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Consider the primitive equations on ◂+▸R2×(◂,▸z0,z1) with initial data a of the form a=◂+▸a1+a2, where ◂+▸a1∈◂◽.▸BUCσ(◂,▸R2;L1(◂,▸z0,z1)) and ◂+▸a2∈L
∞
σ
(◂,▸R2;L1(◂,▸z0,z1)). These spaces are scaling-invariant and represent the anisotropic character of these equations. It is shown that for a1 arbitrary large and a2 sufficiently small, this set of equations admits a unique strong solution which extends to a global one and is thus strongly globally well posed for these data provided a is periodic in the horizontal variables. The approach presented depends crucially on mapping properties of the hydrostatic Stokes semigroup in the L∞(L1)-setting. It can be seen as the counterpart of the classical iteration schemes for the Navier–Stokes equations, now for the primitive equations in the L∞(L1)-setting.
In figure–ground organization, the figure is defined as a region that is both “shaped” and “nearer.” Here we test whether changes in task set and instructions can alter the outcome of the cross-border competition between figural priors that underlies figure assignment. Extremal edge (EE), a relative distance prior, has been established as a strong figural prior when the task is to report “which side is nearer?” In three experiments using bipartite stimuli, EEs competed and cooperated with familiar configuration, a shape prior for figure assignment in a “which side is shaped?” task.” Experiment 1 showed small but significant effects of familiar configuration for displays sketching upright familiar objects, although “shaped-side” responses were predominantly determined by EEs. In Experiment 2, instructions regarding the possibility of perceiving familiar shapes were added. Now, although EE remained the dominant prior, the figure was perceived on the familiar-configuration side of the border on a significantly larger percentage of trials across all display types. In Experiment 3, both task set (nearer/shaped) and the presence versus absence of instructions emphasizing that familiar objects might be present were manipulated within subjects. With familiarity thus “primed,” effects of task set emerged when EE and familiar configuration favored opposite sides as figure. Thus, changing instructions can modulate the weighing of figural priors for shape versus distance in figure assignment in a manner that interacts with task set. Moreover, we show that the influence of familiar parts emerges in participants without medial temporal lobe/ perirhinal cortex brain damage when instructions emphasize that familiar objects might be present.
Cellular membranes can serve as barriers between subcellular compartments, but they can also interact to form dynamically regulated membrane contact sites between a specific pair of organelles. Focussing on plants, this article discusses local redox environments and the current knowledge on membrane contact sites as examples for the dividing and connecting functions of membranes, respectively.
Fragmentation of granular clusters may be studied by experiments and by granular mechanics simulation. When comparing results, it is often assumed that results can be compared when scaled to the same value of E/◂◽.▸Esep, where E denotes the collision energy and ◂◽.▸Esep is the energy needed to break every contact in the granular clusters. The ratio ◂+▸E/◂◽.▸Esep∝v2 depends on the collision velocity v but not on the number of grains per cluster, N. We test this hypothesis using granular-mechanics simulations on silica clusters containing a few thousand grains in the velocity range where fragmentation starts. We find that a good parameter to compare different systems is given by ◂+▸E/(Nα◂◽.▸Esep), where α∼2/3. The occurrence of the extra factor Nα is caused by energy dissipation during the collision such that large clusters request a higher impact energy for reaching the same level of fragmentation than small clusters. Energy is dissipated during the collision mainly by normal and tangential (sliding) forces between grains. For large values of the viscoelastic friction parameter, we find smaller cluster fragmentation, since fragment velocities are smaller and allow for fragment recombination.
Die Möglichkeit einer Prämienanpassung in der deutschen PKV ist vom Wert des sogenannten auslösenden Faktors abhängig, der mittels einer linearen Extrapolation der Schadenquotienten der vergangenen drei Jahre berechnet wird. Seine frühzeitige, verlässliche Vorhersage ist aus Sicht des Risikomanagements von großer Bedeutung. Wir untersuchen deshalb vielfältige Vorhersageansätze, die von klassischen Zeitreihenansätzen und Regression über neuronale Netze bis hin zu hybriden Modellen reichen. Während bei den klassischen Methoden Regression mit ARIMA-Fehlern am besten abschneidet, zeigt ein neuronales Netz, das mit Zeitreihenvorhersage kombiniert oder auf desaisonalisierten und trendbereinigten Daten trainiert wurde, das insgesamt beste Verhalten.
Gliomas are primary brain tumors with a high invasive potential and infiltrative spread. Among them, glioblastoma multiforme (GBM) exhibits microvascular hyperplasia and pronounced necrosis triggered by hypoxia. Histological samples showing garland-like hypercellular structures (so-called pseudopalisades) centered around the occlusion site of a capillary are typical for GBM and hint on poor prognosis of patient survival. We propose a multiscale modeling approach in the kinetic theory of active particles framework and deduce by an upscaling process a reaction-diffusion model with repellent pH-taxis. We prove existence of a unique global bounded classical solution for a version of the obtained macroscopic system and investigate the asymptotic behavior of the solution. Moreover, we study two different types of scaling and compare the behavior of the obtained macroscopic PDEs by way of simulations. These show that patterns (not necessarily of Turing type), including pseudopalisades, can be formed for some parameter ranges, in accordance with the tumor grade. This is true when the PDEs are obtained via parabolic scaling (undirected tissue), while no such patterns are observed for the PDEs arising by a hyperbolic limit (directed tissue). This suggests that brain tissue might be undirected - at least as far as glioma migration is concerned. We also investigate two different ways of including cell level descriptions of response to hypoxia and the way they are related .
