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Sparse Representations for Uncertainty Quantification of a Coupled Field-Circuit ProblemSep 17 2018We consider a model of an electric circuit, where differential algebraic equations for a circuit part are coupled to partial differential equations for an electromagnetic field part. An uncertainty quantification is performed by changing physical parameters ... More

Multiple Right-Hand Side Techniques in Semi-Explicit Time Integration Methods for Transient Eddy Current ProblemsNov 21 2016Sep 23 2017The spatially discretized magnetic vector potential formulation of magnetoquasistatic field problems is transformed from an infinitely stiff differential algebraic equation system into a finitely stiff ordinary differential equation (ODE) system by application ... More

ParaExp using Leapfrog as Integrator for High-Frequency Electromagnetic SimulationsMay 22 2017May 28 2017Recently, ParaExp was proposed for the time integration of linear hyperbolic problems. It splits the time interval of interest into sub-intervals and computes the solution on each sub-interval in parallel. The overall solution is decomposed into a particular ... More

An Application of ParaExp to Electromagnetic Wave ProblemsJul 01 2016Oct 16 2016Recently, ParaExp was proposed for the time integration of hyperbolic problems. It splits the time interval of interest into sub-intervals and computes the solution on each sub-interval in parallel. The overall solution is decomposed into a particular ... More

Parallel-In-Time Simulation of Eddy Current Problems Using PararealJun 19 2017Feb 07 2018In this contribution the usage of the Parareal method is proposed for the time-parallel solution of the eddy current problem. The method is adapted to the particular challenges of the problem that are related to the differential algebraic character due ... More

Waveform Relaxation for the Computational Homogenization of Multiscale Magnetoquasistatic ProblemsJul 19 2016This paper proposes the application of the waveform relaxation method to the homogenization of multiscale magnetoquasistatic problems. In the monolithic heterogeneous multiscale method, the nonlinear macroscale problem is solved using the Newton--Raphson ... More

Stochastic Modeling and Regularity of the Nonlinear Elliptic Curl-Curl EquationJun 24 2016This paper addresses the nonlinear elliptic curl-curl equation with uncertainties in the material law. It is frequently employed in the numerical evaluation of magnetostatic fields, where the uncertainty is ascribed to the so-called B-H curve. A truncated ... More

A Structural Analysis of Field/Circuit Coupled Problems Based on a Generalised Circuit ElementJan 22 2018Mar 05 2018In some applications there arises the need of a spatially distributed description of a physical quantity inside a device coupled to a circuit. Then, the in-space discretised system of partial differential equations is coupled to the system of equations ... More

A Fast Isogeometric BEM for the Three Dimensional Laplace- and Helmholtz ProblemsAug 30 2017Oct 13 2017We present an indirect higher order boundary element method utilising NURBS mappings for exact geometry representation and an interpolation-based fast multipole method for compression and reduction of computational complexity, to counteract the problems ... More

Uncertainty quantification for an optical grating coupler with an adjoint-based Leja adaptive collocation methodJul 19 2018This paper addresses uncertainties arising in the nano-scale fabrication of optical devices. The stochastic collocation method is used to propagate uncertainties in material and geometry to the scattering parameters of the system. A dimension-adaptive ... More

Reduced Order Modelling for the Simulation of Quenches in Superconducting MagnetsOct 13 2017This contributions discusses the simulation of magnetothermal effects in superconducting magnets as used in particle accelerators. An iterative coupling scheme using reduced order models between a magnetothermal partial differential model and an electrical ... More

Model Order Reduction for Rotating Electrical MachinesMay 10 2017The simulation of electric rotating machines is both computationally expensive and memory intensive. To overcome these costs, model order reduction techniques can be applied. The focus of this contribution is especially on machines that contain non-symmetric ... More

Exploring Parallel-in-Time Approaches for Eddy Current ProblemsOct 31 2018We consider the usage of parallel-in-time algorithms of the Parareal and multigrid-reduction-in-time (MGRIT) methodologies for the parallel-in-time solution of the eddy current problem. Via application of these methods to a two-dimensional model problem ... More

Solving nonlinear circuits with pulsed excitation by multirate partial differential equationsOct 17 2017In this paper the concept of Multirate Partial Differential Equations (MPDEs) is applied to obtain an efficient solution for nonlinear low-frequency electrical circuits with pulsed excitation. The MPDEs are solved by a Galerkin approach and a conventional ... More

