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The main goal of this work is to examine various aspects of `inelastic continuum mechanics': first, fundamental aspects of a general finite deformation theory based on a multiplicative decomposition of the deformation gradient with special emphasis on the incompatibility of the so-called intermediate configuration are discussed in detail. Moreover, various balance of linear momentum representations together with the corresponding volume forces are derived in a configurational mechanics context. Subsequent chapters are consequently based on these elaborations so that the applied multiplicative decomposition generally serves as a fundamental modelling concept in this work; after generalised strain measures are introduced, a kinematic hardening model coupled with anisotropic damage, a substructure evolution framework as well as two different growth and remodelling formulations for biological tissues are presented.
Modelling languages are important in the process of software development. The suitability of a modelling language for a project depends on its applicability to the target domain. Here, domain-specific languages have an advantage over more general modelling languages. On the other hand, modelling languages like the Unified Modeling Language can be used in a wide range of domains, which supports the reuse of development knowledge between projects. This thesis treats the syntactical and semantical harmonisation of modelling languages and their combined use, and the handling of complexity of modelling languages by providing language subsets - called language profiles - with tailor-made formal semantics definitions, generated by a profile tool. We focus on the widely-used modelling languages SDL and UML, and formal semantics definitions specified using Abstract State Machines.
In this article, we present an analytic solution for Jiang's constitutive model of elastoplasticity. It is considered in its stress controlled form for proportional stress loading under the assumptions that the one-to-one coupling of the yield surface radius and the memory surface radius is switched off, that the transient hardening is neglected and that the ratchetting exponents are constant.
In the theoretical part of this thesis, the difference of the solutions of the elastic and the elastoplastic boundary value problem is analysed, both for linear kinematic and combined linear kinematic and isotropic hardening material. We consider both models in their quasistatic, rate-independent formulation with linearised geometry. The main result of the thesis is, that the differences of the physical obervables (the stresses, strains and displacements) can be expressed as composition of some linear operators and play operators with respect to the exterior forces. Explicit homotopies between both solutions are presented. The main analytical devices are Lipschitz estimates for the stop and the play operator. We present some generalisations of the standard estimates. They allow different input functions, different initial memories and different scalar products. Thereby, the underlying time involving function spaces are the Sobolov spaces of first order with arbitrary integrability exponent between one and infinity. The main results can easily be generalised for the class of continuous functions with bounded total variation. In the practical part of this work, a method to correct the elastic stress tensor over a long time interval at some chosen points of the body is presented and analysed. In contrast to widespread uniaxial corrections (Neuber or ESED), our method takes multiaxiality phenomena like cyclic hardening/softening, ratchetting and non-masing behaviour into account using Jiang's model of elastoplasticity. It can be easily adapted to other constitutive elastoplastic material laws. The theory for our correction model is developped for linear kinematic hardening material, for which error estimated are derived. Our numerical algorithm is very fast and designed for the case that the elastic stress is piecewise linear. The results for the stresses can be significantly improved with Seeger's empirical strain constraint. For the improved model, a simple predictor-correcor algorithm for smooth input loading is established.
We derive some asymptotics for a new approach to curve estimation proposed by Mr'{a}zek et al. cite{MWB06} which combines localization and regularization. This methodology has been considered as the basis of a unified framework covering various different smoothing methods in the analogous two-dimensional problem of image denoising. As a first step for understanding this approach theoretically, we restrict our discussion here to the least-squares distance where we have explicit formulas for the function estimates and where we can derive a rather complete asymptotic theory from known results for the Priestley-Chao curve estimate. In this paper, we consider only the case where the bias dominates the mean-square error. Other situations are dealt with in subsequent papers.
