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Magnon properties of random alloysOct 19 2018We study magnon properties in terms of spin stiffness, Curie temperatures and magnon spectrum of Fe-Ni, Co-Ni and Fe-Co random alloys using a combination of electronic structure calculations and atomistic spin dynamics simulations. Influence of the disorder ... More

Extended spin model in atomistic simulations of alloysFeb 16 2017An extended atomistic spin model allowing for studies of the finite temperature magnetic properties of alloys is proposed. The model is obtained by extending the Heisenberg Hamiltonian via a parameterization from a first principles basis, interpolating ... More

Spin relaxation signature of colossal magnetic anisotropy in platinum atomic chainsApr 03 2016Recent experimental data demonstrate emerging magnetic order in platinum atomically thin nanowires. Furthermore, an unusual form of magnetic anisotropy -- colossal magnetic anisotropy (CMA) -- was earlier predicted to exist in atomically thin platinum ... More

General method for atomistic spin-lattice dynamics with first principles accuracyApr 09 2018Jul 09 2018We present a computationally efficient general first-principles based method for spin-lattice simulations for solids. Our method is based on a combination of atomistic spin dynamics and molecular dynamics, expressed through a spin-lattice Hamiltonian ... More

A majority gate with chiral magnetic solitonsFeb 02 2017In magnetic materials nontrivial spin textures may emerge owing to the competition among different types of magnetic interactions. Among such spin textures, chiral magnetic solitons represent topologically protected spin configurations with particle-like ... More

Realistic finite temperature simulations of magnetic systems using quantum statisticsAug 02 2017We have performed realistic atomistic simulations at finite temperatures using Monte Carlo and atomistic spin dynamics simulations incorporating quantum (Bose-Einstein) statistics. The description is much improved at low temperatures compared to classical ... More

First principles studies of the Gilbert damping and exchange interactions for half-metallic Heuslers alloysApr 26 2016Heusler alloys have been intensively studied due to the wide variety of properties that they exhibit. One of these properties is of particular interest for technological applications, i.e. the fact that some Heusler alloys are half-metallic. In the following, ... More

Heavy-mass magnetic modes in pyrochlore iridates due to dominant Dzyaloshinskii-Moriya interactionJul 03 2017Materials with strong spin-orbit interactions are presently a main target in the search for systems with novel magnetic properties. Magnetic anisotropies can be very large in such compounds, ranging from strongly frustrated Kitaev exchange in honeycomb ... More

A Note on Support in Triangulated CategoriesApr 24 2008In this note, I define a notion of a compactly supported object in a triangulated category. I prove a number of propositions relating this to traditional notions of support and give an application to the theory of derived Morita equivalence. I also discuss ... More

Undoing Orbifold QuiversFeb 10 2005Apr 11 2005A number of new papers have greatly elucidated the derivation of quiver gauge theories from D-branes at a singularity. A complete story has now been developed for the total space of the canonical line bundle over a smooth Fano 2-fold. In the context of ... More

A new look on the two-dimensional Ising model: thermal artificial spinsJul 04 2015We present a direct experimental investigation of the thermal ordering in an artificial analogue of an asymmetric two dimensional Ising system composed of a rectangular array of nano-fabricated magnetostatically interacting islands. During fabrication ... More

All-thermal switching of amorphous Gd-Fe alloys: analysis of structural properties and magnetization dynamicsAug 24 2015In recent years, there has been an intense interest in understanding the microscopic mechanism of thermally induced magnetization switching driven by a femtosecond laser pulse. Most of the effort has been dedicated to periodic crystalline structures while ... More

Unconventional spin glass state in elemental neodymium in the absence of extrinsic disorderJul 04 2019Spin glasses are a fascinating but highly complex magnetic state of matter, traditionally investigated in materials with a random distribution of exchange interactions. Intricately linked to spin frustration and disorder, spin glasses exhibit no long-range ... More

Topological D-branes from DescentAug 01 2008Sep 06 2010Witten couples the open topological B-model to a holomorphic vector bundle by adding to the boundary of the worldsheet a Wilson loop for an integrable connection on the bundle. Using the descent procedure for boundary vertex operators in this context, ... More

A spin dynamics approach to solitonicsSep 16 2015May 11 2016It is spatial dispersion which is exclusively responsible for the emergence of exchange interaction and magnetic ordering. In contrast, magneto-crystalline anisotropy present in any realistic material brings in a certain non-linearity to the equation ... More

