Eldorado Collection:
http://hdl.handle.net/2003/24992
Tue, 21 Sep 2021 04:58:38 GMT2021-09-21T04:58:38ZTravelling wave solutions for gravity fingering in porous media flows
http://hdl.handle.net/2003/39997
Title: Travelling wave solutions for gravity fingering in porous media flows
Authors: Mitra, Koondanibha; Schweizer, Ben; Rätz, Andreas
Abstract: We study an imbibition problem for porous media. When a wetted layer is above a dry medium, gravity leads to the propagation of the water downwards into the medium. In experiments, the occurence of ﬁngers was observed, a phenomenon that can be described with models that include hysteresis. In the present paper we describe a single ﬁnger in a moving frame and set up a free boundary problem to describe the shape and the motion of one ﬁnger that propagates with a constant speed. We show the existence of solutions to the travelling wave problem and investigate the system numerically.Tue, 01 Dec 2020 00:00:00 GMThttp://hdl.handle.net/2003/399972020-12-01T00:00:00ZConcentration inequalities in random Schrödinger operators
http://hdl.handle.net/2003/39790
Title: Concentration inequalities in random Schrödinger operators
Authors: Schuhmacher, ChristophMon, 21 Jan 2019 00:00:00 GMThttp://hdl.handle.net/2003/397902019-01-21T00:00:00ZLimit theorems and soft edge of freezing random matrix models via dual orthogonal polynomials
http://hdl.handle.net/2003/39789
Title: Limit theorems and soft edge of freezing random matrix models via dual orthogonal polynomials
Authors: Andraus, Sergio; Hermann, Kilian; Voit, MichaelTue, 29 Sep 2020 00:00:00 GMThttp://hdl.handle.net/2003/397892020-09-29T00:00:00ZLimit theorems for Bessel and Dunkl processes of large dimensions and free convolutions
http://hdl.handle.net/2003/39788
Title: Limit theorems for Bessel and Dunkl processes of large dimensions and free convolutions
Authors: Voit, Michael; Woerner, Jeannette H. C.Mon, 28 Sep 2020 00:00:00 GMThttp://hdl.handle.net/2003/397882020-09-28T00:00:00ZSound absorption by perforated walls along boundaries
http://hdl.handle.net/2003/39206
Title: Sound absorption by perforated walls along boundaries
Authors: Donato, Patrizia; Lamacz, Agnes; Schweizer, Ben
Abstract: We analyze the Helmholtz equation in a complex domain.
A sound absorbing structure at a part of the boundary is modelled
by a periodic geometry with periodicity ε > 0. A resonator volume
of thickness ε is connected with thin channels (opening ε^3) with the
main part of the macroscopic domain. For this problem with three
different scales we analyze solutions in the limit ε → 0 and find that
the effective system can describe sound absorption.Wed, 03 Jun 2020 00:00:00 GMThttp://hdl.handle.net/2003/392062020-06-03T00:00:00ZRepresentation of solutions to wave equations with profile functions
http://hdl.handle.net/2003/38166
Title: Representation of solutions to wave equations with profile functions
Authors: Lamacz, Agnes; Schweizer, Ben
Abstract: Solutions to the wave equation with constant coefficients in $\mathbb{R}^d$ ca be represented explicitly in Fourier space. We investigate a reconstruction formula, which provides an approximation of solutions $u(., t)$ to initial data $u_0(.)$ for large times. The reconstruction consists of three steps: 1) Given $u_0$, initial data for a profile equation are extracted. 2) A profile evolution equation determines the shape of the profile at time $\tau = \varepsilon^2 t$. 3) A shell reconstruction operator transforms the profile to a function on $\mathbb{R}^d$. The sketched construction simplifies the wave equation, since only a one-dimensional problem in an $O(1)$ time span has to be solved. We prove that the construction provides a good approximation to the wave evolution operator for times $t$ of order $\varepsilon^{-2}$.Fri, 17 May 2019 00:00:00 GMThttp://hdl.handle.net/2003/381662019-05-17T00:00:00ZSome central limit theorems for random walks associated with hypergeometric functions of type BC
http://hdl.handle.net/2003/38163
Title: Some central limit theorems for random walks associated with hypergeometric functions of type BC
Authors: Artykov, Merdan; Voit, Michael
Abstract: The spherical functions of the noncompact Grassmann manifolds $G_{p,q}(\mathbb F)=G/K$ over $\mathbb F=\mathbb R, \mathbb C, \mathbb H$ with rank $q\ge1$ and
dimension parameter $p>q$ are Heckman-Opdam hypergeometric functions of type BC, when the double coset spaces $G//K$ are identified with the Weyl chamber $C_q^B\subset \mathbb R^q$ of type B. The associated double coset hypergroups on $ C_q^B$ can be embedded into a continuous family of commutative hypergroups $(C_q^B,*_p)$ with $p\in[2q-1,\infty[$ associated with these hypergeometric functions by Rösler. Several limit theorems for random walks on these hypergroups were recently derived by Voit (2017). We here present further limit theorems when the time as well as $p$ tend to $\infty$. For integers $p$, this admits interpretations for group-invariant random walks on the Grassmannians $G/K$.Thu, 01 Feb 2018 00:00:00 GMThttp://hdl.handle.net/2003/381632018-02-01T00:00:00ZContinuous Association Schemes and Hypergroups
http://hdl.handle.net/2003/38162
Title: Continuous Association Schemes and Hypergroups
Authors: Voit, Michael
Abstract: Classical finite association schemes lead to finite-dimensional algebras which are generated by finitely many stochastic matrices. Moreover, there exist associated finite hypergroups. The notion of classical discrete association schemes can be easily extended to the possibly infinite case. Moreover, this notion can be relaxed slightly by using suitably deformed families of stochastic matrices by skipping the integrality conditions. This leads to a larger class of examples which are again associated to discrete hypergroups.
In this paper we propose a topological generalization of association schemes by using a locally compact basis space $X$ and a family of Markov-kernels on $X$ indexed by some locally compact space $D$ where the supports of the associated probability measures satisfy some partition property. These objects, called continuous association schemes, will be related to hypergroup structures on $D$. We study some basic results for this notion and present several classes of examples. It turns out that for a given commutative hypergroup the existence of an associated continuous association scheme implies that the hypergroup has many features of a double coset hypergroup. We in particular show that commutative hypergroups, which are associated with commutative continuous association schemes, carry dual positive product formulas for the characters. On the other hand, we prove some rigidity results in particular in the compact case which say that for given spaces $X,D$ there are only a few continuous association schemes.Thu, 01 Feb 2018 00:00:00 GMThttp://hdl.handle.net/2003/381622018-02-01T00:00:00ZExistence results for the Helmholtz equation in periodic wave-guides with energy methods
http://hdl.handle.net/2003/38161
Title: Existence results for the Helmholtz equation in periodic wave-guides with energy methods
Authors: Schweizer, Ben
Abstract: The Helmholtz equation $ - \nabla \cdot (a \nabla u) - \omega^2 u = f$ is considered in an unbounded wave-guide $\Omega := \mathbb{R} \times S \subset \mathbb{R}^d$, where $S \subset \mathbb{R}^{d-1}$ is a bounded domain. The coefficient $a$ is strictly elliptic and (locally) periodic in the unbounded direction $x_1\in \mathbb{R}$. For non-singular frequencies $\omega$, we show the existence of a solution $u$. While previous proofs of such results were based on operator theory, our proof uses only energy methods.Fri, 10 May 2019 00:00:00 GMThttp://hdl.handle.net/2003/381612019-05-10T00:00:00ZFunctional central limit theorems for multivariate Bessel processes in the freezing regime
http://hdl.handle.net/2003/38160
Title: Functional central limit theorems for multivariate Bessel processes in the freezing regime
Authors: Voit, Michael; Woerner, Jeannette H.C.
Abstract: Multivariate Bessel processes $(X_{t,k})_{t\ge0}$ describe interacting particle systems of Calogero-Moser-Sutherland type and are related with $\beta$-Hermite and $\beta$-Laguerre ensembles. They depend on a root system and a multiplicity $k$ which corresponds to the parameter $\beta$ in random matrix theory. In the recent years, several limit theorems were derived for $k\to\infty$ with fixed $t>0$ and fixed starting point. Only recently, Andraus and Voit used the stochastic differential equations of $(X_{t,k})_{t\ge0}$ to derive limit theorems for $k\to\infty$ with starting points of the form $\sqrt k\cdot x$ with $x$ in the interior of the corresponding Weyl chambers.Here we provide associated functional central limit theorems which are locally uniform in $t$.The Gaussian limiting processes admit explicit representations in terms of matrix exponentials and the solutions of the associated deterministic dynamical systems.Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/2003/381602019-01-01T00:00:00ZRelaxation analysis in a data driven problem with a single outlier
http://hdl.handle.net/2003/38159
Title: Relaxation analysis in a data driven problem with a single outlier
Authors: Röger, Matthias; Schweizer, Ben
Abstract: We study a scalar elliptic problem in the data driven context. Our interest is to study the relaxation of a data set that consists of the union of a linear relation and single outlier. The data driven relaxation is given by the union of the linear relation and a truncated cone that connects the outlier with the linear subspace.Thu, 11 Jul 2019 00:00:00 GMThttp://hdl.handle.net/2003/381592019-07-11T00:00:00ZThe geometric average of curl-free fields in periodic geometries
http://hdl.handle.net/2003/38158
Title: The geometric average of curl-free fields in periodic geometries
Authors: Poelstra, Klaas Hendrik; Schweizer, Ben; Urban, Maik
Abstract: In periodic homogenization problems, one considers a sequence \((u^\eta)_\eta \) of solutions to periodic problems and derives a homogenized equation for an effective quantity $\hat u$. In many applications, $\hat u$ is the weak limit of $(u^\eta)_\eta$, but in some applications $\hat u$ must be defined differently. In the homogenization of Maxwell's equations in periodic media, the effective magnetic field is given by the geometric average of the two-scale limit. The notion of a geometric average has been introduced by Bouchitté and Bourel in [3]; it associates to a curl-free field $Y\setminus \overline{\Sigma} \to \R^3$, where $Y$ is the periodicity cell and $\Sigma$ an inclusion, a vector in $\R^3$. In this article, we extend previous definitions to more general inclusions. The physical relevance of the geometric average is supported by various results, e.g., a convergence property of tangential tracesFri, 31 May 2019 00:00:00 GMThttp://hdl.handle.net/2003/381582019-05-31T00:00:00ZOn a limiting absorption principle for sesquilinear forms with an application to the Helmholtz equation in a waveguide
http://hdl.handle.net/2003/38157
Title: On a limiting absorption principle for sesquilinear forms with an application to the Helmholtz equation in a waveguide
Authors: Schweizer, Ben; Urban, Maik
Abstract: We prove a limiting absorption principle for sesquilinear forms on Hilbert spaces and apply the abstract result to a Helmholtz equation with radiation condition. The limiting absorption principle is based on a Fredholm alternative. It is applied to Helmholtz-type equations in a truncated waveguide geometry. We analyse a problem with radiation conditions on truncated domains, recently introduced in [4]. We improve the previous results by treating the limit δ→0 .Mon, 01 Apr 2019 00:00:00 GMThttp://hdl.handle.net/2003/381572019-04-01T00:00:00ZBeta distributions and Sonine integrals for Bessel functions on symmetric cones
http://hdl.handle.net/2003/37875
Title: Beta distributions and Sonine integrals for Bessel functions on symmetric cones
Authors: Rösler, Margit; Voit, Michael
Abstract: There exist several multivariate extensions of the classical Sonine integral representation for Bessel functions of some index μ + v with respect to such functions of lower index μ. For Bessel functions on matrix cones, Sonine formulas involve beta densities β_(μ,v) on the cone and trace already back to Herz. The Sonine representations known so far on symmetric cones are restricted to continuous ranges Re μ, Re v > μ_0 where the involved Beta densities are probability measures and the limiting index μ_0 ≥ 0 depends on the rank of the cone. It is zero only the one-dimensional case, but larger than zero in all multivariate cases.