Isogeometric Mortar Coupling for Electromagnetic ProblemsDec 27 2018This paper discusses and analyses two domain decomposition approaches for electromagnetic problems that allow the combination of domains discretised by either N\'ed\'elec-type polynomial finite elements or spline-based isogeometric analysis. The first ... More

Application of the Waveform Relaxation Technique to the Co-Simulation of Power Converter Controller and Electrical Circuit ModelsApr 10 2017In this paper we present the co-simulation of a PID class power converter controller and an electrical circuit by means of the waveform relaxation technique. The simulation of the controller model is characterized by a fixed-time stepping scheme reflecting ... More

Optimized Field/Circuit Coupling for the Simulation of Quenches in Superconducting MagnetsFeb 03 2017Jul 06 2017In this paper, we propose an optimized field/circuit coupling approach for the simulation of magnetothermal transients in superconducting magnets. The approach improves the convergence of the iterative coupling scheme between a magnetothermal partial ... More

A 2-D Finite-Element Model for Electro-Thermal Transients in Accelerator MagnetsOct 03 2017Dec 05 2017Superconducting accelerator magnets require sophisticated monitoring and means of protection due to the large energy stored in the magnetic field. Numerical simulations play a crucial role in understanding transient phenomena occurring within the magnet, ... More

Robust Shape Optimization of Electric Devices Based on Deterministic Optimization Methods and Finite Element Analysis With Affine Decomposition and Design ElementsMay 18 2018In this paper, gradient-based optimization methods are combined with finite-element modeling for improving electric devices. Geometric design parameters are considered by affine decomposition of the geometry or by the design element approach, both of ... More

An Application of ParaExp to Electromagnetic Wave ProblemsJul 01 2016Recently, ParaExp was proposed for the time integration of hyperbolic problems. It splits the time interval of interest into sub-intervals and computes the solution on each sub-interval in parallel. The overall solution is decomposed into a particular ... More

Coupling of Magneto-Thermal and Mechanical Superconducting Magnet Models by Means of Mesh-Based InterpolationDec 29 2017In this paper we present an algorithm for the coupling of magneto-thermal and mechanical finite element models representing superconducting accelerator magnets. The mechanical models are used during the design of the mechanical structure as well as the ... More

Modeling of Spatial Uncertainties in the Magnetic ReluctivityOct 10 2016In this paper a computationally efficient approach is suggested for the stochastic modeling of an inhomogeneous reluctivity of magnetic materials. These materials can be part of electrical machines, such as a single phase transformer (a benchmark example ... More

GPU Accelerated Explicit Time Integration Methods for Electro-Quasistatic FieldsDec 30 2016Electro-quasistatic field problems involving nonlinear materials are commonly discretized in space using finite elements. In this paper, it is proposed to solve the resulting system of ordinary differential equations by an explicit Runge-Kutta-Chebyshev ... More

Automatic Generation of Equivalent Electrothermal SPICE Netlists from 3D Electrothermal Field ModelsOct 14 2016Starting from a 3D electrothermal field problem discretized by the Finite Integration Technique, the equivalence to a circuit description is shown by exploiting the analogy to the Modified Nodal Analysis approach. Using this analogy, an algorithm for ... More

Determination of Bond Wire Failure Probabilities in Microelectronic PackagesSep 18 2016This work deals with the computation of industry-relevant bond wire failure probabilities in microelectronic packages. Under operating conditions, a package is subject to Joule heating that can lead to electrothermally induced failures. Manufacturing ... More

Survey on Semi-Explicit Time Integration of Eddy Current ProblemsSep 20 2017The spatial discretization of the magnetic vector potential formulation of magnetoquasistatic field problems results in an infinitely stiff differential-algebraic equation system. It is transformed into a finitely stiff ordinary differential equation ... More

A Defect Corrected Finite Element Approach for the Accurate Evaluation of Magnetic Fields on Unstructured GridsNov 25 2016In electromagnetic simulations of magnets and machines one is often interested in a highly accurate and local evaluation of the magnetic field uniformity. Based on local post-processing of the solution, a defect correction scheme is proposed as an easy ... More

Multiple Right-Hand Side Techniques in Semi-Explicit Time Integration Methods for Transient Eddy Current ProblemsNov 21 2016The spatially discretized magnetic vector potential formulation of magnetoquasistatic field problems is transformed from an infinitely stiff differential algebraic equation system into a finitely stiff ordinary differential equation (ODE) system by application ... More

