Results for "Stuart G. Murdoch"

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Experimental and numerical investigations of switching wave dynamics in a normally dispersive fiber ring resonatorFeb 28 2017Optical frequency combs generated in normally dispersive Kerr microresonators have been observed to correspond to dark temporal structures, and theoretically explained as interlocked switching waves (also known as domain walls or fronts). The time-domain ... More
Coexistence and interactions between nonlinear states with different polarizations in a monochromatically driven passive Kerr resonatorFeb 14 2019We report on experimental observations of coexistence and interactions between nonlinear states with different polarizations in a passive Kerr resonator driven at a single carrier frequency. Using a fiber ring resonator with adjustable birefringence, ... More
Emission of intense resonant radiation by dispersion-managed Kerr cavity solitonsSep 20 2018We report on an experimental and numerical study of temporal Kerr cavity soliton dynamics in dispersion-managed fiber ring resonators. We find that dispersion management can significantly magnify the Kelly-like resonant radiation sidebands emitted by ... More
Nonlinear optics of fibre event horizonsMar 26 2014The nonlinear interaction of light in an optical fibre can mimic the physics at an event horizon. This analogue arises when a weak probe wave is unable to pass through an intense soliton, despite propagating at a different velocity. To date, these dynamics ... More
Origins of clustered frequency combs in Kerr microresonatorsMay 30 2018Recent experiments have demonstrated the generation of widely-spaced parametric sidebands that can evolve into "clustered" optical frequency combs in Kerr microresonators. Here we describe the physics that underpins the formation of such clustered comb ... More
Real-time spectral analysis of ultrafast pulses using a free-space angular chirp enhanced delayMay 14 2019Frequency to time mapping is a powerful technique for observing ultrafast phenomena and non-repetitive events in optics. However, many optical sources operate in wavelength regions, or at power levels, that are not compatible with standard frequency to ... More
Observation of dispersive wave emission by temporal cavity solitonsJun 09 2014We examine a coherently-driven, dispersion-managed, passive Kerr fiber ring resonator and report the first direct experimental observation of dispersive wave emission by temporal cavity solitons. Our observations are in excellent agreement with analytical ... More
Experimental observation of coherent cavity soliton frequency combs in silica microspheresAug 11 2016Aug 15 2016We report on the experimental observation of coherent cavity soliton frequency combs in silica microspheres. Specifically, we demonstrate that careful alignment of the microsphere relative to the coupling fiber taper allows for the suppression of higher-order ... More
Ultra-weak long-range interactions of solitons observed over astronomical distancesMay 29 2013We report what we believe is the weakest interaction between solitons ever observed. Our experiment involves temporal optical cavity solitons recirculating in a coherently-driven passive optical fibre ring resonator. We observe two solitons, separated ... More
Temporal tweezing of light: trapping and manipulation of temporal cavity solitonsOct 17 2014Optical tweezers use laser light to trap and move microscopic particles in space. Here we demonstrate a similar control over ultrashort light pulses, but in time. Our experiment involves temporal cavity solitons that are stored in a passive loop of optical ... More
Writing and erasing of temporal cavity solitons by direct phase modulation of the cavity driving fieldJan 21 2015Temporal cavity solitons (CSs) are persisting pulses of light that can manifest themselves in continuously driven passive resonators, such as macroscopic fiber ring cavities and monolithic microresonators. Experiments so far have demonstrated two techniques ... More
Parameter Estimation for Multiscale DiffusionsMar 28 2006We study the problem of parameter estimation for time-series possessing two, widely separated, characteristic time scales. The aim is to understand situations where it is desirable to fit a homogenized singlescale model to such multiscale data. We demonstrate, ... More