In this paper, we study the extension of Sonine formulas for Bessel functions on symmetric cones to values of v below the critical limit μ_0. This is achieved by an analytic extension of the involved Beta measures as tempered distributions. Following recent ideas by A. Sokal for Riesz distributions on symmetric cones, we analyze for which indices the obtained Beta distributions are still measures. At the same time, we characterize the indices for which a Sonine formula between the related Bessel functions exists. As for Riesz
distributions, there occur gaps in the admissible range of indices which are determined by the so-called Wallach set.Thu, 01 Feb 2018 00:00:00 GMThttp://hdl.handle.net/2003/378752018-02-01T00:00:00ZMathematical analysis of transmission properties of electromagnetic meta-materials
http://hdl.handle.net/2003/37864
Title: Mathematical analysis of transmission properties of electromagnetic meta-materials
Authors: Ohlberger, Mario; Schweizer, Ben; Urban, Maik; Verfürth, Barbara
Abstract: We study time-harmonic Maxwell's equations in meta-materials that use either perfect conductors
or high-contrast materials. Based on known effective equations for perfectly conducting inclusions, we calculate the transmission and reflection coefficients for four different geometries. For high-contrast materials and essentially two-dimensional geometries, we analyze parallel electric and parallel magnetic fields and discuss their potential to exhibit transmission through a sample of meta-material. For a numerical study, one often needs a method that is adapted to heterogeneous media; we consider here a Heterogeneous Multiscale Method for high contrast materials. The qualitative transmission properties, as predicted by the analysis, are confirmed with numerical experiments. The numerical results also underline the applicability of the multiscale method.Mon, 24 Sep 2018 00:00:00 GMThttp://hdl.handle.net/2003/378642018-09-24T00:00:00ZTraveling wave solutions for the Richards equation with hysteresis
http://hdl.handle.net/2003/37863
Title: Traveling wave solutions for the Richards equation with hysteresis
Authors: El Behi-Gornostaeva, Elena; Mitra, Koondanibha; Schweizer, Ben
Abstract: We investigate the one-dimensional non-equilibrium Richards equation with play-type hysteresis. It is known that regularized versions of this equation permit traveling wave solutions that show oscillations and, in particular, the physically relevant effect of a saturation overshoot. We investigate here the non-regularized
hysteresis operator and combine it with a positive τ-term. Our result is that the model has monotone traveling wave solutions. These traveling waves describe the behavior of fronts in a bounded domain. In a two-dimensional interpretation, the result characterizes the speed of fingers in non-homogeneous solutions.Mon, 24 Sep 2018 00:00:00 GMThttp://hdl.handle.net/2003/378632018-09-24T00:00:00ZCentral limit theorems for multivariate Bessel processes in the freezing regime
http://hdl.handle.net/2003/37862
Title: Central limit theorems for multivariate Bessel processes in the freezing regime
Authors: Voit, Michael
Abstract: Multivariate Bessel processes (X_(t,k) )t≥0 are classified via associated root systems and multiplicity constants k ≥ 0. They describe the dynamics of interacting particle systems of Calogero-Moser-Sutherland type. Recently, Andraus, Katori, and Miyashita derived some weak laws of large numbers
for X_(t,k) for fixed times t > 0 and k→∞.
In this paper we derive associated central limit theorems for the root systems of types A, B and D in an elementary way. In most cases, the limits will be normal distributions, but in the B-case there are freezing limits where distributions associated with the root system A or one-sided normal distributions on half-spaces appear. Our results are connected to central limit theorems of Dumitriu and Edelman for β-Hermite and β-Laguerre ensembles.Thu, 01 Nov 2018 00:00:00 GMThttp://hdl.handle.net/2003/378622018-11-01T00:00:00ZLimit theorems for multivariate Bessel processes in the freezing regime
http://hdl.handle.net/2003/37861
Title: Limit theorems for multivariate Bessel processes in the freezing regime
Authors: Andraus, Sergio; Voit, Michael
Abstract: Multivariate Bessel processes describe the stochastic dynamics of
interacting particle systems of Calogero-Moser-Sutherland type and are related
with β-Hermite and Laguerre ensembles. It was shown by Andraus, Katori,
and Miyashita that for fixed starting points, these processes admit interesting
limit laws when the multiplicities k tend to ∞, where in some cases the limits
are described by the zeros of classical Hermite and Laguerre polynomials. In
this paper we use SDEs to derive corresponding limit laws for starting points
of the form √k∙x for k→∞ with x in the interior of the corresponding Weyl
chambers. Our limit results are a.s. locally uniform in time. Moreover, in
some cases we present associated central limit theorems.Thu, 01 Nov 2018 00:00:00 GMThttp://hdl.handle.net/2003/378612018-11-01T00:00:00ZEffective Helmholtz problem in a domain with a Neumann sieve perforation
http://hdl.handle.net/2003/37860
Title: Effective Helmholtz problem in a domain with a Neumann sieve perforation
Authors: Schweizer, Ben
Abstract: A first order model for the transmission of waves through a sound-hard perforation along an interface is derived. Mathematically, we study the Neumann problem for the Helmholtz equation in a complex geometry, the domain contains a periodic array of inclusions of size ε > 0 along a co-dimension 1 manifold.
We derive effective equations that describe the limit as ε → 0. At leading order, the Neumann sieve perforation has no effect; the corrector is given by a Helmholtz equation on the unperturbed domain with jump conditions across the interface. The corrector equations are derived with unfolding methods in L^1-based spaces.Thu, 06 Dec 2018 00:00:00 GMThttp://hdl.handle.net/2003/378602018-12-06T00:00:00ZTraveling wave solutions for the Richards equation with hysteresis
http://hdl.handle.net/2003/37221
Title: Traveling wave solutions for the Richards equation with hysteresis
Authors: El Behi-Gornostaeva, Elena; Mitra, Koondanibha; Schweizer, Ben
Abstract: We investigate the one-dimensional non-equilibrium Richards equation with play-type hysteresis. It is known that regularized versions of this equation permit traveling wave solutions that show oscillations and, in particular, the physically relevant effect of a saturation overshoot. We investigate here the non-regularized
hysteresis operator and combine it with a positive τ-term. Our result is that the model has monotone traveling wave solutions. These traveling waves describe the behavior of fronts in a bounded domain. In a two-dimensional interpretation, the result characterizes the speed of fingers in non-homogeneous solutions.Mon, 24 Sep 2018 00:00:00 GMThttp://hdl.handle.net/2003/372212018-09-24T00:00:00ZMathematical analysis of transmission properties of electromagnetic meta-materials
http://hdl.handle.net/2003/37202
Title: Mathematical analysis of transmission properties of electromagnetic meta-materials
Authors: Ohlberger, Mario; Schweizer, Ben; Urban, Maik; Verfürth, Barbara
Abstract: We study time-harmonic Maxwell's equations in meta-materials that use either perfect conductors
or high-contrast materials. Based on known effective equations for perfectly conducting inclusions, we calculate the transmission and reflection coefficients for four different geometries. For high-contrast materials and essentially two-dimensional geometries, we analyze parallel electric and parallel magnetic fields and discuss their potential to exhibit transmission through a sample of meta-material. For a numerical study, one often needs a method that is adapted to heterogeneous media; we consider here a Heterogeneous Multiscale Method for high contrast materials. The qualitative transmission properties, as predicted by the analysis, are confirmed with numerical experiments. The numerical results also underline the applicability of the multiscale method.Mon, 24 Sep 2018 00:00:00 GMThttp://hdl.handle.net/2003/372022018-09-24T00:00:00ZLattice dynamics on large time scales and dispersive effective equations
http://hdl.handle.net/2003/36361
Title: Lattice dynamics on large time scales and dispersive effective equations
Authors: Schweizer, Ben; Theil, Florian
Abstract: We investigate the long time behavior of waves in crystals. Starting from a linear wave equation on a discrete lattice with periodicity ε > 0, we derive the continuum limit equation for time scales of order ε^(-2). The effective equation is a weakly dispersive wave equation of fourth order. Initial values with bounded support result in ring-like solutions and we characterize the dispersive long-time behavior of the radial profiles with a linearized KdV equation of third order.Tue, 19 Dec 2017 00:00:00 GMThttp://hdl.handle.net/2003/363612017-12-19T00:00:00ZA note on the regularity of matrices with uniform polynomial entries
http://hdl.handle.net/2003/36360
Title: A note on the regularity of matrices with uniform polynomial entries
Authors: Klinker, Frank; Reineke, Christoph
Abstract: In this text we study the regularity of matrices with special polynomial entries. Up to some mild conditions we show that these matrices are regular if a natural limit size is not exceeded. The proof draws connections to generalized Vandermonde matrices and Schur polynomials that are discussed in detail.Fri, 01 Dec 2017 00:00:00 GMThttp://hdl.handle.net/2003/363602017-12-01T00:00:00ZA Bloch wave numerical scheme for scattering problems in periodic wave-guides
http://hdl.handle.net/2003/36118
Title: A Bloch wave numerical scheme for scattering problems in periodic wave-guides
Authors: Dohnal, Tomáš; Schweizer, Ben
Abstract: We present a new numerical scheme to solve the Helmholtz
equation in a wave-guide. We consider a medium that is bounded in
the x2-direction, unbounded in the x1-direction and ε-periodic for large
|x1|, allowing different media on the left and on the right. We suggest
a new numerical method that is based on a truncation of the domain
and the use of Bloch wave ansatz functions in radiation boxes. We prove
the existence and a stability estimate for the infinite dimensional version
of the proposed problem. The scheme is tested on several interfaces of
homogeneous and periodic media and it is used to investigate the effect
of negative refraction at the interface of a photonic crystal with a positive
effective refractive index.Tue, 01 Aug 2017 00:00:00 GMThttp://hdl.handle.net/2003/361182017-08-01T00:00:00ZStrain gradient visco-plasticity with dislocation densities contributing to the energy
http://hdl.handle.net/2003/35963
Title: Strain gradient visco-plasticity with dislocation densities contributing to the energy
Authors: Röger, Matthias; Schweizer, Ben
Abstract: We consider the energetic description of a visco-plastic evolution
and derive an existence result. The energies are convex, but not necessarily
quadratic. Our model is a strain gradient model in which the curl of the
plastic strain contributes to the energy. Our existence results are based on a
time-discretization, the limit procedure relies on Helmholtz decompositions
and compensated compactness.Tue, 18 Apr 2017 00:00:00 GMThttp://hdl.handle.net/2003/359632017-04-18T00:00:00ZThe general non-symmetric, unbalanced star circuit
http://hdl.handle.net/2003/35905
Title: The general non-symmetric, unbalanced star circuit
Authors: Eggert, Christian; Gäer, Ralf; Klinker, Frank
Abstract: We provide the general solution of problems concerning AC star
circuits by turning them into geometric problems. We show that one problem
is strongly related to the Fermat-point of a triangle. We present a solution
that is well adapted to the practical application the problem is based on.
