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Diffusion Anomaly in a three dimensional lattice gasApr 27 2007We investigate the relation between thermodynamic and dynamic properties of an associating lattice gas (ALG) model. The ALG combines a three dimensional lattice gas with particles interacting through a soft core potential and orientational degrees of ... More

Diffusion Anomaly in an Associating Lattice Gas ModelSep 21 2006We investigate the relation between thermodynamic and dynamic properties of an associating lattice gas (ALG) model. The ALG combines a two dimensional lattice gas with particles interacting through a soft core potential and orientational degrees of freedom. ... More

A Hardy-type result on the average of the lattice point error term over long intervalsJul 31 2015Feb 04 2016Suppose $D$ is a suitably admissible compact subset of $\mathbb{R}^k$ having a smooth boundary with possible zones of zero curvature. Let \mbox{$R(T,\theta,x)= N(T,\theta,x) - T^{k}\mathrm{vol}(D)$,} where $N(T,\theta,x)$ is the number of integral lattice ... More

A Short Guide to Anyons and Modular FunctorsOct 17 2016To the working physicist, anyon theory is meant to describe certain quasi-particle excitations occurring in two dimensional topologically ordered systems. A typical calculation using this theory will involve operations such as $\otimes$ to combine anyons, ... More

Growth of torsion of elliptic curves with full 2-torsion over quadratic cyclotomic fieldsFeb 29 2016Let $K = \mathbb{Q}(\sqrt{-3})$ or $\mathbb{Q}(\sqrt{-1})$ and let $C_n$ denote the cyclic group of order $n$. We study how the torsion part of an elliptic curve over $K$ grows in a quadratic extension of $K$. In the case $E(K)[2] \approx C_2 \oplus C_2$ ... More

Spectra of Gauge Code HamiltoniansJan 10 2018We study the spectral gap of frustrated spin (qubit) Hamiltonians constructed from quantum subsystem (gauge) codes. Such a Hamiltonian can be block diagonalized, with blocks labelled by eigenvalues of extensively many integrals of motion (stabilizers ... More

A topological semigroup structure on the space of actions modulo weak equivalenceJan 19 2015We introduce a topology on the space of actions modulo weak equivalence finer than the one previously studied in the literature. We show that the product of actions is a continuous operation with respect to this topology, so that the space of actions ... More

On Sparse Reflexive Generalized InversesJul 09 2018Sep 30 2018We study sparse generalized inverses $H$ of a rank-$r$ real matrix $A$. We give a construction for reflexive generalized inverses having at most $r^2$ nonzeros. For $r=1$ and for $r=2$ with $A$ nonnegative, we demonstrate how to minimize the (vector) ... More

A Particle Model That Produces Feynman Diagrams: Re-examination of Fundamental Entities, Free Particles, and Background FramesAug 11 1999A relativistic quantized particle model avoids difficulties through (1) a Hamiltonian undecomposable into H=H(0)+H(I), (2) a separation of the evolution parameter s from dynamics, (3) "leptons" and "hadrons" composed of "quarks," and (4) the absence of ... More

Efficient treatment of bilinear forms in global optimizationMar 20 2018We efficiently treat bilinear forms in the context of global optimization, by applying McCormick convexification and by extending an approach of Saxena, Bonami and Lee for symmetric quadratic forms to bilinear forms. A key application of our work is in ... More

Naive entropy of dynamical systemsMar 21 2015Feb 20 2016We study an invariant of dynamical systems called naive entropy, which is defined for both measurable and topological actions of any countable group. We focus on nonamenable groups, in which case the invariant is two-valued, with every system having naive ... More

Gluon sivers and experimental considerations for TMDsDec 14 2012The study and characterisation of transverse-momentum-dependent distribution functions (TMDs) is a major goal of the Electron-Ion Collider (EIC) physics programme. The study of gluon TMDs poses a greater challenge than for quark TMDs in DIS measurements, ... More

Completely positive entropy actions of sofic groups with $\mathbb{Z}$ in their centerSep 06 2015Mar 31 2016Let $\Gamma$ be a sofic group with a copy of $\mathbb{Z}$ in its center. We construct an uncountable family of pairwise nonisomorphic measure-preserving $\Gamma$ actions with completely positive entropy, none of which is a factor of a Bernoulli shift. ... More