Suppression of Standing Spin Waves in Low-Dimensional FerromagnetsMar 10 2011May 23 2011We examine the experimental absence of standing spin wave modes in thin magnetic films, by means of atomistic spin dynamics simulations. Using Co on Cu(001) as a model system, we demonstrate that by increasing the number of layers, the "optical" branches ... More

Atomistic spin dynamics of low-dimensional magnetsNov 13 2012Feb 14 2013We investigate the magnetic properties of a range of low-dimensional ferromagnets using a combination of first-principles calculations and atomistic spin dynamics simulations. This approach allows us to evaluate the ground state and finite temperature ... More

A microscopic model for ultrafast remagnetization dynamicsOct 09 2012In this letter, we provide a microscopic model for the ultrafast remagnetization of atomic moments already quenched above Stoner-Curie temperature by a strong laser fluence. Combining first principles density functional theory, atomistic spin dynamics ... More

Accelerating the switching of logical units by anisotropy driven magnetization dynamicsOct 22 2012In this work the magnetization dynamics of clusters supported on non-magnetic substrates is shown to exhibit an unprecedented complex response when subjected to external magnetic fields. The field-driven magnetization reversal of small Co clusters deposited ... More

Ultrafast generation and dynamics of isolated skyrmions in antiferromagnetic insulatorsSep 21 2018Based on atomistic spin dynamics simulations, we report the ultrafast generation of single antiferromagnetic skyrmions in a confined geometry. This process is achieved through an effective magnetic field induced by the inverse Faraday effect from a short ... More

Electronic structure and magnetic properties of L1_0 binary alloysApr 28 2014Jun 13 2014We present a systematic study of the magnetic properties of L1$_0$ binary alloys FeNi, CoNi, MnAl and MnGa via two different density functional theory approaches. Our calculations show large magnetocrystalline anisotropies in the order $1~\text{MJ/m}^3$ ... More

Ultrafast generation and dynamics of isolated skyrmions in antiferromagnetic insulatorsSep 21 2018Feb 21 2019Based on atomistic spin dynamics simulations, we report the ultrafast generation of single antiferromagnetic (AFM) skyrmions in a confined geometry. This process is achieved through an effective magnetic field induced by the athermal inverse Faraday effect ... More

A Weekly Pattern from Hourly Estimates of the Super-Kamiokande-I Neutrino Flux 1996-2001Sep 20 2005A search for a neutrino flux difference between weekdays and weekend days, for the average week of the Super-Kamiokande-I (SK-I) Experiment, was undertaken using the 5-day period version of the SK-I data taken from May 31st, 1996 to July 15th, 2001. A ... More

Simplicial complexes with lattice structuresJan 29 2016May 24 2016If $L$ is a finite lattice, we show that there is a natural topological lattice structure on the geometric realization of its order complex $\Delta(L)$ (definition recalled). Lattice-theoretically, the resulting object is a subdirect product of copies ... More

Submonoids of groups, and group-representability of restricted relation algebrasFeb 20 2017Jul 10 2017Marek Kuczma asked in 1980 whether for every positive integer $n,$ there exists a subsemigroup $M$ of a group $G,$ such that $G$ is equal to the $n$-fold product $M\,M^{-1} M\,M^{-1} \dots\,M^{(-1)^{n-1}},$ but not to any proper initial subproduct of ... More

Which group algebras cannot be made zero by imposing a single non-monomial relation?May 29 2019For which groups $G$ is it true that for all fields $k$, every non-monomial element of the group algebra $k\,G$ generates a <i>proper</i> $2$-sided ideal? The only groups for which we know this are the torsion-free abelian groups. We would like to know ... More

Two SK-I Neutrino Sources?Jun 26 2006A search for a neutrino flux difference between weekdays and weekend days was undertaken for the average week of the Super-Kamiokande-I (SK-I) Experiment, using the 5-day period version of the SK-I data taken from May 31st, 1996 to July 15th, 2001. Arbitrarily ... More

On coproducts in varieties, quasivarieties and prevarietiesJun 10 2008Nov 27 2009If the free algebra F on one generator in a variety V of algebras (in the sense of universal algebra) has a subalgebra free on two generators, must it also have a subalgebra free on three generators? In general, no; but yes if F generates the variety ... More

