Results for "Raphael Wittkowski"

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Dynamical density functional theory for colloidal particles with arbitrary shapeJun 12 2011Starting from the many-particle Smoluchowski equation, we derive dynamical density functional theory for Brownian particles with an arbitrary shape. Both passive and active (self-propelled) particles are considered. The resulting theory constitutes a ... More
The self-propelled Brownian spinning top: dynamics of a biaxial swimmer at low Reynolds numbersOct 10 2011Recently, the Brownian dynamics of self-propelled (active) rod-like particles was explored to model the motion of colloidal microswimmers, catalytically-driven nanorods, and bacteria. Here, we generalize this description to biaxial particles with arbitrary ... More
Stability of liquid crystalline phases in the phase-field-crystal modelMar 01 2011The phase-field-crystal model for liquid crystals is solved numerically in two spatial dimensions. This model is formulated with three position-dependent order parameters, namely the reduced translational density, the local nematic order parameter, and ... More
Microscopic and macroscopic theories for the dynamics of polar liquid crystalsJul 17 2011We derive and analyze the dynamic equations for polar liquid crystals in two spatial dimensions in the framework of classical dynamical density functional theory (DDFT). Translational density variations, polarization, and quadrupolar order are used as ... More
Polar liquid crystals in two spatial dimensions: the bridge from microscopic to macroscopic modelingMar 10 2011Two-dimensional polar liquid crystals have been discovered recently in monolayers of anisotropic molecules. Here, we provide a systematic theoretical description of liquid-crystalline phases for polar particles in two spatial dimensions. Starting from ... 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
Dynamics of a deformable active particle under shear flowJul 08 2013Aug 21 2013The motion of a deformable active particle in linear shear flow is explored theoretically. Based on symmetry considerations, in two spatial dimensions, we propose coupled nonlinear dynamical equations for the particle position, velocity, deformation, ... More
Can the self-propulsion of anisotropic microswimmers be described by using forces and torques?Oct 24 2014The self-propulsion of artificial and biological microswimmers (i.e., active colloidal particles) has often been modelled by using a force and a torque entering into the overdamped equations for the Brownian motion of passive particles. This seemingly ... More
Scalar $φ^4$ field theory for active-particle phase separationNov 06 2013Jul 11 2014Recent theories predict phase separation among orientationally disordered active particles whose propulsion speed decreases rapidly enough with density. Coarse-grained models of this process show time-reversal symmetry (detailed balance) to be restored ... More
Brownian dynamics of a self-propelled particle in shear flowJun 02 2011Brownian dynamics of a self-propelled particle in linear shear flow is studied analytically by solving the Langevin equation and in simulation. The particle has a constant propagation speed along a fluctuating orientation and is additionally subjected ... More
Symmetry-breaking in clogging for oppositely driven particlesNov 10 2015The clogging behavior of a symmetric binary mixture of particles that are driven in opposite directions through constrictions is explored by Brownian dynamics simulations and theory. A dynamical state with a spontaneously broken symmetry occurs where ... More
Microscopic approach to entropy productionDec 08 2012It is a great challenge of nonequilibrium statistical mechanics to calculate entropy production within a microscopic theory. In the framework of linear irreversible thermodynamics, we combine the Mori-Zwanzig-Forster projection operator technique with ... More
Derivation of a three-dimensional phase-field-crystal model for liquid crystals from density functional theoryJul 09 2010Using a generalized order parameter gradient expansion within density functional theory, we derive a phase-field-crystal model for liquid crystals composed by apolar particles in three spatial dimensions. Both the translational density and the orientational ... More
Extended dynamical density functional theory for colloidal mixtures with temperature gradientsSep 28 2012In the past decade, classical dynamical density functional theory (DDFT) has been developed and widely applied to the Brownian dynamics of interacting colloidal particles. One of the possible derivation routes of DDFT from the microscopic dynamics is ... More
