Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems II: Strongly monotone quasi-Newtonian flows

In this article, we develop the a priori and a posteriori error analysis of hp-version interior penalty discontinuous Galerkin finite element methods for strongly monotone quasi-Newtonian fluid flows in a bounded Lipschitz domain Ω ⊂ ℝd, d = 2, 3. In the latter case, computable upper and lower bounds on the error are derived in terms of a natural energy norm, which are explicit in the local mesh size and local polynomial degree of the approximating finite element method. A series of numerical experiments illustrate the performance of the proposed a posteriori error indicators within an automatic hp-adaptive refinement algorithm.

Scheduling of continuous and discontinuous material flows with intermediate storage restrictions

This paper deals with scheduling batch (i.e., discontinuous), continuous, and semicontinuous production in process industries (e.g., chemical, pharmaceutical, or metal casting industries) where intermediate storage facilities and renewable resources (processing units and manpower) of limited capacity have to be observed. First, different storage configurations typical of process industries are discussed. Second, a basic scheduling problem covering the three above production modes is presented. Third, (exact and truncated) branch-and-bound methods for the basic scheduling problem and the special case of batch scheduling are proposed and subjected to an experimental performance analysis. The solution approach presented is flexible and in principle simple, and it can (approximately) solve relatively large problem instances with sufficient accuracy.

Stacking of discontinuous regional palaeoclimate records: Chironomid-based summer temperatures from the Alpine region

Since multi-site reconstructions are less affected by site-specific climatic effects and artefacts, regional palaeotemperature reconstructions based on a number of sites can provide more robust estimates of centennial- to millennial-scale temperature trends than individual, site-specific records. Furthermore, reconstructions based on multiple records are necessary for developing continuous climate records over time scales longer than covered by individual sequences. Here, we present a procedure for developing such reconstructions based on relatively short (centuries to millennia), discontinuously sampled records as are typically developed when using biotic proxies in lake sediments for temperature reconstruction. The approach includes an altitudinal correction of temperatures, an interpolation of individual records to equal time intervals, a stacking procedure for sections of the interval of interest that have the same records available, as well as a splicing procedure to link the individual stacked records into a continuous reconstruction. Variations in the final, stacked and spliced reconstruction are driven by variations in the individual records, whereas the absolute temperature values are determined by the stacked segment based on the largest number of records. With numerical simulations based on the NGRIP δ18O record, we demonstrate that the interpolation and stacking procedure provides an approximation of a smoothed palaeoclimate record if based on a sufficient number of discontinuously sampled records. Finally, we provide an example of a stacked and spliced palaeotemperature reconstruction 15000–90 calibrated 14C yr BP based on six chironomid records from the northern and central Swiss Alps and eastern France to discuss the potential and limitations of this approach.

A total variation discontinuous Galerkin approach for image restoration

The focal point of this paper is to propose and analyze a P 0 discontinuous Galerkin (DG) formulation for image denoising. The scheme is based on a total variation approach which has been applied successfully in previous papers on image processing. The main idea of the new scheme is to model the restoration process in terms of a discrete energy minimization problem and to derive a corresponding DG variational formulation. Furthermore, we will prove that the method exhibits a unique solution and that a natural maximum principle holds. In addition, a number of examples illustrate the effectiveness of the method.

Computational Comparison of Continuous and Discontinuous Galerkin Time-Stepping Methods for Nonlinear Initial Value Problems

This article centers on the computational performance of the continuous and discontinuous Galerkin time stepping schemes for general first-order initial value problems in R n , with continuous nonlinearities. We briefly review a recent existence result for discrete solutions from [6], and provide a numerical comparison of the two time discretization methods.

