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The correctness of model transformations is a crucial element for model-driven engineering of high quality software. In particular, behavior preservation is the most important correctness property avoiding the introduction of semantic errors during the model-driven engineering process. Behavior preservation verification techniques either show that specific properties are preserved, or more generally and complex, they show some kind of behavioral equivalence or refinement between source and target model of the transformation. Both kinds of behavior preservation verification goals have been presented with automatic tool support for the instance level, i.e. for a given source and target model specified by the model transformation. However, up until now there is no automatic verification approach available at the transformation level, i.e. for all source and target models specified by the model transformation.
In this report, we extend our results presented in [27] and outline a new sophisticated approach for the automatic verification of behavior preservation captured by bisimulation resp. simulation for model transformations specified by triple graph grammars and semantic definitions given by graph transformation rules. In particular, we show that the behavior preservation problem can be reduced to invariant checking for graph transformation and that the resulting checking problem can be addressed by our own invariant checker even for a complex example where a sequence chart is transformed into communicating automata. We further discuss today's limitations of invariant checking for graph transformation and motivate further lines of future work in this direction.
Die Bienaymé-Galton-Watson Prozesse können für die Untersuchung von speziellen und sich entwickelnden Populationen verwendet werden. Die Populationen umfassen Individuen, welche sich identisch, zufällig, selbstständig und unabhängig voneinander fortpflanzen und die jeweils nur eine Generation existieren. Die n-te Generation ergibt sich als zufällige Summe der Individuen der (n-1)-ten Generation. Die Relevanz dieser Prozesse begründet sich innerhalb der Historie und der inner- und außermathematischen Bedeutung. Die Geschichte der Bienaymé-Galton-Watson-Prozesse wird anhand der Entwicklung des Konzeptes bis heute dargestellt. Dabei werden die Wissenschaftler:innen verschiedener Disziplinen angeführt, die Erkenntnisse zu dem Themengebiet beigetragen und das Konzept in ihren Fachbereichen angeführt haben. Somit ergibt sich die außermathematische Signifikanz. Des Weiteren erhält man die innermathematische Bedeutsamkeit mittels des Konzeptes der Verzweigungsprozesse, welches auf die Bienaymé-Galton-Watson Prozesse zurückzuführen ist. Die Verzweigungsprozesse stellen eines der aussagekräftigsten Modelle für die Beschreibung des Populationswachstums dar. Darüber hinaus besteht die derzeitige Wichtigkeit durch die Anwendungsmöglichkeit der Verzweigungsprozesse und der Bienaymé-Galton-Watson Prozesse innerhalb der Epidemiologie. Es werden die Ebola- und die Corona-Pandemie als Anwendungsfelder angeführt. Die Prozesse dienen als Entscheidungsstütze für die Politik und ermöglichen Aussagen über die Auswirkungen von Maßnahmen bezüglich der Pandemien. Neben den Prozessen werden ebenfalls der bedingte Erwartungswert bezüglich diskreter Zufallsvariablen, die wahrscheinlichkeitserzeugende Funktion und die zufällige Summe eingeführt. Die Konzepte vereinfachen die Beschreibung der Prozesse und bilden somit die Grundlage der Betrachtungen. Außerdem werden die benötigten und weiterführenden Eigenschaften der grundlegenden Themengebiete und der Prozesse aufgeführt und bewiesen. Das Kapitel erreicht seinen Höhepunkt bei dem Beweis des Kritikalitätstheorems, wodurch eine Aussage über das Aussterben des Prozesses in verschiedenen Fällen und somit über die Aussterbewahrscheinlichkeit getätigt werden kann. Die Fälle werden anhand der zu erwartenden Anzahl an Nachkommen eines Individuums unterschieden. Es zeigt sich, dass ein Prozess bei einer zu erwartenden Anzahl kleiner gleich Eins mit Sicherheit ausstirbt und bei einer Anzahl größer als Eins, die Population nicht in jedem Fall aussterben muss. Danach werden einzelne Beispiele, wie der linear fractional case, die Population von Fibroblasten (Bindegewebszellen) von Mäusen und die Entstehungsfragestellung der Prozesse, angeführt. Diese werden mithilfe der erlangten Ergebnisse untersucht und einige ausgewählte zufällige Dynamiken werden im nachfolgenden Kapitel simuliert. Die Simulationen erfolgen durch ein in Python erstelltes Programm und werden mithilfe der