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Topological and geometrical quantities in active cellular structuresDec 17 2018Topological and geometrical properties and the associated topological defects find a rapidly growing interest in studying the interplay between mechanics and the collective behavior of cells on the tissue level. We here test if well studied equilibrium ... 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

Orientational order on surfaces - the coupling of topology, geometry, and dynamicsJul 21 2016Jun 21 2017We 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

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 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

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

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

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

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

Closing the gap between atomic-scale lattice deformations and continuum elasticityAug 15 2018Jan 24 2019Crystal lattice deformations can be described microscopically by explicitly accounting for the position of atoms or macroscopically by continuum elasticity. In this work, we report on the description of continuous elastic fields derived from an atomistic ... More

Closing the gap between atomic-scale lattice deformations and continuum elasticityAug 15 2018Apr 24 2019Crystal lattice deformations can be described microscopically by explicitly accounting for the position of atoms or macroscopically by continuum elasticity. In this work, we report on the description of continuous elastic fields derived from an atomistic ... More

Topological and geometrical quantities in active cellular structuresDec 17 2018Apr 05 2019Topological and geometrical properties and the associated topological defects find a rapidly growing interest in studying the interplay between mechanics and the collective behavior of cells on the tissue level. We here test if well studied equilibrium ... 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

An efficient numerical framework for the amplitude expansion of the phase-field crystal modelFeb 26 2019The study of polycrystalline materials requires theoretical and computational techniques enabling multiscale investigations. The amplitude expansion of the phase field crystal model (APFC) allows for describing crystal lattice properties on diffusive ... 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

Hydrodynamic interactions in polar liquid crystals on evolving surfacesSep 03 2018Jan 17 2019We consider the derivation and numerical solution of the flow of passive and active polar liquid crystals, whose molecular orientation is subjected to a tangential anchoring on an evolving curved surface. The underlying passive model is a simplified surface ... 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

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

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

An efficient numerical framework for the amplitude expansion of the phase-field crystal modelFeb 26 2019Apr 24 2019The study of polycrystalline materials requires theoretical and computational techniques enabling multiscale investigations. The amplitude expansion of the phase field crystal model (APFC) allows for describing crystal lattice properties on diffusive ... More

The K-theory of free quantum groupsDec 14 2011In this paper we study the $ K $-theory of free quantum groups in the sense of Wang and Van Daele, more precisely, of free products of free unitary and free orthogonal quantum groups. We show that these quantum groups are $ K $-amenable and establish ... More

Increasing sequences of sectorial formsDec 10 2018Apr 05 2019We prove convergence results for `increasing' sequences of sectorial forms. We treat both the case of closed forms and the case of non-closable forms.

Holomorphic families of forms, operators and $C_0$-semigroupsJul 04 2017If $z\mapsto a_z$ is a holomorphic function with values in the sectorial forms in a Hilbert space, then the associated operator valued function $z\mapsto A_z$ is resolvent holomorphic. We give a proof of this result of Kato, on the basis of the Lax-Milgram ... 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

Controlling the energy of defects and interfaces in the amplitude expansion of the phase-field crystal modelApr 25 2017Jul 26 2017One of the major difficulties in employing phase field crystal (PFC) modeling and the associated amplitude (APFC) formulation is the ability to tune model parameters to match experimental quantities. In this work we address the problem of tuning the defect ... 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

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

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

Defects at grain boundaries: A coarse-grained, three-dimensional description by the amplitude expansion of the phase-field crystal modelMar 08 2018May 28 2018We address a three-dimensional, coarse-grained description of dislocation networks at grain boundaries between rotated crystals. The so-called amplitude expansion of the phase-field crystal model is exploited with the aid of finite element method calculations. ... 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

Bands in $L_p$-spacesMar 24 2016Nov 02 2016For a general measure space $(\Omega,\mu)$, it is shown that for every band $M$ in $L_p(\mu)$ there exists a decomposition $\mu=\mu'+\mu^{\prime\prime}$ such that $M=L_p(\mu')=\{f\in L_p(\mu);f=0\ \mu^{\prime\prime}\text{-a.e.}\}$. The theory is illustrated ... More

Convexity splitting in a phase field model for surface diffusionOct 26 2017Convexity splitting like schemes with improved accuracy are proposed for a phase field model for surface diffusion. The schemes are developed to enable large scale simulations in three spatial dimensions describing experimentally observed solid state ... 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

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

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

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

Complex semisimple quantum groups and representation theoryMay 16 2017Mar 03 2018These notes contain an introduction to the theory of complex semisimple quantum groups. Our main aim is to discuss the classification of irreducible Harish-Chandra modules for these quantum groups, following Joseph and Letzter. Along the way we cover ... 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

Analytic solution of an oscillatory migratory alpha^2 stellar dynamoNov 08 2016Nov 25 2016Analytic solutions of the mean-field induction equation predict a nonoscillatory dynamo for homogeneous helical turbulence or constant alpha effect in unbounded or periodic domains. Oscillatory dynamos are generally thought impossible for constant alpha. ... More

On the gauge boson's properties in a candidate technicolor theoryFeb 24 2011Apr 27 2011The technicolor scenario replaces the Higgs sector of the standard model with a strongly interacting sector. One candidate for a realization of such a sector is two-technicolor Yang-Mills theory coupled to two degenerate flavors of adjoint, massless techniquarks. ... More

Turbulent protostellar discsAug 07 2008Aspects of turbulence in protostellar accretion discs are being reviewed. The emergence of dead zones due to poor ionization and alternatives to the magneto-rotational instability are discussed. The coupling between dust and gas in protostellar accretion ... More