Furthermore, we solve a generalization of the geometric situation and discuss
the relation to non-symmetric, unbalanced AC star circuits.Wed, 30 Nov 2016 00:00:00 GMThttp://hdl.handle.net/2003/359052016-11-30T00:00:00ZEffective Maxwell’s equations in general periodic microstructures
http://hdl.handle.net/2003/35904
Title: Effective Maxwell’s equations in general periodic microstructures
Authors: Schweizer, Ben; Urban, Maik
Abstract: We study the time harmonic Maxwell equations in a meta-material
consisting of perfect conductors and void space. The meta-material is assumed to
be periodic with period η > 0; we study the behaviour of solutions ( E^η ,H^η ) in the
limit η → 0 and derive an effective system. In geometries with a non-trivial topology,
the limit system implies that certain components of the effective fields vanish.
We identify the corresponding effective system and can predict, from topological
properties of the meta-material, whether or not it permits the propagation of waves.Wed, 15 Mar 2017 00:00:00 GMThttp://hdl.handle.net/2003/359042017-03-15T00:00:00ZEffective Maxwell´s equations for perfectly conducting split ring resonators
http://hdl.handle.net/2003/35841
Title: Effective Maxwell´s equations for perfectly conducting split ring resonators
Authors: Lipton, Robert; Schweizer, Ben
Abstract: We analyze the time harmonic Maxwell's equations
in a geometry containing perfectly conducting split rings. We
derive the homogenization limit in which the typical size
of the rings tends to zero. The split rings act as resonators
and the assembly can act, effectively, as a magnetically active
material. The frequency dependent effective permeability of
the medium can be large and/or negative.Mon, 19 Dec 2016 00:00:00 GMThttp://hdl.handle.net/2003/358412016-12-19T00:00:00ZResonance meets homogenization - Construction of meta-materials with astonishing properties
http://hdl.handle.net/2003/35840
Title: Resonance meets homogenization - Construction of meta-materials with astonishing properties
Authors: Schweizer, Ben
Abstract: Meta-materials are assemblies of small components. Even though the
single component consists of ordinary materials, the meta-material may
behave effectively in a way that is not known from ordinary materials. In
this text, we discuss some meta-materials that exhibit unusual properties
in the propagation of sound or light. The phenomena are based on
resonance effects in the small components. The small (sub-wavelength)
components can be resonant to the wave-length of an external field if
they incorporate singular features such as a high contrast or a singular
geometry. Homogenization theory allows to derive effective equations for
the macroscopic description of the meta-material and to verify its unusual
properties. We discuss three examples: Sound-absorbing materials,
optical materials with a negative index of refraction, perfect transmission
through grated metals.Sat, 01 Oct 2016 00:00:00 GMThttp://hdl.handle.net/2003/358402016-10-01T00:00:00ZOn Friedrichs inequality, Helmholtz decomposition, vector potentials, and the div-curl lemma
http://hdl.handle.net/2003/35839
Title: On Friedrichs inequality, Helmholtz decomposition, vector potentials, and the div-curl lemma
Authors: Schweizer, Ben
Abstract: We study connections between four different types of results that are concerned with vector-valued functions u : Ω→ℝ³ of class L²(Ω) on a domain Ω ⊂ ℝ³: Coercivity results in H^1(Ω) relying on div and curl, the Helmholtz decomposition, the construction of vector potentials, and the global div-curl lemma.Fri, 23 Sep 2016 00:00:00 GMThttp://hdl.handle.net/2003/358392016-09-23T00:00:00ZGeneralized commutative association schemes, hypergroups, and positive product formulas
http://hdl.handle.net/2003/35838
Title: Generalized commutative association schemes, hypergroups, and positive product formulas
Authors: Voit, Michael
Abstract: It is well known that finite commutative association schemes in the sense of the monograph of Bannai and Ito lead to finite commutative hypergroups with positive dual convolutions and even dual hypergroup structures. In this paper we present several discrete generalizations of association schemes which also lead to associated hypergroups. We show that discrete commutative hypergroups associated with such generalized association schemes admit dual positive convolutions at least on the support of the Plancherel measure. We hope that examples for this theory will lead to the existence of new dual positive product formulas in near future.Mon, 01 Aug 2016 00:00:00 GMThttp://hdl.handle.net/2003/358382016-08-01T00:00:00ZEffective acoustic properties of a meta-material consisting of small Helmholtz resonators
http://hdl.handle.net/2003/34958
Title: Effective acoustic properties of a meta-material consisting of small Helmholtz resonators
Authors: Lamacz, Agnes; Schweizer, Ben
Abstract: We investigate the acoustic properties of meta-materials that are inspired
by sound-absorbing structures. We show that it is possible to construct
meta-materials with frequency-dependent effective properties, with
large and/or negative permittivities. Mathematically, we investigate solutions
υ^ε:Ω^ε→ℝ to a Helmholtz equation in the limit ε→0 with the help
of two-scale convergence. The domain Ωε is obtained by removing from
an open set Ω⊂ℝⁿ in a periodic fashion a large number (order ε⁻ⁿ) of
small resonators (order ε). The special properties of the meta-material are
obtained through sub-scale structures in the perforations.Wed, 16 Mar 2016 00:00:00 GMThttp://hdl.handle.net/2003/349582016-03-16T00:00:00ZThe general treatment of non-symmetric, non-balanced star circuits: On the geometrization of problems in electrical metrology
http://hdl.handle.net/2003/34439
Title: The general treatment of non-symmetric, non-balanced star circuits: On the geometrization of problems in electrical metrology
Authors: Eggert, Christian; Gäer, Ralf; Klinker, Frank
Abstract: In the present note we provide the general solution of a question concerning
non-symmetric AC star circuits that came up in a practical application:
Given a non-symmetric AC star circuit, we need the quantities of the line voltages.
For technical reasons these quantities cannot be measured directly but the
phase-to-phase voltages can be. In this text we present a way to compute the
needed quantities from the measured ones. We translate this problem in electrical
metrology to a geometric one and present in detail a general solution that is well
adapted to the practical problem. Furthermore, we solve the generalization of the
problem that discusses the non-symmetric, non-balanced star circuit. In addition,
we give some further remarks on the mathematical side of the initial problem.Wed, 16 Dec 2015 00:00:00 GMThttp://hdl.handle.net/2003/344392015-12-16T00:00:00ZOscillating Ornstein-Uhlenbeck processes and modelling of electricity prices
http://hdl.handle.net/2003/34269
Title: Oscillating Ornstein-Uhlenbeck processes and modelling of electricity prices
Authors: Kobe, Daniel; Woerner, Jeannette H.C.
Abstract: In this paper we propose an alternative model for electricity spot prices based on
oscillating Ornstein-Uhlenbeck processes. This model captures the characteristics
of empirical data, especially the oscillating shape of the autocorrelation function.
Furthermore, we show that our model leads to explicit formulas for forwards and
options on forwards.Tue, 22 Sep 2015 00:00:00 GMThttp://hdl.handle.net/2003/342692015-09-22T00:00:00ZA distributional limit theorem for the realized power variation of linear fractional stable motions
http://hdl.handle.net/2003/34261
Title: A distributional limit theorem for the realized power variation of linear fractional stable motions
Authors: Glaser, Sven
Abstract: In this article we deduce a distributional theorem for the realized power variation of linear fractional stable
motions. This theorem is proven by choosing the technique of subordination to reduce the proof to a Gaussian limit theorem based on Malliavin-calculus.Tue, 01 Sep 2015 00:00:00 GMThttp://hdl.handle.net/2003/342612015-09-01T00:00:00ZEstimating drift parameters in a fractional Ornstein Uhlenbeck process with periodic mean
http://hdl.handle.net/2003/34260
Title: Estimating drift parameters in a fractional Ornstein Uhlenbeck process with periodic mean
Authors: Dehling, Herold; Franke, Brice; Woerner, Jeannette H.C.