STEAM: A Hierarchical Co-Simulation Framework for Superconducting Accelerator Magnet CircuitsJan 26 2018Simulating the transient effects occurring in superconducting accelerator magnet circuits requires including the mutual electro-thermo-dynamic interaction among the circuit elements, such as power converters, magnets, and protection systems. Nevertheless, ... More

Determination of Bond Wire Failure Probabilities in Microelectronic PackagesSep 18 2016Jan 02 2017This work deals with the computation of industry-relevant bond wire failure probabilities in microelectronic packages. Under operating conditions, a package is subject to Joule heating that can lead to electrothermally induced failures. Manufacturing ... More

A multilevel Monte Carlo method for high-dimensional uncertainty quantification of low-frequency electromagnetic devicesMar 24 2018This work addresses uncertainty quantification of electromagnetic devices determined by the eddy current problem. The multilevel Monte Carlo (MLMC) method is used for the treatment of uncertain parameters while the devices are discretized in space by ... More

Isogeometric Simulation of Lorentz Detuning in Superconducting Accelerator CavitiesJun 27 2016Cavities in linear accelerators suffer from eigenfrequency shifts due to mechanical deformation caused by the electromagnetic radiation pressure, a phenomenon known as Lorentz detuning. Estimating the frequency shift up to the needed accuracy by means ... More

A New Parareal Algorithm for Problems with Discontinuous SourcesMar 14 2018The Parareal algorithm allows to solve evolution problems exploiting parallelization in time. Its convergence and stability have been proved under the assumption of regular (smooth) inputs. We present and analyze here a new Parareal algorithm for ordinary ... More

Efficient simulation of DC-DC switch-mode power converters by multirate partial differential equationsJul 06 2017Apr 17 2018In this paper, Multirate Partial Differential Equations (MPDEs) are used for the efficient simulation of problems with 2-level pulsed excitations as they often occur in power electronics, e.g., DC-DC switch-mode converters. The differential equations ... More

Isogeometric Boundary Elements in Electromagnetism: Rigorous Analysis, Fast Methods, and ExamplesJul 09 2018We present a new approach to three-dimensional electromagnetic scattering problems via fast isogeometric boundary element methods. Starting with an investigation of the theoretical setting around the electric field integral equation within the isogeometric ... More

Low-Dimensional Stochastic Modeling of the Electrical Properties of Biological TissuesNov 22 2016Uncertainty quantification plays an important role in biomedical engineering as measurement data is often unavailable and literature data shows a wide variability. Using state-of-the-art methods one encounters difficulties when the number of random inputs ... More

A New Parareal Algorithm for Time-Periodic Problems with Discontinuous InputsOct 29 2018The Parareal algorithm, which is related to multiple shooting, was introduced for solving evolution problems in a time-parallel manner. The algorithm was then extended to solve time-periodic problems. We are interested here in time-periodic systems which ... More

A Numerical Comparison of an Isogeometric and a Classical Higher-Order Approach to the Electric Field Integral EquationJul 10 2018In this paper, we advocate a novel spline-based isogeometric approach for boundary elements and its efficient implementation. We compare solutions obtained by both an isogeometric approach, and a classical parametric higher-order approach via Raviart-Thomas ... More

An algorithmic comparison of the Hyper-Reduction and the Discrete Empirical Interpolation Method for a nonlinear thermal problemOct 17 2016Dec 19 2017A novel algorithmic discussion of the methodological and numerical differences of competing parametric model reduction techniques for nonlinear problems are presented. First, the Galerkin reduced basis (RB) formulation is presented which fails at providing ... More

Low-Dimensional Stochastic Modeling of the Electrical Properties of Biological TissuesNov 22 2016Sep 23 2017Uncertainty quantification plays an important role in biomedical engineering as measurement data is often unavailable and literature data shows a wide variability. Using state-of-the-art methods one encounters difficulties when the number of random inputs ... More

Uncertainty Quantification for Geometry Deformations of Superconducting Cavities using Eigenvalue TrackingFeb 08 2018The electromagnetic field distribution as well as the resonating frequency of various modes in superconducting cavities are sensitive to small geometry deformations. The occurring variations are motivated by measurements of an available set of resonators ... More

