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The interplay of curvature and vortices in flow on curved surfacesJun 19 2014Incompressible fluids on curved surfaces are considered with respect to the interplay between topology, geometry and fluid properties using a surface vorticity-stream function formulation, which is solved using parametric finite elements. Motivated by ... More

Orientational order on surfaces - the coupling of topology, geometry and dynamicsJul 21 2016We consider the numerical investigation of surface bound orientational order using unit tangential vector fields by means of a gradient-flow equation of a weak surface Frank-Oseen energy. The energy is composed of intrinsic and extrinsic contributions, ... More

Active crystals on a sphereFeb 14 2018Two-dimensional crystals on curved manifolds exhibit nontrivial defect structures. Here, we consider "active crystals" on a sphere, which are composed of self-propelled colloidal particles. Our work is based on a new phase-field-crystal-type model that ... More

Nematic liquid crystals on curved surfaces - a thin film limitSep 27 2017We consider a thin film limit of a Landau-de Gennes Q-tensor model. In the limiting process we observe a continuous transition where the normal and tangential parts of the Q-tensor decouple and various intrinsic and extrinsic contributions emerge. Main ... More

Detached topological charge on capillary bridgesJan 30 2014We numerically investigate crystalline order on negative Gaussian curvature capillary bridges. In agreement with the experimental results in [W. Irvine et al., Nature, "Pleats in crystals on curved surfaces", 2010, (468), 947]} we observe for decreasing ... More

A phase-field-crystal approach to critical nucleiFeb 01 2010We investigate a phase-field-crystal model for homogeneous nucleation. Instead of solving the time evolution of a density field towards equilibrium we use a String Method to identify saddle points in phase space. The saddle points allow to obtain the ... More

Development and Analysis of a Block-Preconditioner for the Phase-Field Crystal EquationJan 27 2015We develop a preconditioner for the linear system arising from a finite element discretization of the Phase Field Crystal (PFC) equation. The PFC model serves as an atomic description of crystalline materials on diffusive time scales and thus offers the ... More

Margination of white blood cells - a computational approach by a hydrodynamic phase field modelJul 03 2015We numerically investigate margination of white blood cells and demonstrate the dependency on a number of conditions including hematocrit, the deformability of the cells and the Reynolds number. A detailed mesoscopic hydrodynamic Helfrich-type model is ... More

Collective migration under hydrodynamic interactions -- a computational approachMay 19 2016Substrate-based cell motility is essential for fundamental biological processes, such as tissue growth, wound healing and immune response. Even if a comprehensive understanding of this motility mode remains elusive, progress has been achieved in its modeling ... More

A Navier Stokes Phase Field Crystal Model for Colloidal SuspensionsOct 21 2013Jan 26 2015We develop a fully continuous model for colloidal suspensions with hydrodynamic interactions. The Navier Stokes Phase Field Crystal (NS-PFC) model combines ideas of dynamic density functional theory with particulate flow approaches and is derived in detail ... More

A multi-mesh finite element method for Lagrange elements of arbitrary degreeMay 26 2010We consider within a finite element approach the usage of different adaptively refined meshes for different variables in systems of nonlinear, time-depended PDEs. To resolve different solution behaviours of these variables, the meshes can be independently ... More

Liquid crystalline growth within a phase-field crystal modelJan 09 2015By using a phase-field crystal (PFC) model, the liquid-crystal growth of the plastic triangular phase is simulated with emphasis on crystal shape and topological defect formation. The equilibrium shape of a plastic triangular crystal (PTC) grown from ... More

On the structure of quantum automorphism groupsNov 07 2014We compute the $ K $-theory of quantum automorphism groups of finite dimensional $ C^* $-algebras in the sense of Wang. The results show in particular that the $ C^* $-algebras of functions on the quantum permutation groups $ S_n^+ $ are pairwise non-isomorphic ... More

The Baum-Connes conjecture for free orthogonal quantum groupsNov 16 2009Jul 11 2011We prove an analogue of the Baum-Connes conjecture for free orthogonal quantum groups. More precisely, we show that these quantum groups have a $ \gamma $-element and that $ \gamma = 1 $. It follows that free orthogonal quantum groups are $ K $-amenable. ... More

Chern character for totally disconnected groupsAug 25 2006In this paper we construct a bivariant Chern character for the equivariant KK-theory of a totally disconnected group with values in bivariant equivariant cohomology in the sense of Baum and Schneider. We prove in particular that the complexified left ... More

