984 results
Search Results
Now showing 1 - 10 of 984
- ItemClassification and clustering: models, software and applications(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Mucha, Hans-Joachim; Ritter, GunterWe are pleased to present the report on the 30th Fall Meeting of the working group ``Data Analysis and Numerical Classification'' (AG-DANK) of the German Classification Society. The meeting took place at the Weierstrass Institute for Applied Analysis and Stochastics (WIAS), Berlin, from Friday Nov. 14 till Saturday Nov. 15, 2008. Already 12 years ago, WIAS had hosted a traditional Fall Meeting with special focus on classification and multivariate graphics (Mucha and Bock, 1996). This time, the special topics were stability of clustering and classification, mixture decomposition, visualization, and statistical software.
- ItemOptimal and robust a posteriori error estimates in L∞(L2) for the approximation of Allen-Cahn equations past singularities(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Bartels, Sören; Müller, RüdigerOptimal a posteriori error estimates in L∞(L2) are derived for the finite element approximation of Allen-Cahn equations. The estimates depend on the inverse of a small parameter only in a low order polynomial and are valid past topological changes of the evolving interface. The error analysis employs an elliptic reconstruction of the approximate solution and applies to a large class of conforming, nonconforming, mixed, and discontinuous Galerkin methods. Numerical experiments illustrate the theoretical results.
- ItemImpact of slippage on the morphology and stability of a dewetting rim(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Münch, Andreas; Wagner, BarbaraIn this study lubrication theory is used to describe the stability and morphology of the rim that forms as a thin polymer film dewets from a hydrophobized silicon wafer. Thin film equations are derived from the governing hydrodynamic equations for the polymer to enable the systematic mathematical and numerical analysis of the properties of the solutions for different regimes of slippage and for a range of time scales. Dewetting rates and the cross sectional profiles of the evolving rims are derived for these models and compared to experimental results. Experiments also show that the rim is typically unstable in the spanwise direction and develops thicker and thinner parts that may grow into ``fingers''. Linear stability analysis as well as nonlinear numerical solutions are presented to investigate shape and growth rate of the rim instability. It is demonstrated that the difference in morphology and the rate at which the instability develops can be directly attributed to the magnitude of slippage. Finally, a derivation is given for the dominant wavelength of the bulges along the unstable rim.
- ItemError control for the approximation of Allen-Cahn and Cahn-Hilliard equations with a logarithmic potential(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Bartels, Sören; Müller, RüdigerA fully computable upper bound for the finite element approximation error of Allen-Cahn and Cahn-Hilliard equations with logarithmic potentials is derived. Numerical experiments show that for the sharp interface limit this bound is robust past topological changes. Modifications of the abstract results to derive quasi-optimal error estimates in different norms for lowest order finite element methods are discussed and lead to weaker conditions on the residuals under which the conditional error estimates hold.
- ItemAnisotropic growth of random surfaces in 2 + 1 dimensions(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Borodin, Alexei; Ferrari, Patrik L.We construct a family of stochastic growth models in $2+1$ dimensions, that belong to the anisotropic KPZ class. Appropriate projections of these models yield $1+1$ dimensional growth models in the KPZ class and random tiling models. We show that correlation functions associated to our models have determinantal structure, and we study large time asymptotics for one of the models. The main asymptotic results are: (1) The growing surface has a limit shape that consists of facets interpolated by a curved piece. (2) The one-point fluctuations of the height function in the curved part are asymptotically normal with variance of order $ln(t)$ for time $tgg 1$. (3) There is a map of the $(2+1)$-dimensional space-time to the upper half-plane $H$ such that on space-like submanifolds the multi-point fluctuations of the height function are asymptotically equal to those of the pullback of the Gaussian free (massless) field on $H$.
- ItemModeling and simulations of beam stabilization in edge-emitting broad area semiconductor devices(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Radziunas, Mindaugas; Cˇ iegis, RaimondasA 2+1 dimensional PDE traveling wave model describing spatial-lateral dynamics of edge-emitting broad area semiconductor devices is considered. A numerical scheme based on a split-step Fourier method is presented and implemented on a parallel compute cluster. Simulations of the model equations are used for optimizing of existing devices with respect to the emitted beam quality, as well as for creating and testing of novel device design concepts
- ItemMoment asymptotics for branching random walks in random environment(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Gün, Onur; König, Wolfgang; Sekulov´c, OzrenWe consider the long-time behaviour of a branching random walk in random environment on the lattice Zd. The migration of particles proceeds according to simple random walk in continuous time, while the medium is given as a random potential of spatially dependent killing/branching rates. The main objects of our interest are the annealed moments m_np , i.e., the p-th moments over the medium of the n-th moment over the migration and killing/branching, of the local and global population sizes. For n = 1, this is well-understood citeGM98, as m_1 is closely connected with the parabolic Anderson model. For some special distributions, citeA00 extended this to ngeq2, but only as to the first term of the asymptotics, using (a recursive version of) a Feynman-Kac formula for m_n. In this work we derive also the second term of the asymptotics, for a much larger class of distributions. In particular, we show that m_n^p m_1^np are asymptotically equal, up to an error e^o(t). The cornerstone of our method is a direct Feynman-Kac-type formula for mn, which we establish using the spine techniques developed in citeHR1.1
- ItemBistability and hysteresis in an optically injected two-section semiconductor laser(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Pimenov, Alexander; Viktorov, Evgeniy A.; Hegarty, Stephen P.; Habruseva, Tatiana; Huyet, Guillaume; Rachinskii, Dmitrii; Vladimirov, Andrei G.The effect of coherent single frequency injection on two-section semiconductor lasers is studied numerically using a model based on a set of delay differential equations. The existence of bistability between different CW and non-stationary regimes of operation is demonstrated in the case of sufficiently large linewidth enhancement factors.
- ItemOn multivariate chi-square distributions and their applications in testing multiple hypotheses(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Dickhaus, Thorsten; Royen, ThomasWe are considered with three different types of multivariate chi-square distributions. Their members play important roles as limiting distributions of vectors of test statistics in several applications of multiple hypotheses testing. We explain these applications and provide formulas for computing multiplicity-adjusted p-values under the respective global hypothesis.
- ItemParameter estimation in time series analysis(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Spokoiny, VladimirThe paper offers a novel unified approach to studying the accuracy of parameter estimation for a time series. Important features of the approach are: (1) The underlying model is not assumed to be parametric. (2) The imposed conditions on the model are very mild and can be easily checked in specific applications. (3) The considered time series need not to be ergodic or stationary. The approach is equally applicable to ergodic, unit root and explosive cases. (4) The parameter set can be unbounded and non-compact. (5) No conditions on parameter identifiability are required. (6) The established risk bounds are nonasymptotic and valid for large, moderate and small samples. (7) The results describe confidence and concentration sets rather than the accuracy of point estimation. The whole approach can be viewed as complementary to the classical one based on the asymptotic expansion of the log-likelihood. In particular, it claims a consistency of the considered estimate in a rather general sense, which usually is assumed to be fulfilled in the asymptotic analysis. In standard situations under ergodicity conditions, the usual rate results can be easily obtained as corollaries from the established risk bounds. The approach and the results are illustrated on a number of popular time series models including autoregressive, Generalized Linear time series, ARCH and GARCH models and meadian/quantile regression.