An algorithmic comparison of the Hyper-Reduction and the Discrete Empirical Interpolation Method for a nonlinear thermal problemOct 17 2016An algorithmic summary and comparison of the methodological and numerical properties of competing parametric model reduction techniques is presented for a planar nonlinear thermal conduction problem. First, the Galerkin reduced basis (RB) formulation ... More

Coupled Simulation of Transient Heat Flow and Electric Currents in Thin Wires: Application to Bond Wires in Microelectronic Chip PackagingSep 24 2018This work addresses the simulation of heat flow and electric currents in thin wires. An important application is the use of bond wires in microelectronic chip packaging. The heat distribution is modeled by an electrothermal coupled problem, which poses ... More

Automated Netlist Generation for 3D Electrothermal and Electromagnetic Field ProblemsSep 23 2018We present a method for the automatic generation of netlists describing general three-dimensional electrothermal and electromagnetic field problems. Using a pair of structured orthogonal grids as spatial discretisation, a one-to-one correspondence between ... More

Systems of Differential Algebraic Equations in Computational ElectromagneticsFeb 19 2018Nov 02 2018Starting from space-discretisation of Maxwell's equations, various classical formulations are proposed for the simulation of electromagnetic fields. They differ in the phenomena considered as well as in the variables chosen for discretisation. This contribution ... More

Uncertainty Quantification for Maxwell's Eigenproblem using Isogeometric AnalysisFeb 08 2018May 30 2018The electromagnetic field distribution as well as the resonating frequency of various modes in superconducting cavities used in particle accelerators for example are sensitive to small geometry deformations. The occurring variations are motivated by measurements ... More

Electrothermal Simulation of Bonding Wire Degradation under Uncertain GeometriesOct 14 2016In this paper, electrothermal field phenomena in electronic components are considered. This coupling is tackled by multiphysical field simulations using the Finite Integration Technique (FIT). In particular, the design of bonding wires with respect to ... More

Proper Generalized Decomposition of Parameterized Electrothermal Problems Discretized by the Finite Integration TechniqueDec 17 2018The proper generalized decomposition is applied to a static electrothermal model subject to uncertainties. A reduced model that circumvents the curse of dimensionality is obtained. The quadratic electrothermal coupling term is non-standard and requires ... More

Multipatch Approximation of the de Rham Sequence and its Traces in Isogeometric AnalysisJun 04 2018We define a conforming B-spline discretisation of the de Rham complex on multipatch geometries. We introduce and analyse the properties of interpolation operators onto these spaces which commute w.r.t. the surface differential operators. Using these results ... More

Recent Advances of Isogeometric Analysis in Computational ElectromagneticsSep 18 2017In this communication the advantages and drawbacks of the isogeometric analysis (IGA) are reviewed in the context of electromagnetic simulations. IGA extends the set of polynomial basis functions, commonly employed by the classical Finite Element Method ... More

Fast and Tiny Structural Self-Indexes for XMLDec 28 2010XML document markup is highly repetitive and therefore well compressible using dictionary-based methods such as DAGs or grammars. In the context of selectivity estimation, grammar-compressed trees were used before as synopsis for structural XPath queries. ... More

XPath Node Selection over Grammar-Compressed TreesNov 21 2013XML document markup is highly repetitive and therefore well compressible using grammar-based compression. Downward, navigational XPath can be executed over grammar-compressed trees in PTIME: the query is translated into an automaton which is executed ... More

Proceedings Second International Workshop on Trends in Tree Automata and Tree TransducersNov 20 2013This volume contains the papers that were presented at the second international workshop on Trends in Tree Automata and Transducers (TTATT 2013) which took place on October 19th, 2013 in Hanoi/Vietnam. The workshop was colocated with the verification ... More

Relation Variables in Qualitative Spatial ReasoningAug 03 2006We study an alternative to the prevailing approach to modelling qualitative spatial reasoning (QSR) problems as constraint satisfaction problems. In the standard approach, a relation between objects is a constraint whereas in the alternative approach ... More

On complements and the factorization problem for Hopf algebrasDec 12 2010Two new results concerning complements in a semisimple Hopf algebra are proved. They extend some well known results from group theory. The uniqueness of Krull Schmidt Remak type decomposition is proved for semisimple completely reducible Hopf algebras. ... More

On coideal subalgebras of cocentral Kac algebras and a generalization of Wall's conjectureMar 25 2012It shown that any coideal subalgebra of a finite dimensional Hopf algebra is a cyclic module over the dual Hopf algebra. Using this we describe all coideal subalgebras of a cocentral abelian extension of Hopf algebras extending some results from [4].