Inversionsmethode realisiert. Die Simulationen stellen beispielhaft die Entwicklungen in den verschiedenen Kritikalitätsfällen der Prozesse dar. Zudem werden die Häufigkeiten der einzelnen Populationsgrößen in Form von Histogrammen angebracht. Dabei lässt sich der Unterschied zwischen den einzelnen Fällen bestätigen und es wird die Anwendungsmöglichkeit der Bienaymé-Galton-Watson Prozesse bei komplexeren Problemen deutlich. Histogramme bekräftigen, dass die einzelnen Populationsgrößen nur endlich oft vorkommen. Diese Aussage wurde von Galton aufgeworfen und in der Extinktions-Explosions-Dichotomie verwendet. Die dargestellten Erkenntnisse über das Themengebiet und die Betrachtung des Konzeptes werden mit einer didaktischen Analyse abgeschlossen. Die Untersuchung beinhaltet die Berücksichtigung der Fundamentalen Ideen, der Fundamentalen Ideen der Stochastik und der Leitidee „Daten und Zufall“. Dabei ergibt sich, dass in Abhängigkeit der gewählten Perspektive die Anwendung der Bienaymé-Galton-Watson Prozesse innerhalb der Schule plausibel ist und von Vorteil für die Schüler:innen sein kann. Für die Behandlung wird exemplarisch der Rahmenlehrplan für Berlin und Brandenburg analysiert und mit dem Kernlehrplan Nordrhein-Westfalens verglichen. Die Konzeption des Lehrplans aus Berlin und Brandenburg lässt nicht den Schluss zu, dass die Bienaymé-Galton-Watson Prozesse angewendet werden sollten. Es lässt sich feststellen, dass die zugrunde liegende Leitidee nicht vollumfänglich mit manchen Fundamentalen Ideen der Stochastik vereinbar ist. Somit würde eine Modifikation hinsichtlich einer stärkeren Orientierung des Lehrplans an den Fundamentalen Ideen die Anwendung der Prozesse ermöglichen. Die Aussage wird durch die Betrachtung und Übertragung eines nordrhein-westfälischen Unterrichtsentwurfes für stochastische Prozesse auf die Bienaymé-Galton-Watson Prozesse unterstützt. Darüber hinaus werden eine Concept Map und ein Vernetzungspentagraph nach von der Bank konzipiert um diesen Aspekt hervorzuheben.
In dieser Arbeit werden nichtlineare Kopplungsmechanismen von akustischen Oszillatoren untersucht, die zu Synchronisation führen können. Aufbauend auf die Fragestellungen vorangegangener Arbeiten werden mit Hilfe theoretischer und experimenteller Studien sowie mit Hilfe numerischer Simulationen die Elemente der Tonentstehung in der Orgelpfeife und die Mechanismen der gegenseitigen Wechselwirkung von Orgelpfeifen identifiziert. Daraus wird erstmalig ein vollständig auf den aeroakustischen und fluiddynamischen Grundprinzipien basierendes nichtlinear gekoppeltes Modell selbst-erregter Oszillatoren für die Beschreibung des Verhaltens zweier wechselwirkender Orgelpfeifen entwickelt. Die durchgeführten Modellrechnungen werden mit den experimentellen Befunden verglichen. Es zeigt sich, dass die Tonentstehung und die Kopplungsmechanismen von Orgelpfeifen durch das entwickelte Oszillatormodell in weiten Teilen richtig beschrieben werden. Insbesondere kann damit die Ursache für den nichtlinearen Zusammenhang von Kopplungsstärke und Synchronisation des gekoppelten Zwei-Pfeifen Systems, welcher sich in einem nichtlinearen Verlauf der Arnoldzunge darstellt, geklärt werden. Mit den gewonnenen Erkenntnissen wird der Einfluss des Raumes auf die Tonentstehung bei Orgelpfeifen betrachtet. Dafür werden numerische Simulationen der Wechselwirkung einer Orgelpfeife mit verschiedenen Raumgeometrien, wie z. B. ebene, konvexe, konkave, und gezahnte Geometrien, exemplarisch untersucht. Auch der Einfluss von Schwellkästen auf die Tonentstehung und die Klangbildung der Orgelpfeife wird studiert. In weiteren, neuartigen Synchronisationsexperimenten mit identisch gestimmten Orgelpfeifen, sowie mit Mixturen wird die Synchronisation für verschiedene, horizontale und vertikale Pfeifenabstände in der Ebene der Schallabstrahlung, untersucht. Die dabei erstmalig beobachteten räumlich isotropen Unstetigkeiten im Schwingungsverhalten der gekoppelten Pfeifensysteme, deuten auf abstandsabhängige Wechsel zwischen gegen- und gleichphasigen Sychronisationsregimen hin. Abschließend wird die Möglichkeit dokumentiert, das Phänomen der Synchronisation zweier Orgelpfeifen durch numerische Simulationen, also der Behandlung der kompressiblen Navier-Stokes Gleichungen mit entsprechenden Rand- und Anfangsbedingungen, realitätsnah abzubilden. Auch dies stellt ein Novum dar.
