Professor of Mathematics
lattice statistical mechanics, enumerative and asymptotic combinatorics, dynamical systems, Monte Carlo algorithms, soft condensed matter
Publications of specific relevance to the Centre for Complex SystemsZeros of conditional Gaussian analytic functions, random sub-unitary
matrices and q-seriesImproving Convergence of Generalised Rosenbluth Sampling for Branched
Polymer Models by Uniform SamplingUniversality class of the special adsorption point of two-dimensional lattice polymersSkew Schur function representation of directed paths in a slitAdsorption of two-dimensional polymers with two- and three-body self-interactions
Adsorption of 2d polymers with two- and three-body self-interactionsAdsorption of interacting self-avoiding trails in two dimensionsEnumerating path diagrams in connection with $q$-tangent and $q$-secant
numbersPhase transitions in solvent-dependent polymer adsorption in three dimensionsPhase transitions in solvent dependent polymer adsorption in three dimensionsAdsorption of interacting self-avoiding trails in two dimensionsExact solution of pulled, directed vesicles with sticky walls in two dimensionsAdsorption of neighbor-avoiding walks on the simple cubic latticeExact solution of pulled, directed vesicles with sticky walls in two dimensionsAdsorption of neighbor-avoiding walks on the simple cubic latticeMulticritical Scaling in a Lattice Model of VesiclesAnomalous polymer collapse winding angle distributions*Universality of crossover scaling for the adsorption transition of lattice polymersUniversality of crossover scaling for the adsorption transition of lattice polymersSolution of semi-flexible self-avoiding trails on a Husimi lattice built
with squaresAnomalous polymer collapse winding angle distributionsPhase diagram of twist storing lattice polymers in variable solvent qualitySolution of semi-flexible self-avoiding trails on a Husimi lattice built with squaresWrithe induced phase transition in unknotted self-avoiding polygonsArea-width scaling in generalised Motzkin pathsArea-width scaling in generalised Motzkin pathsGrand-canonical solution of semi-flexible self-avoiding trails on the
Bethe latticeSelf-attracting polymers in two dimensions with three low-temperature
phasesHigher-order Airy scaling in deformed Dyck pathsGrand-canonical solution of semi-flexible self-avoiding trails on the Bethe latticeHigher-order Airy scaling in deformed Dyck pathsPhase Diagram of Twist Storing Lattice Polymers in Variable Solvent QualityWrithe induced phase transition in unknotted self-avoiding polygonsSelf-attracting polymers in two dimensions with three low-temperature phasesThe role of three-body interactions in two-dimensional polymer collapseDedicated to Professor Tony Guttmann on the occasion of his 70th birthday.Forces and pressures in adsorbing partially directed walksForces and pressures in adsorbing partially directed walksWinding angle distributions for two-dimensional collapsing polymersWinding angle distributions for two-dimensional collapsing polymersThe role of three-body interactions in two-dimensional polymer collapseA semi-flexible attracting-segment model of three-dimensional polymer collapseDataset: Winding angle distributions for two-dimensional collapsing polymersUniform asymptotics of area-weighted Dyck pathsUniform asymptotics of area-weighted Dyck pathsA semi-flexible attracting-segment model of three-dimensional polymer collapseWrithe-induced knotting in a lattice polymerPressure exerted by a vesicle on a surfaceLattice polymers with two competing collapse interactionsNumerical simulation of a lattice polymer model at its integrable pointSemi-flexible interacting self-avoiding trails on the square latticeThe pressure exerted by adsorbing directed lattice paths and staircase polygonsNumerical simulation of a lattice polymer model at its integrable pointSemi-flexible interacting self-avoiding trails on the square latticeSelf-avoiding trails with nearest neighbour interactions on the square
latticeWeighting of topologically different interactions in a model of
two-dimensional polymer collapseWeighting of topologically different interactions in a model of two-dimensional polymer collapseSelf-avoiding trails with nearest neighbour interactions on the square latticeThe pressure exerted by adsorbing directed lattice paths and staircase
polygonsExact power spectra of Brownian motion with solid frictionRare event sampling with stochastic growth algorithmsA Bijection on Bilateral Dyck PathsExact solution of a model of a vesicle attached to a wall subject to mechanical deformationExact power spectra of Brownian motion with solid frictionFrom Rosenbluth Sampling to PERM - rare event sampling with stochastic
growth algorithmsExact solution of a model of a vesicle attached to a wall subject to