Topology and convexity in the space of actions modulo weak equivalenceJan 16 2015Jan 05 2016We analyse the structure of the quotient $\mathrm{A}_\sim(\Gamma,X,\mu)$ of the space of measure-preserving actions of a countable discrete group by the relation of weak equivalence. This space carries a natural operation of convex combination. We show ... More

Stable Configurations of repelling points on compact hyperbolic ManifoldsJul 25 2011It is shown that on compact hyperbolic manifolds, certain stable configurations of points which mutually repel along all interconnecting geodesics become equidistributed as the number of points increases

Conventional Beams or Neutrino Factories: The Next Generation of Accelerator-Based Neutrino ExperimentsAug 21 2000The purpose of this paper is to provoke a discussion about the right next step in accelerator-based neutrino physics. In the next five years many experiments will be done to determine the neutrino mixing parameters. However, the small parameters $\theta_{13}\Delta ... More

Ecosystems, from life, to the Earth, to the GalaxyOct 31 2001Ecosystems are systems where energy flows and material cycles are maintained in an apparently stable, but non-equilibrium state through a process of self-regulation. Such a definition does just apply to biological systems, it can also apply to systems ... More

A quotient-like construction involving elementary submodelsApr 06 2015This article is an investigation of a method of deriving a topology from a space and an elementary submodel containing it. We first define and give the basic properties of this construction, known as $X/M$. In the next section, we construct some examples ... More

Growth of torsion of elliptic curves with odd-order torsion over quadratic cyclotomic fieldsApr 05 2016Apr 28 2016Let $K = \mathbb{Q}(\sqrt{-3})$ or $\mathbb{Q}(\sqrt{-1})$ and let $C_n$ denote the cyclic group of order $n$. We study how the torsion part of an elliptic curve over $K$ grows in a quadratic extension of $K$. In the case $E(K)[2] \approx C_1$ we investigate ... More

Unification of gravity and the harmonic oscillator on a quantum black hole horizon II: Perturbative particle scattering and Feynman amplitudesJul 15 2003Nov 08 2003In Article I, a harmonic-oscillator model of a universe of n quarks is infinitesimally modified to eliminate the background reference frame. As a result, quark trajectories exhibit the unification of gravity and the harmonic oscillator near the horizon ... More

Phase-Boundaries near Critical End points: Applications to Cross-linked CopolymersDec 17 1997The phase behavior of a cross-linked polymer blend made of two incompatible species, $A$ and $B$, of different chemical nature is analyzed. Besides a homogeneous phase, this system also exhibits two microphases and a phase of total segregation. The transition ... More

Dynamic Transitions in a Two Dimensional Associating Lattice Gas ModelFeb 10 2009Using Monte Carlo simulations we investigate some new aspects of the phase diagram and the behavior of the diffusion coefficient in an associating lattice gas (ALG) model on different regions of the phase diagram. The ALG model combines a two dimensional ... More

A Knowledge-based Treatment of Human-Automation SystemsJul 08 2013In a supervisory control system the human agent knowledge of past, current, and future system behavior is critical for system performance. Being able to reason about that knowledge in a precise and structured manner is central to effective system design. ... More

Phase-diagram for Irregular and Non-Symmetric Cross-linked Polymer BlendsDec 17 1997We consider here a blend made of two types of polymers, $A$ and $B$, of different chemical nature. At high temperature the homogeneous mixture is cross-linked. As the temperature is lowered, the two species try to segregate but are kept together by the ... More

Quadrilateral-octagon coordinates for almost normal surfacesApr 20 2009Sep 05 2009Normal and almost normal surfaces are essential tools for algorithmic 3-manifold topology, but to use them requires exponentially slow enumeration algorithms in a high-dimensional vector space. The quadrilateral coordinates of Tollefson alleviate this ... More

Information Rates of Minimal Non-Matroid-Related Access StructuresJan 23 2008In a secret sharing scheme, shares of a secret are distributed to participants in such a way that only certain predetermined sets of participants are qualified to reconstruct the secret. An access structure on a set of participants specifies which sets ... More

The Spectra of Volume and Determinant Densities of LinksJul 07 2015The $\textit{volume density}$ of a hyperbolic link $K$ is defined to be the ratio of the hyperbolic volume of $K$ to the crossing number of $K$. We show that there are sequences of non-alternating links with volume density approaching $v_8$, where $v_8$ ... More