Round Table Summary: Stellar interferometry as a tool to investigate atmospheres and to compare observations with modelsApr 02 2003Long-baseline interferometry at optical and near-infrared wavelengths is an emerging technology which is quickly becoming a useful tool to investigate stellar atmospheres and to compare observations with models. Stellar atmosphere models have so far mainly ... 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
Hard rectangles near curved hard walls: tuning the sign of the Tolman lengthSep 07 2016Combining analytic calculations, computer simulations, and classical density functional theory we determine the interfacial tension of orientable two-dimensional hard rectangles near a curved hard wall. Both a circular cavity holding the particles and ... More
Active Model H: Scalar Active Matter in a Momentum-Conserving FluidApr 28 2015We present a continuum theory of self-propelled particles, without alignment interactions, in a momentum-conserving solvent. To address phase separation we introduce a scalar concentration field $\phi$ with advective-diffusive dynamics. Activity creates ... More
Activity-induced phase separation and self-assembly in mixtures of active and passive particlesAug 21 2014Jan 07 2015We investigate the phase behavior and kinetics of a monodisperse mixture of active (\textit{i.e.}, self-propelled) and passive isometric Brownian particles through Brownian dynamics simulations and theory. As in a purely active system, motility of the ... More
The Formulas for the Distribution of the 3-Smooth, 5-Smooth, 7-Smooth and all other Smooth NumbersAug 24 2016Sep 22 2016In this paper we present rapidly convergent formulas for the distribution of the $3$-smooth, $5$-smooth, $7$-smooth and all other smooth numbers. One of these formulas is another version of a formula due to Hardy and Littlewood for the arithmetic function ... More
Integrable almost complex structures in principal bundles and holomorphic curvesJun 12 2003Jun 12 2003We consider principal fibre bundles with a given connection and construct almost complex structures on the total space if the adjoint bundle is isomorphic to the tangent bundle of the base. We derive the integrability condition. If the structure group ... More
Equitable coloring of k-uniform hypergraphsFeb 22 2002Let $H$ be a $k$-uniform hypergraph with $n$ vertices. A {\em strong $r$-coloring} is a partition of the vertices into $r$ parts, such that each edge of $H$ intersects each part. A strong $r$-coloring is called {\em equitable} if the size of each part ... More
Integer homology 3-spheres admit irreducible representations in SL(2,C)May 27 2016Jul 12 2016We prove that the fundamental group of any integer homology 3-sphere different from the 3-sphere admits irreducible representations of its fundamental group in SL(2,C). For hyperbolic integer homology spheres this comes with the definition, and for Seifert ... More
Computing the diameter polynomially faster than APSPNov 29 2010Jan 13 2011We present a new randomized algorithm for computing the diameter of a weighted directed graph. The algorithm runs in $\Ot(M^{\w/(\w+1)}n^{(\w^2+3)/(\w+1)})$ time, where $\w < 2.376$ is the exponent of fast matrix multiplication, $n$ is the number of vertices ... More
Numerical Green's Function Modeling of One-Dimensional Quantum TransportOct 01 2009Since the initial development of one-dimensional electron gases (1DEG) two decades ago, there has been intense interest in both the fundamental physics and the potential applications, including quantum computation, of these quantum transport systems. ... More
GLAST and Lorentz violationMay 08 2008Aug 13 2008We study possible Lorentz violations by means of gamma-ray bursts (GRB) with special focus on the Large Array Telescope (LAT) of GLAST. We simulate bursts with gtobssim and introduce a Lorentz violating term in the arrival times of the photons. We further ... More
Renormalization of the Nonlinear O(3) Model with Theta-TermAug 29 2012Mar 10 2013The renormalization of the topological term in the two-dimensional nonlinear O(3) model is studied by means of the Functional Renormalization Group. By considering the topological charge as a limit of a more general operator, it is shown that a finite ... More
New Scale Factor MeasureMay 30 2012Jun 01 2012The computation of probabilities in an eternally inflating universe requires a regulator or "measure". The scale factor time measure truncates the universe when a congruence of timelike geodesics has expanded by a fixed volume factor. This definition ... More
Fluctuations relations for semiclassical single-mode laserOct 01 2008Over last decades, the study of laser fluctuations has shown that laser theory may be regarded as a prototypical example of a nonlinear nonequilibrium problem. The present paper discusses the fluctuation relations, recently derived in nonequilibrium statistical ... More
