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A More Accurate Fourier TransformJul 06 2015Fourier transform methods are used to analyze functions and data sets to provide frequencies, amplitudes, and phases of underlying oscillatory components. Fast Fourier transform (FFT) methods offer speed advantages over evaluation of explicit integrals ... More

Evidence for Magnetoreception in Red Drum (Sciaenops ocellatus), Black Drum (Pogonias cromis), and Sea Catfish (Ariopsis felis)Nov 30 2015Over the past few decades, magnetoreception has been discovered in several species of teleost and elasmobranch fishes by employing varied experimental methods including conditioning experiments, observations of alignment with external fields, and experiments ... More

Measuring thrust and predicting trajectory in model rocketryMar 09 2009Methods are presented for measuring thrust using common force sensors and data acquisition to construct a dynamic force plate. A spreadsheet can be used to compute trajectory by integrating the equations of motion numerically. These techniques can be ... More

Impossible? Publication Quality Research with the Weakest 10% of Incoming FreshmenNov 30 2012Undergraduate research is widely regarded as a high impact practice. However, usually only the highest achieving students are rewarded with undergraduate research opportunities. This paper reports on the successful implementation of a student research ... More

High-speed measurement of rifle primer blast wavesFeb 08 2011This article describes a method and results for direct high-speed measurements of rifle primer blast waves employing a high-speed pressure transducer located at the muzzle to record the blast pressure wave produced by primer ignition. Our key findings ... More

Review of Magnetic Shark Deterrents: Hypothetical Mechanisms and Evidence for SelectivityNov 24 2014Several papers published since 2006 describe effects of magnetic fields on elasmobranchs and assess their utility in reducing negative interactions between sharks and humans, including bycatch reduction. Most of these repeat a single untested hypothesis ... More

An Acoustic Demonstration of Galileo's Law of Falling BodiesFeb 08 2011An acoustic method is presented for analyzing the time of falling motion. A ball is dropped from a measured height. The dropping device makes a distinct sound a well-determined time (roughly 14 milliseconds) after release. The ball subsequently makes ... More

Device for Underwater Laboratory Simulation of Unconfined Blast WavesJun 08 2015Shock tubes simulate blast waves to study their effects in air under laboratory conditions; however, few experimental models exist for simulating underwater blast waves that are needed for facilitating experiments in underwater blast transmission, determining ... More

The Evening Tutoring Center at the United States Air Force AcademyFeb 09 2011The United States Air Force Academy (USAFA) has opened an Evening Tutoring Center to provide after-hours tutoring every evening before class days. The center focuses on first and second year courses in challenging quantitative disciplines: mathematics, ... More

Acoustic methods for measuring bullet velocityDec 27 2008This article describes two acoustic methods to measure bullet velocity with an accuracy of 1% or better. In one method, a microphone is placed within 0.1 m of the gun muzzle and a bullet is fired at a steel target 45 m away. The bullet's flight time is ... More

Unions of arcs from Fourier partial sumsFeb 03 2010Mar 03 2010Elementary complex analysis and Hilbert space methods show that a union of at most n arcs on the circle is uniquely determined by the nth Fourier partial sum of its characteristic function. The endpoints of the arcs can be recovered from the coefficients ... More

Is it Possible to Accurately Identify a Shooter's Face as Illuminated by the Muzzle Flash of a 22 LR Pistol?Oct 22 2014The science of firearms muzzle flash has been dominated by three perspectives: 1) Does the muzzle flash reveal friendly positions to naked eye observers so as to draw fire from enemy combatants? 2) Can flash signatures be recognized by electronic surveillance ... More

Performance testing of lead free primers: blast waves, velocity variations, and environmental testingOct 23 2014Results are presented for lead free primers based on diazodinitrophenol (DDNP)compared with tests on lead styphnate based primers. First, barrel friction measurements in 5.56 mm NATO are presented. Second, shot to shot variations in blast waves are presented ... More

Terminal Performance of Lead-Free Pistol Bullets in Ballistic Gelatin Using Retarding Force Analysis from High Speed VideoApr 04 2016Due to concerns about environmental and industrial hazards of lead, a number of military, law enforcement, and wildlife management agencies are giving careful consideration to lead-free ammunition. The goal of lead-free bullets is to gain the advantages ... More

Gyroscopic Stability of Open Tipped Match Style Rifle BulletsJan 16 2014Oct 16 2014Earlier work has produced formulas for predicting stability of rifle bullets of near uniform density and also for plastic-tipped rifle bullets. These formulas have been shown to be accurate within 5%. However, the original Miller stability formula for ... More