Torsion Invariants for FamiliesApr 18 2008May 09 2009We give an overview over the higher torsion invariants of Bismut-Lott, Igusa-Klein and Dwyer-Weiss-Williams, including some more or less recent developments.

Penguin amplitudes in hadronic B decays: NLO spectator scatteringNov 11 2006We present results on the NLO (alpha_s^2) spectator-scattering corrections to the topological penguin amplitudes for charmless hadronic two-body B-decays in QCD factorization. The corrections can be sizable for the colour-suppressed electroweak penguin ... More

Theory of charmless hadronic B-decaysApr 08 2013I summarize results and performance of the dynamical theory of charmless hadronic B decays, based on QCD factorization in the heavy quark limit. On the theoretical side, a number of NNLO (alpha_s^2) amplitudes are now available, all showing a well-behaved ... More

Space-time constructions for the mean curvature flow in a Ricci flow backgroundJun 13 2012Jul 30 2012Given a solution of the (backwards) Ricci flow one can construct a so called canonical soliton metric on space-time, introduced by E. Cabezas-Rivas and P. Topping. We observe that for a mean curvature flow within a (backwards) Ricci flow background, the ... More

Diffraction at the LHC: a non-technical IntroductionMar 22 2010In diffractive interactions of protons or nuclei a violent collision can occur that leaves the forward going particle completely intact -with probability determined by the structure of the proton or nucleus. At very high energies these collisions also ... More

MC3D - 3D Continuum Radiative Transfer, Version 2Jul 18 2002A revised and greatly improved version of the 3D continuum radiative transfer code MC3D is presented. It is based on the Monte-Carlo method and solves the radiative transfer problem self-consistently. It is designed for the simulation of dust temperatures ... More

From Particle Tracks to Velocity and Acceleration Fields Using B-Splines and PenaltiesOct 30 2015In this work a method for reconstructing velocity and acceleration fields is described which uses scattered particle tracking data from flow experiments as input. The goal is to reconstruct these fields faithfully with a limited amount of compute time ... More

First Numerical Implementation of the Loop-Tree Duality MethodOct 14 2015The Loop-Tree Duality (LTD) is a novel perturbative method in QFT that establishes a relation between loop-level and tree-level amplitudes, which gives rise to the idea of treating them simultaneously in a common Monte Carlo. Initially introduced for ... More

Rigidity and Flexibility for Handlebody GroupsAug 10 2016We show that finite index subgroups of the handlebody group are rigid in their ambient mapping class group: any injective map of a finite index subgroup of the genus $g$ handlebody group into the genus $g$ mapping class group is conjugation by a mapping ... More

A non-parametric ensemble transform method for Bayesian inferenceOct 01 2012Jan 14 2013Many applications, such as intermittent data assimilation, lead to a recursive application of Bayesian inference within a Monte Carlo context. Popular data assimilation algorithms include sequential Monte Carlo methods and ensemble Kalman filters (EnKFs). ... More

Gauge Deformations and Embedding Theorems for Special GeometriesSep 30 2009Jul 30 2010We reduce the embedding problem for hypo SU(2) and SU(3)-structures to the embedding problem for hypo G2-structures into parallel Spin(7)-manifolds. The latter will be described in terms of gauge deformations. This description involves the intrinsic torsion ... More

Interacting growth processes and invariant percolationApr 12 2013Jan 19 2015The aim of this paper is to underline the relation between reversible growth processes and invariant percolation. We present two models of interacting branching random walks (BRWs), truncated BRWs and competing BRWs, where survival of the growth process ... More

Classical basis for quantum spectral fluctuations in hyperbolic systemsMar 23 2003Aug 21 2003We reason in support of the universality of quantum spectral fluctuations in chaotic systems, starting from the pioneering work of Sieber and Richter who expressed the spectral form factor in terms of pairs of periodic orbits with self-crossings and avoided ... More

Sorting Discrete i.i.d. Inputs: Quicksort is OptimalAug 17 2016Oct 05 2016We prove the Sedgewick-Bentley conjecture on median-of-$k$ Quicksort on equal keys: The average number of comparisons for Quicksort with fat-pivot (a.k.a. three-way) partitioning is asymptotically only a constant times worse than the information-theoretic ... More