Heterophase polymerization is a technique widely used for the synthesis of high performance polymeric materials with applications including paints, inks, adhesives, synthetic rubber, biomedical applications and many others. Due to the heterogeneous nature of the process, many different relevant length and time scales can be identified. Each of these scales has a direct influence on the kinetics of polymerization and on the physicochemical and performance properties of the final product. Therefore, from the point of view of product and process design and optimization, the understanding of each of these relevant scales and their integration into one single model is a very promising route for reducing the time-to-market in the development of new products, for increasing the productivity and profitability of existing processes, and for designing products with improved performance or cost/performance ratio. The process considered is the synthesis of structured or composite polymer particles by multi-stage seeded emulsion polymerization. This type of process is used for the preparation of high performance materials where a synergistic behavior of two or more different types of polymers is obtained. Some examples include the synthesis of core-shell or multilayered particles for improved impact strength materials and for high resistance coatings and adhesives. The kinetics of the most relevant events taking place in an emulsion polymerization process has been investigated using suitable numerical simulation techniques at their corresponding time and length scales. These methods, which include Molecular Dynamics (MD) simulation, Brownian Dynamics (BD) simulation and kinetic Monte Carlo (kMC) simulation, have been found to be very powerful and highly useful for gaining a deeper insight and achieving a better understanding and a more accurate description of all phenomena involved in emulsion polymerization processes, and can be potentially extended to investigate any type of heterogeneous process. The novel approach of using these kinetic-based numerical simulation methods can be regarded as a complement to the traditional thermodynamic-based macroscopic description of emulsion polymerization. The particular events investigated include molecular diffusion, diffusion-controlled polymerization reactions, particle formation, absorption/desorption of radicals and monomer, and the colloidal aggregation of polymer particles. Using BD simulation it was possible to precisely determine the kinetics of absorption/desorption of molecular species by polymer particles, and to simulate the colloidal aggregation of polymer particles. For diluted systems, a very good agreement between BD simulation and the classical theory developed by Smoluchowski was obtained. However, for concentrated systems, significant deviations from the ideal behavior predicted by Smoluchowski were evidenced. BD simulation was found to be a very valuable tool for the investigation of emulsion polymerization processes especially when the spatial and geometrical complexity of the system cannot be neglected, as is the case of concentrated dispersions, non-spherical particles, structured polymer particles, particles with non-uniform monomer concentration, and so on. In addition, BD simulation was used to describe non-equilibrium monomer swelling kinetics, which is not possible using the traditional thermodynamic approach because it is only valid for systems at equilibrium. The description of diffusion-controlled polymerization reactions was successfully achieved using a new stochastic algorithm for the kMC simulation of imperfectly mixed systems (SSA-IM). In contrast to the traditional stochastic simulation algorithm (SSA) and the deterministic rate of reaction equations, instead of assuming perfect mixing in the whole reactor, the new SSA-IM determines the volume perfectly mixed between two consecutive reactions as a function of the diffusion coefficient of the reacting species. Using this approach it was possible to describe, using a single set of kinetic parameters, typical mass transfer limitations effects during a free radical batch polymerization such as the cage effect, the gel effect and the glass effect. Using multiscale integration it was possible to investigate the formation of secondary particles during the seeded emulsion polymerization of vinyl acetate over a polystyrene seed. Three different cases of radical generation were considered: generation of radicals by thermal decomposition of water-soluble initiating compounds, generation of radicals by a redox reaction at the surface of the particles, and generation of radicals by thermal decomposition of surface-active initiators "inisurfs" attached to the surface of the particles. The simulation results demonstrated the satisfactory reduction in secondary particles formation achieved when the locus of radical generation is controlled close to the particles surface.