Discrete exterior calculus (DEC) for the surface Navier-Stokes equationNov 14 2016We consider a numerical approach for the incompressible surface Navier-Stokes equation. The approach is based on the covariant form and uses discrete exterior calculus (DEC) in space and a semi-implicit discretization in time. The discretization is described ... More

A mechanism for cell motility by active polar gelsDec 17 2014May 05 2015We analyse a generic motility model, with the motility mechanism arising by contractile stress due to the interaction of myosin and actin. A hydrodynamic active polar gel theory is used to model the cytoplasm of a cell and is combined with a Helfrich-type ... More

Equivariant local cyclic homology and the equivariant Chern-Connes characterAug 24 2006We define and study equivariant analytic and local cyclic homology for smooth actions of totally disconnected groups on bornological algebras. Our approach contains equivariant entire cyclic cohomology in the sense of Klimek, Kondracki and Lesniewski ... More

Equivariant cyclic homology for quantum groupsJan 30 2006We define equivariant periodic cyclic homology for bornological quantum groups. Generalizing corresponding results from the group case, we show that the theory is homotopy invariant, stable and satisfies excision in both variables. Along the way we prove ... More

A new description of equivariant cohomology for totally disconnected groupsDec 07 2004We consider smooth actions of totally disconnected groups on simplicial complexes and compare different equivariant cohomology groups associated to such actions. Our main result is that the bivariant equivariant cohomology theory introduced by Baum and ... More

Equivariant periodic cyclic homologyDec 01 2004We define and study equivariant periodic cyclic homology for locally compact groups. This can be viewed as a noncommutative generalization of equivariant de Rham cohomology. Although the construction resembles the Cuntz-Quillen approach to ordinary cyclic ... More

Particles on curved surfaces - a dynamic approach by a phase field crystal modelOct 19 2009Mar 02 2010We present a dynamic model to study ordering of particles on arbitrary curved surfaces. Thereby the particles are represented as maxima in a density field and a surface partial differential equation for the density field is solved to the minimal energy ... More

A mesoscopic field theoretical approach for active systemsApr 22 2016We introduce a mesocopic modeling approach for active systems. The continuum model allows to consider microscopic details as well as emerging macroscopic behavior and can be considered as a minimal continuum model to describe generic properties of active ... More

Bands in $L_p$-spacesMar 24 2016Jun 19 2016For a general measure space $(\Omega,\mu)$, it is shown that for every band $M$ in $L_p(\mu)$ there exists a decomposition $\mu=\mu'+\mu"$ such that $M=L_p(\mu')=\{f\in L_p(\mu);f=0\ \mu"\text{-a.e.}\}$. The theory is illustrated by an example, with an ... More

Morphological stability of electromigration-driven vacancy islandsJan 10 2007Feb 20 2007The electromigration-induced shape evolution of two-dimensional vacancy islands on a crystal surface is studied using a continuum approach. We consider the regime where mass transport is restricted to terrace diffusion in the interior of the island. In ... More

Grain growth beyond the Mullins model, capturing the complex physics behind universal grain size distributionsApr 15 2013Grain growth experiments on thin metallic films have shown the geometric and topological characteristics of the grain structure to be universal and independent of many experimental conditions. The universal size distribution, however, is found to differ ... More

Diffuse interface models of locally inextensible vesicles in a viscous fluidNov 26 2013We present a new diffuse interface model for the dynamics of inextensible vesicles in a viscous fluid. A new feature of this work is the implementation of the local inextensibility condition in the diffuse interface context. Local inextensibility is enforced ... More

Derivation of the phase field crystal model for colloidal solidificationFeb 19 2009May 28 2009The phase-field crystal model is by now widely used in order to predict crystal nucleation and growth. For colloidal solidification with completely overdamped individual particle motion, we show that the phase-field crystal dynamics can be derived from ... More

Equivariant Fredholm modules for the full quantum flag manifold of $SU_q(3)$Dec 11 2014We introduce $C^*$-algebras associated to the foliation structure of a quantum flag manifold. We use these to construct $SL_q(3,\mathbb{C})$-equivariant Fredholm modules for the full quantum flag manifold $X_q = SU_q(3)/T$ of $SU_q(3)$, based on an analytical ... More

