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Molecular gas kinematics of the CMZ: Great oaks from little acorns growSep 30 2016The central molecular zone (CMZ) hosts some of the most massive and dense molecular clouds and star clusters in the Galaxy, offering an important window into star formation under extreme conditions. Star formation in this extreme environment may be closely ... More

Seeding the Galactic Centre gas stream: gravitational instabilities set the initial conditions for the formation of protocluster cloudsSep 06 2016Star formation within the Central Molecular Zone (CMZ) may be intimately linked to the orbital dynamics of the gas. Recent models suggest that star formation within the dust ridge molecular clouds (from G0.253+0.016 to Sgr B2) follows an evolutionary ... More

Seeding the Galactic Centre gas stream: gravitational instabilities set the initial conditions for the formation of protocluster cloudsSep 06 2016Oct 05 2016Star formation within the Central Molecular Zone (CMZ) may be intimately linked to the orbital dynamics of the gas. Recent models suggest that star formation within the dust ridge molecular clouds (from G0.253+0.016 to Sgr B2) follows an evolutionary ... More

A stable partitioned FSI algorithm for incompressible flow and elastic solidsAug 26 2013A stable partitioned algorithm for coupling incompressible flows with compressible elastic solids is described. This added-mass partitioned (AMP) scheme requires no sub-iterations, can be made fully second- or higher-order accurate, and remains stable ... More

A stable partitioned FSI algorithm for incompressible flow and structural shellsAug 27 2013A stable partitioned algorithm for fluid-structure interaction (FSI) problems that couple viscous incompressible flow with structural shells or beams is described. This added-mass partitioned (AMP) scheme uses Robin (mixed) interface conditions for the ... More

A stable FSI algorithm for light rigid bodies in compressible flowAug 16 2012Mar 05 2013In this article we describe a stable partitioned algorithm that overcomes the added mass instability arising in fluid-structure interactions of light rigid bodies and inviscid compressible flow. The new algorithm is stable even for bodies with zero mass ... More

A stable partitioned FSI algorithm for rigid bodies and incompressible flow in three dimensionsNov 13 2017Jun 29 2018This paper describes a novel partitioned algorithm for fluid-structure interaction (FSI) problems that couples the motion of rigid bodies and incompressible flow. This is the first partitioned algorithm that remains stable and second-order accurate, without ... More

A stable partitioned FSI algorithm for rigid bodies and incompressible flow. Part II: General formulationNov 17 2016Apr 24 2017A stable partitioned algorithm is developed for fluid-structure interaction (FSI) problems involving viscous incompressible flow and rigid bodies. This {\em added-mass partitioned} (AMP) algorithm remains stable, without sub-iterations, for light and ... More

A stable partitioned FSI algorithm for rigid bodies and incompressible flow. Part II: General formulationNov 17 2016A stable partitioned algorithm is developed for fluid-structure interaction (FSI) problems involving viscous incompressible flow and rigid bodies. This {\em added-mass partitioned} (AMP) algorithm remains stable, without sub-iterations, for light and ... More

A stable partitioned FSI algorithm for rigid bodies and incompressible flow. Part I: Model problem analysisNov 17 2016A stable partitioned algorithm is developed for fluid-structure interaction (FSI) problems involving viscous incompressible flow and rigid bodies. This {\em added-mass partitioned} (AMP) algorithm remains stable, without sub-iterations, for light and ... More

A stable partitioned FSI algorithm for incompressible flow and deforming beamsJul 22 2015An added-mass partitioned (AMP) algorithm is described for solving fluid-structure interaction (FSI) problems coupling incompressible flows with thin elastic structures undergoing finite deformations. The new AMP scheme is fully second-order accurate ... More

Computed Flow and Fluorescence Over the Ocular SurfaceOct 31 2016Fluorescein is perhaps the most commonly used substance to visualize tear film thickness and dynamics; better understanding of this process aids understanding of dry eye syndrome which afflicts millions of people. We study a mathematical model for tear ... More

Gas Kinematics and Excitation in the Filamentary IRDC G035.39-00.33Jan 10 2014Some theories of dense molecular cloud formation involve dynamical environments driven by converging atomic flows or collisions between preexisting molecular clouds. The determination of the dynamics and physical conditions of the gas in clouds at the ... More