In many procedures of seismic risk mitigation, ground motion simulations are needed to test systems or improve their effectiveness. For example they may be used to estimate the level of ground shaking caused by future earthquakes. Good physical models for ground motion simulation are also thought to be important for hazard assessment, as they could close gaps in the existing datasets. Since the observed ground motion in nature shows a certain variability, part of which cannot be explained by macroscopic parameters such as magnitude or position of an earthquake, it would be desirable that a good physical model is not only able to produce one single seismogram, but also to reveal this natural variability.
In this thesis, I develop a method to model realistic ground motions in a way that is computationally simple to handle, permitting multiple scenario simulations. I focus on two aspects of ground motion modelling. First, I use deterministic wave propagation for the whole frequency range – from static deformation to approximately 10 Hz – but account for source variability by implementing self-similar slip distributions and rough fault interfaces. Second, I scale the source spectrum so that the modelled waveforms represent the correct radiated seismic energy. With this scaling I verify whether the energy magnitude is suitable as an explanatory variable, which characterises the amount of energy radiated at high frequencies – the advantage of the energy magnitude being that it can be deduced from observations, even in real-time.
Applications of the developed method for the 2008 Wenchuan (China) earthquake, the 2003 Tokachi-Oki (Japan) earthquake and the 1994 Northridge (California, USA) earthquake show that the fine source discretisations combined with the small scale source variability ensure that high frequencies are satisfactorily introduced, justifying the deterministic wave propagation approach even at high frequencies. I demonstrate that the energy magnitude can be used to calibrate the high-frequency content in ground motion simulations.
Because deterministic wave propagation is applied to the whole frequency range, the simulation method permits the quantification of the variability in ground motion due to parametric uncertainties in the source description. A large number of scenario simulations for an M=6 earthquake show that the roughness of the source as well as the distribution of fault dislocations have a minor effect on the simulated variability by diminishing directivity effects, while hypocenter location and rupture velocity more strongly influence the variability. The uncertainty in energy magnitude, however, leads to the largest differences of ground motion amplitude between different events, resulting in a variability which is larger than the one observed.
For the presented approach, this dissertation shows (i) the verification of the computational correctness of the code, (ii) the ability to reproduce observed ground motions and (iii) the validation of the simulated ground motion variability. Those three steps are essential to evaluate the suitability of the method for means of seismic risk mitigation.