Equivariant Poincaré duality for quantum group actionsFeb 23 2009Nov 16 2009We extend the notion of Poincar\'e duality in KK-theory to the setting of quantum group actions. An important ingredient in our approach is the replacement of ordinary tensor products by braided tensor products. Along the way we discuss general properties ... More

Structure and dynamics of interfaces between two coexisting liquid crystalline phasesFeb 01 2013The phase-field-crystal model is used to access the structure and thermodynamics of interfaces between two coexisting liquid crystalline phases in two spatial dimensions. Depending on the model parameters there is a variety of possible coexistences between ... More

Complex shape evolution of electromigration-driven single-layer islandsOct 28 2004Mar 24 2005The shape evolution of two-dimensional islands through periphery diffusion biased by an electromigration force is studied numerically using a continuum approach. We show that the introduction of crystal anisotropy in the mobility of edge atoms induces ... More

Polyhedral Voronoi CellsMar 22 2010Voronoi cells of a discrete set in Euclidean space are known as generalized polyhedra. We identify polyhedral cells of a discrete set through a direction cone. For an arbitrary set we distinguish polyhedral from non-polyhedral cells using inversion at ... More

Bernays-Schönfinkel-Ramsey with Simple Bounds is NEXPTIME-completeJan 28 2015Linear arithmetic extended with free predicate symbols is undecidable, in general. We show that the restriction of linear arithmetic inequations to simple bounds extended with the Bernays-Sch\"onfinkel-Ramsey free first-order fragment is decidable and ... More

Limitations of model fitting methods for lensing shear estimationMay 29 2009Gravitational lensing shear has the potential to be the most powerful tool for constraining the nature of dark energy. However, accurate measurement of galaxy shear is crucial and has been shown to be non-trivial by the Shear TEsting Programme. Here we ... More

Twisted identities in Coxeter groupsFeb 07 2007Nov 02 2007Given a Coxeter system (W,S) equipped with an involutive automorphism T, the set of twisted identities is i(T) = {T(w)^{-1}w : w \in W}. We point out how i(T) shows up in several contexts and prove that if there is no s \in S such that sT(s) is of odd ... More

On De Sitter Vacua in Strongly Coupled Heterotic String TheoryMar 31 2004May 19 2004We describe how 4d de Sitter vacua might emerge from 11d heterotic M-theory. Non-perturbative effects and $G$-fluxes play a crucial role leading to vacua with F-term supersymmetry breaking and a positive energy density. Charged scalar matter fields are ... More

Dual Branes, Discrete Chain States and the Entropy of the Schwarzschild Black HoleDec 31 2002We review a recent proposal towards a microscopic understanding of the entropy of non-supersymmetric spacetimes -- with emphasis on the Schwarzschild black hole. The approach is based at an intermediate step on the description of the non-supersymmetric ... More

Bekenstein-Spectrum, Hawking-Temperature and Specific Heat of Schwarzschild Black Holes from Microscopic ChainsMay 30 2002Oct 28 2005We study the thermodynamic consequences of a recently proposed description for a Schwarzschild black hole based on Euclidean (D3,D3)+(\bar{D3},\bar{D3}) brane pairs described in terms of chain-like excitations. A discrete mass-spectrum of Bekenstein-type ... More

Test module filtrations for unit $F$-modulesJul 03 2015Oct 04 2016We extend the notion of test module filtration introduced by Blickle for Cartier modules. We then show that this naturally defines a filtration on unit $F$-modules and prove that this filtration coincides with the notion of $V$-filtration introduced by ... More

$V$-filtrations in positive characteristic and test modulesOct 31 2013Dec 23 2014Let $R$ be a ring essentially of finite type over an $F$-finite field. Given an ideal $\mathfrak{a}$ and a principal Cartier module $M$ we introduce the notion of a $V$-filtration of $M$ along $\mathfrak{a}$. If $M$ is $F$-regular then this coincides ... More

Reactions at surfaces studied by ab initio dynamics calculationsAug 24 1998Due to the development of efficient algorithms and the improvement of computer power it is now possible to map out potential energy surfaces (PES) of reactions at surfaces in great detail. This achievement has been accompanied by an increased effort in ... More

Gluons at finite temperature in Landau gauge Yang--Mills theoryJun 07 2005The infrared behavior of Yang-Mills theory at finite temperature provides access to the role of confinement. In this review recent results on this topic from lattice calculations and especially Dyson-Schwinger studies are discussed. These indicate persistence ... More