Analysis of White Noise Limits for Stochastic Systems with Two Fast Relaxation TimesApr 16 2005In this paper we present a rigorous asymptotic analysis for stochastic systems with two fast relaxation times. The mathematical model analyzed in this paper consists of a Langevin equation for the particle motion with time-dependent force constructed ... More
Monitoring Reactor Anti-Neutrinos Using a Plastic Scintillator Detector in a Mobile LaboratoryNov 02 2018Technology developed for the T2K electromagnetic calorimeter has been adapted to make a small footprint, reliable, segmented detector to characterise anti-neutrinos emitted by nuclear reactors. The device has been developed and demonstrated by the University ... More
A Probabilistic Framework for Quantifying Biological ComplexityMay 09 2017One thing that discriminates living things from inanimate matter is their ability to generate similarly complex or non-random architectures in a large abundance. From DNA sequences to folded protein structures, living cells, microbial communities and ... More
Expanded Alternating Optimization of Nonconvex Functions with Applications to Matrix Factorization and Penalized RegressionDec 12 2014We propose a general technique for improving alternating optimization (AO) of nonconvex functions. Starting from the solution given by AO, we conduct another sequence of searches over subspaces that are both meaningful to the optimization problem at hand ... More
Conditional Modeling and the Jitter Method of Spike Re-sampling: SupplementNov 18 2011This technical report accompanies the manuscript "Conditional Modeling and the Jitter Method of Spike Re-sampling." It contains further details, comments, references, and equations concerning various simulations and data analyses presented in that manuscript, ... More
The Quantum Approximation Optimization Algorithm for MaxCut: A Fermionic ViewJun 09 2017Farhi et al. recently proposed a class of quantum algorithms, the Quantum Approximate Optimization Algorithm (QAOA), for approximately solving combinatorial optimization problems. A level-p QAOA circuit consists of p steps; in each step a classical Hamiltonian, ... More
Tunable long range forces mediated by self-propelled colloidal hard spheresMar 06 2014Dec 11 2014Using Brownian dynamics simulations, we systematically study the effective interaction between two parallel hard walls in a 2D suspension of self-propelled (active) colloidal hard spheres, and we find that the effective force between two hard walls can ... More
Bunching of temporal cavity solitons via forward Brillouin scatteringSep 16 2015We report on the experimental observation of bunching dynamics with temporal cavity solitons in a continuously-driven passive fibre resonator. Specifically, we excite a large number of ultrafast cavity solitons with random temporal separations, and observe ... More
An all-optical buffer based on temporal cavity solitons operating at 10 Gb/sJul 25 2016We demonstrate the operation of an all-optical buffer based on temporal cavity solitons stored in a nonlinear passive fiber ring resonator. Unwanted acoustic interactions between neighboring solitons are suppressed by modulating the phase of the external ... More
Spontaneous creation and annihilation of temporal cavity solitons in a coherently-driven passive fiber resonatorMar 16 2015Mar 29 2015We report on the experimental observation of spontaneous creation and annihilation of temporal cavity solitons (CSs) in a coherently-driven, macroscopic optical fiber resonator. Specifically, we show that CSs are spontaneously created when the frequency ... More
Stimulated Raman Scattering Imposes Fundamental Limits to the Duration and Bandwidth of Temporal Cavity SolitonsAug 16 2017Temporal cavity solitons (CS) are optical pulses that can persist in passive resonators, and they play a key role in the generation of coherent microresonator frequency combs. In resonators made of amorphous materials, such as fused silica, they can exhibit ... More
Observations of spatiotemporal instabilities in the strong-driving regime of an AC-driven nonlinear Schrödinger systemMay 16 2016Localized dissipative structures (LDS) have been predicted to display a rich array of instabilities, yet systematic experimental studies have remained scarce. We have used a synchronously-driven optical fiber ring resonator to experimentally study LDS ... More