In der vorliegenden Arbeit werden die Eigenschaften geschlossener fluider Membranen, sogenannter Vesikeln, bei endlichen Temperaturen untersucht. Dies beinhaltet Betrachtungen zur Form freier Vesikeln, eine Untersuchung des Adhäsionsverhaltens von Vesikeln an planaren Substraten sowie eine Untersuchung der Eigenschaften fluider Vesikeln in eingeschränkten Geometrien. Diese Untersuchungen fanden mit Hilfe von Monte-Carlo-Simulationen einer triangulierten Vesikeloberfläche statt. Die statistischen Eigenschaften der fluktuierenden fluiden Vesikeln wurden zum Teil mittels Freier-Energie-Profile analysiert. In diesem Zusammenhang wurde eine neuartige Histogrammethode entwickelt.<BR> Die Form für eine freie fluide Vesikel mit frei veränderlichem Volumen, die das Konfigurationsenergie-Funktional minimiert, ist im Falle verschwindender Temperatur eine Kugel. Mit Hilfe von Monte-Carlo-Simulationen sowie einem analytisch behandelbaren Modellsystem konnte gezeigt werden, daß sich dieses Ergebnis nicht auf endliche Temperaturen verallgemeinern lässt und statt dessen leicht prolate und oblate Vesikelformen gegenüber der Kugelgestalt überwiegen. Dabei ist die Wahrscheinlichkeit für eine prolate Form ein wenig gröoßer als für eine oblate. Diese spontane Asphärizität ist entropischen Ursprungs und tritt nicht bei zweidimensionalen Vesikeln auf. Durch osmotische Drücke in der Vesikel, die größer sind als in der umgebenden Flüssigkeit, lässt sich die Asphärizität reduzieren oder sogar kompensieren. Die Übergänge zwischen den beobachteten prolaten und oblaten Formen erfolgen im Bereich von Millisekunden in Abwesenheit osmotisch aktiver Partikel. Bei Vorhandensein derartiger Partikel ergeben sich Übergangszeiten im Bereich von Sekunden. Im Rahmen der Untersuchung des Adhäsionsverhaltens fluider Vesikeln an planaren, homogenen Substraten konnte mit Hilfe von Monte-Carlo-Simulationen festgestellt werden, dass die Eigenschaften der Kontaktfläche der Vesikeln stark davon abhängen, welche Kräfte den Kontakt bewirken. Für eine dominierende attraktive Wechselwirkung zwischen Substrat und Vesikelmembran sowie im Falle eines Massendichteunterschieds der Flüssigkeiten innerhalb und außerhalb der Vesikel, der die Vesikel auf das Substrat sinken lässt, fndet man innerhalb der Kontakt ache eine ortsunabhangige Verteilung des Abstands zwischen Vesikelmembran und Substrat. Drückt die Vesikel ohne Berücksichtigung osmotischer Effekte auf Grund einer Differenz der Massendichten der Membran und der umgebenden Flüssigkeit gegen das Substrat, so erhält man eine Abstandsverteilung zwischen Vesikelmembran und Substrat, die mit dem Abstand vom Rand der Kontaktfläche variiert. Dieser Effekt ist zudem temperaturabhängig. Ferner wurde die Adhäsion fluider Vesikeln an chemisch strukturierten planaren Substraten untersucht. Durch das Wechselspiel von entropischen Effekten und Konfigurationsenergien entsteht eine komplexe Abhängigkeit der Vesikelform von Biegesteifigkeit, osmotischen Bedingungen und der Geometrie der attraktiven Domänen. Für die Bestimmung der Biegesteifigkeit der Vesikelmembranen liefern die existierenden Verfahren stark voneinander abweichende Ergebnisse. In der vorliegenden Arbeit konnte mittels Monte-Carlo-Simulationen zur Bestimmung der Biegesteifigkeit anhand des Mikropipettenverfahrens von Evans gezeigt werden, dass dieses Verfahren die a priori für die Simulation vorgegebene Biegesteifigkeit im wesentlichen reproduzieren kann. Im Hinblick auf medizinisch-pharmazeutische Anwendungen ist der Durchgang fluider Vesikeln durch enge Poren relevant. In Monte-Carlo-Simulationen konnte gezeigt werden, dass ein spontaner Transport der Vesikel durch ein Konzentrationsgefälle osmotisch aktiver Substanzen, das den physiologischen Bedingungen entspricht, induziert werden kann. Es konnten die hierfür notwendigen osmotischen Bedingungen sowie die charakteristischen Zeitskalen abgeschätzt werden. Im realen Experiment sind Eindringzeiten in eine enge Pore im Bereich weniger Minuten zu erwarten. Ferner konnte beobachtet werden, dass bei Vesikeln mit einer homogenen, positiven spontanen Krümmung Deformationen hin zu prolaten Formen leichter erfolgen als bei Vesikeln ohne spontane Krümmung. Mit diesem Effekt ist eine Verringerung der Energiebarriere für das Eindringen in eine Pore verbunden, deren Radius nur wenig kleiner als der Vesikelradius ist.