Maximal admissible faces and asymptotic bounds for the normal surface solution spaceApr 15 2010Dec 09 2010The enumeration of normal surfaces is a key bottleneck in computational three-dimensional topology. The underlying procedure is the enumeration of admissible vertices of a high-dimensional polytope, where admissibility is a powerful but non-linear and ... More

Optimizing the double description method for normal surface enumerationAug 29 2008May 20 2009Many key algorithms in 3-manifold topology involve the enumeration of normal surfaces, which is based upon the double description method for finding the vertices of a convex polytope. Typically we are only interested in a small subset of these vertices, ... More

Targeted Fibonacci ExponentiationNov 05 2017A targeted exponentiation algorithm computes a group exponentiation operation $a^k$ with a reversible circuit in such a way that the initial state of the circuit consists of only the base $a$ and fixed values, and the final state consists of only the ... More

Computational topology with Regina: Algorithms, heuristics and implementationsAug 13 2012Feb 22 2013Regina is a software package for studying 3-manifold triangulations and normal surfaces. It includes a graphical user interface and Python bindings, and also supports angle structures, census enumeration, combinatorial recognition of triangulations, and ... More

Detecting genus in vertex links for the fast enumeration of 3-manifold triangulationsJan 16 2011Mar 16 2011Enumerating all 3-manifold triangulations of a given size is a difficult but increasingly important problem in computational topology. A key difficulty for enumeration algorithms is that most combinatorial triangulations must be discarded because they ... More

Searching a bitstream in linear time for the longest substring of any given densityOct 19 2009Jun 07 2010Given an arbitrary bitstream, we consider the problem of finding the longest substring whose ratio of ones to zeroes equals a given value. The central result of this paper is an algorithm that solves this problem in linear time. The method involves (i) ... More

A duplicate pair in the SnapPea censusNov 29 2013Feb 18 2014We identify a duplicate pair in the well-known Callahan-Hildebrand-Weeks census of cusped finite-volume hyperbolic 3-manifolds. Specifically, the six-tetrahedron non-orientable manifolds x101 and x103 are homeomorphic.

Face pairing graphs and 3-manifold enumerationJul 30 2003Nov 20 2003The face pairing graph of a 3-manifold triangulation is a 4-valent graph denoting which tetrahedron faces are identified with which others. We present a series of properties that must be satisfied by the face pairing graph of a closed minimal P^2-irreducible ... More

Point Mutations and Transitions Between Cellular Automata Attractor BasinsJun 17 2003We consider transformations between attractor basins of binary cylindrical cellular automata resulting from mutations. A t-point mutation of a state consists in toggling t sites in that state. Results of such mutations are described by a rule-dependent ... More

High-resolution imaging of compact high-velocity cloudsDec 20 1999Six examples of the compact, isolated high-velocity HI clouds (CHVCs) identified by Braun and Burton (1999) have been imaged with the WSRT. The 65 confirmed objects in this class define a dynamically cold system, with a global minimum for the velocity ... More

Converting between quadrilateral and standard solution sets in normal surface theoryJan 17 2009Sep 03 2009The enumeration of normal surfaces is a crucial but very slow operation in algorithmic 3-manifold topology. At the heart of this operation is a polytope vertex enumeration in a high-dimensional space (standard coordinates). Tollefson's Q-theory speeds ... More

Uniform mixing and completely positive sofic entropyMar 30 2016Let $G$ be a countable discrete sofic group. We define a concept of uniform mixing for measure-preserving $G$-actions and show that it implies completely positive sofic entropy. When $G$ contains an element of infinite order, we use this to produce an ... More

Enumerating fundamental normal surfaces: Algorithms, experiments and invariantsNov 30 2011Oct 01 2013Computational knot theory and 3-manifold topology have seen significant breakthroughs in recent years, despite the fact that many key algorithms have complexity bounds that are exponential or greater. In this setting, experimentation is essential for ... More

Observations from the 8-tetrahedron non-orientable censusSep 15 2005Through computer enumeration with the aid of topological results, we catalogue all 18 closed non-orientable P^2-irreducible 3-manifolds that can be formed from at most eight tetrahedra. In addition we give an overview as to how the 100 resulting minimal ... More

Simplification paths in the Pachner graphs of closed orientable 3-manifold triangulationsOct 27 2011It is important to have effective methods for simplifying 3-manifold triangulations without losing any topological information. In theory this is difficult: we might need to make a triangulation super-exponentially more complex before we can make it smaller ... More

