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- ItemSimulation of microwave circuits and laser structures including PML by means of FIT(München : European Geopyhsical Union, 2004) Hebermehl, G.; Schefter, J.; Schlundt, R.; Tischler, Th.; Zscheile, H.; Heinrich, W.Field-oriented methods which describe the physical properties of microwave circuits and optical structures are an indispensable tool to avoid costly and time-consuming redesign cycles. Commonly the electromagnetic characteristics of the structures are described by the scattering matrix which is extracted from the orthogonal decomposition of the electric field. The electric field is the solution of an eigenvalue and a boundary value problem for Maxwell’s equations in the frequency domain. We discretize the equations with staggered orthogonal grids using the Finite Integration Technique (FIT). Maxwellian grid equations are formulated for staggered nonequidistant rectangular grids and for tetrahedral nets with corresponding dual Voronoi cells. The interesting modes of smallest attenuation are found solving a sequence of eigenvalue problems of modified matrices. To reduce the execution time for high-dimensional problems a coarse and a fine grid is used. The calculations are carried out, using two levels of parallelization. The discretized boundary value problem, a large-scale system of linear algebraic equations with different right-hand sides, is solved by a block Krylov subspace method with various preconditioning techniques. Special attention is paid to the Perfectly Matched Layer boundary condition (PML) which causes non physical modes and a significantly increased number of iterations in the iterative methods.
- ItemAdaptive smoothing of digital images: The R package adimpro(Los Angeles, Calif. : UCLA, Dept. of Statistics, 2007) Polzehl, J.; Tabelow, K.Digital imaging has become omnipresent in the past years with a bulk of applications ranging from medical imaging to photography. When pushing the limits of resolution and sensitivity noise has ever been a major issue. However, commonly used non-adaptive filters can do noise reduction at the cost of a reduced effective spatial resolution only. Here we present a new package adimpro for R, which implements the propagationseparation approach by (Polzehl arid Spokoiriy 2006) for smoothing digital images. This method naturally adapts to different structures of different size in the image and thus avoids oversmoothing edges and fine structures. We extend the method for imaging data with spatial correlation. Furthermore we show how the estimation of the dependence between variance and mean value can be included. We illustrate the use of the package through some examples.
- ItemModification of Newton's law of gravity at very large distances(Amsterdam : Elsevier, 2002) Kirillov, A.A.; Turaev, D.We discuss a Modified Field Theory (MOFT) in which the number of fields can vary. It is shown that when the number of fields is conserved MOFT reduces to the standard field theory but interaction constants undergo an additional renormalization and acquire a dependence on spatial scales. In particular, the renormalization of the gravitational constant leads to the deviation of the law of gravity from the Newton's law in some range of scales rmin < r < rmax, in which the gravitational potential shows essentially logarithmic ∼ ln r (instead of 1/r) behavior. In this range, the renormalized value of the gravitational constant G increases and at scales r > rmax acquires a new constant value G′ ∼ Grmax/rmin. From the dynamical standpoint this looks as if every point source is surrounded with a halo of dark matter. It is also shown that if the maximal scale rmax is absent, the homogeneity of the dark matter in the Universe is consistent with a fractal distribution of baryons in space, in which the luminous matter is located on thin two-dimensional surfaces separated by empty regions of ever growing size.
- ItemA propagation-separation approach to estimate the autocorrelation in a time-series(Göttingen : Copernicus, 2008) Divine, D.V.; Polzehl, J.; Godtliebsen, F.The paper presents an approach to estimate parameters of a local stationary AR(1) time series model by maximization of a local likelihood function. The method is based on a propagation-separation procedure that leads to data dependent weights defining the local model. Using free propagation of weights under homogeneity, the method is capable of separating the time series into intervals of approximate local stationarity. Parameters in different regions will be significantly different. Therefore the method also serves as a test for a stationary AR(1) model. The performance of the method is illustrated by applications to both synthetic data and real time-series of reconstructed NAO and ENSO indices and GRIP stable isotopes.
- 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.
- ItemTetGen : a 3D Delaunay tetrahedral mesh generator version 1.2 user's manual(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2002) Si, HangThis technical report describes the main features and the using of TetGen, a 3D Delaunay tetrahedral mesh generator. Based on the most recent developments in mesh generation algorithms, this program has been specifically designed to fulfill the task of automatically generating high quality tetrahedral meshes, which are suitable for scientific computing using numerical methods such as finite element and finite volume methods. In this document, the user will learn how to create 3D tetrahedral meshes using TetGen's input files and command line switches. Various examples were given for better understanding. This document describes the features of the version 1.2.
- ItemModel-based cluster analysis applied to flow cytometry data of phytoplankton(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2002) Mucha, H.-J.; Simon, U.; Brüggemann, R.Starting from well-known model-based clustering models equivalent formulations for some special models based on pairwise distances are presented. Moreover, these models can be generalized in order to taking into account both weights of observations and weights of variables. Well-known cluster analysis techniques like the iterative partitional K-means method or the agglomerative hierarchical Ward method are useful for discovering partitions or hierarchies in the underlying data. Here these methods are generalised in two ways, firstly by using weighted observations and secondly by allowing different volumes of clusters. Then a more general K-means approach based on pair-wise distances is recommended. Simulation studies are carried out in order to compare the new clustering techniques with the well-known ones. Afterwards a successful application in the field of freshwater ecology is presented. As an example, the cluster analysis of a snapshot from monitoring of phytoplankton (algae) is considered in more detail. Indeed, monitoring by microscope is very time- and work-consuming. Flow cytometry provides the opportunity to investigate algae communities in a semiautomatic way. Statistical data analysis and cluster analysis can at least support the investigations. Here a combination of agglomerative hierarchical clustering and iterative clustering is recommended. In order to give some insight into the data under investigation several univariate, bivariate and multivariate visualizations are proposed.
- ItemBenutzer-Handbuch DIPOG-1.4(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2004) Schmidt, GuntherThis is the manual of the software package DIPOG, version 1.4, which can be used to simulate and optimize binary and multilevel optical gratings. The algorithms are based on the finite--element solution of a system of Helmholtz equations, which are equivalent to the timeharmonic electromagnetic field equations, and on gradient methods for solving optimization problems. The package offers several options to postprocess the calculated electromagnetic fields.
- ItemSimulation der Strahlhärtung von Stahl mit WIAS-SHarP(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2002) Buchwalder, A.; Hömberg, D.; Jurke, Th.; Spies, H.-J.; Weiss, W.Die Software WIAS-SHarP zur Simulation der Oberflaechenhaertung von Stahl mit Laser- und Elektronenstrahl wurde im Rahmen eines zweijaehrigen interdisziplinaeren Forschungsprojektes entwickelt. Das zugrunde liegende mathematische Modell besteht aus einem System gewoehnlicher Differentialgleichungen zur Beschreibung der Gefuegeumwandlungen, gekoppelt mit einer nichtlinearen Waermeleitungsgleichung sowie Komponenten zur Beschreibung der Energieeinkopplung. Um eine moeglichst breite Anwendbarkeit der Software zu gewaehrleisten, wurden werkstoffspezifische Kennwerte zum Umwandlungsverhalten fuer eine grosse Anzahl praxisrelevanter Staehle bereitgestellt. Zur Modellverifikation wurden experimentelle Untersuchungen bei beteiligten Industriepartnern durchgefuehrt und mit den entsprechenden Simulationsrechnungen verglichen.
- ItemDIPOG-2.0 : user guide direct problems for optical gratings over triangular grids(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2003) Rathsfeld, A.[no abstract available]