On the Probability Density of the Nuclei in a Vibrationally Excited MoleculeFeb 20 2019For localized and oriented vibrationally excited molecules, the one-body probability density of the nuclei (one-nucleus density) is studied. Like the familiar and widely used one-electron density that represents the probability of finding an electron ... More

Dynamical Quantum Processes of Molecular Beams at Surfaces: Dissociative Adsorption of Hydrogen on Metal SurfacesMar 05 1996Due to the improvement of computer power and the development of efficient algorithms it is now possible to combine high-dimensional quantum dynamical calculations of the dissociative adsorption of molecular beams with reliable ab-initio potential energy ... More

Measuring the local matter density using Gaia DR2Nov 19 2018Feb 01 2019We determine the total dynamical matter density in the solar neighbourhood using the second Gaia data release (DR2). The dynamical matter density distribution is inferred in a framework of a Bayesian hierarchical model, which accounts for position and ... More

On the generalized Zakharov-Kuznetsov equation at critical regularitySep 30 2015The Cauchy problem for the generalized Zakharov-Kuznetsov equation $$\partial_t u +\partial_x\Delta u=\partial_x u^{k+1}, \qquad \qquad u(0)=u_0$$ is considered in space dimensions $n=2$ and $n=3$ for integer exponents $k \ge 3$. For data $u_0 \in \dot{B}^{s_c}_{2,q}$, ... More

A Remark on the modified Zakharov-Kuznetsov equation in three space dimensionsFeb 26 2013The Cauchy Problem for the modified Zakharov-Kuznetsov equation in three space dimensions is shown to be locally well-posed in $H^s(\R^3)$ for $s > \frac12$. Combined with the conservation of mass and energy this result implies global well-posedness for ... More

The generic gradient-like structure of certain asymptotically autonomous semilinear parabolic equationsDec 13 2017We consider asymptotically autonomous semilinear parabolic equations u_t + Au = f(t,u). Suppose that $f(t,.)\to f^\pm$ as $t\to\pm\infty$, where the semiflows induced by \label{eq:140602-1511} u_t + Au = f^\pm(u) \tag{*} are gradient-like. Under certain ... More

Nonautonomous Conley Index Theory: The Homology Index and Attractor-Repeller decompositionsNov 13 2017In a previous work, the author established a nonautonomous Conley index based on the interplay between a nonautonomous evolution operator and its skew-product formulation. This index is refined to obtain a Conley index for families of nonautonomous evolution ... 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

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

Ambipolar diffusion in large Prandtl number turbulenceMar 21 2019We study the effects of ambipolar diffusion (AD) on hydromagnetic turbulence. We use the strong coupling approximation where the drift velocity between ions and neutrals is proportional to the Lorentz force. We consider the regime of large magnetic Prandtl ... 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

The limited roles of autocatalysis and enantiomeric cross inhibition in achieving homochirality in dilute systemsMar 19 2019To understand the effects of fluctuations on achieving homochirality, we employ a Monte-Carlo method where autocatalysis and enantiomeric cross-inhibition, as well as racemization and deracemization reactions are included. The results of earlier work ... More

Optimal Choice of Weights for Sparse Recovery With Prior InformationJun 30 2015May 24 2016Compressed sensing deals with the recovery of sparse signals from linear measurements. Without any additional information, it is possible to recover an $s$-sparse signal using $m \gtrsim s \log(d/s)$ measurements in a robust and stable way. Some applications ... More

Enclosure of the Numerical Range and Resolvent Estimates of Non-selfadjoint Operator FunctionsNov 30 2017Jul 16 2018In this paper we discuss the relationship between the numerical range of an extensive class of unbounded operator functions and the joint numerical range of the operator coefficients. Furthermore, we derive methods on how to find estimates of the joint ... 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

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

On the Cauchy-problem for generalized Kadomtsev-Petviashvili-II equationsApr 09 2009The Cauchy-problem for the generalized Kadomtsev-Petviashvili-II equation $$u_t + u_{xxx} + \partial_x^{-1}u_{yy}= (u^l)_x, \quad l \ge 3,$$ is shown to be locally well-posed in almost critical anisotropic Sobolev spaces. The proof combines local smoothing ... 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

Analytic solution of an oscillatory migratory alpha^2 stellar dynamoNov 08 2016Analytic solutions of the mean-field induction equation predict a nonoscillatory dynamo for uniform helical turbulence or constant alpha effect in unbounded or periodic domains. Oscillatory dynamos are generally thought impossible for constant alpha. ... 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

A note on weak convergence of the sequential multivariate empirical process under strong mixingApr 18 2013This article investigates weak convergence of the sequential $d$-dimensional empirical process under strong mixing. Weak convergence is established for mixing rates $\alpha_n = O(n^{-a})$, where $a>1$, which slightly improves upon existing results in ... 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

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

Unimodality and convexity of f-vectors of polytopesDec 06 2005We consider unimodality and related properties of f-vectors of polytopes in various dimensions. By a result of Kalai (1988), f-vectors of 5-polytopes are unimodal. In higher dimensions much less can be said; we give an overview on current results and ... More

On top dimensional Lyubeznik numbers in mixed characteristicSep 20 2016Jul 05 2017We prove that the top mixed characteristic Lyubeznik number of a ring $S$ that is a quotient of a complete unramified regular local ring of mixed characteristc with algebraically closed residue field is $1$ provided that depth $S \geq 2$ and dim $S \geq ... 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

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

The spatial Rokhlin property for actions of compact quantum groupsMay 27 2016Oct 07 2016We introduce the spatial Rokhlin property for actions of coexact compact quantum groups on $\mathrm{C}^*$-algebras, generalizing the Rokhlin property for both actions of classical compact groups and finite quantum groups. Two key ingredients in our approach ... 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.

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

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

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