Abstract: We construct a least squares estimator for the drift parameters of a fractional
Ornstein Uhlenbeck process with periodic mean function and long range dependence. For
this estimator we prove consistency and asymptotic normality. In contrast to the classical
fractional Ornstein Uhlenbeck process without periodic mean function the rate of conver-
gence is slower depending on the Hurst parameter H, namely n1-H.Wed, 09 Sep 2015 00:00:00 GMThttp://hdl.handle.net/2003/342602015-09-09T00:00:00ZA coupled surface-Cahn-Hilliard bulk-diffusion system modeling lipid raft formation in cell membranes
http://hdl.handle.net/2003/34257
Title: A coupled surface-Cahn-Hilliard bulk-diffusion system modeling lipid raft formation in cell membranes
Authors: Garcke, Harald; Kampmann, Johannes; Rätz, Andreas; Röger, Matthias
Abstract: We propose and investigate a model for lipid raft formation and dynamics in biological
membranes. The model describes the lipid composition of the membrane and an interaction
with cholesterol. To account for cholesterol exchange between cytosol and cell membrane we couple
a bulk-diffusion to an evolution equation on the membrane. The latter describes a relaxation
dynamics for an energy taking lipid-phase separation and lipid-cholesterol interaction energy into
account. It takes the form of an (extended) Cahn{Hilliard equation. Different laws for the exchange
term represent equilibrium and non-equilibrium models. We present a thermodynamic
justification, analyze the respective qualitative behavior and derive asymptotic reductions of the
model. In particular we present a formal asymptotic expansion near the sharp interface limit,
where the membrane is separated into two pure phases of saturated and unsaturated lipids, respectively.
Finally we perform numerical simulations and investigate the long-time behavior of
the model and its parameter dependence. Both the mathematical analysis and the numerical
simulations show the emergence of raft-like structures in the non-equilibrium case whereas in the
equilibrium case only macrodomains survive in the long-time evolution.Tue, 01 Sep 2015 00:00:00 GMThttp://hdl.handle.net/2003/342572015-09-01T00:00:00ZOutgoing wave conditions in photonic crystals and transmission properties at interfaces
http://hdl.handle.net/2003/34215
Title: Outgoing wave conditions in photonic crystals and transmission properties at interfaces
Authors: Lamacz, Agnes; Schweizer, Ben
Abstract: We analyze the propagation of waves in unbounded photonic crystals, the
waves are described by a Helmholtz equation with x-dependent coefficients. The
scattering problem must be completed with a radiation condition at infinity, which
was not available for x-dependent coefficients. We develop an outgoing wave
condition with the help of a Bloch wave expansion. Our radiation condition
admits a (weak) uniqueness result, formulated in terms of the Bloch measure
of solutions. We use the new radiation condition to analyze the transmission
problem where, at fixed frequency, a wave hits the interface between free space
and a photonic crystal. We derive that the vertical wave number of the incident
wave is a conserved quantity. Together with the frequency condition for the
transmitted wave, this condition leads (for appropriate photonic crystals) to the
effect of negative refraction at the interface.Mon, 31 Aug 2015 00:00:00 GMThttp://hdl.handle.net/2003/342152015-08-31T00:00:00ZVariational approach to coarse-graining of generalized gradient flows
http://hdl.handle.net/2003/34189
Title: Variational approach to coarse-graining of generalized gradient flows
Authors: Duong, Manh Hong; Lamacz, Agnes; Peletier, Mark A.; Sharma, Upanshu
Abstract: In this paper we present a variational technique that handles coarse-graining and passing to a limit in a unified manner. The technique is based on a duality structure, which is present in many gradient flows and other variational evolutions, and which often arises from a large-deviations principle. It has three main features: (A) a natural interaction between the duality structure and the coarse-graining, (B) application to systems with non-dissipative effects, and (C) application to coarse-graining of approximate solutions which solve the equation only to some error. As examples, we use this technique to solve three limit problems, the overdamped limit of the Vlasov-Fokker-Planck equation and the small-noise limit of randomly perturbed Hamiltonian systems with one and with many degrees of freedom.Tue, 04 Aug 2015 00:00:00 GMThttp://hdl.handle.net/2003/341892015-08-04T00:00:00ZA negative index meta-material for Maxwell´s equations
http://hdl.handle.net/2003/34176
Title: A negative index meta-material for Maxwell´s equations
Authors: Schweizer, Ben; Lamacz, Agnes
Abstract: We derive the homogenization limit for time harmonic Maxwell's equations
in a periodic geometry with periodicity length η > 0. The considered
meta-material has a singular sub-structure: the permittivity coefficient in
the inclusions scales like η⁻² and a part of the substructure (corresponding
to wires in the related experiments) occupies only a volume fraction of order
η²; the fact that the wires are connected across the periodicity cells leads
to contributions in the effective system. In the limit η → 0, we obtain a
standard Maxwell system with a frequency dependent effective permeability
μ^eff (ω) and a frequency independent effective permittivity ε^eff. Our formulas
for these coefficients show that both coefficients can have a negative real
part, the meta-material can act like a negative index material. The magnetic
activity μ^eff≠1 is obtained through dielectric resonances as in previous publications.
The wires are thin enough to be magnetically invisible, but, due
to their connectedness property, they contribute to the effective permittivity.
This contribution can be negative due to a negative permittivity in the wires.Wed, 29 Jul 2015 00:00:00 GMThttp://hdl.handle.net/2003/341762015-07-29T00:00:00ZDispersion and limit theorems for random walks associated with hypergeometric functions of type BC
http://hdl.handle.net/2003/34134
Title: Dispersion and limit theorems for random walks associated with hypergeometric functions of type BC
Authors: Voit, Michael
Abstract: The spherical functions of the noncompact Grassmann manifolds Gp,q(F) = G/K over the (skew-)fields F = R,C,H with rank q ≥ 1 and dimension parameter p > q can be described as Heckman-Opdam hypergeometric functions of type BC, where the double coset space G//K is identified with the Weyl chamber CBq ⊂ ℝq of type B. The corresponding product formulas and Harish-Chandra integral representations were recently written down by M. Rösler and the author in an explicit way such that both formulas can be extended analytically to all real parameters p ∈ [2q − 1, ∞[, and that associated commutative convolution structures *p on CBq exist. In this paper we introduce moment functions and the dispersion of probability measures on depeCBqnding on *p and study these functions with the aid of this generalized integral representation. Moreover, we derive strong laws of large numbers and central limit theorems for associated timehomogeneous random walks on (CBq , *p) where the moment functions and the dispersion appear in order to determine drift vectors and covariance matrices of these limit laws explicitely. For integers p, all results have interpretations for G-invariant random walks on the Grassmannians G/K. Besides the BC-cases we also study the spaces GL(q, F)/U(q, F), which are related to Weyl chambers of type A, and for which corresponding results hold. For the rank-one-case q = 1, the results of this paper are well-known in the context of Jacobi-type hypergroups on [0,∞[.Mon, 01 Jun 2015 00:00:00 GMThttp://hdl.handle.net/2003/341342015-06-01T00:00:00ZDiffuse-interface approximations of osmosis free boundary problems
http://hdl.handle.net/2003/34131
Title: Diffuse-interface approximations of osmosis free boundary problems
Authors: Rätz, Andreas
Abstract: Free boundary problems based on mass conservation and surface tension with application in osmotic swelling are the topic of this contribution. We introduce new phase-field approximations of such models, in order to numerically investigate properties of the solutions. Formal justification of the proposed approximations is provided by matched asymptotic expansions supported by numerical tests reproducing the convergence for shrinking interface thickness.Mon, 01 Jun 2015 00:00:00 GMThttp://hdl.handle.net/2003/341312015-06-01T00:00:00ZA multivariate version of the disk convolution
http://hdl.handle.net/2003/34075
Title: A multivariate version of the disk convolution
Authors: Rösler, Margit; Voit, Michael
Abstract: We present an explicit product formula for the spherical functions of the compact
Gelfand pairs (G,K_1) = (SU(p + q), SU(p) × SU(q)) with p ≥ 2q, which can be considered
as the elementary spherical functions of one-dimensional K-type for the Hermitian
symmetric spaces G/K with K = S(U(p) × U(q)). Due to results of Heckman, they can
be expressed in terms of Heckman-Opdam Jacobi polynomials of type BC_q with specific
half-integer multiplicities. By analytic continuation with respect to the multiplicity
parameters we obtain positive product formulas for the extensions of these spherical functions
as well as associated compact and commutative hypergroup structures parametrized
by real p ∈]2q−1,∞[. We also obtain explicit product formulas for the involved continuous
two-parameter family of Heckman-Opdam Jacobi polynomials with regular, but not
necessarily positive multiplicities. The results of this paper extend well known results for
the disk convolutions for q = 1 to higher rank.Wed, 01 Apr 2015 00:00:00 GMThttp://hdl.handle.net/2003/340752015-04-01T00:00:00ZTransmission conditions for the Helmholtzequation in perforated domains
http://hdl.handle.net/2003/34074
Title: Transmission conditions for the Helmholtzequation in perforated domains
Authors: Dörlemann, Christina; Heida, Martin; Schweizer, Ben
Abstract: We study the Helmholtz equation in a perforated domain . The domain Ωε. The domain Ωε is obtained from an open set
Ω⊂ℝ³ by removing small obstacles of typical size ε > 0, the obstacles are located along a 2-dimensional manifold Γ0 ⊂Ω, We derive
effective transmission conditions across Γ0 that characterize solutions in the limit
ε→0O. We obtain that, to leading order O(ε0)=O(1), the perforation is invisible.