Time reversal for radiative transport with applications to inverse and control problemsApr 10 2013Aug 03 2013In this paper we develop a time reversal method for the radiative transport equation to solve two problems: an inverse problem for the recovery of an initial condition from boundary measurements, and the exact boundary controllability of the transport ... More

Assessment of Path Reservation in Distributed Real-Time Vehicle GuidanceApr 23 2013In this paper we assess the impact of path reservation as an additional feature in our distributed real-time vehicle guidance protocol BeeJamA. Through our microscopic simulations we show that na\"{\i}ve reservation of links without any further measurements ... More

LiSK - A C++ Library for Evaluating Classical Polylogarithms and $\text{Li}_{22}$May 31 2016I present a lightweight C++ library for the evaluation of classical polylogarithms Li_n and the special function Li_{22} for arbitrary complex arguments. The evaluation is possible in arbitrary precision arithmetic and features also an explicit double ... More

Diffusion and percolation in anisotropic random barrier modelsFeb 02 2004An anisotropic random barrier model is presented, in which the transition probabilities in different directions have different probability density functions. At low temperatures, the anisotropic long--time diffusion coefficients, obtained using an effective ... More

Computations and Applications of eta invariantsNov 22 2010Apr 27 2011We give a survey on eta invariants including methods of computation and applications in differential topology.

Rational cohomology of \bar R_2 (and \bar S_2)Dec 23 2010We compute the rational cohomology ring of \bar R_2, the (compactified) moduli space of Prym curves of genus 2. We also recompute the rational cohomology ring of \bar S_2, the moduli space of spin curves of genus 2, thereby correcting some errors made ... More

Demonstration of entanglement assisted invariance on IBM's Quantum ExperienceSep 23 2016Quantum entanglement is among the most fundamental, yet from classical intuition also most surprising properties of the fully quantum nature of physical reality. We report several experiments performed on IBM's Quantum Experience demonstrating envariance ... More

Asymptotic link invariants for ergodic vector fieldsMar 06 2008We study the asymptotics of a family of link invariants on the orbits of a smooth volume-preserving ergodic vector field on a compact domain of the 3-space. These invariants, called linear saddle invariants, include many concordance invariants and generate ... More

Totally geodesic submanifolds in Riemannian symmetric spacesOct 24 2008In the first part of this expository article, the most important constructions and classification results concerning totally geodesic submanifolds in Riemannian symmetric spaces are summarized. In the second part, I describe the results of my classification ... More

The Geometrical Description of Feasible Singular Values in the Tensor Train FormatJan 29 2017Tensors have grown in importance and are applied to an increasing number of fields. Crucial in this regard are tensor formats, such as the widespread Tensor Train (TT) decomposition, which represent low rank tensors. This multivariate TT-rank and accordant ... More

On hypersurfaces of positive reach, alternating Steiner formulae and Hadwiger's ProblemApr 15 2013We give new characterisations of sets of positive reach and show that a closed hypersurface has positive reach if and only if it is of class $C^{1,1}$. These results are then used to prove new alternating Steiner formul{\ae} for hypersurfaces of positive ... More

Categoricity of Shimura VarietiesMar 18 2018Dec 15 2018We propose a model-theoretic structure for Shimura varieties and give necessary and sufficient conditions to obtain categoricity. We show that these conditions are directly related to important conjectures in number theory coming from Galois representations ... More

Transportation-cost inequalities for diffusions driven by Gaussian processesMar 11 2014Sep 21 2016We prove transportation-cost inequalities for the law of SDE solutions driven by general Gaussian processes. Examples include the fractional Brownian motion, but also more general processes like bifractional Brownian motion. In case of multiplicative ... More

Harmonic morphisms on conformally flat 3-spheresFeb 26 2009We show that under some non-degeneracy assumption the only submersive harmonic morphism on a conformally flat $3-$sphere is the Hopf fibration. The proof involves an appropriate use the Chern-Simons functional.