Vacuum Structure and the Arrow of TimeDec 14 2011Jun 11 2012We find ourselves in an extended era of entropy production. Unlike most other observations, the arrow of time is usually regarded as a constraint on initial conditions. I argue, however, that it primarily constrains the vacuum structure of the theory. ... More
Stresses in isostatic granular systems and emergence of force chainsFeb 23 2004Jun 14 2004Progress is reported on several questions that bedevil understanding of granular systems: (i) are the stress equations elliptic, parabolic or hyperbolic? (ii) how can the often-observed force chains be predicted from a first-principles continuous theory? ... More
Nonequilibrium brittle fracture propagation: Steady state, oscillations and intermittencyMay 01 1996A minimal model is constructed for two-dimensional fracture propagation. The heterogeneous process zone is presumed to suppress stress relaxation rate, leading to non-quasistatic behavior. Using the Yoffe solution, I construct and solve a dynamical equation ... More
Microreversible recycled chemical systems. Comment on "A Re-Examination of Reversibility in Reaction Models for the Spontaneous Emergence of Homochirality"Apr 24 2008Nov 14 2008The question of the onset of the homochirality on prebiotic Earth still remains a fundamental question in the quest for the origin of life. Recent works in this field introduce the concept of recycling, rather than the traditional open-flow system described ... More
Complementarity Is Not EnoughJul 22 2012Oct 15 2012The near-horizon field B of an old black hole is maximally entangled with the early Hawking radiation R, by unitarity of the S-matrix. But B must be maximally entangled with the black hole interior A, by the equivalence principle. Causal patch complementarity ... More
Noncommutative residue for Heisenberg manifolds. Applications in CR and contact geometryJul 12 2006Aug 23 2007This paper has four main parts. In the first part, we construct a noncommutative residue for the hypoelliptic calculus on Heisenberg manifolds, that is, for the class of Heisenberg PsiDOs introduced by Beals-Greiner and Taylor. This noncommutative residue ... More
Cayley-Hamilton Decomposition and Spectral AsymmetrySep 25 2003Nov 15 2004This paper has been withdrawn due a crucial mistake due to a crucial mistake in the proof of Lemma 2.3.
Spectral Asymmetry, Zeta Functions and the Noncommutative ResidueOct 08 2003Jan 25 2006In this paper we study the spectral asymmetry of (possibly nonselfadjoint) elliptic PsiDO's in terms of the difference of zeta functions coming from different cuttings. Refining previous formulas of Wodzicki in the case of odd class elliptic PsiDO's, ... More
2-Kac-Moody algebrasDec 30 2008We construct a 2-category associated with a Kac-Moody algebra and we study its 2-representations. This generalizes earlier work with Chuang for type A. We relate categorifications relying on K_0 properties and 2-representations.
Dimensions of triangulated categoriesOct 09 2003Sep 16 2004We define a dimension for a triangulated category. We prove a representabilityTheorem for a certain class of functors on finite dimensional triangulatedcategories. We study the dimension of the boundedderived category of an algebra or a scheme and we ... More
Automorphismes, graduations et categories trianguleesAug 11 2010We give a moduli interpretation of the outer automorphism group Out of a finite dimensional algebra similar to that of the Picard group of a scheme. We deduce that Out^0 is invariant under derived and stable equivalences. This allows us to transfer gradings ... More
Rust for functional programmersJul 21 2014This article provides an introduction to Rust, a systems language by Mozilla, to programmers already familiar with Haskell, OCaml or other functional languages.
Categories from scratchMay 13 2014Jul 21 2014The concept of category from mathematics happens to be useful to computer programmers in many ways. Unfortunately, all "good" explanations of categories so far have been designed by mathematicians, or at least theoreticians with a strong background in ... More
Stephane Leduc and the vital exception in the Life SciencesDec 11 2015Mar 04 2016Embryogenesis, the process by which an organism forms and develops, has long been and still is a major field of investigation in the natural sciences. By which means, which forces, are embryonic cells and tissues assembled, deformed, and eventually organized ... More
Extension of Summation Formulas involving Stirling seriesMay 16 2016This paper presents a family of rapidly convergent summation formulas for various finite sums of the form $\sum_{k=0}^{\lfloor x\rfloor}f(k)$, where $x$ is a positive real number.