The North China Plain (NCP) is one of the most productive and intensive agricultural regions in China. High doses of mineral nitrogen (N) fertiliser, often combined with flood irrigation, are applied, resulting in N surplus, groundwater depletion and environmental pollution. The objectives of this thesis were to use the HERMES model to simulate the N cycle in winter wheat (Triticum aestivum L.)–summer maize (Zea mays L.) double crop rotations and show the performance of the HERMES model, of the new ammonia volatilisation sub-module and of the new nitrification inhibition tool in the NCP. Further objectives were to assess the models potential to save N and water on plot and county scale, as well as on short and long-term. Additionally, improved management strategies with the help of a model-based nitrogen fertiliser recommendation (NFR) and adapted irrigation, should be found.
Results showed that the HERMES model performed well under growing conditions of the NCP and was able to describe the relevant processes related to soil–plant interactions concerning N and water during a 2.5 year field experiment. No differences in grain yield between the real-time model-based NFR and the other treatments of the experiments on plot scale in Quzhou County could be found. Simulations with increasing amounts of irrigation resulted in significantly higher N leaching, higher N requirements of the NFR and reduced yields. Thus, conventional flood irrigation as currently practised by the farmers bears great uncertainties and exact irrigation amounts should be known for future simulation studies. In the best-practice scenario simulation on plot-scale, N input and N leaching, but also irrigation water could be reduced strongly within 2 years. Thus, the model-based NFR in combination with adapted irrigation had the highest potential to reduce nitrate leaching, compared to farmers practice and mineral N (Nmin)-reduced treatments. Also the calibrated and validated ammonia volatilisation sub-module of the HERMES model worked well under the climatic and soil conditions of northern China. Simple ammonia volatilisation approaches gave also satisfying results compared to process-oriented approaches. During the simulation with Ammonium sulphate Nitrate with nitrification inhibitor (ASNDMPP) ammonia volatilisation was higher than in the simulation without nitrification inhibitor, while the result for nitrate leaching was the opposite. Although nitrification worked well in the model, nitrification-born nitrous oxide emissions should be considered in future. Results of the simulated annual long-term (31 years) N losses in whole Quzhou County in Hebei Province were 296.8 kg N ha−1 under common farmers practice treatment and 101.7 kg N ha−1 under optimised treatment including NFR and automated irrigation (OPTai). Spatial differences in simulated N losses throughout Quzhou County, could only be found due to different N inputs. Simulations of an optimised treatment, could save on average more than 260 kg N ha−1a−1 from fertiliser input and 190 kg N ha−1a−1 from N losses and around 115.7 mm a−1 of water, compared to farmers practice. These long-term simulation results showed lower N and water saving potential, compared to short-term simulations and underline the necessity of long-term simulations to overcome the effect of high initial N stocks in soil.
Additionally, the OPTai worked best on clay loam soil except for a high simulated denitrification loss, while the simulations using farmers practice irrigation could not match the actual water needs resulting in yield decline, especially for winter wheat. Thus, a precise adaption of management to actual weather conditions and plant growth needs is necessary for future simulations. However, the optimised treatments did not seem to be able to maintain the soil organic matter pools, even with full crop residue input. Extra organic inputs seem to be required to maintain soil quality in the optimised treatments.
HERMES is a relatively simple model, with regard to data input requirements, to simulate the N cycle. It can offer interpretation of management options on plot, on county and regional scale for extension and research staff. Also in combination with other N and water saving methods the model promises to be a useful tool.