Meningial perineurioma: a benign peripheral nerve sheath tumor in a previously unrecognized central nervous system location, mimicking meningioma

Perineurioma is an uncommon, mostly benign, spindle-cell tumor of peripheral nerve sheath origin with a predilection for the soft tissues. Although increasing awareness points to the sites of involvement by perineurioma possibly being as ubiquitous as those frequented by schwannian tumors, only one intracerebral example has been described to date. We report on a surgically resected perineurioma of the falx cerebri in an 86-year-old woman. Preoperative imaging showed an enhancing extraaxial mass of 6 cm × 5.7 cm × 3.7 cm. Histologically, the tumor consisted of a proliferation of spindle cells interwoven by a lattice of basal lamina. Alongside a prevailing soft tissue perineurioma pattern, sclerosing and reticular areas were seen as well. Tumor cells coexpressed EMA and GLUT-1, and a minority immunoreacted for smooth muscle actin. Pericellular basal lamina was decorated with collagen type IV. No staining for S100 protein was detected. Mitotic activity was virtually absent, and the MIB1 labeling index averaged 2%. Ultrastructural examination revealed abundant pinocytotic vesicles within and conspicuous tight junctions between slender cytoplasmic processes which, in turn, were encased by discontinuous basal lamina. FISH analysis confirmed loss of at least part of one chromosome 22q. This observation calls attention to perineurioma as a novel item in the repertoire of low-grade meningial spindle cell neoplasms, in the differential diagnostic context of which it is apt to being misconstrued as either meningioma, solitary fibrous tumor, or neurofibroma. Confusion with the latter bears the risk of overgrading innocuous features of perineurioma as criteria for malignancy.

Establishment and expansion of Lake Malawi rock fish populations after a dramatic Late Pleistocene lake level rise

Major environmental events that fragment populations among multiple island habitats have potential to drive large-scale episodes of speciation and adaptive radiation. A recent palaeolimnological study of sediment cores indicated that Lake Malawi underwent major climate-driven desiccation events 75 000-135 000 years ago that lowered the water level to at least 580 m below the present state and severely reduced surface area. After this period, lake levels rose and stabilized, creating multiple discontinuous littoral rocky habitats. Here, we present evidence supporting the hypothesis that establishment and expansion of isolated philopatric rock cichlid populations occurred after this rise and stabilization of lake level. We studied the Pseudotropheus (Maylandia) species complex, a group with both allopatric and sympatric populations that differ in male nuptial colour traits and tend to mate assortatively. Using coalescent analyses based on mitochondrial DNA, we found evidence that populations throughout the lake started to expand and accumulate genetic diversity after the lake level rise. Moreover, most haplotypes were geographically restricted, and the greatest genetic similarities were typically among sympatric or neighbouring populations. This is indicative of limited dispersal and establishment of assortative mating among populations following the lake level rise. Together, this evidence is compatible with a single large-scale environmental event being central to evolution of spatial patterns of genetic and species diversity in P. (Maylandia) and perhaps other Lake Malawi rock cichlids. Equivalent climate-driven pulses of habitat formation and fragmentation may similarly have contributed to observed rapid and punctuated cladogenesis in other adaptive radiations.

Spatio-temporal dynamics of alpha brain electric fields, and cognitive modes

Brian electric activity is viewed as sequences of momentary maps of potential distribution. Frequency-domain source modeling, estimation of the complexity of the trajectory of the mapped brain field distributions in state space, and microstate parsing were used as analysis tools. Input-presentation as well as task-free (spontaneous thought) data collection paradigms were employed. We found: Alpha EEG field strength is more affected by visualizing mentation than by abstract mentation, both input-driven as well as self-generated. There are different neuronal populations and brain locations of the electric generators for different temporal frequencies of the brain field. Different alpha frequencies execute different brain functions as revealed by canonical correlations with mentation profiles. Different modes of mentation engage the same temporal frequencies at different brain locations. The basic structure of alpha electric fields implies inhomogeneity over time — alpha consists of concatenated global microstates in the sub-second range, characterized by quasi-stable field topographies, and rapid transitions between the microstates. In general, brain activity is strongly discontinuous, indicating that parsing into field landscape-defined microstates is appropriate. Different modes of spontaneous and induced mentation are associated with different brain electric microstates; these are proposed as candidates for psychophysiological ``atoms of thought''.