Theory of dissipationless Nernst effectsOct 13 2009We develop a theory of transverse thermoelectric (Peltier) conductivity, \alpha_{xy}, in finite magnetic field -- this particular conductivity is often the most important contribution to the Nernst thermopower. We demonstrate that \alpha_{xy} of a free ... More

Universal Algebraic Methods for Constraint Satisfaction ProblemsNov 09 2016Mar 10 2017After substantial progress over the last 15 years, the "algebraic CSP-dichotomy conjecture" reduces to the following: every local constraint satisfaction problem (CSP) associated with a finite idempotent algebra is tractable if and only if the algebra ... More

String Webs and 1/4 BPS MonopolesApr 23 1998We argue for the existence of many new 1/4 BPS states in N=4 SU(N_c) Super-Yang-Mills theory with N_c>=3, by constructing them from supersymmetric string webs whose external strings terminate on parallel D3-branes. The masses of the string webs are shown ... More

String Junctions and BPS States in Seiberg-Witten TheoryFeb 05 1998Feb 25 1998We argue that certain BPS states in the D3-brane probe realization of N=2 SU(2) Super-Yang-Mills theory correspond to multi-pronged strings connecting the D3-brane to the background 7-branes. This provides a physical realization of the decay of these ... More

Universal Algebraic Methods for Constraint Satisfaction ProblemsNov 09 2016After substantial progress over the last 15 years, the "algebraic CSP-dichotomy conjecture" reduces to the following: every local constraint satisfaction problem (CSP) associated with a finite idempotent algebra is tractable if and only if the algebra ... More

Completeness results for metrized rings and latticesAug 13 2018Sep 26 2018The Boolean ring $B$ of measurable subsets of the unit interval, modulo sets of measure zero, has proper radical ideals (e.g., $\{0\})$ that are closed under the natural metric, but has no prime ideals closed under that metric; hence closed radical ideals ... More

On group topologies determined by families of setsNov 12 2013Let $G$ be an abelian group, and $F$ a downward directed family of subsets of $G$. The finest topology $\mathcal{T}$ on $G$ under which $F$ converges to $0$ has been described by I.Protasov and E.Zelenyuk. In particular, their description yields a criterion ... More

Internal Symmetry of Space-Time Connections with TorsionNov 19 2014In this brief article an internal symmetry of a generic metric compatible space-time connection, metric and generalized volume element is introduced. The symmetry arises naturally by considering a space-time connection containing a generic torsion tensor, ... More

Loop Groups, Kaluza-Klein Reduction and M-TheoryJun 24 2004Jul 06 2004We show that the data of a principal G-bundle over a principal circle bundle is equivalent to that of a \hat{LG} = U(1) |x LG bundle over the base of the circle bundle. We apply this to the Kaluza-Klein reduction of M-theory to IIA and show that certain ... More

Geometric Aspects of D-branes and T-dualityAug 16 2009Sep 13 2009We explore the differential geometry of T-duality and D-branes. Because D-branes and RR-fields are properly described via K-theory, we discuss the (differential) K-theoretic generalization of T-duality and its application to the coupling of D-branes to ... More

On lattices of convex sets in R^nSep 16 2004Properties of several sorts of lattices of convex subsets of R^n are examined. The lattice of convex sets containing the origin turns out, for n>1, to satisfy a set of identities strictly between those of the lattice of all convex subsets of R^n and the ... More

String Junction Transitions in the Moduli Space of N=2 SYMJun 01 1998The string theory description of BPS states in D-brane world-volume field theories may undergo transitions from open strings to string webs, as well as between different string webs, as one moves in the field theory moduli space. These transitions are ... More

Derivation of the Paraxial Ray Equations in Three Conformal RepresentationsAug 05 2015Acoustic rays can be described by null geodesics of a pseudo-Riemannian manifold. This allows for the immediate generalization of paraxial ray systems via geodesic deviation. The technique has appeared in the literature for the past decade and has been ... More

Critical point for the strong field magnetoresistance of a normal conductor/perfect insulator/perfect conductor composite with a random columnar microstructureJun 23 2000A recently developed self-consistent effective medium approximation, for composites with a columnar microstructure, is applied to such a three-constituent mixture of isotropic normal conductor, perfect insulator, and perfect conductor, where a strong ... More

