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- 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.
- ItemOptimal elliptic Sobolev regularity near three-dimensional, multi-material Neumann vertices(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Haller-Dintelmann, Robert; Höppner, Wolfgang; Kaiser, Hans-Christoph; Rehberg, Joachim; Ziegler, Günter M.We study relative stability properties of different clusters of closely packed one- and two-dimensional localized peaks of the Swift-Hohenberg equation. We demonstrate the existence of a 'spatial Maxwell' point where clusters are almost equally stable, irrespective of the number of pes involved. Above (below) the Maxwell point, clusters become more (less) stable with the increase of the number of peaks
- ItemError bounds: necessary and sufficient conditions(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Fabian, Marian J.; Henrion, Ren´e; Kruger, Alexander Y.; Outrata, Jiˇr´ıThe paper presents a general classification scheme of necessary and sufficient criteria for the error bound property incorporating the existing conditions. Several derivative-like objects both from the primal as well as from the dual space are used to characterize the error bound property of extended-real-valued functions on a Banach space.
- ItemOn a higher order convective Cahn-Hilliard type equation(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Korzec, Maciek Dominik; Rybka, PiotrA convective Cahn-Hilliard type equation of sixth order that describes the faceting of a growing surface is considered with periodic boundary conditions. By using a Galerkin approach the existence of weak solutions to this sixth order partial differential equation is established in $L^2(0,T; dot H^3_per)$. Furthermore stronger regularity results have been derived and these are used to prove uniqueness of the solutions. Additionally a numerical study shows that solutions behave similarly as for the better known convective Cahn-Hilliard equation. The transition from coarsening to roughening is analyzed, indicating that the characteristic length scale decreases logarithmically with increasing deposition rate
- ItemEstimation of the signal subspace without estimation of the inverse covariance matrix(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Panov, Vladimir A.Let a high-dimensional random vector $vecX$ can be represented as a sum of two components - a signal $vecS$, which belongs to some low-dimensional subspace $mathcalS$, and a noise component $vecN$. This paper presents a new approach for estimating the subspace $mathcalS$ based on the ideas of the Non-Gaussian Component Analysis. Our approach avoids the technical difficulties that usually exist in similar methods - it doesn't require neither the estimation of the inverse covariance matrix of $vecX$ nor the estimation of the covariance matrix of $vecN$.
- ItemNon-Gaussian component analysis : new ideas, new proofs, new applications(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Panov, Vladimir A.In this article, we present new ideas concerning Non-Gaussian Component Analysis (NGCA). We use the structural assumption that a high-dimensional random vector $vX$ can be represented as a sum of two components
- ItemASAP : automatic semantics-aware analysis of network payloads(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Krueger, Tammo; Krämer, Nicole; Rieck, KonradAutomatic inspection of network payloads is a prerequisite for effective analysis of network communication. Security research has largely focused on network analysis using protocol specifications, for example for intrusion detection, fuzz testing and forensic analysis. The specification of a protocol alone, however, is often not sufficient for accurate analysis of communication, as it fails to reflect individual semantics of network applications. We propose a framework for semantics-aware analysis of network payloads which automaticylly extracts semantic components from recorded network traffic. Our method proceeds by mapping network payloads to a vector space and identifying semantic templates corresponding to base directions in the vector space. We demonstrate the efficacy of semantics-aware analysis in different security applications: automatic discovery of patterns in honeypot data, analysis of malware communication and network intrusion detection.
- ItemInverse scattering of elastic waves by periodic structures : uniqueness under the third or fourth kind boundary conditions(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Elschner, Johannes; Hu, GuanghuiThe inverse scattering of a time-harmonic elastic wave by a two-dimensional periodic structure in R 2 is investigated. The grating profile is assumed to be a graph given by a piecewise linear function on which the third or fourth kind boundary conditions are satisfied. Via an equivalent variational formulation, existence of quasi-periodic solutions for general Lipschitz grating profiles is proved by applying the Fredholm alternative. However, uniqueness of solution to the direct problem does not hold in general. For the inverse problem, we determine and classify all the unidentifiable grating profiles corresponding to a given incident elastic field, relying on the reflection principle for the Navier equation and the rotational invariance of propagating directions of the total field. Moreover, global uniqueness for the inverse problem is established with a minimal number of incident pressure or shear waves, including the resonance case where a Rayleigh frequency is allowed. The gratings that are unidentifiable by one incident elastic wave provide non-uniqueness examples for appropriately chosen wave number and incident angles
- ItemAn inverse electromagnetic scattering problem for a bi-periodic inhomogeneous layer on a perfectly conducting plate(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Hu, Guanghui; Yang, Jiaqing; Zhang, BoThis paper is concerned with uniqueness for reconstructing a periodic inhomogeneous medium covered on a perfectly conducting plate. We deal with the problem in the frame of time-harmonic Maxwell systems without TE or TM polarization. An orthogonal relation for two refractive indices is obtained, and then inspired by Kirsch's idea, the refractive index can be identified by utilizing the eigenvalues and eigenfunctions of a quasi-periodic Sturm-Liouville eigenvalue problem.