Models and methods for power monolithic microwave integrated circuits

Computer aided design of Monolithic Microwave Integrated Circuits (MMICs) depends critically on active device models that are accurate, computationally efficient, and easily extracted from measurements or device simulators. Empirical models of active electron devices, which are based on actual device measurements, do not provide a detailed description of the electron device physics. However they are numerically efficient and quite accurate. These characteristics make them very suitable for MMIC design in the framework of commercially available CAD tools. In the empirical model formulation it is very important to separate linear memory effects (parasitic effects) from the nonlinear effects (intrinsic effects). Thus an empirical active device model is generally described by an extrinsic linear part which accounts for the parasitic passive structures connecting the nonlinear intrinsic electron device to the external world. An important task circuit designers deal with is evaluating the ultimate potential of a device for specific applications. In fact once the technology has been selected, the designer would choose the best device for the particular application and the best device for the different blocks composing the overall MMIC. Thus in order to accurately reproducing the behaviour of different-in-size devices, good scalability properties of the model are necessarily required. Another important aspect of empirical modelling of electron devices is the mathematical (or equivalent circuit) description of the nonlinearities inherently associated with the intrinsic device. Once the model has been defined, the proper measurements for the characterization of the device are performed in order to identify the model. Hence, the correct measurement of the device nonlinear characteristics (in the device characterization phase) and their reconstruction (in the identification or even simulation phase) are two of the more important aspects of empirical modelling. This thesis presents an original contribution to nonlinear electron device empirical modelling treating the issues of model scalability and reconstruction of the device nonlinear characteristics. The scalability of an empirical model strictly depends on the scalability of the linear extrinsic parasitic network, which should possibly maintain the link between technological process parameters and the corresponding device electrical response. Since lumped parasitic networks, together with simple linear scaling rules, cannot provide accurate scalable models, either complicate technology-dependent scaling rules or computationally inefficient distributed models are available in literature. This thesis shows how the above mentioned problems can be avoided through the use of commercially available electromagnetic (EM) simulators. They enable the actual device geometry and material stratification, as well as losses in the dielectrics and electrodes, to be taken into account for any given device structure and size, providing an accurate description of the parasitic effects which occur in the device passive structure. It is shown how the electron device behaviour can be described as an equivalent two-port intrinsic nonlinear block connected to a linear distributed four-port passive parasitic network, which is identified by means of the EM simulation of the device layout, allowing for better frequency extrapolation and scalability properties than conventional empirical models. Concerning the issue of the reconstruction of the nonlinear electron device characteristics, a data approximation algorithm has been developed for the exploitation in the framework of empirical table look-up nonlinear models. Such an approach is based on the strong analogy between timedomain signal reconstruction from a set of samples and the continuous approximation of device nonlinear characteristics on the basis of a finite grid of measurements. According to this criterion, nonlinear empirical device modelling can be carried out by using, in the sampled voltage domain, typical methods of the time-domain sampling theory.

Safety factors in sheet pile wall design: considerations by using traditional methods and FEM analysis

The purpose of the work is: define and calculate a factor of collapse related to traditional method to design sheet pile walls. Furthermore, we tried to find the parameters that most influence a finite element model representative of this problem. The text is structured in this way: from chapter 1 to 5, we analyzed a series of arguments which are usefull to understanding the problem, while the considerations mainly related to the purpose of the text are reported in the chapters from 6 to 10. In the first part of the document the following arguments are shown: what is a sheet pile wall, what are the codes to be followed for the design of these structures and what they say, how can be formulated a mathematical model of the soil, some fundamentals of finite element analysis, and finally, what are the traditional methods that support the design of sheet pile walls. In the chapter 6 we performed a parametric analysis, giving an answer to the second part of the purpose of the work. Comparing the results from a laboratory test for a cantilever sheet pile wall in a sandy soil, with those provided by a finite element model of the same problem, we concluded that:in modelling a sandy soil we should pay attention to the value of cohesion that we insert in the model (some programs, like Abaqus, don’t accept a null value for this parameter), friction angle and elastic modulus of the soil, they influence significantly the behavior of the system (structure-soil), others parameters, like the dilatancy angle or the Poisson’s ratio, they don’t seem influence it. The logical path that we followed in the second part of the text is reported here. We analyzed two different structures, the first is able to support an excavation of 4 m, while the second an excavation of 7 m. Both structures are first designed by using the traditional method, then these structures are implemented in a finite element program (Abaqus), and they are pushed to collapse by decreasing the friction angle of the soil. The factor of collapse is the ratio between tangents of the initial friction angle and of the friction angle at collapse. At the end, we performed a more detailed analysis of the first structure, observing that, the value of the factor of collapse is influenced by a wide range of parameters including: the value of the coefficients assumed in the traditional method and by the relative stiffness of the structure-soil system. In the majority of cases, we found that the value of the factor of collapse is between and 1.25 and 2. With some considerations, reported in the text, we can compare the values so far found, with the value of the safety factor proposed by the code (linked to the friction angle of the soil).