On the other hand, at order O(ε1)=O(ε), inhomogeneous jump conditions for the
pressure and the flux appear. The jumps can be characterized without cell problems
by elementary expressions that contain the ε0-order limiting pressure function and
the volume of the obstacles.Tue, 07 Apr 2015 00:00:00 GMThttp://hdl.handle.net/2003/340742015-04-07T00:00:00ZInternational Conference Geometric and Algebraic Methods in Mathematical Physics
http://hdl.handle.net/2003/33997
Title: International Conference Geometric and Algebraic Methods in Mathematical PhysicsSun, 01 Mar 2015 00:00:00 GMThttp://hdl.handle.net/2003/339972015-03-01T00:00:00ZAn explicit description of SL (2, ℂ) in terms of SO⁺(3, 1) and vice versa
http://hdl.handle.net/2003/33806
Title: An explicit description of SL (2, ℂ) in terms of SO⁺(3, 1) and vice versa
Authors: Klinker, FrankMon, 01 Dec 2014 00:00:00 GMThttp://hdl.handle.net/2003/338062014-12-01T00:00:00ZIntegral representation and sharp asymptotic results for some Heckman-Opdam hypergeometric functions of type BC
http://hdl.handle.net/2003/33761
Title: Integral representation and sharp asymptotic results for some Heckman-Opdam hypergeometric functions of type BC
Authors: Rösler, Margit; Voit, Michael
Abstract: The Heckman-Opdam hypergeometric functions of type BC extend classical Jacobi functions in one variable and include the spherical functions of non-compact Grassmann manifolds over the real, complex or quaternionic numbers. There are various limit transitions known for such hypergeometric functions, see e.g. [dJ], [RKV]. In the present paper, we use an explicit form of the Harish-Chandra integral representation as well as an interpolated variant, in order to obtain limit results for three continuous classes of hypergeometric functions of type BC which are distinguished by explicit, sharp and uniform error bounds. The first limit realizes the approximation of the spherical functions of infinite dimensional Grassmannians of fixed rank; here hypergeometric functions of type A appear as limits. The second limit is a contraction limit towards Bessel functions of Dunkl type.Mon, 01 Dec 2014 00:00:00 GMThttp://hdl.handle.net/2003/337612014-12-01T00:00:00ZStochastic homogenization of plasticity equations
http://hdl.handle.net/2003/33760
Title: Stochastic homogenization of plasticity equations
Authors: Heida, Martin; Schweizer, BenTue, 02 Dec 2014 00:00:00 GMThttp://hdl.handle.net/2003/337602014-12-02T00:00:00ZA central limit theorem for random walks on the dual of a compact Grassmannian
http://hdl.handle.net/2003/33759
Title: A central limit theorem for random walks on the dual of a compact Grassmannian
Authors: Rösler, Margit; Voit, Michael
Abstract: We consider compact Grassmann manifolds G/K over the real, complex or quaternionic numbers whose spherical functions are Heckman-Opdam polynomials of type BC. From an explicit integral representation of these polynomials we deduce a sharp Mehler-Heine formula, that is an approximation of the Heckman-Opdam polynomials in terms of Bessel functions, with a precise estimate on the error term. This result is used to derive a central limit theorem for random walks on the semi-lattice parametrizing the dual of G/K, which are constructed by successive decompositions of tensor powers of spherical representations of G. The limit is the distribution of a Laguerre ensemble in random matrix theory. Most results of this paper are established for a larger continuous set of multiplicity parameters beyond the group cases.Mon, 01 Dec 2014 00:00:00 GMThttp://hdl.handle.net/2003/337592014-12-01T00:00:00ZEleven-dimensional symmetric supergravity backgrounds, their geometric superalgebras, and a common reduction
http://hdl.handle.net/2003/33657
Title: Eleven-dimensional symmetric supergravity backgrounds, their geometric superalgebras, and a common reduction
Authors: Klinker, Frank
Abstract: We present two different families of eleven-dimensional manifolds that admit non-restricted extensions of their isometry algebras to geometric superalgebras. Both families admit points for which the superalgebra extends to a super Lie algebra; on the one hand, a family of N = 1, 𝜈=3/4 supergravity backgrounds and, on the other hand, an N = 1, 𝜈=1 supergravity background. Furthermore, both families admit a point that can be identified with an N = 4, 𝜈=1/2 six-dimensional supergravity background.Thu, 23 Oct 2014 00:00:00 GMThttp://hdl.handle.net/2003/336572014-10-23T00:00:00ZBifurcation of nonlinear Bloch waves from the spectrum in the Gross-Pitaevskii equation
http://hdl.handle.net/2003/33651
Title: Bifurcation of nonlinear Bloch waves from the spectrum in the Gross-Pitaevskii equation
Authors: Dohnal, Tomáš; Uecker, Hannes
Abstract: We rigorously analyze the bifurcation of so called nonlinear Bloch waves (NLBs)
from the spectrum in the Gross-Pitaevskii (GP) equation with a periodic potential, in arbitrary
space dimensions. These are solutions which can be expressed as finite sums of
quasi-periodic functions, and which in a formal asymptotic expansion are obtained from solutions
of the so called algebraic coupled mode equations. Here we justify this expansion by
proving the existence of NLBs and estimating the error of the formal asymptotics. The analysis
is illustrated by numerical bifurcation diagrams, mostly in 2D. In addition, we illustrate
some relations of NLBs to other classes of solutions of the GP equation, in particular to so
called out{of{gap solitons and truncated NLBs.Mon, 20 Oct 2014 00:00:00 GMThttp://hdl.handle.net/2003/336512014-10-20T00:00:00ZA family of non-restricted D=11 geometric supersymmetries
http://hdl.handle.net/2003/33487
Title: A family of non-restricted D=11 geometric supersymmetries
Authors: Klinker, Frank
Abstract: We construct a two parameter family of irreducible, eleven-dimensional, indecomposable, non-flat Cahen-Wallach spaces with non-restricted geometric supersymmetry of fraction ν = 3/4. Its compactified moduli space can be parametrized by a compact interval with two points corresponding to two non-isometric, decomposable spaces. These singular spaces are associated to a restricted N = 4 geometric supersymmetry with ν = 1/2 in dimension six and a non-restricted N = 2 geometric supersymmetry with ν = 3/4 in dimension nine.Mon, 14 Jul 2014 00:00:00 GMThttp://hdl.handle.net/2003/334872014-07-14T00:00:00ZNon-periodic homogenization of infinitesimal strain plasticity equations
http://hdl.handle.net/2003/33268
Title: Non-periodic homogenization of infinitesimal strain plasticity equations
Authors: Heida, Martin; Schweizer, BenFri, 23 May 2014 00:00:00 GMThttp://hdl.handle.net/2003/332682014-05-23T00:00:00ZThe low frequency spectrum of small Helmholtz resonators
http://hdl.handle.net/2003/33030
Title: The low frequency spectrum of small Helmholtz resonators
Authors: Schweizer, BenSun, 27 Apr 2014 00:00:00 GMThttp://hdl.handle.net/2003/330302014-04-27T00:00:00ZDispersive homogenized models and coefficient formulas for waves in general periodic media
http://hdl.handle.net/2003/33029
Title: Dispersive homogenized models and coefficient formulas for waves in general periodic media
Authors: Dohnal, Tomáš; Lamacz, Agnes; Schweizer, BenWed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/2003/330292014-01-01T00:00:00ZDispersive homogenized models and coefficient formulas for waves in general periodic media
http://hdl.handle.net/2003/32869
Title: Dispersive homogenized models and coefficient formulas for waves in general periodic media
Authors: Dohnal, Tomáš; Lamacz, Agnes; Schweizer, BenFri, 14 Feb 2014 00:00:00 GMThttp://hdl.handle.net/2003/328692014-02-14T00:00:00ZAlmost opposite regression dependence in bivariate distributions
http://hdl.handle.net/2003/31302
Title: Almost opposite regression dependence in bivariate distributions
Authors: Siburg, Karl FriedrichThu, 12 Dec 2013 00:00:00 GMThttp://hdl.handle.net/2003/313022013-12-12T00:00:00ZAn order for asymmetry in copulas, and implications for risk management
http://hdl.handle.net/2003/31301
Title: An order for asymmetry in copulas, and implications for risk management
Authors: Siburg, Karl Friedrich; Stehling, Katharina; Stoimenov, Pavel A.; Woerner, Jeannette H. C.
Abstract: We investigate symmetry properties of bivariate copulas. For this, we introduce an order of asymmetry, as well as measures of asymmetry which are monotone in that order. As for applications, we show that asymmetry does occur in real financial data. This implies that in finance and risk management, asymmetric models should be favored against the usual symmetric ones.Thu, 12 Dec 2013 00:00:00 GMThttp://hdl.handle.net/2003/313012013-12-12T00:00:00ZThe Gumbel test and jumps in the volatility process
http://hdl.handle.net/2003/31294
Title: The Gumbel test and jumps in the volatility process
Authors: Palmes, Christian; Woerner, Jeannette H.C.
Abstract: In the framework of jump detection in stochastic volatility models the Gumbel test based on extreme value theory has recently been introduced. Compared to other jump tests it possesses the advantages that the direction and location of jumps may also be detected. Furthermore, compared to the Barndorff-Nielsen and Shephard test based on bipower variation the Gumbel test possesses a larger power. However, so far one assumption was that the volatility process is Hölder continuous, though there is empirical evidence for jumps in the volatility as well. In this paper we derive that the Gumbel test still works under the setting of finitely many jumps not exceeding a certain size. Furthermore, we show that the given bound on the jump size is sharp.Tue, 10 Dec 2013 00:00:00 GMThttp://hdl.handle.net/2003/312942013-12-10T00:00:00ZProduct formulas for a two-parameter family of Heckman-Opdam hypergeometric functions of type BC
http://hdl.handle.net/2003/31129
Title: Product formulas for a two-parameter family of Heckman-Opdam hypergeometric functions of type BC
Authors: Voit, MichaelThu, 17 Oct 2013 00:00:00 GMThttp://hdl.handle.net/2003/311292013-10-17T00:00:00ZHomogenization of plasticity equations with two-scale convergence methods
http://hdl.handle.net/2003/31083
Title: Homogenization of plasticity equations with two-scale convergence methods
Authors: Schweizer, Ben; Veneroni, M.
Abstract: We investigate the deformation of heterogeneous plastic materials. The
model uses internal variables and kinematic hardening, elastic and plastic strain
are used in an infinitesimal strain theory. For periodic material properties with
periodicity length scale n > 0, we obtain the limiting system as n -> 0. The limiting
two-scale plasticity model coincides with well-known effective models. Our
direct approach relies on abstract tools from two-scale convergence (regarding
convex functionals and monotone operators) and on higher order estimates for
solution sequences.Wed, 09 Oct 2013 00:00:00 GMThttp://hdl.handle.net/2003/310832013-10-09T00:00:00ZA law of large numbers for the power variation of fractional Lévy processes
http://hdl.handle.net/2003/30626
Title: A law of large numbers for the power variation of fractional Lévy processes
Authors: Glaser, Sven
Abstract: We prove a law of large numbers for the power variation of an integrated fractional
process in a pure jump model. This yields consistency of an estimator for the integrated volatility
where we are no longer restricted to a Gaussian model.Mon, 30 Sep 2013 00:00:00 GMThttp://hdl.handle.net/2003/306262013-09-30T00:00:00ZThe Gumbel test for jumps in stochastic volatility models
http://hdl.handle.net/2003/30625
Title: The Gumbel test for jumps in stochastic volatility models
Authors: Palmes, Christian; Woerner, Jeannette H.C.