The present work deals with the (global and local) modeling of the windfield on the real topography of Rheinland-Pfalz. Thereby the focus is on the construction of a vectorial windfield from low, irregularly distributed data given on a topographical surface. The developed spline procedure works by means of vectorial (homogeneous, harmonic) polynomials (outer harmonics) which control the oscillation behaviour of the spline interpoland. In the process the characteristic of the spline curvature which defines the energy norm is assumed to be on a sphere inside the Earth interior and not on the Earth’s surface. The numerical advantage of this method arises from the maximum-minimum principle for harmonic functions.
Annual Report 2006
(2007)
Annual Report, Jahrbuch AG Magnetismus
In this paper we consider a CHARME Model, a class of generalized mixture of nonlinear nonparametric AR-ARCH time series. We apply the theory of Markov models to derive asymptotic stability of this model. Indeed, the goal is to provide some sets of conditions under which our model is geometric ergodic and therefore satisfies some mixing conditions. This result can be considered as the basis toward an asymptotic theory for our model.
Given an undirected connected network and a weight function finding a basis of the cut space with minimum sum of the cut weights is termed Minimum Cut Basis Problem. This problem can be solved, e.g., by the algorithm of Gomory and Hu [GH61]. If, however, fundamentality is required, i.e., the basis is induced by a spanning tree T in G, the problem becomes NP-hard. Theoretical and numerical results on that topic can be found in Bunke et al. [BHMM07] and in Bunke [Bun06]. In the following we present heuristics with complexity O(m log n) and O(mn), where n and m are the numbers of vertices and edges respectively, which obtain upper bounds on the aforementioned problem and in several cases outperform the heuristics of Schwahn [Sch05].
Abstraction is intensively used in the verification of large, complex or infinite-state systems. With abstractions getting more complex it is often difficult to see whether they are valid. However, for using abstraction in model checking it has to be ensured that properties are preserved. In this paper, we use a translation validation approach to verify property preservation of system abstractions. We formulate a correctness criterion based on simulation between concrete and abstract system for a property to be verified. For each distinct run of the abstraction procedure the correctness is verified in the theorem prover Isabelle/HOL. This technique is applied in the verification of embedded adaptive systems. This paper is an extended version a previously published work.
Elastomeric and other rubber-like materials are often simultaneously exposed to short- and long-time loads within engineering applications. When aiming at establishing a general simulation tool for viscoelastic media over these different time scales, a suitable material model and its corresponding material parameters can only be determined if an appropriate number of experimental data is taken into account. In this work an algorithm for the identification of material parameters for large strain viscoelasticity is presented. Thereby, data of multiple experiments are considered. Based on this method the experimental loading intervals for long-time experiments can be shortened in time and the parameter identification procedure is now referred to experimental data of tests under short- and long-time loads without separating the parameters due to these different time scales. The employed viscoelastic material law is based on a nonlinear evolution law and valid far from thermodynamic equilibrium. The identification is carried out by minimizing a least squares functional comparing inhomogeneous displacement fields from experiments and FEM simulations at given (measured) force loads. Within this optimization procedure all material parameters are identified simultaneously by means of a gradient based method for which a semi-analytical sensitivity analysis is calculated. Representative numerical examples are referred to measured data for different polyurethanes. In order to show the general applicability of the identification method for multiple tests, in the last part of this work the parameter identification for small strain plasticity is presented. Thereby three similar test programs on three specimen of the aluminum alloy AlSi9Cu3 are analyzed, and the parameter sets for the respective individual identifications, and for the combination of all tests in one identification, is compared.