Widespread deuteration across the IRDC G035.39-00.33Feb 18 2016Infrared Dark Clouds (IRDCs) are cold, dense regions that are usually found within Giant Molecular Clouds (GMCs). Ongoing star formation within IRDCs is typically still deeply embedded within the surrounding molecular gas. Characterising the properties ... More

Similar complex kinematics within two massive, filamentary infrared dark cloudsJan 19 2018Infrared dark clouds (IRDCs) are thought to be potential hosts of the elusive early phases of high-mass star formation. Here we conduct an in-depth kinematic analysis of one such IRDC, G034.43+00.24 (Cloud F), using high sensitivity and high spectral ... More

Unveiling the Early-Stage Anatomy of a Protocluster Hub with ALMAJul 29 2016Aug 12 2016High-mass stars shape the interstellar medium in galaxies, and yet, largely because the initial conditions are poorly constrained, we do not know how they form. One possibility is that high-mass stars and star clusters form at the junction of filamentary ... More

Investigating the structure and fragmentation of a highly filamentary IRDCJul 25 2016Aug 15 2016We present 3.7 arcsec (~0.05 pc) resolution 3.2 mm dust continuum observations from the IRAM PdBI, with the aim of studying the structure and fragmentation of the filamentary Infrared Dark Cloud G035.39-00.33. The continuum emission is segmented into ... More

Unveiling the Early-Stage Anatomy of a Protocluster Hub with ALMAJul 29 2016Sep 29 2016High-mass stars shape the interstellar medium in galaxies, and yet, largely because the initial conditions are poorly constrained, we do not know how they form. One possibility is that high-mass stars and star clusters form at the junction of filamentary ... More

Recursive polarization of nuclear spins in diamond at arbitrary magnetic fieldsDec 17 2014We introduce an alternate route to dynamically polarize the nuclear spin host of nitrogen-vacancy (NV) centers in diamond. Our approach articulates optical, microwave and radio-frequency pulses to recursively transfer spin polarization from the NV electronic ... More

Widespread SiO and CH3OH emission in Filamentary Infrared Dark CloudsNov 27 2017Infrared-Dark Clouds (IRDCs) are cold, dense regions of high (optical and infrared) extinction, believed to be the birthplace of high-mass stars and stellar clusters. The physical mechanisms leading to the formation of these IRDCs are not completely understood ... More

Direct numerical simulation of particulate flows with an overset grid methodFeb 03 2017We evaluate an efficient overset grid method for two-dimensional and three-dimensional particulate flows for small numbers of particles at finite Reynolds number. The rigid particles are discretised using moving overset grids overlaid on a Cartesian background ... More

15N Fractionation in Infrared-Dark Cloud CoresMay 11 2017Nitrogen is one of the most abundant elements in the Universe and its 14N/15N isotopic ratio has the potential to provide information about the initial environment in which our Sun formed. Recent findings suggest that the Solar System may have formed ... More

Constraining globular cluster formation through studies of young massive clusters - V. ALMA observations of clusters in the AntennaeJan 22 2015Some formation scenarios that have been put forward to explain multiple populations within Globular Clusters (GCs) require that the young massive cluster have large reservoirs of cold gas within them, which is necessary to form future generations of stars. ... More

Quantum Systems Engineering: A structured approach to accelerating the development of a quantum technology industryApr 22 2016The exciting possibilities in the field of new quantum technologies extend far beyond the well-reported application of quantum computing. Precision timing, gravity sensors and imagers, cryptography, navigation, metrology, energy harvesting and recovery, ... More

The challenges for Systems Engineers of non-classical quantum technologiesOct 16 2017Dec 11 2017Non-classical quantum technologies that rely on manipulation of quantum states and exploitation of quantum superposition and entanglement are approaching a level of maturity sufficient to contemplate commercialization as the basis of practical devices ... More

