Flooding and Drying in Discontinuous Galerkin Finite-Element Discretizations of Shallow-Water Equations. Part 1: One Dimension

Free boundaries in shallow-water equations demarcate the time-dependent water line between ‘‘flooded’’ and ‘‘dry’’ regions. We present a novel numerical algorithm to treat flooding and drying in a formally second-order explicit space discontinuous Galerkin finite-element discretization of the one-dimensional or symmetric shallow-water equations. The algorithm uses fixed Eulerian flooded elements and a mixed Eulerian–Lagrangian element at each free boundary. When the time step is suitably restricted, we show that the mean water depth is positive. This time-step restriction is based on an analysis of the discretized continuity equation while using the HLLC flux. The algorithm and its implementation are tested in comparison with a large and relevant suite of known exact solutions. The essence of the flooding and drying algorithm pivots around the analysis of a continuity equation with a fluid velocity and a pseudodensity (in the shallow water case the depth). It therefore also applies, for example, to space discontinuous Galerkin finite-element discretizations of the compressible Euler equations in which vacuum regions emerge, in analogy of the above dry regions. We believe that the approach presented can be extended to finite-volume discretizations with similar mean level and slope reconstruction.This revised version was published online in July 2005 with corrected volume and issue numbers.     

Segregation in thin films: the effect of mass balance and bonding to the support

The effect of mass balance on segregation in thin films is studied by minimizing the free energy of the film with respect to the composition of each layer for a fixed overall mole fraction. It is shown that the Bragg-Williams and quasi-chemical approximationsgive almost identical results. The effect of a difference in bond strength of the two components with the support is shown to lead to large variations in the composition of the outer film surface, even for thick (more than about 30 layers) films.     

Approximate analysis of exponential queueing systems with blocking

Summary A network of service stations Q ₀ Q ₁,...,Q_M is studied. Requests arrive at the centers according to independent Poisson processes; they travel through (part of) the network demanding amounts of service, with independent and negative exponentially distributed lengths, from those centers which they enter, and finally depart from the network. The waiting rooms or buffers at each service station in this exponential service system are finite. When the capacity at Q _i is reached, service at all nodes which are currently processing a request destined next for Q _i is instantaneously interrupted. The interruption lasts until the service of the request in the saturated node Q _i is. completed. This blocking phenomenon makes an exact analysis intractable and a numerical solution computationally infeasible for most exponential systems. We introduce an approximation procedure for a class of exponential systems with blocking and show that it leads to accurate approximations for the marginal equilibrium queue length distributions. The applicability of the approximation method may not be limited to blocking systems.Mathematical Sciences Department Postdoctoral Fellow 1978–79.     

The Identification of Small Molecule Inhibitors That Reduce Invasion and Metastasis of Aggressive Cancers

Transformed epithelial cells can activate programs of epithelial plasticity and switch from a sessile, epithelial phenotype to a motile, mesenchymal phenotype. This process is linked to the acquisition of an invasive phenotype and the formation of distant metastases. The development of compounds that block the acquisition of an invasive phenotype or revert the invasive mesenchymal phenotype into a more differentiated epithelial phenotype represent a promising anticancer strategy. In a high-throughput assay based on E-cadherin (re)induction and the inhibition of tumor cell invasion, 44,475 low molecular weight (LMW) compounds were screened. The screening resulted in the identification of candidate compounds from the PROAM02 class. Selected LMW compounds activated E-cadherin promoter activity and inhibited cancer cell invasion in multiple metastatic human cancer cell lines. The intraperitoneal administration of selected LMW compounds reduced the tumor burden in human prostate and breast cancer in vivo mouse models. Moreover, selected LMW compounds decreased the intra-bone growth of xenografted human prostate cancer cells. This study describes the identification of the PROAM02 class of small molecules that can be exploited to reduce cancer cell invasion and metastases. Further clinical evaluation of selected candidate inhibitors is warranted to address their safety, bioavailability and antitumor efficacy in the management of patients with aggressive cancers.     

From discrete particles to continuum fields near a boundary

An expression for the stress tensor near an external boundary of a discrete mechanical system is derived explicitly in terms of the constituents’ degrees of freedom and interaction forces. Starting point is the exact and general coarse graining formulation presented by Goldhirsch (Granul Mat 12(3):239–252, 2010), which is consistent with the continuum equations everywhere but does not account for boundaries. Our extension accounts for the boundary interaction forces in a self-consistent way and thus allows the construction of continuous stress fields that obey the macroscopic conservation laws even within one coarse-graining width of the boundary. The resolution and shape of the coarse-graining function used in the formulation can be chosen freely, such that both microscopic and macroscopic effects can be studied. The method does not require temporal averaging and thus can be used to investigate time-dependent flows as well as static or steady situations. Finally, the fore-mentioned continuous field can be used to define ‘fuzzy’ (very rough) boundaries. Discrete particle simulations are presented in which the novel boundary treatment is exemplified, including chute flow over a base with roughness greater than one particle diameter.     