The IEEE 802.11 networks have a tremendous growth in the last years, but also now there is a rapid development of the wireless LAN technologies. High transmission rates, simple deployment and especially low costs make this network technology an efficient and cheap way to get access to the Internet. Fon is the world-wide greatest WIFI community and in January 2007 this community offers more than 11.000 access points in Germany and nearly 55.000 all over the world. However, this technology has also his shady sides. For example, it is possible for everyone to receive data from the wireless medium. So a protection against this open data traffic is a encryption mechanism called Wired Equivalent Privacy (WEP). The tragic end of theWired Equivalent Privacy (WEP) and the simplicity of various Denial-of-Service (DoS) attacks on the wireless medium have resulted in giving up the security at the logical-link layer and shifting it to upper layers (or in the best case leaving it within virtual private networks (VPNs)). Nevertheless, there is an enormous growth in using public access to the Internet via HotSpots in cafés, libraries, schools or at airports, train stops etc. Therefore, it is important for the Wireless Internet Service Provider (WISP) to make sure that anyone with a usual wireless device can connect to their access points. Offering this service to anybody makes giving a sufficient level of security very difficult. On the one hand it should be easy for everyone to use this access, on the other hand there is, in most cases, no security. A businessman is not very pleased about phishing his account data for a great enterprise or for his online office like the KIS at the University of Technology in Kaiserslautern. In most cases the WISPs use a simple web based authentication mechanism. By connecting to the WISPs services, the user is redirected to a webpage requesting his login data or credit card information. Therefore the user only needs a wireless LAN device and a webbrowser to authenticate. An attacker could sniff on the wireless medium to phish delicate data from a legal connected user or use DoS attacks as initial point for various other attacks. In most cases, this can be done with no or only small effort. On the other side, in some cases, the WISP has to do a hard reset on his wireless devices after a DoS attack. Therefore an analysis of access points is done in this work. So, the first part is to show how "‘new"’ access points react to flooding attacks and what mechanisms are used to protect them. The second part implements an attack using an anomaly of some access points that are discovered in the first part. And the last chapter deals with some information about using an Intrusion Detection System (IDS) to protect the devices against such attacks.
In this article a new data-adaptive method for smoothing of bivariate functions is developed. The smoothing is done by kernel regression with rotational invariant bivariate kernels. Two or three local bandwidth parameters are chosen automatically by a two-step plug-in approach. The algorithm starts with small global bandwidth parameters, which adapt during a few iterations to the noisy image. In the next step local bandwidths are estimated. Some general asymptotic results about Gasser-Müller-estimators and optimal bandwidth selection are given. The derived local bandwidth estimators converge and are asymptotically normal.
Embedded systems have become ubiquitous in everyday life, and especially in the automotive industry. New applications challenge their design by introducing a new class of problems that are based on a detailed analysis of the environmental situation. Situation analysis systems rely on models and algorithms of the domain of computational geometry. The basic model is usually an Euclidean plane, which contains polygons to represent the objects of the environment. Usual implementations of computational geometry algorithms cannot be directly used for safety-critical systems. First, a strict analysis of their correctness is indispensable and second, nonfunctional requirements with respect to the limited resources must be considered. This thesis proposes a layered approach to a polygon-processing system. On top of rational numbers, a geometry kernel is formalised at first. Subsequently, geometric primitives form a second layer of abstraction that is used for plane sweep and polygon algorithms. These layers do not only divide the whole system into manageable parts but make it possible to model problems and reason about them at the appropriate level of abstraction. This structure is used for the verification as well as the implementation of the developed polygon-processing library.
On the Complexity of the Uncapacitated Single Allocation p-Hub Median Problem with Equal Weights
(2007)
The Super-Peer Selection Problem is an optimization problem in network topology construction. It may be cast as a special case of a Hub Location Problem, more exactly an Uncapacitated Single Allocation p-Hub Median Problem with equal weights. We show that this problem is still NP-hard by reduction from Max Clique.