First-principles derivation of the AdS/CFT Y-systemsAug 24 2011Oct 25 2011We provide a first-principles, perturbative derivation of the AdS5/CFT4 Y-system that has been proposed to solve the spectrum problem of N=4 SYM. The proof relies on the computation of quantum effects in the fusion of some loop operators, namely the transfer ... More
The Formulas for the Distribution of the 3-Smooth, 5-Smooth, 7-Smooth and all other Smooth NumbersAug 24 2016Oct 23 2016In this paper we present and prove rapidly convergent formulas for the distribution of the $3$-smooth, $5$-smooth, $7$-smooth and all other smooth numbers. One of these formulas is another version of a formula due to Hardy and Littlewood for the arithmetic ... More
The evolution of massive stars in the context of V838 MonocerotisJul 25 2006The aim of this paper is to look at the evolution of massive stars in order to determine whether or not the progenitor of V838 Mon may be a massive star. In the first part of this paper, the evolution of massive stars around solar metallicity is described, ... More
Comments on: "Operator $K$-theory for the group SU(n,1)" by P. Julg and G. KasparovJan 22 2006Apr 25 2006In this note we point out and fill a gap in the proof by Julg-Kasparov of the Baum-Connes conjecture with coefficients for discrete subgroups of $\op{SU}(n,1)$. The issue at stake is the proof that the complex powers of the contact Laplacian are element ... More
Traces on pseudodifferential operators and sums of commutatorsJul 28 2007Jan 08 2008The aim of this paper is to show that various known characterizations of traces on classical pseudodifferentials operators (PsiDOs) can actually be obtained by very elementary considerations on PsiDOs, using only basic properties of these operators. Thereby, ... More
Complex powers of the contact Laplacian and the Baum-Connes conjecture for SU(n,1)Jan 22 2006Apr 25 2006This paper is an extended version of math.OA/0601528 where we point out and remedy a gap in the proof by P. Julg and G. Kasparov of the Baum-Connes conjecture for discrete subgroups of SU(n,1). In particular, here we explain in details why the non-microlocality ... More
A new proof of the local regularity of the eta invariant of a Dirac operatorNov 05 2004Dec 02 2005In this paper we give a new proof of Bismut-Freed's result on the local regularity of the eta invariant of a Dirac operator in odd dimension.
Classification of 3D consistent quad-equationsSep 21 2010Nov 03 2010We consider 3D consistent systems of six independent quad-equations assigned to the faces of a cube. The well-known classification of 3D consistent quad-equations, the so-called ABS-list, is included in this situation. The extension of these equations ... More
Two-dimensional Laplacian growth can be mapped onto Hamiltonian dynamicsJan 28 1994Jan 31 1994It is shown that the dynamics of the growth of a two dimensional surface in a Laplacian field can be mapped onto Hamiltonian dynamics. The mapping is carried out in two stages: first the surface is conformally mapped onto the unit circle, generating a ... More
PIN Skimming: Exploiting the Ambient-Light Sensor in Mobile DevicesMay 15 2014In this paper, we propose a new type of side channel which is based on the ambient-light sensor employed in today's mobile devices. The pervasive usage of mobile devices, i.e., smartphones and tablet computers and their vast amount of sensors represent ... More
Noncommutative residue invariants for CR and contact manifoldsOct 04 2005Jul 21 2006In this paper we produce several new invariants for CR and contact manifolds by looking at the noncommutative residue traces of various geometric projections. In the CR setting these operators arise from the Kohn-Rossi complex and include the Szeg\"o ... More
Families of trees decompose the random graph in any arbitrary wayOct 22 2002Let $F=\{H_1,...,H_k\}$ be a family of graphs. A graph $G$ with $m$ edges is called {\em totally $F$-decomposable} if for {\em every} linear combination of the form $\alpha_1 e(H_1) + ... + \alpha_k e(H_k) = m$ where each $\alpha_i$ is a nonnegative integer, ... More
Consistency and Stability of a Milstein-Galerkin Finite Element Scheme for Semilinear SPDEJul 15 2013We present an abstract concept for the error analysis of numerical schemes for semilinear stochastic partial differential equations (SPDEs) and demonstrate its usefulness by proving the strong convergence of a Milstein-Galerkin finite element scheme. ... More
Optimal Error Estimates of Galerkin Finite Element Methods for Stochastic Partial Differential Equations with Multiplicative NoiseMar 23 2011We consider Galerkin finite element methods for semilinear stochastic partial differential equations (SPDEs) with multiplicative noise and Lipschitz continuous nonlinearities. We analyze the strong error of convergence for spatially semidiscrete approximations ... More
On whether and how D-RISC and Microgrids can be kept relevant (self-assessment report)Mar 20 2013This report lays flat my personal views on D-RISC and Microgrids as of March 2013. It reflects the opinions and insights that I have gained from working on this project during the period 2008-2013. This report is structed in two parts: deconstruction ... More
SL: a "quick and dirty" but working intermediate language for SVP systemsAug 22 2012The CSA group at the University of Amsterdam has developed SVP, a framework to manage and program many-core and hardware multithreaded processors. In this article, we introduce the intermediate language SL, a common vehicle to program SVP platforms. SL ... More
Haskell for OCaml programmersMay 13 2014Jul 21 2014This introduction to Haskell is written to optimize learning by programmers who already know OCaml.