Solving a Set of Truncated Dyson-Schwinger Equations with a Globally Converging MethodApr 14 2005Mar 08 2006A globally converging numerical method to solve coupled sets of non-linear integral equations is presented. Such systems occur e.g. in the study of Dyson-Schwinger equations of Yang-Mills theory and QCD. The method is based on the knowledge of the qualitative ... More

The High-Temperature Phase of Yang-Mills Theory in Landau GaugeJan 17 2005The high-temperature phase of Yang-Mills theory in Landau gauge is studied using Dyson-Schwinger equations. The propagators of the gluon and the Faddeev-Popov ghosts are obtained at finite and infinite temperature, partially analytically. The results ... More

On the Flattening of Negative Curvature via T-Duality with a Non-Constant B-FieldNov 24 1999Nov 14 2003In an earlier paper, Alvarez, Alvarez-Gaume, Barbon and Lozano pointed out, that the only way to "flatten" negative curvature by means of a T-duality is by introducing an appropriate, non-constant NS-NS B-field. In this paper, we are investigating this ... More

Testing Stability of M-Theory on an S^1/Z_2 OrbifoldSep 27 1999Jun 23 2000We analyse perturbatively, whether a flat background with vanishing G-flux in Horava-Witten supergravity represents a vacuum state, which is stable with respect to interactions between the ten-dimensional boundaries, mediated through the D=11 supergravity ... More

The case for a distributed solar dynamo shaped by near-surface shearFeb 15 2005Arguments for and against the widely accepted picture of a solar dynamo being seated in the tachocline are reviewed and alternative ideas concerning dynamos operating in the bulk of the convection zone, or perhaps even in the near-surface shear layer, ... More

The solar interior - radial structure, rotation, solar activity cycleMar 28 2007Some basic properties of the solar convection zone are considered and the use of helioseismology as an observational tool to determine its depth and internal angular velocity is discussed. Aspects of solar magnetism are described and explained in the ... More

Location of the solar dynamo and near-surface shearDec 29 2005The location of the solar dynamo is discussed in the context of new insights into the theory of nonlinear turbulent dynamos. It is argued that, from a dynamo-theoretic point of view, the bottom of the convection zone is not a likely location and that ... More

On base change of the fundamental group schemeMay 30 2012Nov 04 2013We provide for all prime numbers $p$ examples of smooth projective curves over a field of characteristic $p$ for which base change of the fundamental group scheme fails. This is intimately related to how $F$-trivial vector bundles, i.e. bundles trivialized ... More

The combinatorics of twisted involutions in Coxeter groupsNov 19 2004May 04 2005The open intervals in the Bruhat order on twisted involutions in a Coxeter group are shown to be PL spheres. This implies results conjectured by F. Incitti and sharpens the known fact that these posets are Gorenstein* over Z_2. We also introduce a Boolean ... More

Fixed points of zircon automorphismsMar 16 2007A zircon is a poset in which every principal order ideal is finite and equipped with a so-called special matching. We prove that the subposet induced by the fixed points of any automorphism of a zircon is itself a zircon. This provides a natural context ... More

On the Bekenstein-Hawking Entropy, Non-Commutative Branes and Logarithmic CorrectionsDec 30 2003Jun 21 2006We extend earlier work on the origin of the Bekenstein-Hawking entropy to higher-dimensional spacetimes. The mechanism of counting states is shown to work for all spacetimes associated with a Euclidean doublet $(E_1,M_1)+(E_2,M_2)$ of electric-magnetic ... More

A Small Cosmological Constant and Backreaction of Non-Finetuned ParametersJul 28 2000Sep 29 2003We include the backreaction on the warped geometry induced by non-finetuned parameters in a two domain-wall set-up to obtain an exponentially small Cosmological Constant $\Lambda_4$. The mechanism to suppress the Cosmological Constant involves one classical ... More

Near-surface shear layer dynamicsJan 03 2007The outer surface layers of the sun show a clear deceleration at low latitudes. This is generally thought to be the result of a strong dominance of vertical turbulent motions associated with strong downdrafts. This strong negative radial shear should ... More

Computational aspects of astrophysical MHD and turbulenceSep 27 2001The advantages of high-order finite difference scheme for astrophysical MHD and turbulence simulations are highlighted. A number of one-dimensional test cases are presented ranging from various shock tests to Parker-type wind solutions. Applications to ... More