Symmetry constrained machine learningNov 16 2018Symmetry, a central concept in understanding the laws of nature, has been used for centuries in physics, mathematics, and chemistry, to help make mathematical models tractable. Yet, despite its power, symmetry has not been used extensively in machine ... More

Can one factor the classical adjoint of a generic matrix?Jun 08 2003Aug 08 2004Let k be a field, n a positive integer, X a generic nxn matrix over k (i.e., a matrix (x_{ij}) of n^2 independent indeterminates over the polynomial ring k[x_{ij}]), and adj(X) its classical adjoint. It is shown that if char k=0 and n is odd, then adj(X) ... More

Every module is an inverse limit of injective modulesApr 15 2011Aug 16 2011It is shown that any left module A over a ring R can be written as the intersection of a downward directed system of injective submodules of an injective module; equivalently, as an inverse limit of one-to-one homomorphisms of injectives. If R is left ... More

Exact analysis of a Veselago lens in the quasi-static regimeMay 15 2014The resolution of conventional optical lenses is limited by the wavelength. Materials with negative refractive index have been shown to enable the generation of an enhanced resolution image where both propagating and non-propagating waves are employed. ... More

Moduli spaces for Bondal quiversDec 07 2005Sep 06 2007Given a sufficiently nice collection of sheaves on an algebraic variety V, Bondal explained how to build a quiver Q along with an ideal of relations in the path algebra of Q such that the derived category of representations of Q subject to these relations ... More

Dipoles, Twists and Noncommutative Gauge TheoryAug 02 2000Aug 18 2000T-duality of gauge theories on a noncommutative $T^d$ can be extended to include fields with twisted boundary conditions. The resulting T-dual theories contain novel nonlocal fields. These fields represent dipoles of constant magnitude. Several unique ... More

Theory of characteristics for first order partial differential equationsNov 25 2010We use the method of synthetic differential geometry to revisit the geometric reasoning employed by Lie, Klein and others in their study of partial differential equations.

On the invariants of the splitting algebraMay 23 2011For a given monic polynomial $p(t)$ of degree $n$ over a commutative ring $k$, the splitting algebra is the universal $k$-algebra in which $p(t)$ has $n$ roots, or, more precisely, over which $p(t)$ factors, $p(t)=(t-\xi_1)...(t-\xi_n)$. The symmetric ... More

First neighbourhood of the diagonal, and geometric distributionsJun 07 2002We describe the geometric notion of distribution in synthetic terms, utilizing the notion of "first neighbourhood of the diagonal" from algebraic geometry. We characterize involutive distributions in combinatorial terms.

Multi-Adaptive Galerkin Methods for ODEs IMay 12 2012We present multi-adaptive versions of the standard continuous and discontinuous Galerkin methods for ODEs. Taking adaptivity one step further, we allow for individual time-steps, order and quadrature, so that in particular each individual component has ... More

The Kellogg property and boundary regularity for p-harmonic functions with respect to the Mazurkiewicz boundary and other compactificationsMay 05 2017Oct 30 2018In this paper boundary regularity for p-harmonic functions is studied with respect to the Mazurkiewicz boundary and other compactifications. In particular, the Kellogg property (which says that the set of irregular boundary points has capacity zero) is ... More

A $q$-analogue of the FKG inequality and some applicationsJun 07 2009Aug 21 2009Let $L$ be a finite distributive lattice and $\mu : L \to {\mathbb R}^{+}$ a log-supermodular function. For functions $k: L \to {\mathbb R}^{+}$ let $$E_{\mu} (k; q) \defeq \sum_{x\in L} k(x) \mu (x) q^{{\mathrm rank}(x)} \in {\mathbb R}^{+}[q].$$ We ... More

Commutation StructuresNov 02 2005For a fixed object X in a monoidal category, an X-commutation structure on an object A is just a map from XA to AX. We study aspects of such structure in case A has a dual.