Ensemble wind forecasting based on the HARMONIE model and adaptive finite elements in complex orography

[EN]Ensemble forecasting is a methodology to deal with uncertainties in the numerical wind prediction. In this work we propose to apply ensemble methods to the adaptive wind forecasting model presented in. The wind field forecasting is based on a mass-consistent model and a log-linear wind profile using as input data the resulting forecast wind from Harmonie, a Non-Hydrostatic Dynamic model used experimentally at AEMET with promising results. The mass-consistent model parameters are estimated by using genetic algorithms. The mesh is generated using the meccano method and adapted to the geometry…

A new insight in stress recovery tecniques and hessian reconstruction methods

Stress recovery techniques have been an active research topic in the last few years since, in 1987, Zienkiewicz and Zhu proposed a procedure called Superconvergent Patch Recovery (SPR). This procedure is a last-squares fit of stresses at super-convergent points over patches of elements and it leads to enhanced stress fields that can be used for evaluating finite element discretization errors. In subsequent years, numerous improved forms of this procedure have been proposed attempting to add equilibrium constraints to improve its performances. Later, another superconvergent technique, called Recovery by Equilibrium in Patches (REP), has been proposed. In this case the idea is to impose equilibrium in a weak form over patches and solve the resultant equations by a last-square scheme. In recent years another procedure, based on minimization of complementary energy, called Recovery by Compatibility in Patches (RCP) has been proposed in. This procedure, in many ways, can be seen as the dual form of REP as it substantially imposes compatibility in a weak form among a set of self-equilibrated stress fields. In this thesis a new insight in RCP is presented and the procedure is improved aiming at obtaining convergent second order derivatives of the stress resultants. In order to achieve this result, two different strategies and their combination have been tested. The first one is to consider larger patches in the spirit of what proposed in [4] and the second one is to perform a second recovery on the recovered stresses. Some numerical tests in plane stress conditions are presented, showing the effectiveness of these procedures. Afterwards, a new recovery technique called Last Square Displacements (LSD) is introduced. This new procedure is based on last square interpolation of nodal displacements resulting from the finite element solution. In fact, it has been observed that the major part of the error affecting stress resultants is introduced when shape functions are derived in order to obtain strains components from displacements. This procedure shows to be ultraconvergent and is extremely cost effective, as it needs in input only nodal displacements directly coming from finite element solution, avoiding any other post-processing in order to obtain stress resultants using the traditional method. Numerical tests in plane stress conditions are than presented showing that the procedure is ultraconvergent and leads to convergent first and second order derivatives of stress resultants. In the end, transverse stress profiles reconstruction using First-order Shear Deformation Theory for laminated plates and three dimensional equilibrium equations is presented. It can be seen that accuracy of this reconstruction depends on accuracy of first and second derivatives of stress resultants, which is not guaranteed by most of available low order plate finite elements. RCP and LSD procedures are than used to compute convergent first and second order derivatives of stress resultants ensuring convergence of reconstructed transverse shear and normal stress profiles respectively. Numerical tests are presented and discussed showing the effectiveness of both procedures.