The complexity of the normal surface solution spaceNov 30 2009Mar 11 2010Normal surface theory is a central tool in algorithmic three-dimensional topology, and the enumeration of vertex normal surfaces is the computational bottleneck in many important algorithms. However, it is not well understood how the number of such surfaces ... More

Molecular Hydrogen in the Lagoon: H2 line emission from Messier 8Jan 30 2002The 2.12 micron v=1-0 S(1) line of molecular hydrogen has been imaged in the Hourglass region of M8. The line is emitted from a roughly bipolar region, centred around the O7 star Herschel 36. The peak H2 1-0 S(1) line intensity is 8.2 x 10E-15 erg s-1 ... More

Modelling collisions in a relativistic plasmaOct 22 2009Generalising the work of Lenard and Bernstein, we introduce a new, fully relativistic model to describe collisional plasmas. Like the Fokker-Planck operator, this equation represents velocity diffusion and conserves particle number. However, unlike the ... More

Points of order 13 on elliptic curvesAug 30 2016Oct 15 2016We pick up the study of 13-torsion in elliptic curves where Mazur and Tate left off 45 years ago. We consider various questions concerning elliptic curves defined over the maximal totally real subfield of the 13th cyclotomic field (where J_1(13) acquires ... More

Points of order 13 on elliptic curvesAug 30 2016Sep 16 2016We pick up the study of 13-torsion in elliptic curves where Mazur and Tate left off 45 years ago. We consider various questions concerning elliptic curves defined over the maximal totally real subfield of the 13th cyclotomic field (where J_1(13) acquires ... More

Enumeration of non-orientable 3-manifolds using face pairing graphs and union-findApr 27 2006Drawing together techniques from combinatorics and computer science, we improve the census algorithm for enumerating closed minimal P^2-irreducible 3-manifold triangulations. In particular, new constraints are proven for face pairing graphs, and pruning ... More

Structures of small closed non-orientable 3-manifold triangulationsNov 07 2003Sep 15 2005A census is presented of all closed non-orientable 3-manifold triangulations formed from at most seven tetrahedra satisfying the additional constraints of minimality and P^2-irreducibility. The eight different 3-manifolds represented by these 41 different ... More

Stable configurations of repelling points on compact manifolds IIOct 14 2014This paper describes, in the case of the unit circle, several applications of a geometrically intrinsic treatment of counterparts of classical electrostatics, previously developed in [4] and [5].

Complementary vertices and adjacency testing in polytopesFeb 18 2012Aug 26 2012Our main theoretical result is that, if a simple polytope has a pair of complementary vertices (i.e., two vertices with no facets in common), then it has at least two such pairs, which can be chosen to be disjoint. Using this result, we improve adjacency ... More

The Pachner graph and the simplification of 3-sphere triangulationsNov 18 2010Feb 23 2011It is important to have fast and effective methods for simplifying 3-manifold triangulations without losing any topological information. In theory this is difficult: we might need to make a triangulation super-exponentially more complex before we can ... More

The cusped hyperbolic census is completeMay 12 2014From its creation in 1989 through subsequent extensions, the widely-used "SnapPea census" now aims to represent all cusped finite-volume hyperbolic 3-manifolds that can be obtained from <= 8 ideal tetrahedra. Its construction, however, has relied on inexact ... More

Uniform mixing and completely positive sofic entropyMar 30 2016Nov 02 2016Let $G$ be a countable discrete sofic group. We define a concept of uniform mixing for measure-preserving $G$-actions and show that it implies completely positive sofic entropy. When $G$ contains an element of infinite order, we use this to produce an ... More

Mixing times via super-fast couplingSep 20 2006Sep 15 2011We provide a coupling proof that the transposition shuffle on a deck of n cards is mixing of rate Cn(log{n}) with a moderate constant, C. This rate was determined by Diaconis and Shahshahani, but the question of a natural probabilistic coupling proof ... More

Combinatorial Seifert fibred spaces with transitive cyclic automorphism groupApr 11 2014Jul 10 2015In combinatorial topology we aim to triangulate manifolds such that their topological properties are reflected in the combinatorial structure of their description. Here, we give a combinatorial criterion on when exactly triangulations of 3-manifolds with ... More