Measurement of microresonator frequency comb stability by spectral interferometryOct 28 2015We demonstrate a new technique for the experimental measurement of the spectral coherence of microresonator optical frequency combs. Specifically, we use a spectral interference method, typically used in the context of supercontinuum generation, to explore ... More
Asymmetric balance in symmetry breakingApr 15 2019Spontaneous symmetry breaking is central to our understanding of physics and explains many natural phenomena, from cosmic scales to sub-atomic particles. It can also be exploited for applications, but engineered systems naturally present some deviations ... More
Writing and Erasing of Temporal Kerr Cavity Solitons via Intensity Modulation of the Cavity Driving FieldFeb 21 2018We experimentally and numerically study the use of intensity modulation for the controlled addressing of temporal Kerr cavity solitons. Using a coherently driven fiber ring resonator, we demonstrate that a single temporally broad intensity modulation ... More
Observation of Spatiotemporal Chaos Induced by a Cavity Soliton in a Fiber Ring ResonatorFeb 11 2016We report on the experimental observation of temporal cavity soliton destabilization via spatiotemporal chaos in a coherently-driven optical fiber ring resonator. Numerical simulations and theoretical analyses are in good agreement with experimental observations. ... More
Widely tunable optical parametric oscillation in a Kerr microresonatorOct 03 2017We report on the first experimental demonstration of widely-tunable parametric sideband generation in a Kerr microresonator. Specifically, by pumping a silica microsphere in the normal dispersion regime, we achieve the generation of phase-matched four-wave ... More
Controlled merging and annihilation of localized dissipative structures in an AC-driven damped nonlinear Schrödinger systemApr 27 2015We report studies of controlled interactions of localized dissipative structures in a system described by the AC-driven damped nonlinear Schr\"odinger equation. Extensive numerical simulations reveal a diversity of interaction scenarios that are governed ... More
Impact of de-synchronization and drift on soliton-based Kerr frequency combs in the presence of pulsed driving fieldsMay 23 2019Pulsed driving of Kerr microresonators represents a promising avenue for the efficient generation of soliton states associated with coherent optical frequency combs. The underlying physics has not, however, yet been comprehensively investigated. Here, ... More
Universal mechanism for the binding of temporal cavity solitonsMar 30 2017We present theoretical and experimental evidence of a universal mechanism through which temporal cavity solitons of externally-driven, passive, Kerr resonators can form robust long-range bound states. These bound states, sometime also referred to as multi-soliton ... More
Hierarchical interpretations for neural network predictionsJun 14 2018Jan 16 2019Deep neural networks (DNNs) have achieved impressive predictive performance due to their ability to learn complex, non-linear relationships between variables. However, the inability to effectively visualize these relationships has led to DNNs being characterized ... More
Spontaneous symmetry breaking and trapping of temporal Kerr cavity solitons by pulsed or amplitude modulated driving fieldsMar 27 2018May 02 2018We report on a systematic study of temporal Kerr cavity soliton dynamics in the presence of pulsed or amplitude modulated driving fields. In stark contrast to the more extensively studied case of phase modulations, we find that Kerr cavity solitons are ... More
Patterns of Selection of Human Movements II: Movement Limits, Mechanical Energy, and Very Slow Walking GaitsOct 03 2016The biomechanics of the human body allow humans a range of possible ways of executing movements to attain specific goals. This range of movement is limited by a number of mechanical, biomechanical, or cognitive constraints. Shifts in these limits result ... More
Constructions with bundle gerbesDec 09 2003This thesis develops the theory of bundle gerbes and examines a number of useful constructions in this theory. These allow us to gain a greater insight into the structure of bundle gerbes and related objects. Furthermore they naturally lead to some interesting ... More
Reducing almost Lagrangian structures and almost CR geometries to partially integrable structuresJul 08 2008Jul 10 2008This paper demostrates a method for analysing almost CR geometries $(H,J)$, by uniquley defining a partially integrable structure $(H,K)$ from the same data. Thus two almost CR geometries $(H,J)$ and $(H',J')$ are equivalent if and and only if they generate ... More