Machine learning methods for prediction of disulphide bonding states of cysteine residues in proteins

The goal of this thesis work is to develop a computational method based on machine learning techniques for predicting disulfide-bonding states of cysteine residues in proteins, which is a sub-problem of a bigger and yet unsolved problem of protein structure prediction. Improvement in the prediction of disulfide bonding states of cysteine residues will help in putting a constraint in the three dimensional (3D) space of the respective protein structure, and thus will eventually help in the prediction of 3D structure of proteins. Results of this work will have direct implications in site-directed mutational studies of proteins, proteins engineering and the problem of protein folding. We have used a combination of Artificial Neural Network (ANN) and Hidden Markov Model (HMM), the so-called Hidden Neural Network (HNN) as a machine learning technique to develop our prediction method. By using different global and local features of proteins (specifically profiles, parity of cysteine residues, average cysteine conservation, correlated mutation, sub-cellular localization, and signal peptide) as inputs and considering Eukaryotes and Prokaryotes separately we have reached to a remarkable accuracy of 94% on cysteine basis for both Eukaryotic and Prokaryotic datasets, and an accuracy of 90% and 93% on protein basis for Eukaryotic dataset and Prokaryotic dataset respectively. These accuracies are best so far ever reached by any existing prediction methods, and thus our prediction method has outperformed all the previously developed approaches and therefore is more reliable. Most interesting part of this thesis work is the differences in the prediction performances of Eukaryotes and Prokaryotes at the basic level of input coding when ‘profile’ information was given as input to our prediction method. And one of the reasons for this we discover is the difference in the amino acid composition of the local environment of bonded and free cysteine residues in Eukaryotes and Prokaryotes. Eukaryotic bonded cysteine examples have a ‘symmetric-cysteine-rich’ environment, where as Prokaryotic bonded examples lack it.

Hybrid Methods for Resource Allocation and Scheduling Problems in Deterministic and Stochastic Environments

This work presents exact, hybrid algorithms for mixed resource Allocation and Scheduling problems; in general terms, those consist into assigning over time finite capacity resources to a set of precedence connected activities. The proposed methods have broad applicability, but are mainly motivated by applications in the field of Embedded System Design. In particular, high-performance embedded computing recently witnessed the shift from single CPU platforms with application-specific accelerators to programmable Multi Processor Systems-on-Chip (MPSoCs). Those allow higher flexibility, real time performance and low energy consumption, but the programmer must be able to effectively exploit the platform parallelism. This raises interest in the development of algorithmic techniques to be embedded in CAD tools; in particular, given a specific application and platform, the objective if to perform optimal allocation of hardware resources and to compute an execution schedule. On this regard, since embedded systems tend to run the same set of applications for their entire lifetime, off-line, exact optimization approaches are particularly appealing. Quite surprisingly, the use of exact algorithms has not been well investigated so far; this is in part motivated by the complexity of integrated allocation and scheduling, setting tough challenges for ``pure'' combinatorial methods. The use of hybrid CP/OR approaches presents the opportunity to exploit mutual advantages of different methods, while compensating for their weaknesses. In this work, we consider in first instance an Allocation and Scheduling problem over the Cell BE processor by Sony, IBM and Toshiba; we propose three different solution methods, leveraging decomposition, cut generation and heuristic guided search. Next, we face Allocation and Scheduling of so-called Conditional Task Graphs, explicitly accounting for branches with outcome not known at design time; we extend the CP scheduling framework to effectively deal with the introduced stochastic elements. Finally, we address Allocation and Scheduling with uncertain, bounded execution times, via conflict based tree search; we introduce a simple and flexible time model to take into account duration variability and provide an efficient conflict detection method. The proposed approaches achieve good results on practical size problem, thus demonstrating the use of exact approaches for system design is feasible. Furthermore, the developed techniques bring significant contributions to combinatorial optimization methods.

Finite-strain analysis in orthogneiss of the Gran Paradiso massif, Western Alps, Italy