A stable added-mass partitioned (AMP) algorithm for elastic solids and incompressible flow: model problem analysisDec 07 2018A stable added-mass partitioned (AMP) algorithm is developed for fluid-structure interaction (FSI) problems involving viscous incompressible flow and compressible elastic-solids. The AMP scheme remains stable and second-order accurate even when added-mass ... More

A stable added-mass partitioned (AMP) algorithm for elastic solids and incompressible flowDec 13 2018A stable added-mass partitioned (AMP) algorithm is developed for fluid-structure interaction (FSI) problems involving viscous incompressible flow and compressible elastic solids. Deforming composite grids are used to effectively handle the evolving geometry ... More

Complex, Quiescent Kinematics in a Highly Filamentary Infrared Dark CloudOct 25 2012Infrared Dark Clouds (IRDCs) host the initial conditions under which massive stars and stellar clusters form. We have obtained high sensitivity and high spectral resolution observations with the IRAM 30m antenna, which allowed us to perform detailed analysis ... More

The dynamical properties of dense filaments in the infrared dark cloud G035.39-00.33Mar 06 2014Infrared Dark Clouds (IRDCs) are unique laboratories to study the initial conditions of high-mass star and star cluster formation. We present high-sensitivity and high-angular resolution IRAM PdBI observations of N2H+ (1-0) towards IRDC G035.39-00.33. ... More

Young massive star cluster formation in the Galactic Centre is driven by global gravitational collapse of high-mass molecular cloudsMar 14 2019Young massive clusters (YMCs) are the most compact, high-mass stellar systems still forming at the present day. The precursor clouds to such systems are, however, rare due to their large initial gas mass reservoirs and rapid dispersal timescales due to ... More

'The Brick' is not a brick: A comprehensive study of the structure and dynamics of the Central Molecular Zone cloud G0.253+0.016Feb 07 2019In this paper we provide a comprehensive description of the internal dynamics of G0.253+0.016 (a.k.a. 'the Brick'); one of the most massive and dense molecular clouds in the Galaxy to lack signatures of widespread star formation. As a potential host to ... More

Molecular gas kinematics within the central 250 pc of the Milky WayJan 14 2016Feb 10 2016Using spectral-line observations of HNCO, N2H+, and HNC, we investigate the kinematics of dense gas in the central ~250 pc of the Galaxy. We present SCOUSE (Semi-automated multi-COmponent Universal Spectral-line fitting Engine), a line fitting algorithm ... More

Lattice point counting and height bounds over number fields and quaternion algebrasAug 05 2013An important problem in analytic and geometric combinatorics is estimating the number of lattice points in a compact convex set in a Euclidean space. Such estimates have numerous applications throughout mathematics. In this note, we exhibit applications ... More

Star formation in a high-pressure environment: An SMA view of the Galactic centre dust ridgeNov 02 2017The star formation rate in the Central Molecular Zone (CMZ) is an order of magnitude lower than predicted according to star formation relations that have been calibrated in the disc of our own and nearby galaxies. Understanding how and why star formation ... More

The dynamical evolution of molecular clouds near the Galactic Centre - II. Spatial structure and kinematics of simulated cloudsFeb 05 2019Feb 07 2019The evolution of molecular clouds in galactic centres is thought to differ from that in galactic discs due to a significant influence of the external gravitational potential. We present a set of numerical simulations of molecular clouds orbiting on the ... More

New Measurement of Compton Scattering from the Deuteron and an Improved Extraction of the Neutron Electromagnetic PolarizabilitiesSep 12 2014Nov 13 2014The electromagnetic polarizabilities of the nucleon are fundamental properties that describe its response to external electric and magnetic fields. They can be extracted from Compton-scattering data --- and have been, with good accuracy, in the case of ... More

Ionised gas kinematics in bipolar H II regionsMay 01 2018Stellar feedback plays a fundamental role in shaping the evolution of galaxies. Here we explore the use of ionised gas kinematics in young, bipolar H II regions as a probe of early feedback in these star-forming environments. We have undertaken a multiwavelength ... More

A Brief Update on the CMZoom SurveyOct 18 2016The inner few hundred parsecs of the Milky Way, the Central Molecular Zone (CMZ), is our closest laboratory for understanding star formation in the extreme environments (hot, dense, turbulent gas) that once dominated the universe. We present an update ... More