Sodium Chloride, NaCl/ε : New Force FieldAug 08 2015A new computational model for Sodium Chloride, the NaCl/{\epsilon}, is proposed. The Force Fields employed here for the description of the NaCl is based on a set of radial particle-particle pair potentials involving Lennard-Jones (LJ) and Coulombic forces. ... More

Enabling Robots to Infer how End-Users Teach and Learn through Human-Robot InteractionFeb 02 2019During human-robot interaction (HRI), we want the robot to understand us, and we want to intuitively understand the robot. In order to communicate with and understand the robot, we can leverage interactions, where the human and robot observe each other's ... More

A water-like model under confinement for hydrophobic and hydrophilic particle-plate interaction potentialsSep 24 2013Molecular dynamic simulations were employed to study a water-like model confined between hydrophobic and hydrophilic plates. The phase behavior of this system is obtained for different distances between the plates and particle-plate potentials. For both ... More

Liquid Polymorphism and Density Anomaly in a Lattice Gas ModelJul 29 2004We present a simple model for an associating liquid in which polymorphism and density anomaly are connected. Our model combines a two dimensional lattice gas with particles interacting through a soft core potential and orientational degrees of freedom ... More

Ion-ion correlations: an improved one-component plasma correctionOct 22 1999Based on a Debye-Hueckel approach to the one-component plasma we propose a new free energy for incorporating ionic correlations into Poisson-Boltzmann like theories. Its derivation employs the exclusion of the charged background in the vicinity of the ... More

Finite Lattice and Phenomenological Approximations for the Anomaly in the Density of a Water-like Lattice Gas ModelNov 18 2011We propose a model for a two dimensional, associative water-like lattice gas with one single variable representing both long and short-range interactions. The corresponding hamiltonian was solved exactly, by state enumeration in a finite lattice, so to ... More

Nonlinear Stability of Periodic Travelling Wave Solutions for the Regularized Benjamin-Ono and BBM EquationsApr 29 2009This paper has various goals: first, we develop a local and global well-posedness theory for the regularized Benjamin-Ono equation in the periodic setting, second, we show that the Cauchy problem for this equation (in both periodic and non-periodic case) ... More

Flow and structure of fluids in functionalized nanoporesOct 16 2015May 15 2016We investigate through non-equilibrium Molecular Dynamics simulations the structure and flow of fluids in functionalized nanopores. The nanopores are modeled as cylindrical structures with solvophilic and solvophobic sites. Two fluids are modeled. The ... More

Phase Diagram and Thermodynamic and Dynamic Anomalies in a Pure Repulsive ModelFeb 04 2014Using Monte Carlo simulations a lattice gas model with only repulsive interactions was checked for the presence of anomalies. We show that this system exhibits the density (temperature of maximum density - TMD) and diffusion anomalies as present in liquid ... More

Charge reversal of colloidal particlesSep 23 2005A theory is presented for the effective charge of colloidal particles in suspensions containing multivalent counterions. It is shown that if colloids are sufficiently strongly charged, the number of condensed multivalent counterion can exceed the bare ... More

Flexible Polyelectrolytes with Monovalent SaltJul 23 2004We present a model for describing flexible polyelectrolytes in a good solvent a nd in the presence of monovalent salt . The molecule composed by $N$ monomers is characterized by the end to end distanc e $R_e=b (Z-1)^\gamma$ and the number of associated ... More

Anomalies in a waterlike model confined between platesDec 14 2012Using molecular dynamic simulations we study a waterlike model confined between two fixed hydrophobic plates. The system is tested for density, diffusion and structural anomalous behavior and compared with the bulk results. Within the range of confining ... More

Potassium bromide, KBr/ε : New Force FieldNov 09 2016Nov 14 2016The correct description of the ionic interaction and stable equilibrium of the simulations of biomolecular structure, dynamics, folding, catalysis, and function, an accurate model of the monovalent ions is very important. The force field needs to reproduce ... More

Thermodynamic and dynamic anomalous behavior in the TIP4P/ε water modelAug 08 2015Aug 11 2015The model Tip4p/{\epsilon} for water is tested for the presence of thermodynamic and dy- namic anomalies. Molecular dynamic simulations for this model were performed and we show that for this system the density versus temperature at constant pressure ... More

Computing the crosscap number of a knot using integer programming and normal surfacesJul 12 2011Mar 06 2012The crosscap number of a knot is an invariant describing the non-orientable surface of smallest genus that the knot bounds. Unlike knot genus (its orientable counterpart), crosscap numbers are difficult to compute and no general algorithm is known. We ... More

