Multilevel Monte Carlo for Random Degenerate Scalar Convection Diffusion Equation

We consider the numerical solution of scalar, nonlinear degenerate convection-diffusion problems with random diffusion coefficient and with random flux functions. Building on recent results on the existence, uniqueness and continuous dependence of weak solutions on data in the deterministic case, we develop a definition of random entropy solution. We establish existence, uniqueness, measurability and integrability results for these random entropy solutions, generalizing \cite{Mishr478,MishSch10a} to possibly degenerate hyperbolic-parabolic problems with random data. We next address the numerical approximation of random entropy solutions, specifically the approximation of the deterministic first and second order statistics. To this end, we consider explicit and implicit time discretization and Finite Difference methods in space, and single as well as Multi-Level Monte-Carlo methods to sample the statistics. We establish convergence rate estimates with respect to the discretization parameters, as well as with respect to the overall work, indicating substantial gains in efficiency are afforded under realistic regularity assumptions by the use of the Multi-Level Monte-Carlo method. Numerical experiments are presented which confirm the theoretical convergence estimates.Comment: 24 Page

Epitaxial lateral overgrowth of a-plane GaN by metalorganic chemical vapor deposition

We report on epitaxial lateral overgrowth (ELO) of (112¯0) a-plane GaN by metalorganic chemical vapor deposition. Different growth rates of Ga- and N-polar wings together with wing tilt create a major obstacle for achieving a smooth, fully coalesced surface in ELOa-plane GaN. To address this issue a two-step growth method was employed to provide a large aspect ratio of height to width in the first growth step followed by enhanced lateral growth in the second by controlling the growth temperature. By this method, the average ratio of Ga- to N-polar wing growth rate has been reduced from 4–6 to 1.5–2, which consequently reduced the wing-tilt induced height difference between the two approaching wings at the coalescence front, thereby making their coalescence much easier. Transmission electron microscopy showed that the threading dislocation density in the wing regions was 1.0×108 cm−2, more than two orders of magnitude lower than that in the window regions (4.2×1010 cm−2). However, a relatively high density of basal stacking faults of 1.2×104 cm−1 was still present in the wing regions as compared to c -plane GaN, where they are rarely observed away from the substrate. Atomic force microscopy(AFM) measurements showed two orders of magnitude higher density of surface pits in the window than in the wing regions, which were considered to be terminated by dislocations (partial ones related to stacking faults and full ones) on the surface. The existence of basal stacking faults was also revealed by AFM measurements on the a-plane ELO sample after wet chemical etching in hot H3PO4∕H2SO4 (1:1). The extensions of Ga-polar wings near the meeting fronts were almost free of stacking faults. The improvement of crystalline quality in the overgrown layer by ELO was also verified by near field scanning optical microscopy and time-resolved photoluminescence measurements; the former showing strongly enhanced luminescence from the wing regions, and the latter indicating longer decay times (0.25 ns) compared to a standard a-plane GaN template (40 ps)

Gemcitabine and carboplatin in intensively pretreated patients with metastatic breast cancer

Background: Patients with metastatic breast cancer (MBC) are increasingly exposed to anthracyclines and taxanes either during treatment of primary breast cancer or during initial therapy of metastatic disease. The combination of gemcitabine and carboplatin was therefore investigated as an anthracycline- and taxane-free treatment option. Patients and Methods: MBC patients previously treated with chemotherapy were enrolled in a multicenter phase II study. Treatment consisted of gemcitabine (1,000 mg/m(2) i.v. on days 1 and 8) and carboplatin (AUC 4 i.v. on day 1) applied every 3 weeks. Results: Thirty-nine patients were recruited, and a total of 207 treatment cycles were applied with a median of 5 cycles per patient. One complete response and 11 partial responses were observed for an overall response rate of 31% (95% CI: 17-48%). Twelve patients (31%) had stable disease. Median time to progression was 5.3 months (95% CI: 2.6-6.7 months) and median overall survival from start of treatment was 13.2 months (95% CI: 8.7-16.7 months). Grade 3/4 hematological toxicity included leukopenia (59%/5%), thrombo-cytopenia (26%/23%) and anemia (10%/0%). Nonhematological toxicity was rarely severe. Conclusion: Combination chemotherapy with gemcitabine and carboplatin is an effective and generally well-tolerated treatment option for intensively pretreated patients with MBC. Due to a considerable incidence of severe thrombocytopenia it would be reasonable to consider starting gemcitabine at the lower dose level of 800 mg/m(2). Copyright (c) 2008 S. Karger AG, Basel

Vidarabin-monophosphate, BCNU, VM26--an in vitro comparative study of active agents in the treatment of malignant human brain tumours.

BCNU (carmustine), VM26 (teniposide) and ARA-A5'P (vidarabin-monophosphate) were compared in their activity against 30 cell lines of primary (N = 21) and metastatic (N = 9) human brain tumours, which were characterized in tissue culture by cytochemical, immunological and cytogenetic criteria. In vivo achievable concentration-time products c X t were correlated with in vitro pharmacokinetic data in order to evaluate in vitro drug sensitivity at relevant exposure doses. A microcytotoxicity assay was employed to screen for drug toxicity in individual tumour cell lines. Following drug exposure and 5 to 8 population doubling times of untreated controls, RNA-synthesis - as a parameter of cell metabolism and proliferation - was determined by incorporation of [5,6-3H]-uridine into cellular RNA (liquid scintillation counting protocol). The cytotoxic effect of each drug on individual cell lines was expressed in terms of a sensitivity index (SI); by these means effects of different drugs on individual tumour cell lines could be compared. Mean sensitivity indices of ARA-A5'P, BCNU and VM26 for primary brain tumour cell lines were 0.59, 0.82 and 0.54. ARA-A5'P and VM26 had almost similar activities against brain tumour cell lines, whereas BCNU was significantly (P less than 0.001) less active. High grade gliomas were less sensitive to all three agents than low grade and infratentorial gliomas. ARA-A5'P was also able to effectively reduce colony formation in brain tumour cell lines. A cross-resistance of ARA-A5'P to either BCNU or VM26 could not be observed. Clearly, ARA-A5'P is an effective drug in treatment of brain tumour cells in vitro

Coulomb correlation effects in zinc monochalcogenides

Electronic structure and band characteristics for zinc monochalcogenides with zinc-blende- and wurtzite-type structures are studied by first-principles density-functional-theory calculations with different approximations. It is shown that the local-density approximation underestimates the band gap and energy splitting between the states at the top of the valence band, misplaces the energy levels of the Zn-3d states, and overestimates the crystal-field-splitting energy. Regardless of the structure type considered, the spin-orbit-coupling energy is found to be overestimated for ZnO and underestimated for ZnS with wurtzite-type structure, and more or less correct for ZnSe and ZnTe with zinc-blende-type structure. The order of the states at the top of the valence band is found to be anomalous for ZnO in both zinc-blende- and wurtzite-type structure, but is normal for the other zinc monochalcogenides considered. It is shown that the Zn-3d electrons and their interference with the O-2p electrons are responsible for the anomalous order. The typical errors in the calculated band gaps and related parameters for ZnO originate from strong Coulomb correlations, which are found to be highly significant for this compound. The LDA+U approach is by and large found to correct the strong correlation of the Zn-3d electrons, and thus to improve the agreement with the experimentally established location of the Zn-3d levels compared with that derived from pure LDA calculations