Compton scattering from 12C using tagged photons in the energy range 65 - 115 MeVJan 16 2014Elastic scattering of photons from 12C has been investigated using quasi-monoenergetic tagged photons with energies in the range 65 - 115 MeV at laboratory angles of 60 deg, 120 deg, and 150 deg at the Tagged-Photon Facility at the MAX IV Laboratory in ... More

H2O Southern Galactic Plane Survey (HOPS): Paper III - Properties of Dense Molecular Gas across the Inner Milky WayApr 11 2017The H2O Southern Galactic Plane Survey (HOPS) has mapped 100 square degrees of the Galactic plane for water masers and thermal molecular line emission using the 22-m Mopra telescope. We describe the automated spectral-line fitting pipelines used to determine ... More

Topological origins of bound states in the continuum for systems with conical intersectionsOct 24 2017Bound states in the continuum (BSCs) were reported in a linear vibronic coupling model with a conical intersection (CI) [Cederbaum et al. Phys. Rev. Lett. 90, 013001 (2003)]. It was also found that these states are destroyed within the Born-Oppenheimer ... More

Subsonic islands within a high-mass star-forming IRDCFeb 20 2018Feb 27 2018High-mass star forming regions are typically thought to be dominated by supersonic motions. We present combined Very Large Array and Green Bank Telescope (VLA+GBT) observations of NH$_3$ (1,1) and (2,2) in the infrared dark cloud (IRDC) G035.39-00.33, ... More

Time Projection Chamber (TPC) Detectors for Nuclear Astrophysics Studies With Gamma BeamsDec 22 2018Gamma-Beams at the HIgS facility in the USA and anticipated at the ELI-NP facility, now constructed in Romania, present unique new opportunities to advance research in nuclear astrophysics; not the least of which is resolving open questions in oxygen ... More

Multicomponent kinematics in a massive filamentary IRDCDec 22 2018To probe the initial conditions for high-mass star and cluster formation, we investigate the properties of dense filaments within the infrared dark cloud G035.39-00.33 (IRDC G035.39) in a combined Very Large Array (VLA) and the Green Bank Telescope (GBT) ... More

Temperature structure and kinematics of the IRDC G035.39-00.33Jun 27 2017Aims. Infrared dark clouds represent the earliest stages of high-mass star formation. Detailed observations of their physical conditions on all physical scales are required to improve our understanding of their role in fueling star formation. Methods. ... More

Using young massive star clusters to understand star formation and feedback in high-redshift-like environmentsJan 11 2016The formation environment of stars in massive stellar clusters is similar to the environment of stars forming in galaxies at a redshift of 1 - 3, at the peak star formation rate density of the Universe. As massive clusters are still forming at the present ... More

Small zeros of quadratic forms outside of a union of varietiesJul 02 2013Let $F$ be a quadratic form in $N \geq 2$ variables defined on a vector space $V \subseteq K^N$ over a global field $K$, and $\Z \subseteq K^N$ be a finite union of varieties defined by families of homogeneous polynomials over $K$. We show that if $V ... More

System Energy Assessment (SEA), Defining a Standard Measure of EROI for Energy Businesses as Whole SystemsApr 18 2011A more objective method for measuring the energy needs of businesses, System Energy Assessment (SEA), identifies the natural boundaries of businesses as self-managing net-energy systems, of controlled and self-managing parts. The method is demonstrated ... More

Unambiguous Identification of the Second 2+ State in 12C and the Structure of the Hoyle StateMar 18 2013The second 2+ state of 12C, predicted over fifty years ago as an excitation of the Hoyle state, has been unambiguously identified using the 12C(g,a_0)8Be reaction. The alpha particles produced by the photodisintegration of 12C were detected using an Optical ... More

Spin readout via spin-to-charge conversion in bulk diamond nitrogen-vacancy ensemblesSep 19 2018We demonstrate optical readout of ensembles of nitrogen-vacancy(NV) center spins in a bulk diamond sample via spin-to-charge conversion. A high power 594 nm laser is utilized to selectively ionize these paramagnetic defects in the spin state with a contrast ... More