The inverse cascade in turbulent dynamosDec 05 2000The emergence of a large scale magnetic field from randomly forced isotropic strongly helical flows is discussed in terms of the inverse cascade of magnetic helicity and the alpha-effect. In simulations of such flows the maximum field strength exceeds ... More

Differential Hopf Algebras on Quantum Groups of Type AMay 29 1998Let A be a Hopf algebra and $Gamma$ be a bicovariant first order differential calculus over A. It is known that there are three possibilities to construct a differential Hopf algebra $Gamma^wedge$ that contains $Gamma$ as its first order part; namely ... More

Sequential Implementation of Monte Carlo Tests with Uniformly Bounded Resampling RiskDec 17 2006Jul 07 2008This paper introduces an open-ended sequential algorithm for computing the p-value of a test using Monte Carlo simulation. It guarantees that the resampling risk, the probability of a different decision than the one based on the theoretical p-value, is ... More

Bi- and trilinear Schroedinger estimates in one space dimension with applications to cubic NLS and DNLSMay 22 2005The Fourier transforms of the products of two respectively three solutions of the free Schroedinger equation in one space dimension are estimated in mixed and, in the first case weighted, L^p - norms. Inserted into an appropriate variant of the Fourier ... More

Towards Dark Energy from String-TheoryDec 31 2007Mar 12 2008We discuss vacuum energy in string and M-theory with a focus on heterotic M-theory. In the latter theory a mechanism is described for maintaining zero vacuum energy after supersymmetry breaking. Higher-order corrections can be expected to give a sufficiently ... More

Large Gravitational Waves and Lyth Bound in Multi Brane InflationAug 31 2007Sep 30 2008It is shown that multi M5-brane inflation in heterotic M-theory gives rise to a detectable gravitational wave power spectrum with tensor fraction $r$ typically larger than the projected experimental sensitivity, $r_{exp} = 0.01$. A measurable gravitational ... More

Supersymmetry Breaking with Zero Vacuum Energy in M-Theory Flux CompactificationsDec 31 2006Sep 13 2007An attractive mechanism to break supersymmetry in vacua with zero vacuum energy arose in E_8 x E_8 heterotic models with hidden sector gaugino condensate. An H-flux balances the exponentially small condensate on shell and fixes the complex structure moduli. ... More

Black Holes, Space-Filling Chains and Random WalksDec 30 2003Jul 30 2006Many approaches to a semiclassical description of gravity lead to an integer black hole entropy. In four dimensions this implies that the Schwarzschild radius obeys a formula which describes the distance covered by a Brownian random walk. For the higher-dimensional ... More

Schwarzschild Black Holes from Brane-Antibrane PairsApr 24 2002May 07 2002We show that D=4 Schwarzschild black holes can arise from a doublet of Euclidean D3-antiD3 pairs embedded in D=10 Lorentzian spacetime. By starting from a D=10 type IIB supergravity description for the D3-antiD3 pairs and wrapping one of them over an ... More

Dual Brane Pairs, Chains and the Bekenstein-Hawking EntropyJan 30 2002Oct 28 2005A proposal towards a microscopic understanding of the Bekenstein-Hawking entropy for D=4 spacetimes with event horizon is made. Since we will not rely on supersymmetry these spacetimes need not be supersymmetric. Euclidean D-branes which wrap the event ... More

A Small Cosmological Constant, Grand Unification and Warped GeometryJun 29 2000May 28 2006We explore a mechanism to obtain the observational small value for the 4-dimensional vacuum energy through an exponential warp-factor suppression. Intriguingly the required suppression scale relates directly to the GUT scale. We demonstrate the mechanism ... More

Distributed versus tachocline dynamosDec 29 2005Arguments are presented in favor of the idea that the solar dynamo may operate not just at the bottom of the convection zone, i.e. in the tachocline, but it may operate in a more distributed fashion in the entire convection zone. The near-surface shear ... More

Numerical simulations of turbulent dynamosOct 24 2000Using a periodic box calculation it is shown that, owing to helicity conservation, a large scale field can only develop on a resistive timescale. This behaviour can be reproduced by a mean-field dynamo with alpha and eta_t quenchings that are equally ... More

Magnetic helicity in primordial and dynamo scenarios of galaxiesJan 23 2006Some common properties of helical magnetic fields in decaying and driven turbulence are discussed. These include mainly the inverse cascade that produces fields on progressively larger scales. Magnetic helicity also restricts the evolution of the large ... More