Free 3-distributions: holonomy, Fefferman constructions and dual distributionsAug 22 2007Mar 27 2008This paper analyses the parabolic geometries generated by a free 3-distribution in the tangent space of a manifold. It shows the existence of normal Fefferman constructions over CR and Lagrangian contact structures corresponding to holonomy reductions ... More
Generalised Einstein condition and cone construction for parabolic geometriesMay 16 2007Aug 14 2008This paper attempts to define a generalisation of the standard Einstein condition (in conformal/metric geometry) to any parabolic geometry. To do so, it shows that any preserved involution $\sigma$ of the adjoint bundle $\mc{A}$ gives rise, given certain ... More
From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator AnsatzSep 11 2017Feb 28 2019The next few years will be exciting as prototype universal quantum processors emerge, enabling implementation of a wider variety of algorithms. Of particular interest are quantum heuristics, which require experimentation on quantum hardware for their ... More
On the Principled Description of Human MovementsSep 22 2015While the use of technology to provide accurate and objective measurements of human movement performance is presently an area of great interest, efforts to quantify the performance of movement are hampered by the lack of a principled model that describes ... More
Co-Production of Cement and Carbon Nanotubes with a Carbon Negative FootprintAug 02 2016C2CNT (Carbon dioxide to carbon nanotube) cement plants have been introduced and analyzed which provide a significant economic incentive to eliminate the massive CO2 greenhouse gas emissions of current plants and serves as a template for carbon mitigation ... More
Note on pre-Courant algebroid structures for parabolic geometriesSep 06 2007Mar 01 2011This note aims to demonstrate that every parabolic geometry has a naturally defined per-Courant algebro\"id structure. This structure is a Courant algebro\"id if and only if the the curvature $\kappa$ of the Cartan connection vanishes. In all other cases, ... More
Ricci-Flat Holonomy: a ClassificationFeb 27 2006Sep 12 2006The reductive holonomy algebras for a torsion-free affine connection are analysed, with the goal of establishing which ones can correspond to a Ricci-flat connection with the same properties. Various families of holonomies are eliminated through different ... More
A bundle gerbe construction of a spinor bundle from the smooth free loop of a vector bundleJul 18 2012A bundle gerbe is constructed from an oriented smooth vector bundle of even rank with a fiberwise inner product, over a compact connected orientable smooth manifold with Riemannian metric. From a trivialization of the bundle gerbe is constructed an irreducible ... More
Near-infrared [Fe II] and H$_{2}$ Emission-line Study of Galactic Supernova Remnants in the First QuadrantFeb 11 2019We report the detection of near-infrared (NIR) [Fe II] (1.644 $\mu$m) and H$_{2}$ 1-0 S(1) (2.122 $\mu$m) line features associated with Galactic supernova remnants (SNRs) in the first quadrant using two narrowband imaging surveys, UWIFE and UWISH2. Among ... More
The rapid growth phase of supermassive black holesMay 21 2018Sep 07 2018We investigate the rapid growth phase of supermassive black holes (BHs) within the hydrodynamical cosmological \eagle simulation. This non-linear phase of BH growth occurs within $\sim$$L_{*}$ galaxies, embedded between two regulatory states of the galaxy ... More
Astrometric Discovery of GJ 164BSep 09 2004We discovered a low-mass companion to the M-dwarf GJ 164 with the CCD-based imaging system of the Stellar Planet Survey (STEPS) astrometric program. The existence of GJ 164B was confirmed with Hubble Space Telescope NICMOS imaging observations. A high-dispersion ... More
World-line Quantisation of a Reciprocally Invariant SystemJun 26 2007We present the world-line quantisation of a system invariant under the symmetries of reciprocal relativity (pseudo-unitary transformations on ``phase space coordinates" $(x^\mu(\tau),p^\mu(\tau))$ which preserve the Minkowski metric and the symplectic ... More
Quantifying the pathways to life using assembly spacesJul 06 2019We have developed the concept of pathway assembly to explore the amount of extrinsic information required to build an object. To quantify this information in an agnostic way, we present a method to determine the amount of pathway assembly information ... More