On-Demand Generation of Neutral and Negatively-Charged Silicon-Vacancy Centers in DiamondMar 17 2018Point defects in wide-bandgap semiconductors are emerging as versatile resources for nanoscale sensing and quantum information science but our understanding of the photo-ionization dynamics is presently incomplete. Here we use two-color confocal microscopy ... More

Long-term data storage in diamondOct 27 2016The negatively-charged nitrogen-vacancy (NV-) center in diamond is the focus of widespread attention for applications ranging from quantum information processing to nanoscale metrology. Although most work so far has focused on the NV- optical and spin ... More

Totally isotropic subspaces of small height in quadratic spacesSep 16 2014Let $K$ be a global field or $\overline{\mathbb Q}$, $F$ a nonzero quadratic form on $K^N$, $N \geq 2$, and $V$ a subspace of $K^N$. We prove the existence of an infinite collection of finite families of small-height maximal totally isotropic subspaces ... More

An Optical Readout TPC (O-TPC) for Studies in Nuclear Astrophysics With Gamma-Ray Beams at HIgSJan 10 2011We report on the construction, tests, calibrations and commissioning of an Optical Readout Time Projection Chamber (O-TPC) detector operating with a CO2(80%) + N2(20%) gas mixture at 100 and 150 Torr. It was designed to measure the cross sections of several ... More

Distributed star formation throughout the Galactic Center cloud Sgr B2Jan 15 2018We report ALMA observations with resolution $\approx0.5$" at 3 mm of the extended Sgr B2 cloud in the Central Molecular Zone (CMZ). We detect 271 compact sources, most of which are smaller than 5000 AU. By ruling out alternative possibilities, we conclude ... More

The Survey of Water and Ammonia in the Galactic Center (SWAG): Molecular Cloud Evolution in the Central Molecular ZoneOct 18 2017The Survey of Water and Ammonia in the Galactic Center (SWAG) covers the Central Molecular Zone (CMZ) of the Milky Way at frequencies between 21.2 and 25.4 GHz obtained at the Australia Telescope Compact Array at $\sim 0.9$ pc spatial and $\sim 2.0$ km ... More

On well-rounded ideal lattices - IIJul 11 2012We study well-rounded lattices which come from ideals in quadratic number fields, generalizing some recent results of the first author with K. Petersen. In particular, we give a characterization of ideal well-rounded lattices in the plane and show that ... More

On integral well-rounded lattices in the planeMay 23 2012We investigate distribution of integral well-rounded lattices in the plane, parameterizing the set of their similarity classes by solutions of the family of Pell-type Diophantine equations of the form $x^2+Dy^2=z^2$ where $D>0$ is squarefree. We apply ... More

High-Order Coupled Cluster Method (CCM) Formalism 2 -- "Generalised" Expectation Values: Spin-Spin Correlation Functions for Frustrated and Unfrustrated 2D AntiferromagnetsNov 27 2009Recent developments of high-order CCM have been to extend existing formalism and codes to $s \ge \frac 12$ for both the ground and excited states. In this article, we describe how "generalised" expectation values for a wide range of one- and two-body ... More

Two-electron-spin ratchets as a platform for microwave-free dynamic nuclear polarization of arbitrary material targetsApr 18 2019Optically-pumped color centers in semiconductor powders can potentially induce high levels of nuclear spin polarization in surrounding solids or fluids at or near ambient conditions, but complications stemming from the random orientation of the particles ... More

High-Order Coupled Cluster Method (CCM) Formalism 3: Finite-Size CCMFeb 23 2010Recent developments of high-order CCM have been to extend existing formalism and codes to $s \ge \frac 12$ for both the ground and excited states, and independently to "generalised" expectation values for a wide range of one- and two-body spin operators. ... More

High-Order Coupled Cluster Method (CCM) Formalism 1: Ground- and Excited-State Properties of Lattice Quantum Spin Systems with $s >= 1/2$Sep 07 2009Sep 11 2009The coupled cluster method (CCM) is a powerful and widely applied technique of modern-day quantum many-body theory. It has been used with great success in order to understand the properties of quantum magnets at zero temperature. This is due largely to ... More