Variational modelling of wave–structure interactions with an offshore wind-turbine mast

We consider the development of a mathematical model of water waves interacting with the mast of an offshore wind turbine. A variational approach is used for which the starting point is an action functional describing a dual system comprising a potential-flow fluid, a solid structure modelled with nonlinear elasticity, and the coupling between them. We develop a linearized model of the fluid–structure or wave–mast coupling, which is a linearization of the variational principle for the fully coupled nonlinear model. Our numerical results for the linear case indicate that our variational approach yields a stable numerical discretization of a fully coupled model of water waves and an elastic beam. The energy exchange between the subsystems is seen to be in balance, yielding a total energy that shows only small and bounded oscillations amplitude of which tends to zero with the second-order convergence as the timestep approaches zero. Similar second-order convergence is observed for spatial mesh refinement. The linearized model so far developed can be extended to a nonlinear regime.     

Identification of Molecular Fingerprints in Human Heat Pain Thresholds by Use of an Interactive Mixture Model R Toolbox (AdaptGauss)

Biomedical data obtained during cell experiments, laboratory animal research, or human studies often display a complex distribution. Statistical identification of subgroups in research data poses an analytical challenge. Here were introduce an interactive R-based bioinformatics tool, called “AdaptGauss”. It enables a valid identification of a biologically-meaningful multimodal structure in the data by fitting a Gaussian mixture model (GMM) to the data. The interface allows a supervised selection of the number of subgroups. This enables the expectation maximization (EM) algorithm to adapt more complex GMM than usually observed with a noninteractive approach. Interactively fitting a GMM to heat pain threshold data acquired from human volunteers revealed a distribution pattern with four Gaussian modes located at temperatures of 32.3, 37.2, 41.4, and 45.4 °C. Noninteractive fitting was unable to identify a meaningful data structure. Obtained results are compatible with known activity temperatures of different TRP ion channels suggesting the mechanistic contribution of different heat sensors to the perception of thermal pain. Thus, sophisticated analysis of the modal structure of biomedical data provides a basis for the mechanistic interpretation of the observations. As it may reflect the involvement of different TRP thermosensory ion channels, the analysis provides a starting point for hypothesis-driven laboratory experiments.     

Local acceptance of renewable energy—A case study from southeast Germany

The European 20–20–20 goals, as well as national targets for the next decade, require a substantial increase in installed renewable capacity in Germany. While public support for such measures is high on an abstract level, the situation in the local context is often very different. Here, the impact of renewable energy might cause resistance. Empirical research shows that a community ownership model can have a positive effect on local acceptance. Our study explores whether such an effect can also be demonstrated in a community co-ownership model. The question is relevant since larger projects exceed the financial possibilities of most communities, leaving them with only co-ownership as an option. The research design is based on a comparative case study, utilizing a questionnaire-based survey. The results of the survey clearly show that a significant difference in local acceptance exists between the two cases. The residents of Zschadraß, where a community co-ownership model exists, are consistently more positive towards local renewable energy and also towards renewable energy in general. The results provide evidence that the co-ownership model is a means to reconcile local acceptance with an increased use of renewable energy in Germany.     

Somatoform dissociative symptoms as related to animal defensive reactions to predatory imminence and injury.

The authors hypothesized that there would be a similarity between animal defensive responses to variable predatory imminence and injury and certain somatoform dissociative symptoms of trauma-reporting patients who have dissociative disorder. As a first test of this hypothesis, 12 somatoform symptom clusters consisting of clinically observed somatoform dissociative phenomena were constructed. All clusters discriminated between patients with dissociative disorders (n?=?50) and patients with other psychiatric diagnoses (n?=?50). Those expressive of the hypothesized similarity—freezing, anesthesia-analgesia, and disturbed eating—belonged to the 5 most characteristic symptoms of dissociative disorder patients. Anesthesia-analgesia, urogenital pain, and freezing symptom clusters independently contributed to predicted presence of dissociative disorder. Using an independent sample, it appeared that anesthesia-analgesia best predicted presence of dissociative disorder after controlling for symptom severity. The results were largely consistent with the hypothesized similarity. (PsycINFO Database Record (c) 2010 APA, all rights reserved)