Octave-spanning tunable parametric oscillation in crystalline Kerr microresonatorsApr 10 2019Parametric nonlinear optical processes allow for the generation of new wavelengths of coherent electromagnetic radiation. Their ability to create radiation that is widely tunable in wavelength is particularly appealing, with applications ranging from ... More
On Sun-to-Earth Propagation of Coronal Mass EjectionsApr 13 2013We investigate how coronal mass ejections (CMEs) propagate through, and interact with, the inner heliosphere between the Sun and Earth, a key question in CME research and space weather forecasting. CME Sun-to-Earth kinematics are constrained by combining ... More
Numerical simulations of granular dynamics. I. Hard-sphere discrete element method and testsJun 11 2013We present a new particle-based (discrete element) numerical method for the simulation of granular dynamics, with application to motions of particles on small solar system body and planetary surfaces. The method employs the parallel N-body tree code pkdgrav ... More
Improved measurements of the intergalactic medium temperature around quasars: possible evidence for the initial stages of He-II reionisation at z~6Oct 03 2011We present measurements of the intergalactic medium (IGM) temperature within ~5 proper Mpc of seven luminous quasars at z~6. The constraints are obtained from the Doppler widths of Lyman-alpha absorption lines in the quasar near-zones and build upon our ... More
Higher-Order Topological InsulatorsAug 11 2017Jun 03 2018Three-dimensional topological (crystalline) insulators are materials with an insulating bulk, but conducting surface states which are topologically protected by time-reversal (or spatial) symmetries. Here, we extend the notion of three-dimensional topological ... More
A first direct measurement of the intergalactic medium temperature around a quasar at z=6Jan 19 2010Mar 25 2010The thermal state of the intergalactic medium (IGM) provides an indirect probe of both the HI and HeII reionisation epochs. Current constraints on the IGM temperature from the Lya forest are restricted to the redshift range 2<z<4.5, limiting the ability ... More
Music from the heavens - Gravitational waves from supermassive black hole mergers in the EAGLE simulationsJan 21 2016Jul 29 2016We estimate the expected event rate of gravitational wave signals from mergers of supermassive black holes that could be resolved by a space-based interferometer, such as the Evolved Laser Interferometer Space Antenna (eLISA), utilising the reference ... More
Accurate mass and radius determinations of a cool subdwarf in an eclipsing binaryMar 07 2019Cool subdwarfs are metal-poor low-mass stars that formed during the early stages of the evolution of our Galaxy. Because they are relatively rare in the vicinity of the Sun, we know of few cool subdwarfs in the solar neighbourhood, and none with both ... More
Self-induced Scattering of Strahl Electrons in the Solar WindJun 06 2019We investigate the scattering of strahl electrons by micro-instabilities as a mechanism for creating the electron halo in the solar wind. We develop a mathematical framework for the description of electron-driven micro-instabilities and discuss the associated ... More
The Interplay of Topological Surface and Bulk Electronic States in Bi2Se3Oct 05 2012In this Letter we present scanning tunneling microscopy density-of-states measurements and electronic structure calculations of the topological insulator Bi2Se3. The measurements show significant background states in addition to the expected Dirac cone. ... More
The gas fractions of dark matter haloes hosting simulated $\sim L^\star$ galaxies are governed by the feedback history of their black holesOct 17 2018Jun 04 2019We examine the origin of scatter in the relationship between the gas fraction and mass of dark matter haloes hosting present-day $\sim L^\star$ central galaxies in the EAGLE simulations. The scatter is uncorrelated with the accretion rate of the central ... More
Constraint Control of Nonholonomic Mechanical SystemsOct 08 2016Oct 17 2016We derive an optimal control formulation for a nonholonomic mechanical system using the nonholonomic constraint itself as the control. We focus on Suslov's problem, which is defined as the motion of a rigid body with a vanishing projection of the body ... More
