution of inter-particle distance can oscillate. This is underlined in the thermodynamic limit by an improved mean-field theory which shows a remarkably good agreement with simulations. The main focus of this work is the exact solution of lattice models by matrix-product ansatz. We finally obtain stationary states also for related processes. Especially considerable is a new formulation of steady states for parallel dynamics like the ASEP with open boundaries as a product of a pair-factorized and a matrix-product state.Die vorliegende Arbeit beschäftigt sich im Wesentlichen mit dem vollkommen asymmetrischen Exklusionsprozess (ASEP) mit periodischen Randbedingungen. Der ASEP ist auf einem eindimensionalen Gitter definiert, auf dem jede Zelle entweder leer oder von genau einem Teilchen besetzt sein kann. In der ursprünglichen Definition können sich die Teilchen unter der Voraussetzung, dass die Zielzelle frei ist, genau um eine Zelle nach rechts bewegen. Hier betrachten wir die Möglichkeit, eine oder zwei Zellen zu hüpfen. Sowohl zufällig-sequentielle als auch parallele Dynamik werden behandelt. Besonderes Interesse gilt dem Hochgeschwindigkeitsfall, in dem sich die Teilchen wenn möglich immer zwei Zellen vorwärts bewegen. Der stationäre Zustand wird mit Hilfe des Matrixproduktansatzes exakt bestimmt. Unabhängig vom Update entwickelt sich dieser Prozess in Unterräume des Konfigurationsraumes und kann zu dynamischer Defektbildung in Form einer überschüssigen Leerstelle führen. Man beobachtet zwei Phasen, wo die Defektgeschwindigkeit verschiedene Werte annimmt, welche jeweils ausgehend von der erzeugenden Funktion der Normierung exakt berechnet werden. Numerisch bestimmte Dichteprofile zeigen eine interessante algebraische Form als Grenzfall eines Schockprofils. Für kontinuierliche Zeit stellt sich heraus, dass der Prozess mit dem wohlbekannten ASEP mit einem Defektteilchen verwandt ist. Für parallele Dynamik erhält man erhält man eine neue natürliche Defektdynamik. Für die allgemeine Definition des Prozesses mit Maximalgeschwindigkeit zwei wird ausgehend von einer Analyse des Zweiteilchensektors gezeigt, dass die Abstandsverteilung der Teilchen oszillieren kann. Diese Beobachtung wird unterstrichen im thermodynamischen Limes mit Hilfe einer verbesserten Mean-Field-Theorie, welche bemerkenswert gute Übereinstimmung mit Simulationen zeigt. Das Hauptaugenmerk dieser Arbeit liegt in der exakten Beschreibung von Gittermodellen mit dem Matrixproduktansatz. Mit diesem Ansatz werden schließlich Lösungen für verwandte Modelle abgeleitet. Besonders beachtenswert ist eine neue Formulierung der stationären Zustände für parallele Dynamik, wie für den ASEP mit offenen Rändern als ein Produkt eines paarfaktorisierten und eines Matrixproduktzustandes

Characterizing correlations of flow oscillations at bottlenecks

"Oscillations" occur in quite different kinds of many-particle-systems when two groups of particles with different directions of motion meet or intersect at a certain spot. We present a model of pedestrian motion that is able to reproduce oscillations with different characteristics. The Wald-Wolfowitz test and Gillis' correlated random walk are shown to hold observables that can be used to characterize different kinds of oscillations

Optimizing evacuation flow in a two-channel exclusion process

We use a basic setup of two coupled exclusion processes to model a stylised situation in evacuation dynamics, in which evacuees have to choose between two escape routes. The coupling between the two processes occurs through one common point at which particles are injected, the process can be controlled by directing incoming individuals into either of the two escape routes. Based on a mean-field approach we determine the phase behaviour of the model, and analytically compute optimal control strategies, maximising the total current through the system. Results are confirmed by numerical simulations. We also show that dynamic intervention, exploiting fluctuations about the mean-field stationary state, can lead to a further increase in total current.Comment: 16 pages, 6 figure

Investigation of masking concepts for influencing the austenitization process during press hardening

One possibility to adjust tailored properties in hot stamping is the application of a masking concept to prevent a complete austenitization. In this study different concepts were investigated in order to use them as a suitable masking. A simulation model of the heating phase was developed for the purpose of predicting the resulting microstructure and hardness. Experimentally determined temperature profiles were used for the numerical model. The numerical results of the temperature profile and hardness were validated by experimental investigations and non-destructive hardness measurements. The simulated hardness is in adequate agreement with the measured hardness

Tailoring Soft Local Zones in Quenched Blanks of the Steel 22MnB5 by Partial Pre-cooling with Compressed Air