Coherent manipulation of cold Rydberg atoms near the surface of an atom chipAug 08 2013Oct 06 2013Coherent superpositions of the 49s and 48s Rydberg states of cold Rb atoms were studied near the surface of an atom chip. The superpositions were created and manipulated using microwaves resonant with the two-photon 49s-48s transition. Coherent behavior ... More

Energy shifts of Rydberg atoms due to patch fields near metal surfacesAug 09 2010Mar 07 2011The statistical properties of patch electric fields due to a polycrystalline metal surface are calculated. The fluctuations in the electric field scale like 1/z^2, when z >> w, where z is the distance to the surface, and w is the characteristic length ... More

Renormalization automated by Hopf algebraOct 13 1998It was recently shown that the renormalization of quantum field theory is organized by the Hopf algebra of decorated rooted trees, whose coproduct identifies the divergences requiring subtraction and whose antipode achieves this. We automate this process ... More

Knots and Numbers in $φ^4$ Theory to 7 Loops and BeyondApr 21 1995We evaluate all the primitive divergences contributing to the 7--loop $\beta$\/--function of $\phi^4$ theory, i.e.\ all 59 diagrams that are free of subdivergences and hence give scheme--independent contributions. Guided by the association of diagrams ... More

Combinatoric explosion of renormalization tamed by Hopf algebra: 30-loop Pade-Borel resummationDec 11 1999Jan 07 2000It is easy to sum chain-free self-energy rainbows, to obtain contributions to anomalous dimensions. It is also easy to resum rainbow-free self-energy chains. Taming the combinatoric explosion of all possible nestings and chainings of a primitive self-energy ... More

Localization of a Polymer with Internal ConstraintsMar 06 1996We argue that Kantor and Kardar's assertion that their simulation results contradict our criterion for the localization of a softly constrainted ideal polymer is incorrect. Our criterion is inapplicable to the model used in these simulations. We argue ... More

Unfolding a Codimension-Two, Discontinuous, Andronov-Hopf BifurcationApr 18 2008We present an unfolding of the codimension-two scenario of the simultaneous occurrence of a discontinuous bifurcation and an Andronov-Hopf bifurcation in a piecewise-smooth, continuous system of autonomous ordinary differential equations in the plane. ... More

Quasi-conservation laws for compressible 3D Navier-Stokes flowJun 15 2012Oct 06 2012We formulate the quasi-Lagrangian fluid transport dynamics of mass density $\rho$ and the projection $q=\bom\cdot\nabla\rho$ of the vorticity $\bom$ onto the density gradient, as determined by the 3D compressible Navier-Stokes equations for an ideal gas, ... More

Enstrophy bounds and the range of space-time scales in the hydrostatic primitive equationsApr 03 2011Sep 14 2011The hydrostatic primitive equations (HPE) form the basis of most numerical weather, climate and global ocean circulation models. Analytical (not statistical) methods are used to find a scaling proportional to $(Nu\,Ra\,Re)^{1/4}$ for the range of horizontal ... More

Stretching and folding diagnostics in solutions of the three-dimensional Euler and Navier-Stokes equationsDec 16 2010Two possible diagnostics of stretching and folding (S&F) in fluid flows are discussed, based on the dynamics of the gradient of potential vorticity ($q = \bom\cdot\nabla\theta$) associated with solutions of the three-dimensional Euler and Navier-Stokes ... More

Stretching and folding processes in the 3D Euler and Navier-Stokes equationsNov 02 2013Stretching and folding dynamics in the incompressible, stratified 3D Euler and Navier-Stokes equations are reviewed in the context of the vector $\bdB = \nabla q\times\nabla\theta$ where $q=\bom\cdot\nabla\theta$. The variable $\theta$ is the temperature ... More

Lagrangian particle paths and ortho-normal quaternion framesJul 11 2006Feb 16 2007Experimentalists now measure intense rotations of Lagrangian particles in turbulent flows by tracking their trajectories and Lagrangian-average velocity gradients at high Reynolds numbers. This paper formulates the dynamics of an orthonormal frame attached ... More