The Fermi Surface Effect on Magnetic Interlayer CouplingFeb 03 2004The oscillating magnetic interlayer coupling of Fe over spacer layers consisting of Cu$_{x}$Pd$_{1-x}$ alloys is investigated by first principles density functional theory. The amplitude, period and phase of the coupling, as well as the disorder-induced ... More

Thermally driven domain wall motion in Fe on W(1 1 0)Aug 05 2013It has recently been shown that domain walls in ferromagnets can be moved in the presence of thermal gradients. In this work we study the motion of narrow domain walls in low-dimensional systems when subjected to thermal gradients. The system chosen is ... More

Topological excitations in a Kagomé magnetJan 19 2014Jan 21 2014It is shown here that a Kagom\'e magnet, with Heisenberg and Dzyaloshinskii-Moriya interactions causes non trivial topological and chiral magnetic properties. Chirality---that is, left or right handedness---is a very important concept in a broad range ... More

Anomalous phonon lifetime shortening in paramagnetic CrN caused by magneto-lattice coupling: A combined spin and ab initio molecular dynamics studyFeb 08 2018We study the mutual coupling of spin fluctuations and lattice vibrations in paramagnetic CrN by combining atomistic spin dynamics and ab initio molecular dynamics. The two degrees of freedom are dynamically coupled leading to non-adiabatic effects. Those ... More

A systematic study of magnetodynamic properties at finite temperatures in doped permalloy from first principles calculationsFeb 19 2016Jun 23 2016By means of first principles calculations, we have systematically investigated how the magnetodynamic properties Gilbert damping, magnetization and exchange stiffness are affected when permalloy (Py) (Fe$_{0.19}$Ni$_{0.81}$) is doped with 4d or 5d transition ... More

Moduli Spaces for D-branes at the Tip of a ConeOct 18 2005For physicists: We show that the quiver gauge theory derived from a Calabi-Yau cone via an exceptional collection of line bundles on the base has the original cone as a component of its classical moduli space. For mathematicians: We use data from the ... More

Generating an electromagnetic multipole by oscillating currentsJun 25 2017Based on the relation between a plane phased array and plane waves we show that a spherical current layer or a current sphere proportional to a multipole electric field and situated in a uniform medium generates the same multipole field in all space. ... More

A thermodynamic measure of the Magneto-electric coupling in the 3D topological insulatorJan 14 2012Nov 04 2012We show that the magneto-electric coupling in 3D (strong) topological insulators is related to a second derivative of the bulk magnetization. The formula we derive is the non-linear response analog of the Streda formula for Hall conductivity (P. Streda, ... More

Bulk metals with helical surface statesMar 15 2010May 21 2010In the flurry of experiments looking for topological insulator materials, it has been recently discovered that some bulk metals very close to topological insulator electronic states, support the same topological surface states that are the defining characteristic ... More

A theoretical analysis of inertia-like switching in magnets: applications to a synthetic antiferromagnetSep 07 2011The magnetization dynamics of a synthetic antiferromagnet subject to a short magnetic field pulse, has been studied by using a combination of first-principles and atomistic spin dynamics simulations. We observe switching phenomena on the time scale of ... More

Quantum mechanics as "space-time statistical mechanics"?Jan 24 2005In this paper we discuss and analyse the idea of trying to see (non-relativistic) quantum mechanics as a ``space-time statistical mechanics'', by using the classical statistical mechanical method on objective microscopic space-time configurations. It ... More

SUSY Flat Direction Decay - the prospect of particle production and preheating investigated in the unitary gaugeJan 04 2008Apr 22 2010We look at the possibility of non-perturbative particle production after inflation from SUSY flat directions produced by rotating eigenstates thereby avoiding the standard adiabaticity conditions. This might lead to preheating and prevent the delay of ... More

First-passage percolation on Cartesian power graphsJun 29 2015We consider first-passage percolation with standard exponential edge weights on the class of "high-dimensional" graphs that can be written as an iterated Cartesian product $G\square G \square \dots \square G$ of some base graph $G$ as the number of factors ... More

Thermal state entanglement in harmonic latticesMar 07 2008Jun 18 2008We investigate the entanglement properties of thermal states of the harmonic lattice in one, two and three dimensions. We establish the value of the critical temperature for entanglement between neighbouring sites and give physical reasons. Further sites ... More

A classification of smooth convex 3-polytopes with at most 16 lattice pointsJun 21 2012We provide a complete classification up to isomorphism of all smooth convex lattice 3-polytopes with at most 16 lattice points. There exist in total 103 different polytopes meeting these criteria. Of these, 99 are strict Cayley polytopes and the remaining ... More

Completeness of the ring of polynomialsDec 19 2013Let $k$ be an uncountable field. We prove that the polynomial ring $R:=k[X_1,\dots,X_n]$ in $n\ge 2$ variables over $k$ is complete in its adic topology. In addition we prove that also the localization $R_{\goth m}$ at a maximal ideal $\goth m\subset ... More