Understanding human crowd behaviour has been an intriguing topic of interdisciplinary research in recent decades. Modelling of crowd dynamics using differential equations is an indispensable approach to unraveling the various complex dynamics involved in such interacting particle systems. Numerical simulation of pedestrian crowd via these mathematical models allows us to study different realistic scenarios beyond the limitations of studies via controlled experiments.
In this thesis, the main objective is to understand and analyse the dynamics in a domain shared by both pedestrians and moving obstacles. We model pedestrian motion by combining the social force concept with the idea of optimal path computation. This leads to a system of ordinary differential equations governing the dynamics of individual pedestrians via the interaction forces (social forces) between them. Additionally, a non-local force term involving the optimal path and desired velocity governs the pedestrian trajectory. The optimal path computation involves solving a time-independent Eikonal equation, which is coupled to the system of ODEs. A hydrodynamic model is developed from this microscopic model via the mean-field limit.
To consider the interaction with moving obstacles in the domain, we model a set of kinematic equations for the obstacle motion. Two kinds of obstacles are considered - "passive", which move in their predefined trajectories and have only a one-way interaction with pedestrians, and "dynamic", which have a feedback interaction with pedestrians and have their trajectories changing dynamically. The coupled model of pedestrians and obstacles is used to discern pedestrian collision avoidance behaviour in different computational scenarios in a long rectangular domain. We observe that pedestrians avoid collisions through route choice strategies that involve changes in speed and path. We extend this model to consider the interaction between pedestrians and vehicular traffic. We appropriately model the interactions of vehicles, following lane traffic, based on the car-following approach. We observe how the deceleration and braking mechanism of vehicles is executed at pedestrian crossings depending on the right of way on the roads.
As a second objective, we study the disease contagion in moving crowds. We consider the influence of the crowd motion in a complex dynamical environment on the course of infection of pedestrians. A hydrodynamic model for multi-group pedestrian flow is derived from the kinetic equations based on a social force model. It is coupled along with an Eikonal equation to a non-local SEIS contagion model for disease spread. Here, apart from the description of local contacts, the influence of contact times has also been modelled. We observe that the nature of the flow and the geometry of the domain lead to changes in density which affect the contact time and, consequently, the rate of spread of infection.
Finally, the social force model is compared to a variable speed based rational behaviour pedestrian model. We derive a hierarchy of the heuristics-based model from microscopic to macroscopic scales and numerically investigate these models in different density scenarios. Various numerical test cases are considered, including uni- and bi-directional flows and scenarios with and without obstacles. We observe that in low-density scenarios, collision avoidance forces arising from the behavioural heuristics give valid results. Whereas in high-density scenarios, repulsive force terms are essential.
The numerical simulations of all the models are carried out using a mesh-free particle method based on least square approximations. The meshfree numerical framework provides an efficient and elegant way to handle complex geometric situations involving boundaries and stationary or moving obstacles.
The precise regulation of synaptic connectivity is essential for the processing of information in the brain. Any aberrant loss of synaptic connectivity due to genetic mutations will disrupt information flow in the nervous system and may represent the underlying cause of psychiatric or neurodegenerative diseases. Therefore, identification of the molecular mechanisms controlling synaptic plasticity and maintenance is essential for our understanding of neuronal circuits in development and disease.
Maturity model for determining digitalization levels within different product lifecycle phases
(2021)
Maintaining pace with ongoing changes due to digitalization is challenging for manufacturing companies. For successful
implementation of digitalization, manufacturing companies must consider their existing technical systems, organizational
structures, and processes, as well as social aspects. With the support of a maturity model, a company-specific digitalization
level can be evaluated to provide manufacturing companies with an initial insight into their particular status quo; this
can serve as a starting point for future optimization and digitalization projects. Furthermore, the results of such an analysis
allow objective comparison of different areas within the company and with competitors. In this paper, the “Integrierte Arbeitssystemgestaltung
in digitalisierten Produktionsunternehmen” (InAsPro) maturity model is presented, which considers
the Development, Production, and Assembly product lifecycle phases, as well as Aftersales, and assesses their digitalization
level focusing on the four dimensions of Technology, Organization, Social Issues, and Corporate Strategy. The maturity
model’s rating scale distinguishes between four maturity levels. The results given by the InAsPro maturity model for an
entire company are presented, along with those for each product lifecycle phase. Extensive descriptions for each specific
maturity level are also provided.
Consider a linear realization of a matroid over a field. One associates with it a configuration
polynomial and a symmetric bilinear form with linear homogeneous coefficients.
The corresponding configuration hypersurface and its non-smooth locus support the
respective first and second degeneracy scheme of the bilinear form.We showthat these
schemes are reduced and describe the effect of matroid connectivity: for (2-)connected
matroids, the configuration hypersurface is integral, and the second degeneracy scheme
is reduced Cohen–Macaulay of codimension 3. If the matroid is 3-connected, then also
the second degeneracy scheme is integral. In the process, we describe the behavior
of configuration polynomials, forms and schemes with respect to various matroid
constructions.