Abstract: In this paper we develop a test for jumps based on extreme value theory.We consider a continuous-
time stochastic volatility model with a general continuous volatility process, allowing for long- and
short-range dependence and observe it under a high-frequency sampling scheme. We show that a
certain test statistics based on the maximum of increments converges to the Gumbel distribution
under the null hypothesis of no additive jump component and to infinity otherwise. In contrast to
most other tests based on power variation our test naturally allows to distinguish between positive
and negative jumps. As a by-product of our analysis we also deduce an optimal pathwise estimator
for the spot volatility process. In addition we provide a small simulation study and show that our
test is more sensitive to jumps with a larger power than the Barndorff-Nielsen and Shephard test
based on bipower variation. Finally we apply our results to a real data set of the world stock index.Mon, 30 Sep 2013 00:00:00 GMThttp://hdl.handle.net/2003/306252013-09-30T00:00:00ZMoment bounds for the corrector in stochastic homogenization of a percolation model
http://hdl.handle.net/2003/30624
Title: Moment bounds for the corrector in stochastic homogenization of a percolation model
Authors: Lamacz, Agnes; Neukamm, Stefan; Otto, Felix
Abstract: We study the corrector equation in stochastic homogenization for a simplified Bernoulli
percolation model on Z^d, d > 2. The model is obtained from the classical {0,1}-Bernoulli
bond percolation by conditioning all bonds parallel to the first coordinate direction to be
open. As a main result we prove (in fact for a slightly more general model) that stationary
correctors exist and that all finite moments of the corrector are bounded. This extends a
previous result in [8], where uniformly elliptic conductances are treated, to the degenerate
case. Our argument is based on estimates on the gradient of the elliptic Green's function.Mon, 30 Sep 2013 00:00:00 GMThttp://hdl.handle.net/2003/306242013-09-30T00:00:00ZConnections on Cahen-Wallach spaces
http://hdl.handle.net/2003/30579
Title: Connections on Cahen-Wallach spaces
Authors: Klinker, Frank
Abstract: We systematically discuss connections on spinor bundles of Cahen-
Wallach symmetric spaces. A large class of these connections is closely connected
with a quadratic relation on a Clifford algebra. This relation in turn is
associated to a symmetric linear map that defines the underlying space. We
present various solutions of this relation. Moreover, we show that the solutions
we present here provide a complete list with respect to a particular algebraic
condition.Fri, 06 Sep 2013 00:00:00 GMThttp://hdl.handle.net/2003/305792013-09-06T00:00:00ZSymmetry breaking in a bulk-surface reaction-diffusion model for signaling networks
http://hdl.handle.net/2003/30359
Title: Symmetry breaking in a bulk-surface reaction-diffusion model for signaling networks
Authors: Rätz, Andreas; Röger, Matthias
Abstract: Signaling molecules play an important role for many cellular functions. We investigate here a general system of two membrane reaction-diffusion equations coupled to a diffusion equation inside the cell by a Robin-type boundary condition and a flux term in the membrane equations. A specific model of this form was recently proposed by the authors for the GTPase cycle in cells. We investigate here a putative role of diffusive instabilities in cell polarization. By a linearized stability analysis we identify two different mechanisms. The first resembles a classical Turing instability for the membrane subsystem and requires (unrealistically) large differences in the lateral diffusion of activator and substrate. The second possibility on the other hand is induced by the difference in cytosolic and lateral diffusion and appears much more realistic. We complement our theoretical analysis by numerical simulations that confirm the new stability mechanism and allow to investigate the evolution beyond the regime where the linearization applies.Mon, 03 Jun 2013 00:00:00 GMThttp://hdl.handle.net/2003/303592013-06-03T00:00:00ZA doubly non-linear system in small-strain visco-plasticity
http://hdl.handle.net/2003/30358
Title: A doubly non-linear system in small-strain visco-plasticity
Authors: Francfort, Gilles; Schweizer, Ben
Abstract: We study a system of small strain visco-plasticity. We use an additive decomposition of the strain into elastic and plastic part, and allow for non-linear relations in the Hooke's law and in the flow rule. We show the existence of solutions, using a time-discrete approximation scheme. The limit procedure is based on a strong convergence result for the time-discrete solution sequence.Mon, 03 Jun 2013 00:00:00 GMThttp://hdl.handle.net/2003/303582013-06-03T00:00:00ZTraveling Solitary Waves in the Periodic Nonlinear Schrödinger Equation with Finite Band Potentials
http://hdl.handle.net/2003/30321
Title: Traveling Solitary Waves in the Periodic Nonlinear Schrödinger Equation with Finite Band Potentials
Authors: Dohnal, Tomáš
Abstract: The paper studies asymptotics of moving gap solitons in nonlinear periodic structures
of finite contrast ("deep grating") within the one dimensional periodic nonlinear Schr¨odinger equation
(PNLS). Periodic structures described by a finite band potential feature transversal crossings of band
functions in the linear band structure and a periodic perturbation of the potential yields new small
gaps. An approximation of gap solitons in such a gap is given by slowly varying envelopes which
satisfy a system of generalized Coupled Mode Equations (gCME) and by Bloch waves at the crossing
point. The eigenspace at the crossing point is two dimensional and it is necessary to select Bloch
waves belonging to the two band functions. This is achieved by an optimization algorithm. Traveling
solitary wave solutions of the gCME then result in nearly solitary wave solutions of PNLS moving at
an O(1) velocity across the periodic structure. A number of numerical tests are performed to confirm
the asymptotics.Thu, 16 May 2013 00:00:00 GMThttp://hdl.handle.net/2003/303212013-05-16T00:00:00ZForecasting Portfolio-Value-at-Risk with Nonparametric Lower Tail Dependence Estimates
http://hdl.handle.net/2003/30287
Title: Forecasting Portfolio-Value-at-Risk with Nonparametric Lower Tail Dependence Estimates
Authors: Siburg, Karl Friedrich; Stoimenov, Pavel; Weiß, Gregor N. F.
Abstract: We propose to forecast the Value-at-Risk of bivariate portfolios using copulas which are calibrated on
the basis of nonparametric sample estimates of the coefficient of lower tail dependence. We compare our proposed
method to a conventional copula-GARCH model where the parameter of a Clayton copula is estimated via Canonical
Maximum-Likelihood. The superiority of our proposed model is exemplified by analyzing a data sample of nine
different financial portfolios. A comparison of the out-of-sample forecasting accuracy of both models confirms that
our model yields economically significantly better Value-at-Risk forecasts than the competing parametric calibration
strategy.Mon, 29 Apr 2013 00:00:00 GMThttp://hdl.handle.net/2003/302872013-04-29T00:00:00ZOn thermodynamics of fluid interfaces
http://hdl.handle.net/2003/30147
Title: On thermodynamics of fluid interfaces
Authors: Heida, Martin
Abstract: A recently introduced method for the derivation of thermodynamically consistent boundary
conditions will be used in order to study the interaction of two fluids at the common interface and the
contact line to a solid body. The calculations allow for temperature dependent surface energy/ surface tension
and yield thermodynamical conditions on dynamic contact angles. Furthermore, we will show how Mean
Curvature Flow and Mullins-Sekerka models fit into this general framework and give a possible explanation
for the Dussan and Davis experiment [10] compared to the Huh and Scriven Paradox [17] within the presented
theory.
[10] E. B. Dussan V. and S.H. Davis. On the motion of a fluid-fluid interface along a solid surface. Journal of Fluid Mechanics,
65(01):71–95, 1974.
[17] C. Huh and LE Scriven. Hydrodynamic model of steady movement of a solid/liquid/fluid contact line. Journal of Colloid
and Interface Science, 35(1):85–101, 1971.Wed, 17 Apr 2013 00:00:00 GMThttp://hdl.handle.net/2003/301472013-04-17T00:00:00ZExistence of solutions for two types of generalized versions of the Cahn-Hilliard equation
http://hdl.handle.net/2003/30146
Title: Existence of solutions for two types of generalized versions of the Cahn-Hilliard equation
Authors: Heida, MartinWed, 17 Apr 2013 00:00:00 GMThttp://hdl.handle.net/2003/301462013-04-17T00:00:00ZDispersive effective equations for waves in heterogeneous media on large time scales
http://hdl.handle.net/2003/29943
Title: Dispersive effective equations for waves in heterogeneous media on large time scales
Authors: Dohnal, T.; Lamacz, A.; Schweizer, B.Wed, 20 Feb 2013 00:00:00 GMThttp://hdl.handle.net/2003/299432013-02-20T00:00:00ZOn gradient flows of nonconvex functionals in Hilbert spaces with Riemannian metric and application to Cahn-Hilliard equations
http://hdl.handle.net/2003/29794
Title: On gradient flows of nonconvex functionals in Hilbert spaces with Riemannian metric and application to Cahn-Hilliard equations
Authors: Heida, MartinFri, 16 Nov 2012 00:00:00 GMThttp://hdl.handle.net/2003/297942012-11-16T00:00:00ZA variational perspective on cloaking by anomalous localized resonance
http://hdl.handle.net/2003/29714
Title: A variational perspective on cloaking by anomalous localized resonance
Authors: Kohn, R. V.; Lu, J.; Schweizer, Ben; Weinstein, M. I.Tue, 16 Oct 2012 00:00:00 GMThttp://hdl.handle.net/2003/297142012-10-16T00:00:00ZOlshanski spherical functions for infinite dimensional motion groups of fixed rank
http://hdl.handle.net/2003/29659
Title: Olshanski spherical functions for infinite dimensional motion groups of fixed rank
Authors: Rösler, Margit; Voit, MichaelMon, 08 Oct 2012 00:00:00 GMThttp://hdl.handle.net/2003/296592012-10-08T00:00:00ZColliding Interfaces in Old and New Diffuse-interface Approximations of Willmore-flow
http://hdl.handle.net/2003/29653
Title: Colliding Interfaces in Old and New Diffuse-interface Approximations of Willmore-flow
Authors: Esedoglu, Selim; Rätz, Andreas; Röger, Matthias
Abstract: This paper is concerned with diffuse-interface approximations of the Willmore flow. We first present numerical results of standard diffuse-interface models for colliding one dimensional interfaces. In such a scenario evolutions towards interfaces with corners can occur that do not necessarily describe the adequate sharp-interface dynamics. We therefore propose and investigate alternative diffuse-interface approximations that lead to a different and more regular behavior if interfaces collide. These dynamics are derived from approximate energies that converge to the L1-lower-semicontinuous envelope of the Willmore energy, which is in general not true for the more standard Willmore approximation.Mon, 01 Oct 2012 00:00:00 GMThttp://hdl.handle.net/2003/296532012-10-01T00:00:00ZAn adaptive multiscale finite element method
http://hdl.handle.net/2003/29586
Title: An adaptive multiscale finite element method
Authors: Henning, Patrick; Ohlberger, Mario; Schweizer, Ben
Abstract: This work is devoted to an adaptive multiscale finite element method
(MsFEM) for solving elliptic problems with rapidly oscillating coeefficients.