A finite-strain study in the Gran Paradiso massif of the Italian Western Alps has been carried out to elucidate whether ductile strain shows a relationship to nappe contacts and to shed light on the nature of the subhorizontal foliation typical of the gneiss nappes in the Alps. The Rf/_ and Fry methods used on feldspar porphyroclasts from 143 augengneiss and 11 conglomerate samples of the Gran Paradiso unit (upper tectonic unit of the Gran Paradiso massif), as well as, 9 augengneiss (Erfaulet granite) and 3 quartzite conglomerate samples from the underlying Erfaulet unit (lower unit of the Gran Paradiso massif), and 1 sample from mica schist. Microstructures and thermobarometric data show that feldspar ductility at temperatures >~450°C occurred only during high-pressure metamorphism, when the rocks were underplated beneath the overriding Adriatic plate. Therefore, the finite-strain data can be related to high-pressure metamorphism in the Alpine subduction zone. The augen gneiss was heterogeneously deformed and axial ratios of the strain ellipse in XZ sections range from 2.1 to 69.8. The long axes of the finite-strain ellipsoids trend W/WNW and the short axes are subvertical associated with a subhorizontal foliation. The strain magnitudes do not increase towards the nappe contacts. Geochemical work shows that the accumulation of finite strain was not associated with any significant volume strain. Hence, the data indicate flattening strain type in the Gran Paradiso unit and constrictional strain type in the Erfaulet unit and prove deviations from simple shear. In addition, electron microprobe work was undertaken to determine if the analysed fabrics formed during high-P metamorphism. The chemistry of phengites in the studied samples suggests that deformation and final structural juxtaposition of the Gran Paradiso unit against the Erfaulet took place during high-pressure metamorphism. On the other hand, nappe stacking occurred early during subduction probably by brittle imbrication and that ductile strain was superimposed on and modified the nappe structure during high-pressure underplating in the Alpine subduction zone. The accumulation of ductile strain during underplating was not by simple shear and involved a component of vertical shortening, which caused the subhorizontal foliation in the Gran Paradiso massif. It is concluded that this foliation formed during thrusting of the nappes onto each other suggesting that nappe stacking was associated with vertical shortening. The primary evidence for this interpretation is an attenuated metamorphic section with high-pressure metamorphic rocks of the Gran Paradiso unit juxtaposed against the Erfaulet unit. Therefore, the exhumation during high-pressure metamorphism in the Alpine subduction zone involved a component of vertical shortening, which is responsible for the subhorizontal foliation within the nappes.

Finite element models of coseismic deformation due to the 2009 L'Aquila (Italy) and 2008 Wenchuan(China) earthquakes

The topic of my Ph.D. thesis is the finite element modeling of coseismic deformation imaged by DInSAR and GPS data. I developed a method to calculate synthetic Green functions with finite element models (FEMs) and then use linear inversion methods to determine the slip distribution on the fault plane. The method is applied to the 2009 L’Aquila Earthquake (Italy) and to the 2008 Wenchuan earthquake (China). I focus on the influence of rheological features of the earth's crust by implementing seismic tomographic data and the influence of topography by implementing Digital Elevation Models (DEM) layers on the FEMs. Results for the L’Aquila earthquake highlight the non-negligible influence of the medium structure: homogeneous and heterogeneous models show discrepancies up to 20% in the fault slip distribution values. Furthermore, in the heterogeneous models a new area of slip appears above the hypocenter. Regarding the 2008 Wenchuan earthquake, the very steep topographic relief of Longmen Shan Range is implemented in my FE model. A large number of DEM layers corresponding to East China is used to achieve the complete coverage of the FE model. My objective was to explore the influence of the topography on the retrieved coseismic slip distribution. The inversion results reveals significant differences between the flat and topographic model. Thus, the flat models frequently adopted are inappropriate to represent the earth surface topographic features and especially in the case of the 2008 Wenchuan earthquake.

Toeplitz operators on finite and infinite dimensional spaces with associated psi *-Fréchet algebras