Constraint Control of Nonholonomic Mechanical SystemsOct 08 2016Oct 19 2016We derive an optimal control formulation for a nonholonomic mechanical system using the nonholonomic constraint itself as the control. We focus on Suslov's problem, which is defined as the motion of a rigid body with a vanishing projection of the body ... More
Parametric Manifolds II: Intrinsic ApproachJul 12 1994A parametric manifold is a manifold on which all tensor fields depend on an additional parameter, such as time, together with a parametric structure, namely a given (parametric) 1-form field. Such a manifold admits natural generalizations of Lie differentiation, ... More
Convergence Analysis of Ensemble Kalman Inversion: The Linear, Noisy CaseFeb 25 2017Aug 08 2017We present an analysis of ensemble Kalman inversion, based on the continuous time limit of the algorithm. The analysis of the dynamical behaviour of the ensemble allows us to establish well-posedness and convergence results for a fixed ensemble size. ... More
Adiabatic limit and the slow motion of vortices in a Chern-Simons-Schrödinger systemMay 07 2009Jun 25 2009We study a nonlinear system of partial differential equations in which a complex field (the Higgs field) evolves according to a nonlinear Schroedinger equation, coupled to an electromagnetic field whose time evolution is determined by a Chern-Simons term ... More
The Schwinger model on $S^1$: Hamiltonian formulation, vacuum and anomalyJun 18 2012We present a Hamiltonian formulation of the Schwinger model on the circle in Coulomb gauge as a semi-bounded self-adjoint operator which is invariant under the modular group ${\cal M}=\Z$ of large gauge transformations. There is a nontrivial action of ... More
Approximating Ground and Excited State Energies on a Quantum ComputerAug 06 2015Approximating ground and a fixed number of excited state energies, or equivalently low order Hamiltonian eigenvalues, is an important but computationally hard problem. Typically, the cost of classical deterministic algorithms grows exponentially with ... More
The Imprint of Cosmic Reionization on Galaxy ClusteringJun 26 2007We consider the effect of reionization on the clustering properties of galaxy samples at intermediate redshifts (z~0.3-5.5). Current models for the reionization of intergalactic hydrogen predict that overdense regions will be reionized early, thus delaying ... More
Numerical Simulations of a Rolling Ball Robot Actuated by Internal Point MassesApr 30 2019The controlled motion of a rolling ball actuated by internal point masses that move along arbitrarily-shaped rails fixed within the ball is considered. The controlled equations of motion are solved numerically using a predictor-corrector continuation ... More
Small amplitude solitary waves in the Dirac-Maxwell systemOct 26 2012Sep 27 2017We study nonlinear bound states, or solitary waves, in the Dirac-Maxwell system proving the existence of solutions in which the Dirac wave function is of the form $\phi(x,\omega)e^{-i\omega t}$, $\omega\in(-m,\omega_*)$, with some $\omega_*>-m$, such ... More
Calibrating the Galaxy Halo - Black Hole Relation Based on the Clustering of QuasarsMar 31 2004The observed number counts of quasars may be explained either by long-lived activity within rare massive hosts, or by short-lived activity within smaller, more common hosts. It has been argued that quasar lifetimes may therefore be inferred from their ... More
Cosmic Hydrogen Was Significantly Neutral a Billion Years After the Big BangJan 12 2004The ionization fraction of cosmic hydrogen, left over from the big bang, provides crucial fossil evidence for when the first stars and quasar black holes formed in the infant universe. Spectra of the two most distant quasars known show nearly complete ... More
Reionization of Hydrogen and Helium by Early Stars and QuasarsSep 03 2002Nov 14 2002We compute the reionization histories of hydrogen and helium due to the ionizing radiation fields produced by stars and quasars. For the quasars we use a model based on halo-merger rates that reproduces all known properties of the quasar luminosity function ... More
Constraints on the Process that Regulates the Growth of Supermassive Black Holes Based on the Intrinsic Scatter in the M_bh-sigma RelationJun 14 2005We show that the observed scatter in the relations between the mass of supermassive black holes (SMBHs), M_bh, and the velocity dispersion sigma or mass M_sph of their host spheroid, place interesting constraints on the process that regulates SMBH growth ... More