The high-strength boron steel 22MnB5 steel is widely used for automotive lightweight constructions. A novel approach is promising to tailor strength and ductility in the hardened condition using locally pre-tempered sheets for the hot stamping process. It results in the formation of locally soft spots where mechanical joining is subsequently intended. A slow pre-cooling of the later joining zones with cooling rates below a certain critical cooling rate for obtaining a decreased strength in these regions is required. A tubular air cooling system suited for this task is presented and tested in a process where the subsequent quenching of the overall sheet is realized by rapid cooling in a water bath. Varying the air pressure and cooling duration allows controlling the size of the softened local spot in a wide range and still obtaining a bainitic microstructure. Using two-stage cooling with point jet nozzles and a subsequent hot stamping process with water-cooled dies resulted in a main sheet hardness of about 470 HV5 and of 260 HV5 in the pre-cooled spots, respectively

Frozen shuffle update for an asymmetric exclusion process on a ring

We introduce a new rule of motion for a totally asymmetric exclusion process (TASEP) representing pedestrian traffic on a lattice. Its characteristic feature is that the positions of the pedestrians, modeled as hard-core particles, are updated in a fixed predefined order, determined by a phase attached to each of them. We investigate this model analytically and by Monte Carlo simulation on a one-dimensional lattice with periodic boundary conditions. At a critical value of the particle density a transition occurs from a phase with `free flow' to one with `jammed flow'. We are able to analytically predict the current-density diagram for the infinite system and to find the scaling function that describes the finite size rounding at the transition point.Comment: 16 page

Poseidon Berichte - Paphsanias Volcano Cruise POS512, 25.04.2017 – 06.05.2017, Heraklion (Griechenland) – Heraklion (Griechenland)

Summary Cruise POS512 was scheduled for ten working days from 25.4. to 6.5.2017 in order to (1) produce a bathymetric map of the Epidavros Basin near the peninsula of Methana, (2) survey the volcanic structures of the Paphsanias Volcanic Field with the ROV PHOCA, and (3) sample the volcanic rocks. The Paphsanias Volcanic Field was found in 1987 but only one rock sample had been recovered and the size, age and composition of the lavas were unknown. Historic reports suggested an eruption on Methana and potentially off the coast some 2000 years ago. The bathymetric survey showed that six volcanic structures form the volcanic field ranging from simple lava flows on the seafloor, small cone-like structures to relatively complex crater-like structures with small volcanic domes. The largest volcanoes are about 200 m high and have diameters of about 2 km. The northern two complex Volcanoes 1 and 2 are relatively young and consist of steep lava flows and dome-like structures with little sediment. No indication of very young volcanism and hydrothermal activity was found. In contrast, the four southern structures are mostly sediment-covered and outcrops of volcanic rocks are rare and often covered by thick carbonate and MnOOH crusts. These four edifices are older than the northern two. Lava samples range from olivine-bearing basalts to plagioclase-amphibole-biotite-phyric andesites and dacites. All lavas appear to be fresh but few show signs of submarine extrusion and quenching. Volcaniclastic material was rarely observed and sampled indicating that explosive volcanic activity did not occur. During cruise POS512 13 ROV dives recovered 163 samples including 131 fresh lavas from four different volcanoes of the Paphsanias Volcanic Field and 427 nm of bathymetric survey was carried out

Calibration of the Particle Density in Cellular-Automaton Models for Traffic Flow

We introduce density dependence of the cell size in cellular-automaton models for traffic flow, which allows a more precise correspondence between real-world phenomena and what observed in simulation. Also, we give an explicit calibration of the particle density particularly for the asymmetric simple exclusion process with some update rules. We thus find that the present method is valid in that it reproduces a realistic flow-density diagram.Comment: 2 pages, 2 figure

Intersection of two TASEP traffic lanes with frozen shuffle update

Motivated by interest in pedestrian traffic we study two lanes (one-dimensional lattices) of length $L$ that intersect at a single site. Each lane is modeled by a TASEP (Totally Asymmetric Exclusion Process). The particles enter and leave lane $\sigma$ (where $\sigma=1,2$) with probabilities $\alpha_\sigma$ and $\beta_\sigma$, respectively. We employ the `frozen shuffle' update introduced in earlier work [C. Appert-Rolland et al, J. Stat. Mech. (2011) P07009], in which the particle positions are updated in a fixed random order. We find analytically that each lane may be in a `free flow' or in a `jammed' state. Hence the phase diagram in the domain $0\leq\alpha_1,\alpha_2\leq 1$ consists of four regions with boundaries depending on $\beta_1$ and $\beta_2$. The regions meet in a single point on the diagonal of the domain. Our analytical predictions for the phase boundaries as well as for the currents and densities in each phase are confirmed by Monte Carlo simulations.Comment: 7 figure

Posterpräsentation der Promovierenden : Abstract-Band ; Promovierendentag 2023

Diese Sammlung enthält die Abstracts der Poster, die im Rahmen des Promovierendentages 2023 von kooperativ promovierenden Doktorandinnen und Doktoranden an der Hochschule für Angewandte Wissenschaften Hamburg (HAW Hamburg) präsentiert werden. Sie geben einen Einblick in spannende, durch wissenschaftliches Niveau und Praxisnähe geprägte Forschungsvorhaben.NonPeerReviewe