Lattice Vertex Algebras on General Even, Self-dual LatticesOct 30 2002Feb 11 2003In this note we analyse the Lie algebras of physical states stemming from lattice constructions on general even, self-dual lattices Gamma^{p,q} with p greater or equal to q. It is known that if the lattice is at most Lorentzian, the resulting Lie algebra ... More

Relativistic Bound StatesAug 27 2003In this contribution, I will give a brief survey of present techniques to treat the bound state problem in relativistic quantum field theories. In particular, I will discuss the Bethe-Salpeter equation, various quasi-potential equations, the Feynman-Schwinger ... More

Bloch-Wilson Hamiltonian and a Generalization of the Gell-Mann-Low TheoremNov 25 1999The effective Hamiltonian introduced many years ago by Bloch and generalized later by Wilson, appears to be the ideal starting point for Hamiltonian perturbation theory in quantum field theory. The present contribution derives the Bloch-Wilson Hamiltonian ... More

Directed and multi-directed animals on the king's latticeJan 07 2013Oct 28 2015This article introduces a new, simple solvable lattice for directed animals: the directed king's lattice, or square lattice with next nearest neighbor bonds and preferred directions {W, NW, N, NE, E}. We show that the directed animals in this lattice ... More

Magnetic Prandtl number dependence of kinetic to magnetic dissipation ratioApr 28 2014Jul 18 2014Using direct numerical simulations of three-dimensional hydromagnetic turbulence, either with helical or non-helical forcing, we show that the ratio of kinetic-to-magnetic energy dissipation always increases with the magnetic Prandtl number, i.e., the ... More

Extending ArXiv.org to Achieve Open Peer Review and PublishingNov 23 2010Today's peer review process for scientific articles is unnecessarily opaque and offers few incentives to referees. Likewise, the publishing process is unnecessarily inefficient and its results are only rarely made freely available to the public. Here ... More

Bound-state/elementary-particle duality in the Higgs sector and the case for an excited 'Higgs' within the standard modelMay 30 2012Nov 22 2012Though being weakly interacting, QED can support bound states. In principle, this can be expected for the weak interactions in the Higgs sector as well. In fact, it has been argued long ago that there should be a duality between bound states and the elementary ... More

Counting supersymmetric branesSep 09 2011Dec 06 2011Maximal supergravity solutions are revisited and classified, with particular emphasis on objects of co-dimension at most two. This class of solutions includes branes whose tension scales with g_s^{-\sigma} for \sigma>2. We present a group theory derivation ... More

Chandrasekhar-Kendall functions in astrophysical dynamosMar 25 2011Some of the contributions of Chandrasekhar to the field of magnetohydrodynamics are highlighted. Particular emphasis is placed on the Chandrasekhar-Kendall functions that allow a decomposition of a vector field into right- and left-handed contributions. ... More

Simulations of astrophysical dynamosDec 22 2010Numerical aspects of dynamos in periodic domains are discussed. Modifications of the solutions by numerically motivated alterations of the equations are being reviewed using the examples of magnetic hyperdiffusion and artificial diffusion when advancing ... More

Gauges, propagators, and physicsNov 24 2010When a theory shall be described at all scales, it is necessary to start from its elementary degrees of freedom. Herein, one possible chain of steps for this purpose will be briefly outlined for the example of a gauge theory, like QCD. Starting with the ... More

Paradigm shifts in solar dynamo modelingJan 23 2009May 09 2009Selected topics in solar dynamo theory are being highlighted. The possible relevance of the near-surface shear layer is discussed. The role of turbulent downward pumping is mentioned in connection with earlier concerns that a dynamo-generated magnetic ... More

VIEWPOINT: A New Twist in Simulating Solar FlaresMar 07 2016Simulations show for the first time how the magnetic fields that produce solar flares can extend out of the Sun by acquiring a twist.