In this thesis, the quasi-static Biot poroelasticity system in bounded multilayered domains in one and three dimensions is studied. In more detail, in the one-dimensional case, a finite volume discretization for the Biot system with discontinuous coefficients is derived. The discretization results in a difference scheme with harmonic averaging of the coefficients. Detailed theoretical analysis of the obtained discrete model is performed. Error estimates, which establish convergence rates for both primary as well as flux unknowns are derived. Besides, modified and more accurate discretizations, which can be applied when the interface position coincides with a grid node, are obtained. These discretizations yield second order convergence of the fluxes of the problem. Finally, the solver for the solution of the produced system of linear equations is developed and extensively tested. A number of numerical experiments, which confirm the theoretical considerations are performed. In the three-dimensional case, the finite volume discretization of the system involves construction of special interpolating polynomials in the dual volumes. These polynomials are derived so that they satisfy the same continuity conditions across the interface, as the original system of PDEs. This technique allows to obtain such a difference scheme, which provides accurate computation of the primary as well as of the flux unknowns, including the points adjacent to the interface. Numerical experiments, based on the obtained discretization, show second order convergence for auxiliary problems with known analytical solutions. A multigrid solver, which incorporates the features of the discrete model, is developed in order to solve efficiently the linear system, produced by the finite volume discretization of the three-dimensional problem. The crucial point is to derive problem-dependent restriction and prolongation operators. Such operators are a well-known remedy for the scalar PDEs with discontinuous coefficients. Here, these operators are derived for the system of PDEs, taking into account interdependence of different unknowns within the system. In the derivation, the interpolating polynomials from the finite volume discretization are employed again, linking thus the discretization and the solution processes. The developed multigrid solver is tested on several model problems. Numerical experiments show that, due to the proper problem-dependent intergrid transfer, the multigrid solver is robust with respect to the discontinuities of the coefficients of the system. In the end, the poroelasticity system with discontinuous coefficients is used to model a real problem. The Biot model, describing this problem, is treated numerically, i.e., discretized by the developed finite volume techniques and then solved by the constructed multigrid solver. Physical characteristics of the process, such as displacement of the skeleton, pressure of the fluid, components of the stress tensor, are calculated and then presented at certain cross-sections.
Haustoria of the rust fungus pathogen Uromyces fabae deliver RTP1 (Rust Transferred Protein1) into host plant cells. In this work, different heterologous expression systems were used to study RTP1 biological function as well as RTP1 transfer mechanism. The first part of this thesis focused on the identification of the subcellular target compartment of RTP1 in plant cells. In this respect we could identify a functional bipartite nuclear localization signal within RTP1. However, stable and transient expression studies of RTP1 in different plant species, including the host plant Vicia faba, interfered with plant cell vitality but did not result in detection of RTP1 protein. These findings led us to propose that RTP1 interferes with plant gene expression. However, the molecular basis of this interference remains unclear. By deletion studies, we could localize the active region of RTP1 within a 45 amino acid central domain. In the second part of this study, two different lines of approaches were taken to study RTP1 transfer mechanism. First, transient expression of secreted RTP1 (sRTP1) also interfered with plant cell vitality. Addition of an endoplasmic reticulum retention signal abolished sRTP1 interference with plant cell vitality, suggesting that RTP1 can reenter the plant cell from the apoplast after secretion in the absence of the pathogen. We have identified a PEST-like region within RTP1, however, contribution of this region to the stability of RTP1 is not clear. Site directed mutagenesis analysis showed that the PEST-like region is likely to play a role during the transfer of RTP1 through plant plasma membrane. In the second line of approach, we established a recombinant delivery model, using Ustilago maydis/Zea mays pathosystem, to pursue RTP1 translocation into the plant cell. Our results indicate that U. maydis is capable of secreting high amounts of recombinant RTP1, showing similar glycosylation pattern as RTP1 secreted from rust haustoria. Our data propose the use of this model system to study RTP1 domains mediating its entry into the plant cell. Haustoria of the rust fungus pathogen Uromyces fabae deliver RTP1 (Rust Transferred Protein1) into host plant cells. In this work, different heterologous expression systems were used to study RTP1 biological function as well as RTP1 transfer mechanism. The first part of this thesis focused on the identification of the subcellular target compartment of RTP1 in plant cells. In