Morse theory and higher torsion invariants IIMay 20 2003Let p: M -> B be a family of compact manifolds equipped with a unitarily flat vector bundle F -> M. We generalize Igusa's higher Franz-Reidemeister torsion \tau(M/B;F) to the case that the fibre-wise cohomology H^*(M/B;F) -> B carries a parallel metric. ... More

On the irreducible representations of generalized quantum doublesFeb 20 2012A description of all the irreducible representations of generalized quantum doubles associated to skew pairings of semisimple Hopf algebras is given. In particular a description of the irreducible representations of semisimple Drinfeld doubles is obtained. ... More

Backward-Backward Splitting in Hadamard SpacesSep 23 2013Sep 30 2013The backward-backward algorithm is a tool for finding minima of a regularization of the sum of two convex functions in Hilbert spaces. We generalize this setting to Hadamard spaces and prove the convergence of an error-tolerant version of the backward-backward ... More

Mellin moments of heavy flavor contributions to F_2(x,Q^2) at NNLOOct 16 2009This thesis is concerned with the calculation of fixed moments of the O(a_s^3) heavy flavor contributions to the Wilson coefficients of the structure function F_2(x,Q^2) in the limit Q^2 >> m^2, neglecting power corrections. The massive Wilson coefficients ... More

One-dimensional quantum wires: A pedestrian approach to bosonizationAug 01 2007Sep 08 2009In these lecture notes we will consider systems in which the motion of electrons is confined to one dimension (1D). In these so-called quantum wires electron-electron interaction effects play an important role because the restricted dimensions enhance ... More

Numerical Evidence for Multiplicative Logarithmic Corrections from Marginal OperatorsFeb 06 1996May 28 1996Field theory calculations predict multiplicative logarithmic corrections to correlation functions from marginally irrelevant operators. However, for the numerically most suitable model - the spin-1/2 chain - these corrections have been controversial. ... More

An Accurate Determination of the Exchange Constant in Sr_2CuO_3 from Recent Theoretical ResultsAug 10 1995Feb 08 1996Data from susceptibility measurements on Sr_2CuO_3 are compared with recent theoretical predictions for the magnetic susceptibility of the antiferromagnetic spin-1/2 Heisenberg chain. The experimental data fully confirms the theoretical predictions and ... More

Accurate variational electronic structure calculations with the density matrix renormalization groupMay 06 2014During the past 15 years, the density matrix renormalization group (DMRG) has become increasingly important for ab initio quantum chemistry. The underlying matrix product state (MPS) ansatz is a low-rank decomposition of the full configuration interaction ... More

R-Matrix Poisson Algebras and Their DeformationsJun 03 2007We classify in this paper Poisson structures on modules over semisimple Lie algebras arising from classical r-matrices. We then study their quantizations and the relation to classical invariant theory.

Equivariant Quantizations of Symmetric AlgebrasOct 12 2008Dec 09 2008Let g be a Lie bialgebra and let V be a finite-dimensional g-module. We study deformations of the symmetric algebra of V which are equivariant with respect to an action of the quantized enveloping algebra of g. In particular we investigate such quantizations ... More

Turbulent spectra in real-time gauge field evolutionDec 12 2008We investigate ultraviolet fixed points in the real-time evolution of non-Abelian gauge fields. Classical-statistical lattice simulations reveal equal-time correlation functions with a spectral index 3/2. Analytical understanding of this result is achieved ... More

Validation of credit default probabilities via multiple testing proceduresJun 25 2010We apply multiple testing procedures to the validation of estimated default probabilities in credit rating systems. The goal is to identify rating classes for which the probability of default is estimated inaccurately, while still maintaining a predefined ... More

Supersymmetry beyond minimal flavour violationAug 14 2008Nov 18 2008We review the sources and phenomenology of non-minimal flavour violation in the MSSM. We discuss in some detail the most important theoretical and experimental constraints, as well as promising observables to look for supersymmetric effects at the LHC ... More

On strategies for determination and characterization of the underlying eventSep 04 2010Sep 22 2010We discuss the problem of the separation and description of the underlying event (UE) within two existing approaches to UE measurement: the "traditional" method, widely used at Tevatron, and a recently proposed jet-area/median method. A simple toy model ... More

Wilson Loops, Bianchi Constraints and Duality in Abelian Lattice ModelsAug 05 1998Nov 18 1998We introduce new modified Abelian lattice models, with inhomogeneous local interactions, in which a sum over topological sectors are included in the defining partition function. The dual models, on lattices with arbitrary topology, are constructed and ... More

Bipartite Field Theories: from D-Brane Probes to Scattering AmplitudesJul 03 2012Dec 20 2012We introduce and initiate the investigation of a general class of 4d, N=1 quiver gauge theories whose Lagrangian is defined by a bipartite graph on a Riemann surface, with or without boundaries. We refer to such class of theories as Bipartite Field Theories ... More