The present thesis is a contribution to the multi-variable theory of Bergman and Hardy Toeplitz operators on spaces of holomorphic functions over finite and infinite dimensional domains. In particular, we focus on certain spectral invariant Frechet operator algebras F closely related to the local symbol behavior of Toeplitz operators in F. We summarize results due to B. Gramsch et.al. on the construction of Psi_0- and Psi^*-algebras in operator algebras and corresponding scales of generalized Sobolev spaces using commutator methods, generalized Laplacians and strongly continuous group actions. In the case of the Segal-Bargmann space H^2(C^n,m) of Gaussian square integrable entire functions on C^n we determine a class of vector-fields Y(C^n) supported in complex cones K. Further, we require that for any finite subset V of Y(C^n) the Toeplitz projection P is a smooth element in the Psi_0-algebra constructed by commutator methods with respect to V. As a result we obtain Psi_0- and Psi^*-operator algebras F localized in cones K. It is an immediate consequence that F contains all Toeplitz operators T_f with a symbol f of certain regularity in an open neighborhood of K. There is a natural unitary group action on H^2(C^n,m) which is induced by weighted shifts and unitary groups on C^n. We examine the corresponding Psi^*-algebra A of smooth elements in Toeplitz-C^*-algebras. Among other results sufficient conditions on the symbol f for T_f to belong to A are given in terms of estimates on its Berezin-transform. Local aspects of the Szegö projection P_s on the Heisenbeg group and the corresponding Toeplitz operators T_f with symbol f are studied. In this connection we apply a result due to Nagel and Stein which states that for any strictly pseudo-convex domain U the projection P_s is a pseudodifferential operator of exotic type (1/2, 1/2). The second part of this thesis is devoted to the infinite dimensional theory of Bergman and Hardy spaces and the corresponding Toeplitz operators. We give a new proof of a result observed by Boland and Waelbroeck. Namely, that the space of all holomorphic functions H(U) on an open subset U of a DFN-space (dual Frechet nuclear space) is a FN-space (Frechet nuclear space) equipped with the compact open topology. Using the nuclearity of H(U) we obtain Cauchy-Weil-type integral formulas for closed subalgebras A in H_b(U), the space of all bounded holomorphic functions on U, where A separates points. Further, we prove the existence of Hardy spaces of holomorphic functions on U corresponding to the abstract Shilov boundary S_A of A and with respect to a suitable boundary measure on S_A. Finally, for a domain U in a DFN-space or a polish spaces we consider the symmetrizations m_s of measures m on U by suitable representations of a group G in the group of homeomorphisms on U. In particular,in the case where m leads to Bergman spaces of holomorphic functions on U, the group G is compact and the representation is continuous we show that m_s defines a Bergman space of holomorphic functions on U as well. This leads to unitary group representations of G on L^p- and Bergman spaces inducing operator algebras of smooth elements related to the symmetries of U.

Non linear application of an in-house finite elements software

Questa tesi si pone come obiettivo l'analisi delle componenti di sollecitazione statica di un serbatoio, in acciaio API 5L X52, sottoposto a carichi di flessione e pressione interna attraverso il programma agli elementi finiti PLCd4, sviluppato presso l'International Center for Numerical Methods in Engineering (CIMNE - Barcelona). Questo tipo di analisi rientra nel progetto europeo ULCF, il cui traguardo è lo studio della fatica a bassissimo numero di cicli per strutture in acciaio. Prima di osservare la struttura completa del serbatoio è stato studiato il comportamento del materiale per implementare all'interno del programma una nuova tipologia di curva che rappresentasse al meglio l'andamento delle tensioni interne. Attraverso il lavoro di preparazione alla tesi è stato inserito all'interno del programma un algoritmo per la distribuzione delle pressioni superficiali sui corpi 3D, successivamente utilizzato per l'analisi della pressione interna nel serbatoio. Sono state effettuate analisi FEM del serbatoio in diverse configurazioni di carico ove si è cercato di modellare al meglio la struttura portante relativa al caso reale di "full scale test". Dal punto di vista analitico i risultati ottenuti sono soddisfacenti in quanto rispecchiano un corretto comportamento del serbatoio in condizioni di pressioni molto elevate e confermano la bontà del programma nell'analisi computazionale.

Finite-element discretization of 3D energy-transport equations for semiconductors

In this thesis a mathematical model was derived that describes the charge and energy transport in semiconductor devices like transistors. Moreover, numerical simulations of these physical processes are performed. In order to accomplish this, methods of theoretical physics, functional analysis, numerical mathematics and computer programming are applied. After an introduction to the status quo of semiconductor device simulation methods and a brief review of historical facts up to now, the attention is shifted to the construction of a model, which serves as the basis of the subsequent derivations in the thesis. Thereby the starting point is an important equation of the theory of dilute gases. From this equation the model equations are derived and specified by means of a series expansion method. This is done in a multi-stage derivation process, which is mainly taken from a scientific paper and which does not constitute the focus of this thesis. In the following phase we specify the mathematical setting and make precise the model assumptions. Thereby we make use of methods of functional analysis. Since the equations we deal with are coupled, we are concerned with a nonstandard problem. In contrary, the theory of scalar elliptic equations is established meanwhile. Subsequently, we are preoccupied with the numerical discretization of the equations. A special finite-element method is used for the discretization. This special approach has to be done in order to make the numerical results appropriate for practical application. By a series of transformations from the discrete model we derive a system of algebraic equations that are eligible for numerical evaluation. Using self-made computer programs we solve the equations to get approximate solutions. These programs are based on new and specialized iteration procedures that are developed and thoroughly tested within the frame of this research work. Due to their importance and their novel status, they are explained and demonstrated in detail. We compare these new iterations with a standard method that is complemented by a feature to fit in the current context. A further innovation is the computation of solutions in three-dimensional domains, which are still rare. Special attention is paid to applicability of the 3D simulation tools. The programs are designed to have justifiable working complexity. The simulation results of some models of contemporary semiconductor devices are shown and detailed comments on the results are given. Eventually, we make a prospect on future development and enhancements of the models and of the algorithms that we used.