A Size of ~10 Mpc for the Ionized Bubbles at the End of Cosmic ReionizationSep 16 2004The first galaxies to appear in the universe at redshifts z>20 created ionized bubbles in the intergalactic medium of neutral hydrogen left over from the Big-Bang. It is thought that the ionized bubbles grew with time, surrounded clusters of dwarf galaxies ... More
Self-Regulated Growth of Supermassive Black Holes in Galaxies as the Origin of the Optical and X-ray Luminosity Functions of QuasarsApr 09 2003We postulate that supermassive black-holes grow in the centers of galaxies until they unbind the galactic gas that feeds them. We show that the corresponding self-regulation condition yields a correlation between black-hole mass (Mbh) and galaxy velocity ... More
Constraint Control of Nonholonomic Mechanical SystemsOct 08 2016Nov 30 2016We derive an optimal control formulation for a nonholonomic mechanical system using the nonholonomic constraint itself as the control. We focus on Suslov's problem, which is defined as the motion of a rigid body with a vanishing projection of the body ... More
Potential Impact of Global Navigation Satellite Services on Total Power HI Intensity Mapping SurveysMar 16 2018Mar 27 2019Future total-power single-dish HI intensity mapping (HI IM) surveys have the potential to provide unprecedented insight into late time ($z < 1$) cosmology that are competitive with Stage IV dark energy surveys. However, redshifts between $0 < z < 0.2$ ... More
The Shutdown Problem: How Does a Blockchain System End?Feb 19 2019We define and examine the shutdown problem for blockchain systems: how to gracefully end the system's operation at the end of its useful life. A particular focus is those blockchain systems that hold archival data of long-lived interest. We outline what ... More
The correlation between the distribution of galaxies and 21cm emission at high redshiftsSep 27 2006Deep surveys have recently discovered galaxies at the tail end of the epoch of reionization. In the near future, these discoveries will be complemented by a new generation of low-frequency radio observatories that will map the distribution of neutral ... More
Adaptive time-stepping for Stochastic Partial Differential Equations with non-Lipschitz driftDec 21 2018We introduce an explicit, adaptive time-stepping scheme for simulation of SPDEs with non-Lipschitz drift coefficients. Strong convergence is proven for the full space-time discretisation with multiplicative noise by considering the space and time discretisation ... More
On the Dynamics of a Rolling Ball Actuated by Internal Point MassesJan 28 2018Dec 30 2018The motion of a rolling ball actuated by internal point masses that move inside the ball's frame of reference is considered. The equations of motion are derived by applying Euler-Poincar\'e's symmetry reduction method in concert with Lagrange-d'Alembert's ... More
Heterotic/$F$-theory Duality and Narasimhan-Seshadri EquivalenceJun 17 2019Finding the $F$-theory dual of a Heterotic model with Wilson-line symmetry breaking presents the challenge of achieving the dual $\mathbb{Z}_{2}$-action on the $F$-theory model in such a way that the $\mathbb{Z}_{2}$-quotient is Calabi-Yau with an Enriques ... More
Projective indecomposable modules and quivers for monoid algebrasJun 16 2017We give a construction of the projective indecomposable modules and a description of the quiver for a large class of monoid algebras including the algebra of any finite monoid whose principal right ideals have at most one idempotent generator. Our results ... More
Flow of Planets Raises Short Period Fall OffNov 08 2012After finding more planets than expected at the shortest period, there has been an effort to explain their numbers by weak tidal friction. However, we find that the strength of tidal dissipation that would produce the occurence distribution found from ... More
Ensembles, Dynamics, and Cell Types: Revisiting the Statistical Mechanics Perspective on Cellular RegulationFeb 01 2019Genetic regulatory networks control ontogeny. For fifty years Boolean networks have served as models of such systems, ranging from ensembles of random Boolean networks as models for generic properties of gene regulation to working dynamical models of ... More