On the presence of twinlike models in cosmologyFeb 27 2012We study cosmological models described by a single real scalar field. We work within the first-order framework, and we show how the first-order equations simplify the investigation, leading to a direct search of twinlike theories. The procedure is used ... More

Direct Dark Matter Detection with Velocity Distribution in the Eddington approachMar 26 2006Aug 14 2006Exotic dark matter together with the vacuum energy (associated with the cosmological constant) seem to dominate the Universe. Thus its direct detection is central to particle physics and cosmology. Supersymmetry provides a natural dark matter candidate, ... More

Towards cohomology of renormalization: bigrading the combinatorial Hopf algebra of rooted treesJan 28 2000Jan 29 2000The renormalization of quantum field theory twists the antipode of a noncocommutative Hopf algebra of rooted trees, decorated by an infinite set of primitive divergences. The Hopf algebra of undecorated rooted trees, ${\cal H}_R$, generated by a single ... More

Association of multiple zeta values with positive knots via Feynman diagrams up to 9 loopsSep 16 1996Nov 18 1996It is found that the number, $M_n$, of irreducible multiple zeta values (MZVs) of weight $n$, is generated by $1-x^2-x^3=\prod_n (1-x^n)^{M_n}$. For $9\ge n\ge3$, $M_n$ enumerates positive knots with $n$ crossings. Positive knots to which field theory ... More

Exact solutions of Dyson-Schwinger equations for iterated one-loop integrals and propagator-coupling dualityDec 17 2000The Hopf algebra of undecorated rooted trees has tamed the combinatorics of perturbative contributions, to anomalous dimensions in Yukawa theory and scalar $\phi^3$ theory, from all nestings and chainings of a primitive self-energy subdivergence. Here ... More

Feynman diagrams as a weight system: four-loop test of a four-term relationDec 01 1996Dec 15 1997At four loops there first occurs a test of the four-term relation derived by the second author in the course of investigating whether counterterms from subdivergence-free diagrams form a weight system. This test relates counterterms in a four-dimensional ... More

Comparison of Two Numerical Methods for Computation of American Type of the Floating Strike Asian OptionMay 31 2011We present a numerical approach for solving the free boundary problem for the Black-Scholes equation for pricing American style of floating strike Asian options. A fixed domain transformation of the free boundary problem into a parabolic equation defined ... More

Canonical Maps to Twisted RingsSep 21 2004Dec 14 2004If A is a strongly noetherian graded algebra generated in degree one, then there is a canonically constructed graded ring homomorphism from A to a twisted homogeneous coordinate ring B(X, L, sigma), which is surjective in large degree. This result is ... More

Exact Kohn-Sham eigenstates versus quasiparticles in simple models of strongly correlated electronsJul 21 2011Jan 12 2012We present analytic expressions for the exact density functional and Kohn-Sham Hamiltonian of simple tight-binding models of correlated electrons. These are the single- and double-site versions of the Anderson, Hubbard and spinless fermion models. The ... More

Long Range Hydration Effects in Electrolytic Free Suspended Black FilmsJun 16 1998The force law within free suspended black films made of negatively charged Aerosol-OT (AOT) with added LiCl or CsCl is studied accurately using X-ray reflectivity (ca. 1{\AA}). We find an electrolyte concentration threshold above which a substantial additional ... More

The umbral--penumbral boundary in sunspsots in the context of magneto-convectionFeb 25 2019Jurcak et al (2018) have reported that, in a sample of more than 100 umbral cores in sunspots, the umbral-penumbral boundary (UPB) is characterized by a remarkably narrowly-defined numerical value (1867 G) of the vertical component of the magnetic field. ... More

Can we rely on hybrid-DFT energies of solid-state problems with local-DFT geometries?Feb 01 2019Hybrid functionals often improve considerably the accuracy of density-functional calculations, in particular of quantities resulting from the band structure. In plane-wave (PW) calculations this benefit comes at the cost of an increase in computation ... More

Norm convergence of partial sums of $H^1$ functionsMar 28 2018Apr 11 2018A classical observation of Riesz says that truncations of a general $\sum_{n=0}^\infty a_n z^n$ in the Hardy space $H^1$ do not converge in $H^1$. A substitute positive result is proved: these partial sums always converge in the Bergman norm $A^1$. The ... More