One of the rules-of-thumb of colloid and surface physics is that most surfaces are charged when in contact with a solvent, usually water. This is the case, for instance, in charge-stabilized colloidal suspensions, where the surface of the colloidal particles are charged (usually with a charge of hundreds to thousands of e, the elementary charge), monolayers of ionic surfactants sitting at an air-water interface (where the water-loving head groups become charged by releasing counterions), or bilayers containing charged phospholipids (as cell membranes). In this work, we look at some model-systems that, although being a simplified version of reality, are expected to capture some of the physical properties of real charged systems (colloids and electrolytes). We initially study the simple double layer, composed by a charged wall in the presence of its counterions. The charges at the wall are smeared out and the dielectric constant is the same everywhere. The Poisson-Boltzmann (PB) approach gives asymptotically exact counterion density profiles around charged objects in the weak-coupling limit of systems with low-valent counterions, surfaces with low charge density and high temperature (or small Bjerrum length). Using Monte Carlo simulations, we obtain the profiles around the charged wall and compare it with both Poisson-Boltzmann (in the low coupling limit) and the novel strong coupling (SC) theory in the opposite limit of high couplings. In the latter limit, the simulations show that the SC leads in fact to asymptotically correct density profiles. We also compare the Monte Carlo data with previously calculated corrections to the Poisson-Boltzmann theory. We also discuss in detail the methods used to perform the computer simulations. After studying the simple double layer in detail, we introduce a dielectric jump at the charged wall and investigate its effect on the counterion density distribution. As we will show, the Poisson-Boltzmann description of the double layer remains a good approximation at low coupling values, while the strong coupling theory is shown to lead to the correct density profiles close to the wall (and at all couplings). For very large couplings, only systems where the difference between the dielectric constants of the wall and of the solvent is small are shown to be well described by SC. Another experimentally relevant modification to the simple double layer is to make the charges at the plane discrete. The counterions are still assumed to be point-like, but we constraint the distance of approach between ions in the plane and counterions to a minimum distance D. The ratio between D and the distance between neighboring ions in the plane is, as we will see, one of the important quantities in determining the influence of the discrete nature of the charges at the wall over the density profiles. Another parameter that plays an important role, as in the previous case, is the coupling as we will demonstrate, systems with higher coupling are more subject to discretization effects than systems with low coupling parameter. After studying the isolated double layer, we look at the interaction between two double layers. The system is composed by two equally charged walls at distance d, with the counterions confined between them. The charge at the walls is smeared out and the dielectric constant is the same everywhere. Using Monte-Carlo simulations we obtain the inter-plate pressure in the global parameter space, and the pressure is shown to be negative (attraction) at certain conditions. The simulations also show that the equilibrium plate separation (where the pressure changes from attractive to repulsive) exhibits a novel unbinding transition. We compare the Monte Carlo results with the strong-coupling theory, which is shown to describe well the bound states of systems with moderate and high couplings. The regime where the two walls are very close to each other is also shown to be well described by the SC theory. Finally, Using a field-theoretic approach, we derive the exact low-density ("virial") expansion of a binary mixture of positively and negatively charged hard spheres (two-component hard-core plasma, TCPHC). The free energy obtained is valid for systems where the diameters d_+ and d_- and the charge valences q_+ and q_- of positive and negative ions are unconstrained, i.e., the same expression can be used to treat dilute salt solutions (where typically d_+ ~ d_- and q_+ ~ q_-) as well as colloidal suspensions (where the difference in size and valence between macroions and counterions can be very large). We also discuss some applications of our results.
Volatile supply and sales markets, coupled with increasing product individualization and complex production processes, present significant challenges for manufacturing companies. These must navigate and adapt to ever-shifting external and internal factors while ensuring robustness against process variabilities and unforeseen events. This has a pronounced impact on production control, which serves as the operational intersection between production planning and the shop- floor resources, and necessitates the capability to manage intricate process interdependencies effectively. Considering the increasing dynamics and product diversification, alongside the need to maintain constant production performances, the implementation of innovative control strategies becomes crucial.