q-Schur algebras and complex reflection groups, ISep 12 2005Dec 03 2007We show that the category O for a rational Cherednik algebra of type A is equivalent to modules over a q-Schur algebra (parameter not a half integer), providing thus character formulas for simple modules. We give some generalization to B_n(d). We prove ... More
Categories derivees et geometrie birationnelleMar 24 2005Originally a technical tool, the derived category of coherent sheaves over an algebraic variety has become over the last twenty years an important invariant in the birational study of algebraic varieties. Problems of birational invariance and of minimization ... More
Universal Limit on CommunicationNov 17 2016I derive a universal upper bound on the capacity of any communication channel between two distant systems. The Holevo quantity, and hence the mutual information, is at most of order $E \Delta t / \hbar$, where $E$ the average energy of the signal, and ... More
Heisenberg calculus and spectral theory of hypoelliptic operators on Heisenberg manifoldsSep 14 2005Dec 06 2005This memoir deals with the hypoelliptic calculus on Heisenberg manifolds, or Heisenberg calculus. The Heisenberg manifolds generalize CR and contact manifolds and in this context the main differential operators at stake include the H\"ormander's sum of ... More
Intrinsic notion of principal symbol for the Heisenberg calculusApr 04 2005Dec 06 2005In this paper we define an intrinsic notion of principal for the Hypoelliptic calculus on Heisenberg manifolds. More precisely, the principal symbol of a \psivdo appears as a homogeneous section over the linear dual of the tangent Lie algebra bundle of ... More
Packing 4-cycles in Eulerian and bipartite Eulerian tournaments with an application to distances in interchange graphsOct 26 2003We prove that every Eulerian orientation of $K_{m,n}$ contains $\frac{1}{4+\sqrt{8}}mn(1-o(1))$ arc-disjoint directed 4-cycles, improving earlier lower bounds. Combined with a probabilistic argument, this result is used to prove that every regular tournament ... More
The S-Procedure via Dual Cone CalculusMay 10 2013Given a quadratic function $h$ that satisfies a Slater condition, Yakubovich's S-Procedure (or S-Lemma) gives a characterization of all other quadratic functions that are copositive with $h$ in a form that is amenable to numerical computations. In this ... More
Macroscopic diffusion from a Hamilton-like dynamicsNov 03 2012Mar 20 2013We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of Hamiltonian ... More
Macroscopic fluctuation theory of local collisional dynamicsMay 08 2012We explain why the macroscopic fluctuations of deterministic local collision dynamics should be characterized by a non strictly convex functional.
