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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

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

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

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

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

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

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

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

Sparse Representations for Uncertainty Quantification of a Coupled Field-Circuit ProblemSep 17 2018Mar 08 2019We 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

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

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

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

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

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

Multigrid-reduction-in-time for Eddy Current problemsMay 16 2019Parallel-in-time methods have shown success for reducing the simulation time of many time-dependent problems. Here, we consider applying the multigrid-reduction-in-time (MGRIT) algorithm to a voltage-driven eddy current model problem.

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

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

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

Multilevel Monte Carlo Simulation of the Eddy Current Problem With Random ParametersMay 23 2017The multilevel Monte Carlo method is applied to an academic example in the field of electromagnetism. The method exhibits a reduced variance by assigning the samples to multiple models with a varying spatial resolution. For the given example it is found ... 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

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

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

Explicit Time Integration of Transient Eddy Current ProblemsJan 11 2017For time integration of transient eddy current problems commonly implicit time integration methods are used, where in every time step one or several nonlinear systems of equations have to be linearized with the Newton-Raphson method due to ferromagnetic ... 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

Accelerated Steady-State Torque Computation for Induction Machines using Parallel-In-Time AlgorithmsFeb 21 2019This paper focuses on efficient steady-state computations of induction machines. In particular, the periodic Parareal algorithm with initial-value coarse problem (PP-IC) is considered for acceleration of classical time-stepping simulations via non-intrusive ... More

Isogeometric Analysis Simulation of TESLA Cavities Under UncertaintyNov 06 2017In the design of electromagnetic devices the accurate representation of the geometry plays a crucial role in determining the device performance. For accelerator cavities, in particular, controlling the frequencies of the eigenmodes is important in order ... 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

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

Robust Optimization Approaches for the Design of an Electric MachineDec 05 2017Aug 06 2018In this paper two formulations for the robust optimization of the size of the permanent magnet in a synchronous machine are discussed. The optimization is constrained by a partial differential equation to describe the electromagnetic behavior of the machine. ... 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

An Extended Analytic Model for the Heating of BondwiresSep 28 2017We present an extended analytic formula for the calculation of the temperature profile along a bondwire embedded in a package. The resulting closed formula is built by coupling the heat transfer equations of the bondwire and the surrounding moulding compound ... 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

Uncertainty Quantification for Maxwell's Eigenproblem based on Isogeometric Analysis and Mode TrackingFeb 08 2018Mar 06 2019The 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

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

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

A Space-Time Approach for the Time-Domain Simulation in a Rotating Reference FrameJun 19 2017We approach the discretisation of Maxwell's equations directly in space-time without making any non-relativistic assumptions with the particular focus on simulations in rotating reference frames. As a research example we study Sagnac's effect in a rotating ... 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

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

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

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

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

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

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

Proper Generalized Decomposition of Parameterized Electrothermal Problems Discretized by the Finite Integration TechniqueDec 17 2018Mar 21 2019The 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

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

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

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

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

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

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

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

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

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

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].

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

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

SLE and spidernetsFeb 12 2018Oct 05 2018We regard SLE from a quantum probability point of view and approximate the underlying quantum process by the growth of a random graph, which arises from the comb product of a certain spidernet and its complement. We obtain a stronger result for the deterministic ... 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

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

Smash nilpotent cycles on products of curvesJul 31 2012Aug 01 2012Voevodsky has conjectured that numerical and smash equivalence coincide on a smooth projective variety. We prove the conjecture for one dimensional cycles on an arbitrary product of curves. As a consequence we get that numerically trivial 1-cycles on ... 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

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

Linear systems over localizations of ringsSep 24 2017Dec 18 2017We describe a method for solving linear systems over the localization of a commutative ring $R$ at a multiplicatively closed subset $S$ that works under the following hypotheses: the ring $R$ is coherent, i.e., we can compute finite generating sets of ... More

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.

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.

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

Two-term spectral asymptotics for the Dirichlet pseudo-relativistic kinetic energy operator on a bounded domainJun 27 2017Aug 06 2018Continuing the series of works following Weyl's one-term asymptotic formula for the counting function $N(\lambda)=\sum_{n=1}^\infty(\lambda_n{-}\lambda)_-$ of the eigenvalues of the Dirichlet Laplacian and the much later found two-term expansion on domains ... 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

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.

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

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

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

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

On the second cohomology group of a simplicial groupNov 15 2009Sep 29 2010We give an algebraic proof for the result of Eilenberg and Mac Lane that the second cohomology group of a simplicial group G can be computed as a quotient of a fibre product involving the first two homotopy groups and the first Postnikov invariant of ... More

Spectral data for simply-periodic solutions of the sinh-Gordon equationJan 11 2017This note summarizes results that were obtained by the author in his habilitation thesis (arXiv:1607.08792) concerning the development of a spectral theory for simply periodic, 2-dimensional, complex-valued solutions of the sinh-Gordon equation. Spectral ... More

On an analogue of a Brauer theorem for fusion categoriesMar 16 2015In this paper we prove an analogue of Brauer's theorem for faithful objects in fusion categories. Other notions, such as the order and the index associated to faithful objects of fusion categories are also discussed. We show that the index of a faithful ... More

Resolutions for unit groups of ordersSep 28 2016We present a general algorithm for constructing a free resolution for unit groups of orders in semisimple rational algebras. The approach is based on computing a contractible $G$-complex employing the theory of minimal classes of quadratic forms and Opgenorth's ... More

Equivalence Problems for Tree Transducers: A Brief SurveyMay 22 2014The decidability of equivalence for three important classes of tree transducers is discussed. Each class can be obtained as a natural restriction of deterministic macro tree transducers (MTTs): (1) no context parameters, i.e., top-down tree transducers, ... More

Theoretical overview of b->s hadronic decaysFeb 10 2010A wealth of data on hadronic b -> s transitions is available from the B-factories and will be improved at the LHCb experiment and possible future super-B-factories. I review the theory of these decays as it pertains to the search for physics beyond the ... More