Numerical methods for the dispersion analysis of Guided Waves

The use of guided ultrasonic waves (GUW) has increased considerably in the fields of non-destructive (NDE) testing and structural health monitoring (SHM) due to their ability to perform long range inspections, to probe hidden areas as well as to provide a complete monitoring of the entire waveguide. Guided waves can be fully exploited only once their dispersive properties are known for the given waveguide. In this context, well stated analytical and numerical methods are represented by the Matrix family methods and the Semi Analytical Finite Element (SAFE) methods. However, while the former are limited to simple geometries of finite or infinite extent, the latter can model arbitrary cross-section waveguides of finite domain only. This thesis is aimed at developing three different numerical methods for modelling wave propagation in complex translational invariant systems. First, a classical SAFE formulation for viscoelastic waveguides is extended to account for a three dimensional translational invariant static prestress state. The effect of prestress, residual stress and applied loads on the dispersion properties of the guided waves is shown. Next, a two-and-a-half Boundary Element Method (2.5D BEM) for the dispersion analysis of damped guided waves in waveguides and cavities of arbitrary cross-section is proposed. The attenuation dispersive spectrum due to material damping and geometrical spreading of cavities with arbitrary shape is shown for the first time. Finally, a coupled SAFE-2.5D BEM framework is developed to study the dispersion characteristics of waves in viscoelastic waveguides of arbitrary geometry embedded in infinite solid or liquid media. Dispersion of leaky and non-leaky guided waves in terms of speed and attenuation, as well as the radiated wavefields, can be computed. The results obtained in this thesis can be helpful for the design of both actuation and sensing systems in practical application, as well as to tune experimental setup.

Semi-synthetic bile acids as novel drug candidate in liver diseases: physico-chemical characterization and HPLC-ES-MS/MS methods for their quali-quantitative analysis in different experimental animal models

The physico-chemical characterization, structure-pharmacokinetic and metabolism studies of new semi synthetic analogues of natural bile acids (BAs) drug candidates have been performed. Recent studies discovered a role of BAs as agonists of FXR and TGR5 receptor, thus opening new therapeutic target for the treatment of liver diseases or metabolic disorders. Up to twenty new semisynthetic analogues have been synthesized and studied in order to find promising novel drugs candidates. In order to define the BAs structure-activity relationship, their main physico-chemical properties (solubility, detergency, lipophilicity and affinity with serum albumin) have been measured with validated analytical methodologies. Their metabolism and biodistribution has been studied in “bile fistula rat”, model where each BA is acutely administered through duodenal and femoral infusion and bile collected at different time interval allowing to define the relationship between structure and intestinal absorption and hepatic uptake ,metabolism and systemic spill-over. One of the studied analogues, 6α-ethyl-3α7α-dihydroxy-5β-cholanic acid, analogue of CDCA (INT 747, Obeticholic Acid (OCA)), recently under approval for the treatment of cholestatic liver diseases, requires additional studies to ensure its safety and lack of toxicity when administered to patients with a strong liver impairment. For this purpose, CCl4 inhalation to rat causing hepatic decompensation (cirrhosis) animal model has been developed and used to define the difference of OCA biodistribution in respect to control animals trying to define whether peripheral tissues might be also exposed as a result of toxic plasma levels of OCA, evaluating also the endogenous BAs biodistribution. An accurate and sensitive HPLC-ES-MS/MS method is developed to identify and quantify all BAs in biological matrices (bile, plasma, urine, liver, kidney, intestinal content and tissue) for which a sample pretreatment have been optimized.