Aspects of Bifurcation Theory for Piecewise-Smooth, Continuous SystemsJun 21 2010Systems that are not smooth can undergo bifurcations that are forbidden in smooth systems. We review some of the phenomena that can occur for piecewise-smooth, continuous maps and flows when a fixed point or an equilibrium collides with a surface on which ... More

Shrinking Point Bifurcations of Resonance Tongues for Piecewise-Smooth, Continuous MapsSep 20 2008Resonance tongues are mode-locking regions of parameter space in which stable periodic solutions occur; they commonly occur, for example, near Neimark-Sacker bifurcations. For piecewise-smooth, continuous maps these tongues typically have a distinctive ... More

Resonance near Border-Collision Bifurcations in Piecewise-Smooth, Continuous MapsFeb 11 2010Mode-locking regions (resonance tongues) formed by border-collision bifurcations of piecewise-smooth, continuous maps commonly exhibit a distinctive sausage-like geometry with pinch points called "shrinking points". In this paper we extend our unfolding ... More

New Velocity Distribution in the Context of the Eddington TheoryMar 19 2002Jan 14 2003Exotic dark matter together with the vacuum energy (associated with the cosmological constant) seem to dominate the Universe. Thus its direct detection is central to particle physics and cosmology. Supersymmetry provides a natural dark matter candidate, ... More

Making a Science of Model SearchSep 23 2012Many computer vision algorithms depend on a variety of parameter choices and settings that are typically hand-tuned in the course of evaluating the algorithm. While such parameter tuning is often presented as being incidental to the algorithm, correctly ... More

Andronov-Hopf Bifurcations in Planar, Piecewise-Smooth, Continuous FlowsJan 17 2007An equilibrium of a planar, piecewise-$C^1$, continuous system of differential equations that crosses a curve of discontinuity of the Jacobian of its vector field can undergo a number of discontinuous or border-crossing bifurcations. Here we prove that ... More

Localized basis sets for unbound electrons in nanoelectronicsDec 20 2007It is shown how unbound electron wave functions can be expanded in a suitably chosen localized basis sets for any desired range of energies. In particular, we focus on the use of gaussian basis sets, commonly used in first-principles codes. The possible ... More

The gradient of potential vorticity, quaternions and an orthonormal frame for fluid particlesJun 19 2010The gradient of potential vorticity (PV) is an important quantity because of the way PV (denoted as $q$) tends to accumulate locally in the oceans and atmospheres. Recent analysis by the authors has shown that the vector quantity $\bdB = \bnabla q\times ... More

The dynamics of the gradient of potential vorticityNov 08 2009Mar 19 2010The transport of the potential vorticity gradient $\bnabla{q}$ along surfaces of constant temperature $\theta$ is investigated for the stratified Euler, Navier-Stokes and hydrostatic primitive equations of the oceans and atmosphere using the divergenceless ... More

Lagrangian analysis of alignment dynamics for isentropic compressible magnetohydrodynamicsAug 07 2006After a review of the isentropic compressible magnetohydrodynamics (ICMHD) equations, a quaternionic framework for studying the alignment dynamics of a general fluid flow is explained and applied to the ICMHD equations.

Homogeneous variational complexes and bicomplexesDec 16 2005We present a family of complexes playing the same role, for homogeneous variational problems, that the horizontal parts of the variational bicomplex play for variational problems on a fibred manifold. We show that, modulo certain pullbacks, each of these ... More

Dark solitons in atomic Bose-Einstein condensates: from theory to experimentsApr 23 2010This review paper presents an overview of the theoretical and experimental progress on the study of matter-wave dark solitons in atomic Bose-Einstein condensates. Upon introducing the general framework, we discuss the statics and dynamics of single and ... More

Trapped-ion qutrit spin molecule quantum computerJun 03 2005We present a qutrit quantum computer design using trapped ions in the presence of a magnetic field gradient. The magnetic field gradient induces a "spin-spin" type coupling, similar to the J-coupling observed in molecules, between the qutrits which allows ... More