In recent years, the integration of Industry 4.0 technologies and machine learning methods has gained prominence in addressing emerging challenges in production applications. Within this context, this cumulative thesis analyzes deep learning based production systems based on five publications. Particular attention is paid to the applications of deep reinforcement learning, aiming to explore its potential in dynamic control contexts. Analysis reveal that deep reinforcement learning excels in various applications, especially in dynamic production control tasks. Its efficacy can be attributed to its interactive learning and real-time operational model. However, despite its evident utility, there are notable structural, organizational, and algorithmic gaps in the prevailing research. A predominant portion of deep reinforcement learning based approaches is limited to specific job shop scenarios and often overlooks the potential synergies in combined resources. Furthermore, it highlights the rare implementation of multi-agent systems and semi-heterarchical systems in practical settings. A notable gap remains in the integration of deep reinforcement learning into a hyper-heuristic.
To bridge these research gaps, this thesis introduces a deep reinforcement learning based hyper- heuristic for the control of modular production systems, developed in accordance with the design science research methodology. Implemented within a semi-heterarchical multi-agent framework, this approach achieves a threefold reduction in control and optimisation complexity while ensuring high scalability, adaptability, and robustness of the system. In comparative benchmarks, this control methodology outperforms rule-based heuristics, reducing throughput times and tardiness, and effectively incorporates customer and order-centric metrics. The control artifact facilitates a rapid scenario generation, motivating for further research efforts and bridging the gap to real-world applications. The overarching goal is to foster a synergy between theoretical insights and practical solutions, thereby enriching scientific discourse and addressing current industrial challenges.
Situated in an active tectonic region, Santiago de Chile, the country´s capital with more than six million inhabitants, faces tremendous earthquake hazard. Macroseismic data for the 1985 Valparaiso and the 2010 Maule events show large variations in the distribution of damage to buildings within short distances indicating strong influence of local sediments and the shape of the sediment-bedrock interface on ground motion. Therefore, a temporary seismic network was installed in the urban area for recording earthquake activity, and a study was carried out aiming to estimate site amplification derived from earthquake data and ambient noise. The analysis of earthquake data shows significant dependence on the local geological structure with regards to amplitude and duration. Moreover, the analysis of noise spectral ratios shows that they can provide a lower bound in amplitude for site amplification and, since no variability in terms of time and amplitude is observed, that it is possible to map the fundamental resonance frequency of the soil for a 26 km x 12 km area in the northern part of the Santiago de Chile basin. By inverting the noise spectral rations, local shear wave velocity profiles could be derived under the constraint of the thickness of the sedimentary cover which had previously been determined by gravimetric measurements. The resulting 3D model was derived by interpolation between the single shear wave velocity profiles and shows locally good agreement with the few existing velocity profile data, but allows the entire area, as well as deeper parts of the basin, to be represented in greater detail. The wealth of available data allowed further to check if any correlation between the shear wave velocity in the uppermost 30 m (vs30) and the slope of topography, a new technique recently proposed by Wald and Allen (2007), exists on a local scale. While one lithology might provide a greater scatter in the velocity values for the investigated area, almost no correlation between topographic gradient and calculated vs30 exists, whereas a better link is found between vs30 and the local geology. When comparing the vs30 distribution with the MSK intensities for the 1985 Valparaiso event it becomes clear that high intensities are found where the expected vs30 values are low and over a thick sedimentary cover. Although this evidence cannot be generalized for all possible earthquakes, it indicates the influence of site effects modifying the ground motion when earthquakes occur well outside of the Santiago basin. Using the attained knowledge on the basin characteristics, simulations of strong ground motion within the Santiago Metropolitan area were carried out by means of the spectral element technique. The simulation of a regional event, which has also been recorded by a dense network installed in the city of Santiago for recording aftershock activity following the 27 February 2010 Maule earthquake, shows that the model is capable to realistically calculate ground motion in terms of amplitude, duration, and frequency and, moreover, that the surface topography and the shape of the sediment bedrock interface strongly modify ground motion in the Santiago basin. An examination on the dependency of ground motion on the hypocenter location for a hypothetical event occurring along the active San Ramón fault, which is crossing the eastern outskirts of the city, shows that the unfavorable interaction between fault rupture, radiation mechanism, and complex geological conditions in the near-field may give rise to large values of peak ground velocity and therefore considerably increase the level of seismic risk for Santiago de Chile.