Spectral theory of differential operators on finite metric graphs and on bounded domains

Die vorliegende Arbeit widmet sich der Spektraltheorie von Differentialoperatoren auf metrischen Graphen und von indefiniten Differentialoperatoren auf beschränkten Gebieten. Sie besteht aus zwei Teilen. Im Ersten werden endliche, nicht notwendigerweise kompakte, metrische Graphen und die Hilberträume von quadratintegrierbaren Funktionen auf diesen betrachtet. Alle quasi-m-akkretiven Laplaceoperatoren auf solchen Graphen werden charakterisiert, und Abschätzungen an die negativen Eigenwerte selbstadjungierter Laplaceoperatoren werden hergeleitet. Weiterhin wird die Wohlgestelltheit eines gemischten Diffusions- und Transportproblems auf kompakten Graphen durch die Anwendung von Halbgruppenmethoden untersucht. Eine Verallgemeinerung des indefiniten Operators $-tfrac{d}{dx}sgn(x)tfrac{d}{dx}$ von Intervallen auf metrische Graphen wird eingeführt. Die Spektral- und Streutheorie der selbstadjungierten Realisierungen wird detailliert besprochen. Im zweiten Teil der Arbeit werden Operatoren untersucht, die mit indefiniten Formen der Art $langlegrad v, A(cdot)grad urangle$ mit $u,vin H_0^1(Omega)subset L^2(Omega)$ und $OmegasubsetR^d$ beschränkt, assoziiert sind. Das Eigenwertverhalten entspricht in Dimension $d=1$ einer verallgemeinerten Weylschen Asymptotik und für $dgeq 2$ werden Abschätzungen an die Eigenwerte bewiesen. Die Frage, wann indefinite Formmethoden für Dimensionen $dgeq 2$ anwendbar sind, bleibt offen und wird diskutiert.

Computer simulation methods to study interfacial tensions : from the Ising model to colloidal crystals

In condensed matter systems, the interfacial tension plays a central role for a multitude of phenomena. It is the driving force for nucleation processes, determines the shape and structure of crystalline structures and is important for industrial applications. Despite its importance, the interfacial tension is hard to determine in experiments and also in computer simulations. While for liquid-vapor interfacial tensions there exist sophisticated simulation methods to compute the interfacial tension, current methods for solid-liquid interfaces produce unsatisfactory results.rnrnAs a first approach to this topic, the influence of the interfacial tension on nuclei is studied within the three-dimensional Ising model. This model is well suited because despite its simplicity, one can learn much about nucleation of crystalline nuclei. Below the so-called roughening temperature, nuclei in the Ising model are not spherical anymore but become cubic because of the anisotropy of the interfacial tension. This is similar to crystalline nuclei, which are in general not spherical but more like a convex polyhedron with flat facets on the surface. In this context, the problem of distinguishing between the two bulk phases in the vicinity of the diffuse droplet surface is addressed. A new definition is found which correctly determines the volume of a droplet in a given configuration if compared to the volume predicted by simple macroscopic assumptions.rnrnTo compute the interfacial tension of solid-liquid interfaces, a new Monte Carlo method called ensemble switch method'' is presented which allows to compute the interfacial tension of liquid-vapor interfaces as well as solid-liquid interfaces with great accuracy. In the past, the dependence of the interfacial tension on the finite size and shape of the simulation box has often been neglected although there is a nontrivial dependence on the box dimensions. As a consequence, one needs to systematically increase the box size and extrapolate to infinite volume in order to accurately predict the interfacial tension. Therefore, a thorough finite-size scaling analysis is established in this thesis. Logarithmic corrections to the finite-size scaling are motivated and identified, which are of leading order and therefore must not be neglected. The astounding feature of these logarithmic corrections is that they do not depend at all on the model under consideration. Using the ensemble switch method, the validity of a finite-size scaling ansatz containing the aforementioned logarithmic corrections is carefully tested and confirmed. Combining the finite-size scaling theory with the ensemble switch method, the interfacial tension of several model systems, ranging from the Ising model to colloidal systems, is computed with great accuracy.