mechanical deformationAnomalous critical behaviour in the polymer collapse transition of
three-dimensional lattice trailsAnomalous critical behaviour in the polymer collapse transition of three-dimensional lattice trailsEnumeration of area-weighed Dyck paths with restricted heightAn Infinite Family of Adsorption Models and Restricted Lukasiewicz PathsAn infinite family of adsorption models and restricted Lukasiewicz pathsAn infinite family of adsorption models and restricted Lukasiewicz pathsCounting the number of elements in the mutation classes of (A)over-tilde(n)-quiversExact solution of the discrete (1+1)-dimensional RSOS model in a slit with field and wall interactionsForcing Adsorption of a Tethered Polymer by PullingA semi-flexible attracting segment model of two-dimensional polymer collapseIdentification of a polymer growth process with an equilibrium
multi-critical collapse phase transition: the meeting point of swollen,
collapsed and crystalline polymersIdentification of a polymer growth process with an equilibrium multi-critical collapse phase transition: the meeting point of swollen, collapsed and crystalline polymersExact Solution of the Discrete (1+1)-dimensional RSOS Model in a Slit
with Field and Wall InteractionsEnumeration of area-weighed Dyck paths with restricted heightExact Solution of the Discrete (1+1)-dimensional RSOS Model in a Slit with Field and Wall InteractionsA simple model of a vesicle drop in a confined geometryAsymptotic enumeration of 2-covers and line graphsExact solution of the discrete (1+1)-dimensional RSOS model with field and surface interactionsExact solution of the discrete (1+1)-dimensional RSOS model with field and surface interactionsAsymptotics of the Farey Fraction Spin Chain Free Energy at the Critical PointAsymptotics of the Farey Fraction Spin Chain Free Energy at the Critical
PointExact Solution of the Discrete (1+1)-dimensional RSOS Model with Field and Surface InteractionsCounting the number of elements in the mutation classes of
\tilde{A}_n-quiversA note on the distribution of the maximum of a set of Poisson random
variablesA self-interacting partially directed walk subject to a forceSemi-flexible hydrogen-bonded and non-hydrogen bonded lattice polymersMatrix Ansatz, lattice paths and rook placementsA self-interacting partially directed walk subject to a forceScaling of the atmosphere of self-avoiding walksCounting defective parking functionsPolymers with self-attraction and stiffness: a generic phase structureSemi-flexible hydrogen-bonded and non-hydrogen bonded lattice polymersDecoding generalised hyperoctahedral groups and asymptotic analysis of
correctible error patternsScaling of the atmosphere of self-avoiding walksPartially directed paths in a wedgeFinite-size scaling functions for directed polymers confined between attracting wallsPartially directed paths in a symmetric wedgeDirected paths in a wedgeOn the location of the surface-attached globule phase in collapsing polymersExact solution of semi-flexible and super-flexible interacting partially directed walksFinite-size scaling functions for directed polymers confined between attracting wallsOn the location of the surface-attached globule phase in collapsing polymersExact Solution of Semi-Flexible and Super-Flexible Interacting Partially Directed WalksThe competition of hydrogen-like and isotropic interactions on polymer collapseAsymptotic enumeration of 2-covers and line graphsDirected Paths in a WedgeThe competition of hydrogen-like and isotropic interactions on polymer collapseControlling Secondary Structures of Bio-Polymers with Hydrogen-Like
BondingControlling Secondary Structures of Bio-Polymers with Hydrogen-Like BondingCollapse transition of self-avoiding trails on the square latticeAsymptotics for incidence matrix classesPartially directed paths in a wedgeSelf-avoiding random walk with multiple site weightings and restrictionsAsymptotics for incidence matrix classesCluster approximation for the Farey fraction spin chainOn a Type of Self-Avoiding Random Walk with Multiple Site Weightings and RestrictionsCollapse transition of self-avoiding trails on the square latticeAsymptotic enumeration of incidence matricesPolymer Simulations with a flat histogram stochastic growth algorithmPolymer Simulations with a Flat Histogram Stochastic Growth AlgorithmAsymptotic enumeration of incidence matricesCluster Approximation for the Farey Fraction Spin ChainLayering transitions for adsorbing polymers in poor solventsPulling absorbing and collapsing polymers from a surfacePulling absorbing and collapsing polymers from a surfaceStretching of a chain polymer adsorbed at a surfaceLayering transitions for adsorbing polymers in poor solventsStretching of a chain