this respect we could identify a functional bipartite nuclear localization signal within RTP1. However, stable and transient expression studies of RTP1 in different plant species, including the host plant Vicia faba, interfered with plant cell vitality but did not result in detection of RTP1 protein. These findings led us to propose that RTP1 interferes with plant gene expression. However, the molecular basis of this interference remains unclear. By deletion studies, we could localize the active region of RTP1 within a 45 amino acid central domain. In the second part of this study, two different lines of approaches were taken to study RTP1 transfer mechanism. First, transient expression of secreted RTP1 (sRTP1) also interfered with plant cell vitality. Addition of an endoplasmic reticulum retention signal abolished sRTP1 interference with plant cell vitality, suggesting that RTP1 can reenter the plant cell from the apoplast after secretion in the absence of the pathogen. We have identified a PEST-like region within RTP1, however, contribution of this region to the stability of RTP1 is not clear. Site directed mutagenesis analysis showed that the PEST-like region is likely to play a role during the transfer of RTP1 through plant plasma membrane. In the second line of approach, we established a recombinant delivery model, using Ustilago maydis/Zea mays pathosystem, to pursue RTP1 translocation into the plant cell. Our results indicate that U. maydis is capable of secreting high amounts of recombinant RTP1, showing similar glycosylation pattern as RTP1 secreted from rust haustoria. Our data propose the use of this model system to study RTP1 domains mediating its entry into the plant cell.
In the present work the modelling and numerical treatment of discontinuities in thermo-mechanical solids is investigated and applied to diverse physical problems. From this topic a structure for this work results, which considers the formulation of thermo-mechanical processes in continua in the first part and which forms the mechanical and thermodynamical framework for the description of discontinuities and interfaces, that is performed in the second part. The representation of the modelling of solid materials bases on the detailed derivation of geometrically nonlinear kinematics, that yields different strain and stress measures for the material and spatial configuration. Accordingly, this results in different formulations of the mechanical and thermodynamical balance equations. On these foundations we firstly derive by means of the concepts of the plasticity theory an elasto-plastic prototype-model, that is extended subsequently. In the centre of interest is the formulation of damage models in consideration of rate-dependent material behaviour. In the next step follows the extension of the isothermal material models to thermo-mechanically coupled problems, whereby also the special case of adiabatic processes is discussed. Within the representation of the different constitutive laws, the importance is attached to their modular structure. Moreover, a detailed discussion of the isothermal and the thermo-mechanically coupled problem with respect to their numerical treatment is performed. For this purpose the weak forms with respect to the different configurations and the corresponding linearizations are derived and discretized. The derived material models are highlighted by numerical examples and also proved with respect to plausibility. In order to take discontinuities into account appropriate kinematics are introduced and the mechanical and thermodynamical balance equations have to be modified correspondingly. The numerical description is accomplished by so-called interface-elements, which are based on an adequate discretization. In this context two application fields are distinguished. On the one side the interface elements provide a tool for the description of postcritical processes in the framework of localization problems, which include material separation and therefore they are appropriate for the description of cutting processes. Here in turn one has to make the difference between the domain-dependent and the domain-independent formulation, which mainly differ in the definition of the interfacial strain measure. On the other side material properties are attached to the interfaces whereas the spatial extension is neglectable. A typical application of this type of discontinuities can be found in the scope of the modelling of composites, for instance. In both applications the corresponding thermo-mechanical formulations are derived. Finally, the different interface formulations are highlighted by some numerical examples and they are also proved with respect to plausibility.
The main aim of this work was to obtain an approximate solution of the seismic traveltime tomography problems with the help of splines based on reproducing kernel Sobolev spaces. In order to be able to apply the spline approximation concept to surface wave as well as to body wave tomography problems, the spherical spline approximation concept was extended for the case where the domain of the function to be approximated is an arbitrary compact set in R^n and a finite number of discontinuity points is allowed. We present applications of such spline method to seismic surface wave as well as body wave tomography, and discuss the theoretical and numerical aspects of such applications. Moreover, we run numerous numerical tests that justify the theoretical considerations.