Towards Distortion-Predictable Embedding of Neural NetworksAug 01 2015Current research in Computer Vision has shown that Convolutional Neural Networks (CNN) give state-of-the-art performance in many classification tasks and Computer Vision problems. The embedding of CNN, which is the internal representation produced by ... More

Local and global gauge-fixingJan 14 2013Gauge-fixing as a sampling procedure of gauge copies provides a possibility to construct well-defined gauges also beyond perturbation theory. The implementation of such sampling strategies in lattice gauge theory is briefly outlined, and examples are ... More

On the hierarchies of higher order mKdV and KdV equationsSep 16 2009Oct 28 2009The Cauchy problem for the higher order equations in the mKdV hierarchy is investigated with data in the spaces $\hat{H}^r_s(\R)$ defined by the norm $$\n{v_0}{\hat{H}^r_s(\R)} := \n{< \xi > ^s\hat{v_0}}{L^{r'}_{\xi}},\quad < \xi >=(1+\xi^2)^{\frac12}, ... More

A Geometrical Stability Condition for Compressed SensingOct 28 2015Jul 06 2016During the last decade, the paradigm of compressed sensing has gained significant importance in the signal processing community. While the original idea was to utilize sparsity assumptions to design powerful recovery algorithms of vectors $x \in \mathbb{R}^d$, ... More

Sparse Blind Deconvolution and Demixing Through $\ell_{1,2}$-MinimizationSep 08 2016This paper concerns solving the sparse deconvolution and demixing problem using $\ell_{1,2}$-minimization. We show that under a certain structured random model, robust and stable recovery is possible. The results extend results of Ling and Strohmer [Self ... More

An explicit computation of a family of trivialising étale coversNov 09 2011We explicitly compute \'etale covers of the smooth Fermat curves $Y_{p+1} = \Proj k[u,v,w]/(u^{p+1} + v^{p+1} - w^{p+1})$ which trivialise the vector bundles $\Syz(u^2, v^2, w^2)(3)$, where $k$ is a field of characteristic $p \geq 3$.

Stellar mixing length theory with entropy rainApr 13 2015Aug 22 2016The effects of a nongradient flux term originating from the motion of convective elements with entropy perturbations of either sign are investigated and incorporated into a modified version of stellar mixing length theory (MLT). Such a term, first studied ... More

Fixed points of involutive automorphisms of the Bruhat orderMar 04 2004Oct 14 2004Applying a classical theorem of Smith, we show that the poset property of being Gorenstein$^*$ over $\mathbb{Z}_2$ is inherited by the subposet of fixed points under an involutive poset automorphism. As an application, we prove that every interval in ... More

Two Exterior Algebras for orthogonal and symplectic Quantum GroupsJun 08 1999Let \Gamma be one of the N^2-dimensional bicovariant first order differential calculi on the orthogonal or symplectic quantum group O_q(N) or Sp_q(N). The parameter q is not a root of unity. We show that the second antisymmetrizer exterior algebra is ... More

Why coronal mass ejections are necessary for the dynamoJan 03 2007Large scale dynamo-generated fields are a combination of interlocked poloidal and toroidal fields. Such fields possess magnetic helicity that needs to be regenerated and destroyed during each cycle. A number of numerical experiments now suggests that ... More

The helicity issue in large scale dynamosJul 18 2002The connection between helically isotropic MHD turbulence and mean-field dynamo theory is reviewed. The nonlinearity in the mean-field theory is not yet well established, but detailed comparison with simulations begin to help select viable forms of the ... More

The solar dynamo: old, recent, and new problemsNov 30 2000A number of problems of solar and stellar dynamo theory are briefly reviewed and the current status of possible solutions is discussed. Results of direct numerical simulations are described in view of mean-field dynamo theory and the relation between ... More

The inverse cascade and nonlinear alpha-effect in simulations of isotropic helical hydromagnetic turbulenceJun 13 2000Dec 07 2000A numerical model of isotropic homogeneous turbulence with helical forcing is investigated. The resulting flow, which is essentially the prototype of the alpha^2 dynamo of mean-field dynamo theory, produces strong dynamo action with an additional large ... More

Hydrogen dissociation on metal surfaces - a model system for reactions on surfacesAug 24 1998Reactions on surfaces play an important role in many technological applications. Since these processes are often rather complex, one tries to understand single steps of these complicated reactions by investigating simpler system. In particular the hydrogen ... More

Two- and three-point Green's functions in two-dimensional Landau-gauge Yang-Mills theoryApr 05 2007Apr 13 2007The ghost and gluon propagator and the ghost-gluon and three-gluon vertex of two-dimensional SU(2) Yang-Mills theory in (minimal) Landau gauge are studied using lattice gauge theory. It is found that the results are qualitatively similar to the ones in ... More

The finite antichain property in Coxeter groupsDec 09 2005Jan 19 2006We prove that the weak order on an infinite Coxeter group contains infinite antichains if and only if the group is not affine.