Langevin molecular dynamics derived from Ehrenfest dynamicsDec 21 2007Mar 30 2011Stochastic Langevin molecular dynamics for nuclei is derived from the Ehrenfest Hamiltonian system (also called quantum classical molecular dynamics) in a Kac-Zwanzig setting, with the initial data for the electrons stochastically perturbed from the ground ... More

Algebra of Principal Fibre Bundles, and ConnectionsMay 12 2000We put together some of the efforts by several people of making aspects of fibre bundle theory into algebra. The initiator of these efforts was Charles Ehresmann, who put the notion of groupoid and groupoid action in the focus of fibre bundle theory in ... More

A geometric theory of harmonic and semi-conformal mapsJun 12 2003We describe for any Riemannian manifold a certain infinitesimal neighbourhood of the diagonal. Semi-conformal maps are analyzed as those that preserve such neighbourhoods; harmonic maps are analyzed as those that preserve mirror image formation for pairs ... More

A computation of Poisson kernels for some standard weighted biharmonic operators in the unit discJul 03 2007We compute Poisson kernels for integer weight parameter standard weighted biharmonic operators in the unit disc with Dirichlet boundary conditions. The computations performed extend the supply of explicit examples of such kernels and suggest similar formulas ... More

Infinitesimal aspects of the Laplace operatorJun 23 2000In the context of synthetic differential geometry, we study the Laplace operator an a Riemannian manifold. The main new aspect is a neighbourhood of the diagonal, smaller than the second neighbourhood usually required as support for second order differential ... More

The random strategy in Maker-Breaker graph minor gamesJul 10 2019In a $(1:b)$ biased Maker-Breaker game, how good a strategy is for a player can be measured by the bias range for which its rival can win, choosing an appropriate counterstrategy. Bednarska and {\L}uczak proved that, in the $H$-subgraph game, the uniformly ... More

Bundle functors and fibrationsMay 10 2015We give an account, in terms of fibered categories and their fibrewise duals, of aspects of the theory of bundle functors and star-bundle functors in differential geometry.

Unoriented first-passage percolation on the n-cubeFeb 12 2014Jun 05 2014The $n$-dimensional binary hypercube is the graph whose vertices are the binary $n$-tuples $\{0, 1\}^n$ and where two vertices are connected by an edge if they differ at exactly one coordinate. We prove that if the edges are assigned independent mean ... More

Magnetic interactions of supported magnetic clustersNov 22 2005It is demonstrated that the magnetic interactions can be drastically different for nano-sized systems compared to those of bulk or surfaces. Using a real-space formalism we have developed a method to calculate non-collinear magnetization structures and ... More

Magnon softening in a ferromagnetic monolayer: a first-principles spin dynamics studyJan 11 2010Apr 26 2010We study the Fe/W(110) monolayer system through a combination of first principles calculations and atomistic spin dynamics simulations. We focus on the dispersion of the spin waves parallel to the [001] direction. Our results compare favorably with the ... More

Magnetic structure of Fe, Mn, and Cr clusters supported on Cu(111)Aug 14 2006Apr 20 2007The magnetic structures of small clusters of Fe, Mn, and Cr supported on a Cu(111) surface have been studied with non-collinear first principles theory. Different geometries such as triangles, pyramids and wires are considered and the cluster sizes have ... More

On the large magnetic anisotropy of Fe_{2}PApr 11 2012Jul 03 2012We present an investigation on the large magnetic anisotropy of Fe_{2}P, based on {\it Ab Initio} density-functional theory calculations, with a full potential linear muffin-tin orbital (FP-LMTO) basis. We obtain an uniaxial magnetic anisotropy energy ... More

Control Synthesis with Localizability and Passivity ConstraintsDec 19 2018A compact formulation of the most central idea in system level synthesis is given, namely that controller localizability can be enforced using convex constraints on the closed loop. Moreover, it is noted that for passive open loop systems, a passivity ... More

Projective lines as groupoids with projection structureOct 20 2013The coordinate projective line over a field is seen as a groupoid with a further `projection' structure. We investigate conversely to what extent such an, abstractly given, groupoid may be coordinatized by a suitable field constructed out of the geometry. ... More