Starting from a general version of the MsFEM with oversampling, we de-
rive an a posteriori estimate for the H1-error between the exact solution
of the problem and a corresponding MsFEM approximation. Our esti-
mate holds without any assumptions on scale separation or on the type of
the heterogeneity. The estimator splits into different contributions which
account for the coarse grid error, the fine grid error and the oversampling
error. Based on the error estimate we construct an adaptive algorithm
that is validated in numerical experiments.Wed, 08 Aug 2012 00:00:00 GMThttp://hdl.handle.net/2003/295862012-08-08T00:00:00ZPositive topological entropy for multi-bump magnetic fields
http://hdl.handle.net/2003/29575
Title: Positive topological entropy for multi-bump magnetic fields
Authors: Knauf, Andreas; Schulz, Frank; Siburg, Karl Friedrich
Abstract: We study the dynamics of a charged particle in a planar magnetic field which consists of n >= 1 disjoint localized peaks. We show that, under mild geometric conditions, this system is semi-conjugated to the full shift on n symbols and, hence, carries positive topological entropy.Tue, 07 Aug 2012 00:00:00 GMThttp://hdl.handle.net/2003/295752012-08-07T00:00:00ZLimit transition between hypergeometric functions of type BC and Type A
http://hdl.handle.net/2003/29494
Title: Limit transition between hypergeometric functions of type BC and Type A
Authors: Koornwinder, Tom; Rösler, Margit; Voit, MichaelWed, 04 Jul 2012 00:00:00 GMThttp://hdl.handle.net/2003/294942012-07-04T00:00:00ZGeneralization of the Blumenthal-Getoor Index to the Class of Homogeneous Di usions with Jumps and some Applications
http://hdl.handle.net/2003/29493
Title: Generalization of the Blumenthal-Getoor Index to the Class of Homogeneous Di usions with Jumps and some Applications
Authors: Schnurr, Alexander
Abstract: We introduce the probabilistic symbol for the class of homogeneous diffusions with jumps (in
the sense of Jacod/Shiryaev). This concept generalizes the well known characteristic exponent
of a Lévy process. Using the symbol we introduce eight indices which generalize the Blumenthal-
Getoor index beta and the Pruitt index delta These indices are used afterwards to obtain growth and
Hölder conditions of the process. In the future the technical main results will be used to derive
further fine properties. Since virtually all examples of homogeneous diffusions in the literature
are Markovian, we construct a process which does not have this property.Wed, 04 Jul 2012 00:00:00 GMThttp://hdl.handle.net/2003/294932012-07-04T00:00:00ZRemarks on pseudo stable laws on contractible groups
http://hdl.handle.net/2003/29492
Title: Remarks on pseudo stable laws on contractible groups
Authors: Hazod, Wilfried
Abstract: In this note we discuss a class of probability distributions
on homogeneous groups, called pseudo stable laws which were
investigated in [5] for the real line. In particular it is shown that
under mild assumptions these distributions belong to the domain
of normal attraction of stable laws.Wed, 04 Jul 2012 00:00:00 GMThttp://hdl.handle.net/2003/294922012-07-04T00:00:00ZLimit theorems for radial random walks on Euclidean spaces of high dimensions
http://hdl.handle.net/2003/29488
Title: Limit theorems for radial random walks on Euclidean spaces of high dimensions
Authors: Grundmann, WaldemarWed, 27 Jun 2012 00:00:00 GMThttp://hdl.handle.net/2003/294882012-06-27T00:00:00ZA two-scale model of two-phase ow in porous media ranging from porespace to the macro scale
http://hdl.handle.net/2003/29480
Title: A two-scale model of two-phase ow in porous media ranging from porespace to the macro scale
Authors: Heida, Martin
Abstract: We will derive two-scale models for two-phase flow in porous media, with the microscale
given by the porescale. The resulting system will account for balance of mass, momentum
and energy. To this aim, we will combine a generalization of Rajagopal’s and Srinivasa’s assumption
of maximum rate of entropy production [39, 20, 21] with formal asymptotic expansion. The
microscopic model will be based on phase fields, in particular to the full Cahn-Hilliard-Navier-
Stokes-Fourier model derived in [23] with the boundary conditions from [20]. Using a generalized
notion of characteristic functions, we will show that the solutions to the two-scale model macroscopically
behave like classical solutions to a system of porous media flow equations. Relative
permeabilities and capillary pressure relations are outcomes of the theory and exist only for special
cases. Therefore, the two-scale model can be considered as a true generalization of classical
models providing more information on the microscale thereby making the introduction of hysteresis
superfluous.Fri, 15 Jun 2012 00:00:00 GMThttp://hdl.handle.net/2003/294802012-06-15T00:00:00ZOn the derivation of thermodynamically consistent boundary conditions for the Cahn-Hilliard-Navier-Stokes system
http://hdl.handle.net/2003/29479
Title: On the derivation of thermodynamically consistent boundary conditions for the Cahn-Hilliard-Navier-Stokes system
Authors: Heida, Martin
Abstract: A new method will be introduced for the derivation of thermodynamically consistent boundary
conditions for the full Cahn-Hilliard-Navier-Stokes-Fourier system for two immiscible fluids, where the phase
field variable (order parameter) is given in terms of concentrations or partial densities. Five different types
of models will be presented and discussed. The article can be considered as a continuation of a previous work
by Heida, Málek and Rajagopal [16], which focused on the derivation and generalization of Cahn-Hilliard-
Navier-Stokes models. The method is based on the assumption of maximum rate of entropy production by
Rajagopal and Srinivasa [30]. This assumption will be generalized to surfaces of bounded domains using
an integral formulation of the balance of entropy. Following [30], the calculations are based on constitutive
equations for the bulk energy, the surface energy and the rates of entropy production in the bulk and on
the surface. The resulting set of boundary conditions will consist of dynamic boundary conditions for the
Cahn-Hilliard equation and either generalized Navier-slip, perfect slip or no-slip boundary conditions for the
balance of linear momentum. Additionally, we will find that we also have to impose a boundary condition on
the normal derivative of the normal component of the velocity field. The new approach has the advantage
that the calculations are very transparent, the resulting equations come up very naturally and it is obvious
how the calculations can be generalized to more than two fluids or more general constitutive assumptions
for the energies. Additionally to former approaches, the approach also yields the full balance of energy for
thewhole system. Finally, a possible explanation will be given for the “rolling” movement of the contact line,
first observed in Dussan and Davis [8].Fri, 15 Jun 2012 00:00:00 GMThttp://hdl.handle.net/2003/294792012-06-15T00:00:00ZUniform oscillatory behavior of spherical functions of GL_n/U_n at the identity and a central limit theorem
http://hdl.handle.net/2003/29453
Title: Uniform oscillatory behavior of spherical functions of GL_n/U_n at the identity and a central limit theorem
Authors: Voit, MichaelWed, 23 May 2012 00:00:00 GMThttp://hdl.handle.net/2003/294532012-05-23T00:00:00ZEffective Maxwell equations in a geometry with flat rings of arbitrary shape
http://hdl.handle.net/2003/29427
Title: Effective Maxwell equations in a geometry with flat rings of arbitrary shape
Authors: Lamacz, Agnes; Schweizer, Ben
Abstract: We analyze the time harmonic Maxwell’s equations in a complex
geometry. The homogenization process is performed in the case that many
small, thin conductors are distributed in a subdomain of R^3. Each single
conductor is, topologically, a split ring resonator, but we allow arbitrary
flat shapes. In the limit of large conductivities in the rings and small
ring diameters we obtain an effective Maxwell system. Depending on the
frequency, the effective system can exhibit a negative effective permeability.Mon, 23 Apr 2012 00:00:00 GMThttp://hdl.handle.net/2003/294272012-04-23T00:00:00ZEin optimiertes Gättungsverfahren motiviert durch eine technische Fragestellung
http://hdl.handle.net/2003/29414
Title: Ein optimiertes Gättungsverfahren motiviert durch eine technische Fragestellung
Authors: Klinker, Frank; Skoruppa, Günter
Abstract: Ausgehend von einer konkreten technischen Fragestellung
diskutieren wir in dieser Notiz die Anwendung verschiedener Glättungsverfahren
auf Datensätze mit vorgegebener Struktur. Wir stellen die Verfahren im
Detail vor und besprechen die Vor- und Nachteile. Insbesondere stellen wir hier
die symmetrisierte exponentielle Glättung vor, die ein sehr gutes Glättungsverhalten
mit einem hohen Maß an Symmetrieerhaltung kombiniert.Thu, 12 Apr 2012 00:00:00 GMThttp://hdl.handle.net/2003/294142012-04-12T00:00:00ZHomogenization of the degenerate two-phase flow equations
http://hdl.handle.net/2003/29407
Title: Homogenization of the degenerate two-phase flow equations
Authors: Henning, Patrick; Ohlberger, Mario; Schweizer, Ben
Abstract: We analyze two-phase flow in highly heterogeneous media.