Loop Quantum Cosmology on a TorusSep 14 2009In this paper we study the effect of a torus topology on Loop Quantum Cosmology. We first derive the Teichmueller space parametrizing all possible tori using Thurston's theorem and construct a Hamiltonian describing the dynamics of these torus universes. ... More
A new short proof of the local index formula and some of its applicationsNov 20 2002Nov 15 2004We give a new short proof of the index formula of Atiyah and Singer based on combining Getzler's rescaling with Greiner's approach of the heat kernel asymptotics. As application we can easily compute the Connes-Moscovici cyclic cocycle of even and odd ... More
Two-dimensional variational systems on the root lattice $Q(A_{N})$Jan 20 2016We study certain two-dimensional variational systems, namely pluri-Lagrangian systems on the root lattice $Q(A_{N})$. Here, we follow the scheme which was already used to define two-dimensional pluri-Lagrangian systems on the lattice $\mathbb{Z}^{N}$ ... More
Asymptotically optimal $K_k$-packings of dense graphs via fractional $K_k$-decompositionsNov 25 2003Let $H$ be a fixed graph. A {\em fractional $H$-decomposition} of a graph $G$ is an assignment of nonnegative real weights to the copies of $H$ in $G$ such that for each $e \in E(G)$, the sum of the weights of copies of $H$ containing $e$ in precisely ... More
Structural evolution of granular systems: TheoryDec 22 2014May 01 2015A first-principles theory is developed for the general evolution of a key structural characteristic of planar granular systems - the cell order distribution. The dynamic equations are constructed and solved in closed form for a number of examples: dense ... More
Formulating a first-principles statistical theory of growing surfaces in two-dimensional Laplacian fieldsAug 11 1994A statistical theory of two-dimensional Laplacian growths is formulated from first-principles. First the area enclosed by the growing surface is mapped conformally to the interior of the unit circle, generating a set of dynamically evolving quasi-particles. ... More
Threshold phenomena on product spaces: BKKKL revisited (once more)Sep 26 2007We revisit the work of Bourgain, Kahn, Kalai, Katznelson and Linial (1992) -- referred to as ``BKKKL'' in the title -- about influences on Boolean functions in order to give a precise statement of threshold phenomenon on the product space $\{1,..., r\}^\NN$, ... More
Rapidly Convergent Summation Formulas involving Stirling SeriesJan 31 2016This paper presents a family of rapidly convergent summation formulas for various finite sums of analytic functions. These summation formulas are obtained by applying a series acceleration transformation involving Stirling numbers of the first kind to ... More
Explicit contraction rates for a class of degenerate and infinite-dimensional diffusionsMay 25 2016Jul 20 2016Given a separable and real Hilbert space $\mathbb{H}$ and a trace-class, symmetric and non-negative operator $\mathcal{G}:\mathbb{H}\rightarrow\mathbb{H}$, we examine the equation \begin{align*} dX_t = -X_t\, dt + b(X_t) \, dt + \sqrt{2} \, dW_t, \qquad ... More
Logarithmic singularities of Schwartz kernels and local invariants of conformal and CR structuresOct 31 2007This paper consists of two parts. In the first part we show that in odd dimension, as well as in even dimension below the critical weight (i.e. half the dimension), the logarithmic singularities of Schwartz kernels and Green kernels of conformal invariant ... More
Functional calculus and spectral asymptotics for hypoelliptic operators on Heisenberg Manifolds. IFeb 25 2005Dec 06 2005This paper is part of a series papers devoted to geometric and spectral theoretic applications of the hypoelliptic calculus on Heisenberg manifolds. More specifically, in this paper we make use of the Heisenberg calculus of Beals-Greiner and Taylor to ... More
The number of edge disjoint transitive triples in a tournamentApr 14 2003We prove that a tournament with $n$ vertices has more than $0.13n^2(1+o(1))$ edge-disjoint transitive triples. We also prove some results on the existence of large packings of $k$-vertex transitive tournaments in an $n$-vertex tournament. Our proofs combine ... More
On the maximum number of spanning copies of an orientation in a tournamentNov 24 2015For an orientation $H$ with $n$ vertices, let $T(H)$ denote the maximum possible number of labeled copies of $H$ in an $n$-vertex tournament. It is easily seen that $T(H) \ge n!/2^{e(H)}$ as the latter is the expected number of such copies in a random ... More
Firewalls From Double PurityAug 12 2013Aug 21 2013The firewall paradox is often presented as arising from double entanglement, but I argue that more generally the paradox is double purity. Near-horizon modes are purified by the interior, in the infalling vacuum. Hence they cannot also be pure alone, ... More