Geometric estimates from spanning surfacesAug 17 2016We derive bounds on the length of the meridian and the cusp volume of hyperbolic knots in terms of the topology of essential surfaces spanned by the knot. We provide an algorithmically checkable criterion that guarantees that the meridian length of a ... More

L-band (3.5 micron) IR-excess in massive star formation, I. 30 DoradusApr 27 2005L-band data of 30 Doradus at 3.5 micron taken with SPIREX (South Pole Infrared Explorer) is presented. The photometry was combined with 2MASS JHK data at 1.25-2.2 micron. Colour-colour and colour-magnitude diagrams are constructed and used to determine ... More

On the entropy of radiation reactionOct 22 2013The inexorable development of ever more powerful laser systems has re-ignited interest in electromagnetic radiation reaction and its significance for the collective behaviour of charged matter interacting with intense electromagnetic fields. The classical ... More

Projective geometry and the outer approximation algorithm for multiobjective linear programmingJun 15 2010A key problem in multiobjective linear programming is to find the set of all efficient extreme points in objective space. In this paper we introduce oriented projective geometry as an efficient and effective framework for solving this problem. The key ... More

Computing closed essential surfaces in 3-manifoldsDec 31 2018We present a practical algorithm to test whether a 3-manifold given by a triangulation or an ideal triangulation contains a closed essential surface. This property has important theoretical and algorithmic consequences. As a testament to its practicality, ... More

Computationally proving triangulated 4-manifolds to be diffeomorphicMar 12 2014We present new computational methods for proving diffeomorphy of triangulated 4-manifolds, including algorithms and topological software that can for the first time effectively handle the complexities that arise in dimension four and be used for large ... More

Bootstrap Markov chain Monte Carlo and optimal solutions for the Law of Categorical Judgment (Corrected)Aug 09 2010A novel procedure is described for accelerating the convergence of Markov chain Monte Carlo computations. The algorithm uses an adaptive bootstrap technique to generate candidate steps in the Markov Chain. It is efficient for symmetric, convex probability ... More

Density anomaly in a competing interactions lattice gas modelSep 06 2004We study a very simple model of a short-range attraction and an outer shell repulsion as a test system for demixing phase transition and density anomaly. The phase-diagram is obtained by applying mean field analysis and Monte Carlo simulations to a two ... More

Sine-Gordon mean field theory of a Coulomb GasFeb 14 1997Sine-Gordon field theory is used to investigate the phase diagram of a neutral Coulomb gas. A variational mean field free energy is constructed and the corresponding phase diagrams in two (2d) and three dimensions (3d) are obtained. When analyzed in terms ... More

A Neutral Polyampholyte in an ionic solutionMay 13 1996The behavior of a neutral polyampholyte ($PA$) chain with $N$ monomers, in an ionic solution, is analyzed in the framework of the full Debye-H$\ddot u $ckel-Bjerrum-Flory $(DHBjF)$ theory. A $PA$ chain, that in addition to the neutral monomers, also contains ... More

Charge renormalization and phase separation in colloidal suspensionsOct 23 2000We explore the effects of counterion condensation on fluid-fluid phase separation in charged colloidal suspensions. It is found that formation of double layers around the colloidal particles stabilizes suspensions against phase separation. Addition of ... More

Connection Between Minimum of Solubility and Temperature of Maximum Density in an Associating Lattice Gas ModelMay 09 2012In this paper we investigate the solubility of a hard - sphere gas in a solvent modeled as an associating lattice gas (ALG). The solution phase diagram for solute at 5% is compared with the phase diagram of the original solute free model. Model properties ... More

Diffusion anomaly and dynamic transitions in the Bell-Lavis water modelJun 07 2010In this paper we investigate the dynamic properties of the minimal Bell-Lavis (BL) water model and their relation to the thermodynamic anomalies. The Bell-Lavis model is defined on a triangular lattice in which water molecules are represented by particles ... More

Embeddings of 3-manifolds in S^4 from the point of view of the 11-tetrahedron censusOct 14 2008Sep 26 2012This is a collection of notes on embedding problems for 3-manifolds. The main question explored is `which 3-manifolds embed smoothly in the 4-sphere?' The terrain of exploration is the Burton/Martelli/Matveev/Petronio census of triangulated prime closed ... More