On the uniform equidistribution of closed horospheres in hyperbolic manifoldsMar 17 2011We prove asymptotic equidistribution results for pieces of large closed horospheres in cofinite hyperbolic manifolds of arbitrary dimension. This extends earlier results by Hejhal and Str\"ombergsson in dimension 2. Our proofs use spectral methods, and ... More

On the value distribution of the Epstein zeta function in the critical stripMay 13 2011We study the value distribution of the Epstein zeta function $E_n(L,s)$ for $0<s<\frac{n}{2}$ and a random lattice $L$ of large dimension $n$. For any fixed $c\in(1/4,1/2)$ and $n\to\infty$, we prove that the random variable $V_n^{-2c}E_n(\cdot,cn)$ has ... More

A comparison theorem for $f$-vectors of simplicial polytopesMay 12 2006Nov 07 2006Let $f_i(P)$ denote the number of $i$-dimensional faces of a convex polytope $P$. Furthermore, let $S(n,d)$ and $C(n,d)$ denote, respectively, the stacked and the cyclic $d$-dimensional polytopes on $n$ vertices. Our main result is that for every simplicial ... More

Multiadaptive Galerkin Methods for ODEs III: A Priori Error EstimatesMay 14 2012The multiadaptive continuous/discontinuous Galerkin methods mcG(q) and mdG(q) for the numerical solution of initial value problems for ordinary differential equations are based on piecewise polynomial approximation of degree q on partitions in time with ... More

Fibrations as Eilenberg-Moore algebrasDec 05 2013We give an elementary exposition of some fundamental facts about fibered (or rather opfibered) categories, in terms of monads and 2-categories. The account avoids any mention of category-valued functors and pseudofunctors.

Two extensions of Thurston's spectral theorem for surface diffeomorphismsAug 18 2012Thurston obtained a classification of individual surface homeomorphisms via the dynamics of the corresponding mapping class elements on Teichm\"uller space. In this paper we present certain extended versions of this, first, to random products of homeomorphisms ... More

Integration of 1-forms and connectionsFeb 28 2019We give a combinatorial/geometric argument of the classical result that an affine connection, which is both torsion free and curvature free, is locally an affine space.

Realizability and Internal Model Control on NetworksDec 19 2018Mar 30 2019It is proved that network realizability of controllers can be enforced without conservatism using convex constraints on the closed loop transfer function. Once a network realizable closed loop transfer matrix has been found, a corresponding controller ... More

Random walks, arrangements, cell complexes, greedoids, and self-organizing librariesMay 01 2008The starting point is the known fact that some much-studied random walks on permutations, such as the Tsetlin library, arise from walks on real hyperplane arrangements. This paper explores similar walks on complex hyperplane arrangements. This is achieved ... More

The 2PI coupling expansion revisitedNov 01 2005Recently, out-of-equilibrium field theory has been studied using approximations based on truncations of the 2PI effective action. Although results are promising, the convergence of subsequent orders of the approximation is difficult to get a handle on, ... More

Efficient Representation of Computational MeshesMay 14 2012We present a simple yet general and efficient approach to representation of computational meshes. Meshes are represented as sets of mesh entities of different topological dimensions and their incidence relations. We discuss a straightforward and efficient ... More

Distributed Control of Positive SystemsFeb 29 2012May 14 2014A system is called positive if the set of non-negative states is left invariant by the dynamics. Stability analysis and controller optimization are greatly simplified for such systems. For example, linear Lyapunov functions and storage functions can be ... More

Automating the Finite Element MethodDec 02 2011The finite element method can be viewed as a machine that automates the discretization of differential equations, taking as input a variational problem, a finite element and a mesh, and producing as output a system of discrete equations. However, the ... More

$ν$MSSM superpotential to 6th order - normalised and with no superfluous couplingsNov 30 2009Apr 28 2010We expand the superpotential of $\nu$MSSM to 6th order. This is the order at which all flat directions can be lifted. All 5179 couplings are independent ie. the superpotential cannot be zero for all fields, without all couplings being zero. Likewise, ... More

SUSY Flat Directions -- to get a VEV or not?Nov 13 2009We investigate the potential of SUSY flat directions (FDs). Large FD vacuum expectation values (VEVs) can delay thermalisation and solve the gravitino problem - if FDs decay perturbatively. This depends on how many and which directions get the VEVs. Recently ... More