Fluctuation Relations for Diffusions Thermally Driven by a Non-Stationnary BathAug 02 2009In the context of the dynamical evolution in a non-stationary thermal bath, we construct a family of fluctuation relations for the entropy production that are not verified by the work performed on the system. We exhibit fluctuation relations which are ... More
$PU(N)$ monopoles, higher rank instantons, and the monopole invariantsFeb 29 2008A famous conjecture in gauge theory mathematics, attributed to Witten, suggests that the polynomial invariants of Donaldson are expressible in terms of the Seiberg-Witten invariants if the underlying four-manifold is of simple type. Mathematicians have ... More
Dense graphs with a large triangle cover have a large triangle packingSep 02 2010It is well known that a graph with $m$ edges can be made triangle-free by removing (slightly less than) $m/2$ edges. On the other hand, there are many classes of graphs which are hard to make triangle-free in the sense that it is necessary to remove roughly ... More
A vanishing result for a Casson-type instanton invariantNov 14 2009Casson-type invariants emerging from Donaldson theory over certain negative definite 4-manifolds were recently suggested by Andrei Teleman. These are defined by a count of a zero-dimensional moduli space of flat instantons. Motivated by the cobordism ... More
Projection effects in cluster mass estimates : the case of MS2137Mar 31 2005Jul 08 2005We revisit the mass properties of the lensing cluster of galaxies MS2137-23 and assess the mutual agreement between cluster mass estimates based on lensing, X-rays and stellar dynamics. We perform a thorough elliptical lens modelling using arcs in the ... More
Noncommutative geometry and lower dimensional volumes in Riemannian geometryJul 28 2007In this paper we explain how to define "lower dimensional'' volumes of any compact Riemannian manifold as the integrals of local Riemannian invariants. For instance we give sense to the area and the length of such a manifold in any dimension. Our reasoning ... More
Around rationality of cyclesNov 17 2011Dec 07 2011In this article we prove certain results comparing rationality of algebraic cycles over the function fi?eld of a quadric and over the base field. Those results have already been proved by Alexander Vishik in the case of characteristic 0, which allowed ... More
Stress transmission and isostatic states of non-rigid particulate systemsJan 28 2005The isostaticity theory for stress transmission in macroscopic planar particulate assemblies is extended here to non-rigid particles. It is shown that, provided that the mean coordination number in $d$ dimensions is $d+1$, macroscopic systems can be mapped ... More
Large fluctuations of disentaglement force and implications for polymer dynamicsAug 28 2001This paper examines the effect of cooling on disentanglement forces in polymers and the implications for both single chain pullout and polymer dynamics. I derive the explicit dependence of the distribution of these forces on temperature, which is found ... More
Towards a theory of growing surfaces: Mapping two-dimensional Laplacian growth onto Hamiltonian dynamics and statisticsJan 28 1994Jan 31 1994I show that the evolution of a two dimensional surface in a Laplacian field can be described by Hamiltonian dynamics. First the growing region is mapped conformally to the interior of the unit circle, creating in the process a set of mathematical zeros ... More
Szego projections and new invariants for CR and contact manifoldsJan 15 2006In this paper we give a survey of the constructions in math.DG/0510061 of several new invariants for CR and contact manifolds. The latter extend previous constructions of Hirachi and Boutet de Monvel. In addition, we give simple algebro-geometric arguments ... More
Representations of rational Cherednik algebrasApr 29 2005Apr 30 2005This paper surveys the representation theory of rational Cherednik algebras. We also discuss the representations of the spherical subalgebras. We describe in particular the results on category O. For type A, we explain relations with the Hilbert scheme ... More
Representation spaces of pretzel knotsDec 13 2010May 08 2012We study the representation spaces $R(K;\bf{i})$ as appearing in Kronheimer and Mrowka's framed instanton knot Floer homology, for a class of pretzel knots. In particular, for pretzel knots $P(p,q,r)$ with $p, q, r$ pairwise coprime, these appear to be ... More
On the Asymptotic Completeness of the Volterra CalculusOct 13 2003Aug 30 2004The Volterra calculus is a simple and powerful pseudodifferential tool for inverting parabolic equations and it has also found many applications in geometric analysis. On the other hand, an important property in the theory of pseudodifferential operators ... More
A New Hypoelliptic Operator on Almost CR ManifoldsAug 27 2008Mar 14 2011The aim of this paper is to present the construction, out of the Kohn-Rossi complex, of a new hypoelliptic operator $Q_{L}$ on almost CR manifolds equipped with a real structure. The operator acts on all (p,q)-forms, but when restricted to (p,0)-forms ... More