A fast branching algorithm for unknot recognition with experimental polynomial-time behaviourNov 05 2012Oct 09 2014It is a major unsolved problem as to whether unknot recognition - that is, testing whether a given closed loop in R^3 can be untangled to form a plain circle - has a polynomial time algorithm. In practice, trivial knots (which can be untangled) are typically ... More

Longitudinal wave-breaking limits in a unified geometric model of relativistic warm plasmasAug 31 2009The covariant Vlasov-Maxwell system is used to study breaking of relativistic warm plasma waves. The well-known theory of relativistic warm plasmas due to Katsouleas and Mori (KM) is subsumed within a unified geometric formulation of the `waterbag' paradigm ... More

Non-linear electrostatic waves in Born-Infeld plasmasNov 25 2010Motivated by the suggestion that Born-Infeld plasmas could have significance for electron acceleration in neutron star crusts, we obtain an upper bound on the amplitude of electrostatic waves propagating parallel to a longitudinal magnetic field in a ... More

Compact High-Velocity Clouds at High ResolutionDec 22 1999Six examples of the compact, isolated high-velocity clouds catalogued by Braun & Burton (1999) and identified with a dynamically cold ensemble of primitive objects falling towards the barycenter of the Local Group have been imaged with the Westerbork ... More

Weak containment of measure preserving group actionsNov 23 2016We survey recent progress in the theory of weak containment of measure preserving group actions.

A tree traversal algorithm for decision problems in knot theory and 3-manifold topologyOct 29 2010Mar 30 2012In low-dimensional topology, many important decision algorithms are based on normal surface enumeration, which is a form of vertex enumeration over a high-dimensional and highly degenerate polytope. Because this enumeration is subject to extra combinatorial ... More

The complexity of detecting taut angle structures on triangulationsJul 04 2012Oct 03 2012There are many fundamental algorithmic problems on triangulated 3-manifolds whose complexities are unknown. Here we study the problem of finding a taut angle structure on a 3-manifold triangulation, whose existence has implications for both the geometry ... More

Locating regions in a sequence under density constraintsApr 05 2011Apr 02 2013Several biological problems require the identification of regions in a sequence where some feature occurs within a target density range: examples including the location of GC-rich regions, identification of CpG islands, and sequence matching. Mathematically, ... More

Fixed parameter tractable algorithms in combinatorial topologyFeb 17 2014May 05 2014To enumerate 3-manifold triangulations with a given property, one typically begins with a set of potential face pairing graphs (also known as dual 1-skeletons), and then attempts to flesh each graph out into full triangulations using an exponential-time ... More

How to Lose with Least ProbabilityDec 09 2011Dec 13 2011Two players alternate tossing a biased coin where the probability of getting heads is p. The current player is awarded alpha points for tails and alpha+beta for heads. The first player reaching n points wins. For a completely unfair coin the player going ... More

The Warped HI Layer of the Outer GalaxyJan 27 2006Using the Leiden/Dwingeloo Survey (Hartmann & Burton 1997) of the Galactic sky north of declination -30 degrees as the principal component of a composite data cube, the structure of the warped HI layer of the outer Galaxy was displayed by converting the ... More

Geometrical description of non-linear electrostatic oscillations in relativistic thermal plasmasJul 23 2008Jul 30 2008We develop a method for investigating the relationship between the shape of a 1-particle distribution and non-linear electrostatic oscillations in a collisionless plasma, incorporating transverse thermal motion. A general expression is found for the maximum ... More

Aspects of electromagnetic radiation reaction in strong fieldsSep 26 2014With the recent advances in laser technology, experimental investigation of radiation reaction phenomena is at last becoming a realistic prospect. A pedagogical introduction to electromagnetic radiation reaction is given with the emphasis on matter driven ... More

Status of HI searches for CHVCs beyond the Local GroupApr 04 2000Jun 15 2001Growing evidence supports the suggestion that the compact high-velocity clouds of HI (CHVCs) are located throughout the Local Group and continue to fuel galactic evolution. Recent distance estimates to individual objects lie in the range 150-850 kpc, ... More

Morphological Characteristics of Compact High-Velocity Clouds Revealed by High-Resolution WSRT ImagingDec 22 1999A class of compact, isolated high-velocity clouds which plausibly represents a homogeneous subsample of the HVC phenomenon in a single physical state was objectively identified by Braun and Burton (1999). Six examples of the CHVCs, unresolved in single-dish ... More