The algebra of the Catalan monoid as an incidence algebra: A simple proofJun 18 2018We give a direct straightforward proof that there is an isomorphism between the algebra of the Catalan monoid C_n that is, the monoid of all order-preserving, weakly increasing self-maps f of [n] = {1,...,n}, over any commutative ring with identity and ... More
Lessons from a Restricted Turing TestApr 04 1994We report on the recent Loebner prize competition inspired by Turing's test of intelligent behavior. The presentation covers the structure of the competition and the outcome of its first instantiation in an actual event, and an analysis of the purpose, ... More
Utility Optimization in Congested Queueing NetworksAug 26 2009Nov 24 2010We consider a multi-class single server queueing network as a model of a packet switching network. The rates packets are sent into this network are controlled by queues which act as congestion windows. By considering a sequence of congestion controls, ... More
Basis invariant description of chemical equilibrium with implications for a recent axionic leptogenesis modelJul 30 2015Dec 29 2015We provide a systematic treatment of chemical equilibrium in the presence of a specific type of time dependent background. The type of time dependent background we consider appears, for example, in recently proposed axion/Majoron leptogenesis models [1,2]. ... More
Effective dynamics for solitons in the nonlinear Klein Gordon Maxwell system and the Lorentz force lawMay 07 2009We consider the nonlinear Klein Gordon Maxwell system on four dimensional Minkowski space-time. For appropriate nonlinearities the system admits soliton solutions which are gauge invariant generalizations of the non-topological solitons introduced and ... More
Empirical Performance Evaluation of Enhanced Throughput Schemes of IEEE802.11 Technology in Wireless Area NetworksSep 11 2013The success in the growing wireless standards can be measured by the achievement of quality of service (QoS) specifications by the designers. The IEEE802.11 wireless standards are widely accepted as wireless technology for wireless LAN. Efforts have been ... More
On the Normal Force and Static Friction Acting on a Rolling Ball Actuated by Internal Point MassesOct 07 2018Apr 11 2019The goal of this paper is to investigate the normal and tangential forces acting at the point of contact between a horizontal surface and a rolling ball actuated by internal point masses moving in the ball's frame of reference. The normal force and static ... More
On the Optimal Control of a Rolling Ball Robot Actuated by Internal Point MassesAug 12 2017May 01 2019The controlled motion of a rolling ball actuated by internal point masses that move along arbitrarily-shaped rails fixed within the ball is considered. Application of the variational Pontryagin's minimum principle yields the ball's controlled equations ... More
Constraint Control of Nonholonomic Mechanical SystemsOct 08 2016Nov 10 2018We derive an optimal control formulation for a nonholonomic mechanical system using the nonholonomic constraint itself as the control. We focus on Suslov's problem, which is defined as the motion of a rigid body with a vanishing projection of the body ... More
Flow level convergence and insensitivity for multi-class queueing networksFeb 15 2011We consider a multi-class queueing network as a model of packet transfer in a communication network. We define a second stochastic model as a model document transfer in a communication network where the documents transferred have a general distribution. ... More
Cartan subalgebras in uniform Roe algebrasAug 13 2018May 16 2019In this paper we study structural and uniqueness questions for Cartan subalgebras of uniform Roe algebras. We characterise when an inclusion $B\subseteq A$ of $\mathrm{C}^*$-algebras is isomorphic to the canonical inclusion of $\ell^\infty(X)$ inside ... More
Semi-regular masas of transfinite lengthNov 20 2006In 1965 Tauer produced a countably infinite family of semi-regular masas in the hyperfinite $\mathrm{II}_1$ factor, no pair of which are conjugate by an automorphism. This was achieved by iterating the process of passing to the algebra generated by the ... More
Iron abundance correlations and an occurrence distribution discrepancy from ongoing planet migrationMay 22 2013Sep 12 2013Whether the higher occurrence of giant planets being hosted by metal-rich versus metal-poor stars results from formation or from "pollution" has been a question of intense debate. We present new patterns that emerge when planet/star systems are separated ... More