Problems related to the degeneracy of the permeability coefficient
functions are treated with a new concept of weighted solutions. Instead
of the pressure variables we formulate the problem with the weighted
pressure function ψ, which is obtained as the product of permeability
and pressure. We perform the homogenization limit and obtain effective
equations in the form of a two-scale limit system. The nonlinear effective
system is of the classical form in the non-degenerate case. In the
degenerate case, the two-scale system uses again a weighted pressure
variable. Our approach allows to work without the global pressure
function. Even though internal interfaces are included, our approach
provides the homogenization limit without any smallness assumptions
on permeabilities or capillary pressures.Mon, 02 Apr 2012 00:00:00 GMThttp://hdl.handle.net/2003/294072012-04-02T00:00:00ZA new diffuse-interface model for step flow in epitaxial growth
http://hdl.handle.net/2003/29391
Title: A new diffuse-interface model for step flow in epitaxial growth
Authors: Rätz, Andreas
Abstract: In this work, we consider epitaxial growth of thin crystalline films. Thereby, we propose
a new diffuse-interface approximation of a semi-continuous model resolving atomic distances in the
growth direction but being coarse-grained in the lateral directions. Mathematically, this leads to a free
boundary problem proposed by Burton, Cabrera and Frank for steps separating terraces of different
atomic heights. The evolution of the steps is coupled to a diffusion equation for the adatom (adsorbed
atom) concentration fulfilling Robin-type boundary conditions at the steps. Our approach allows to
incorporate an Ehrlich-Schwoebel barrier as well as diffusion along step edges into a diffuse-interface
model.
This model results in a Cahn-Hilliard equation with a degenerate mobility coupled to diffusion
equations on the terraces with a diffuse-interface description of the boundary conditions at the steps.
We provide a justification by matched asymptotic expansions formally showing the convergence of the
diffuse-interface model towards the sharp-interface model as the interface width shrinks to zero. The
results of the asymptotic analysis are numerically reproduced by a finite element discretisation.Mon, 19 Mar 2012 00:00:00 GMThttp://hdl.handle.net/2003/293912012-03-19T00:00:00ZHysteresis models and gravity fingering in porous media
http://hdl.handle.net/2003/29390
Title: Hysteresis models and gravity fingering in porous media
Authors: Rätz, Andreas; Schweizer, Ben
Abstract: We study flow problems in unsaturated porous media. Our main interest is the gravity driven penetration of a dry material, a situation in which fingering effects can be observed experimentally and numerically. The flow is described by either a Richards or a two-phase model. The important modelling aspect regards the capillary pressure relation which can include static hysteresis and dynamic corrections. We report on analytical existence and instability results for the corresponding models and present numerical
calculations. We show that fingering effects can be observed in various models and discuss the importance of the static hysteresis term.Fri, 16 Mar 2012 00:00:00 GMThttp://hdl.handle.net/2003/293902012-03-16T00:00:00ZIntrinsic topologies on H-contraction groups with applications to semistability
http://hdl.handle.net/2003/29311
Title: Intrinsic topologies on H-contraction groups with applications to semistability
Authors: Hazod, Wilfried
Abstract: Semistable continuous convolution semigroups on Lie groups with non-trivial idempotent are characterized by semistable continuous convolution semigroups with trivial idempotent on a contractible, hence homogeneous Lie group. (Cf., e.g. [9], [10], III, theorem 3.5.4.) In fact, this homogeneous group is obtained by a retopologization of the contractible subgroup on which the original semistable laws are concentrated. In [26] E. Siebert investigated such intrinsic topologies for contractible subgroups of Polish groups, generalizing partially the before mentioned situation of Lie groups. Here we use these ideas to obtain intrinsic topologies for H-contractible subgroups of Polish groups, where H denotes a compact subgroup. This allows, under additional assumptions (which are satisfied in the Lie group case) to obtain similar characterization of semistable laws with non-trivial idempotents.Mon, 20 Feb 2012 00:00:00 GMThttp://hdl.handle.net/2003/293112012-02-20T00:00:00ZPlasmonic waves allow perfect transmission through sub-wavelength metallic gratings
http://hdl.handle.net/2003/29229
Title: Plasmonic waves allow perfect transmission through sub-wavelength metallic gratings
Authors: Bouchitté, Guy; Schweizer, Ben
Abstract: We perform a mathematical analysis of the transmission
properties of a metallic layer with narrow slits. Our analysis is inspired by
recent measurements and numerical calculations that report an unexpected
high transmission coefficient of such a structure in a subwavelength regime.
We analyze the time harmonic Maxwell’s equations in the H-parallel case
for a fixed incident wavelength. Denoting by ? the typical size of the grated
structure, we analyze the limit n -> 0 and derive effective equations that
take into account the role of plasmonic waves. We obtain a formula for the
effective transmission coefficient.Mon, 19 Dec 2011 00:00:00 GMThttp://hdl.handle.net/2003/292292011-12-19T00:00:00ZMoment functions and Central Limit Theorem for Jacobi hypergroups on [0;∞[
http://hdl.handle.net/2003/29197
Title: Moment functions and Central Limit Theorem for Jacobi hypergroups on [0;∞[
Authors: Grundmann, WaldemarTue, 22 Nov 2011 00:00:00 GMThttp://hdl.handle.net/2003/291972011-11-22T00:00:00ZTwo-phase flow equations with a dynamic capillary pressure
http://hdl.handle.net/2003/29193
Title: Two-phase flow equations with a dynamic capillary pressure
Authors: Koch, Jan; Rätz, Andreas; Schweizer, Ben
Abstract: We investigate the motion of two immiscible fluids in a porous medium described by the two-phase flow system. In the capillary pressure relation, we include static and dynamic hysteresis. The model is wellestablished in the context of the Richards equation, which is obtained by assuming a constant pressure for one of the two phases. We derive an existence result for this hysteresis-two-phase model for non-degenerate permeability and capillary pressure curves. A discretization scheme is introduced and numerical results for fingering experiments are obtained. The main analytical tool is a compactness result for two variables that are couled by an hysteresis relation.Wed, 16 Nov 2011 00:00:00 GMThttp://hdl.handle.net/2003/291932011-11-16T00:00:00ZCentral limit theorems for hyperbolic spaces and Jacobi processes on [0;Central limit theorems for hyperbolic spaces and Jacobi processes on [0;∞[
http://hdl.handle.net/2003/29150
Title: Central limit theorems for hyperbolic spaces and Jacobi processes on [0;Central limit theorems for hyperbolic spaces and Jacobi processes on [0;∞[
Authors: Voit, MichaelWed, 12 Oct 2011 00:00:00 GMThttp://hdl.handle.net/2003/291502011-10-12T00:00:00ZThe Richards equation with hysteresis and degenerate capillary pressure
http://hdl.handle.net/2003/29032
Title: The Richards equation with hysteresis and degenerate capillary pressure
Authors: Schweizer, Ben
Abstract: We study the Richards equation with a dynamic capillary pressure, including hysteresis. We provide existence and approximation results for degenerate capillary pressure curves pc, treating two cases. In the first case, the permeability function k can be degenerate, but the initial saturation does not take the critical values. In the second case, the permeability function k is strictly positive, but the capillary pressure function can be multi-valued. In both cases, the degenerate behavior of pc leads to the physically desired uniform bounds for the saturation variable. Our approach exploits maximum principles and relies on the corresponding uniform bounds for pressure and saturation. A new compactness result for the saturation variable allows to take limits in nonlinear terms. The solution concept uses tools of convex analysis.Tue, 23 Aug 2011 00:00:00 GMThttp://hdl.handle.net/2003/290322011-08-23T00:00:00ZTuring Instabilities in a Mathematical Model for Signaling Networks
http://hdl.handle.net/2003/28907
Title: Turing Instabilities in a Mathematical Model for Signaling Networks
Authors: Rätz, Andreas; Röger, Matthias
Abstract: GTPase molecules are important regulators in cells that continuously run through
an activation/deactivation and membrane-attachment/membrane-detachment cycle. Activated
GTPase is able to localize in parts of the membranes and to induce cell polarity. As feedback loops
contribute to the GTPase cycle and as the coupling between membrane-bound and cytoplasmic
processes introduces different diffusion coefficients a Turing mechanism is a natural candidate for
this symmetry breaking. We formulate a mathematical model that couples a reaction-diffusion
system in the inner volume to a reaction-diffusion system on the membrane via a
flux condition and an attachment/detachment law at the membrane. We present a reduction to a simpler nonlocal
reaction-diffusion model and perform a stability analysis and numerical simulations for this
reduction. Our model in principle does support Turing instabilities but only if the lateral diffusion
of inactivated GTPase is much faster than the diffusion of activated GTPase.Mon, 11 Jul 2011 00:00:00 GMThttp://hdl.handle.net/2003/289072011-07-11T00:00:00ZControl of the isoperimetric deficit by the Willmore deficit
http://hdl.handle.net/2003/28895
Title: Control of the isoperimetric deficit by the Willmore deficit
Authors: Röger, Matthias; Schätzle, Reiner
Abstract: In the class of smoothly embedded surfaces of sphere type we prove
that the isoperimetric deficit can be controlled by the Willmore deficit.Fri, 01 Jul 2011 00:00:00 GMThttp://hdl.handle.net/2003/288952011-07-01T00:00:00ZGeneralized duality for k-forms
http://hdl.handle.net/2003/28015
Title: Generalized duality for k-forms
Authors: Klinker, Frank
Abstract: We give the definition of a duality that is applicable to arbitrary k-forms. The operator that defines the duality depends on a fixed form omega.
Our definition extends in a very natural way the Hodge duality of n-forms in 2n dimensional spaces and the generalized duality of two-forms. We discuss the properties of the duality in the case where omega is invariant with respect to a subalgebra of so(V). Furthermore, we give examples for the invariant case as well as for the case of discrete symmetry.Wed, 08 Jun 2011 00:00:00 GMThttp://hdl.handle.net/2003/280152011-06-08T00:00:00ZBuckling instability of viral capsides
http://hdl.handle.net/2003/27658
Title: Buckling instability of viral capsides
Authors: Aland, Sebastian; Rätz, Andreas; Röger, Matthias; Voigt, Axel
Abstract: The crystallographic structure of spherical viruses is modeled using a multiscale approach combining a macroscopic Helfrich model for morphology evolution with a microscopic approximation of a classical density functional theory for the protein interactions. The derivation of the model is based on energy dissipation and conservation of protein number density. The resulting set of equations is solved within a diffuse domain approach using finite elements and shows buckling transitions of spherical into faceted viral shapes.Tue, 22 Mar 2011 00:00:00 GMThttp://hdl.handle.net/2003/276582011-03-22T00:00:00Z