polymer adsorbed at a surfacePolymer Simulations with a flat histogram stochastic growth algorithmProof of a monotonicity conjectureMonte carlo investigation of lattice models of polymer collapse in five dimensionsTowards a complete determination of the spectrum of a transfer operator associated with intermittencyScaling near the theta point for isolated polymers in solutionPolymer collapse in high dimensions: Monte Carlo simulation of lattice modelsNonlinear contact mechanics based on ring-down experiments with quartz crystal resonatorsComment on `Stretched polymers in a poor solvent'Monte Carlo Investigation of Lattice Models of Polymer Collapse in Five DimensionsPseudo-first-order transition in interacting self-avoiding walks and trailsScaling of self-avoiding walks and self-avoiding trails in three dimensionsScaling of Self-Avoiding Walks and Self-Avoiding Trails in Three DimensionsPseudo-First-Order Transition in Interacting Self-avoiding Walks and TrailsFour-dimensional polymer collapse II: interacting self-avoiding trailsScaling of self-avoiding walks in high dimensionsFour-dimensional polymer collapse II: Interacting self-avoiding trailsScaling of Self-Avoiding Walks in High DimensionsOn the Asymptotics of Takeuchi NumbersFour-dimensional polymer collapse: pseudo-first-order transition in interacting self-avoiding walks.First-order scaling near a second-order phase transition: Tricritical polymer collapseOn the Asymptotics of Takeuchi NumbersViscoelastic Depinning of Driven Systems: Mean-Field Plastic ScallopsViscoelastic Depinning of Driven Systems: Mean-Field Plastic ScallopsFirst-order scaling near a second-order phase transition: Tricritical polymer collapseFour-dimensional polymer collapse II: Pseudo-First-Order Transition in Interacting Self-avoiding WalksOn the asymptotics of the finite-perimeter partition function of two-dimensional lattice vesiclesExistence of four-dimensional polymer collapse I. Kinetic growth trailsOn the Asymptotics of the Finite-Perimeter Partition Function of Two-Dimensional Lattice VesiclesDynamics of a single particle in a horizontally shaken boxWinding angles for two-dimensional polymers with orientation-dependent interactionsWinding-angle distribution for two-dimensional polymers at the theta-pointThe statistical mechanics of vesiclesDynamics of a single particle in a horizontally shaken boxWinding angles for two-dimensional polymers with orientation dependent interactionsSTACKING MODELS OF VESICLES AND COMPACT CLUSTERSTHE COLLAPSE POINT OF INTERACTING TRAILS IN 2 DIMENSIONS FROM KINETIC GROWTH SIMULATIONSRECENT DEVELOPMENTS IN THE STUDY OF WALKS, POLYGONS AND THE ISING-MODELUNIFORM Q-SERIES ASYMPTOTICS FOR STAIRCASE POLYGONSModels of polymer collapse in three dimensions: Evidence from kinetic growth simulations.CRITICAL EXPONENTS FROM NONLINEAR FUNCTIONAL-EQUATIONS FOR PARTIALLY DIRECTED CLUSTER-MODELSUNIVERSAL DISTANCE RATIOS FOR INTERACTING 2-DIMENSIONAL POLYMERSEXACT SCALING BEHAVIOR OF PARTIALLY CONVEX VESICLESCROSSOVER IN SMART KINETIC GROWTH WALKSINTERACTING PARTIALLY DIRECTED WALKS - A MODEL OF POLYMER COLLAPSEMANHATTAN LATTICE THETA-POINT EXPONENTS FROM KINETIC GROWTH WALKS AND EXACT RESULTS FROM THE NIENHUIS O(N) MODELLOW-TEMPERATURE 2D POLYMER PARTITION-FUNCTION SCALING - SERIES ANALYSIS RESULTSOwczarek, Prellberg, and Brak reply.EXACT SCALING FORM FOR THE COLLAPSED 2D POLYMER PHASE - REPLYON THE SYMMETRY CLASSES OF PLANAR SELF-AVOIDING WALKSFinite-length scaling of collapsing directed walks.A SCALING THEORY OF THE COLLAPSE TRANSITION IN GEOMETRIC CLUSTER-MODELS OF POLYMERS AND VESICLESTHE TRICRITICAL BEHAVIOR OF SELF-INTERACTING PARTIALLY DIRECTED WALKSStaircase polygons, elliptic integrals, Heun functions, and lattice Green functions.EXACT SOLUTION OF THE DISCRETE (1 + 1)-DIMENSIONAL SOS MODEL WITH FIELD AND SURFACE INTERACTIONSNew scaling form for the collapsed polymer phase.MAPS OF INTERVALS WITH INDIFFERENT FIXED-POINTS - THERMODYNAMIC FORMALISM AND PHASE-TRANSITIONSNO-3-IN-LINE FOR 17 AND 19No-three-in-line for seventeen and nineteenThe combinatorics of the leading root of the partial theta functionMulticritical Scaling in a Lattice Model of VesiclesSkew Schur Function Representation of Directed Paths in a SlitGrants of specific relevance to the Centre for Complex SystemsManoj Kumar NIF Alumni: Phase transitions and critical behaviour of polymer collapse on disordered latticesTen talented undergraduate students from across a wide range of Science and Engineering programmes are embarking on exciting summer research internships under the mentorship of academic supervisors. This fantastic opportunity has been made possible through the QMUL Summer Training Research Initiative to Support Diversity and Equality (STRIDE) and the London ... [more]