Aerodynamic Drag and Gyroscopic StabilityAug 15 2013Oct 16 2014This paper describes the effects on aerodynamic drag of rifle bullets as the gyroscopic stability is lowered from 1.3 to 1.0. It is well known that a bullet can tumble for stability less than 1.0. The Sierra Loading Manuals (4th and 5th Editions) have ... More

EI VideosApr 11 2012The Quantitative Reasoning Center (QRC) at USAFA has the institution's primary responsibility for offering after hours extra instruction (EI) in core technical disciplines (mathematics, chemistry, physics, and engineering mechanics). Demand has been tremendous, ... More

Illuminating Fourier Series with AudacityNov 20 2012This paper briefly describes some simple techniques for illuminating Fourier series and Fourier analysis with the Audacity sound recording program. These techniques are easily applied in the classroom and help students move beyond formula roulette in ... More

Studying the Internal Ballistics of a Combustion Driven Potato Cannon using High-speed VideoMay 04 2013A potato cannon was designed to accommodate several different experimental propellants and have a transparent barrel so the movement of the projectile could be recorded on high-speed video (at 2000 frames per second). Both combustion chamber and barrel ... More

Lifting endomorphisms to automorphismsMar 04 2007Mar 13 2007Normal endomorphisms of von Neumann algebras need not be extendable to automorphisms of a larger von Neumann algebra, but they always have asymptotic lifts. We describe the structure of endomorphisms and their asymptotic lifts in some detail, and apply ... More

A Tentative Role for FOXP2 in the Evolution of Dual Processing Modes and Generative AbilitiesAug 11 2014It has been suggested that the origins of cognitive modernity in the Middle/Upper Paleolithic following the appearance of anatomically modern humans was due to the onset of dual processing or contextual focus (CF), the ability to shift between different ... More

Is Carbon Cycling Keeping Pace with Increases in Atmospheric Carbon Dioxide?Dec 20 2018Carbon dioxide (CO2) increase has been well documented, and global net primary production is of importance to a variety of ecological topics. Since CO2 increases primary production in laboratory experiments, the global effects of increasing CO2 on global ... More

Photometric Trends in the Visible Solar Continuum and Their Sensitivity to the Center-to-Limb ProfileFeb 23 2015Jun 25 2015Solar irradiance variations over solar rotational time-scales are largely determined by the passage of magnetic structures across the visible solar disk. Variations on solar cycle time scales are thought to be similarly due to changes in surface magnetism ... More

Small-Network Approximations for Geometrically Frustrated Ising SystemsJul 14 2011The study of frustrated spin systems often requires time-consuming numerical simulations. As the simplest approach, the classical Ising model is often used to investigate the thermodynamic behavior of such systems. Exploiting the small correlation lengths ... More

Generalized network structures: The configuration model and the canonical ensemble of simplicial complexesFeb 12 2016Jun 06 2016Simplicial complexes are generalized network structures able to encode interactions occurring between more than two nodes. Simplicial complexes describe a large variety of complex interacting systems ranging from brain networks, to social and collaboration ... More

Demonstrating an Improved Length-weight Model in Largemouth Bass, Chain Pickerel, Yellow Perch, Black Crappie, and Brown Bullhead in Stilwell Reservoir, West Point, New YorkJul 02 2011The traditional power law model, W(L) = aL^b, is widely applied to describe weight (W) vs. length (L) in fish. The model, W(L) = (L/L1)^b, is proposed as an improvement. The Levenberg-Marquardt non-linear least squares technique is used to determine the ... More

High-speed measurement of firearm primer blast wavesMar 13 2012This article describes a method and results for direct high-speed measurements of firearm primer blast waves employing a high-speed pressure transducer located at the muzzle to record the blast pressure wave produced by primer ignition. Key findings are: ... More

The two-star model: exact solution in the sparse regime and condensation transitionApr 24 2015Apr 28 2015The $2$-star model is the simplest exponential random graph model that displays complex behavior, such as degeneracy and phase transition. Despite its importance, this model has been solved only in the regime of dense connectivity. In this work we solve ... More

Lectures on controlled topology: mapping cylinder neighborhoodsJan 22 2002The existence theorem for mapping cylinder neighborhoods is discussed as a prototypical example of controlled topology and its applications. The first of a projected series developed from lectures at the Summer School on High-Dimensional Topology, Trieste ... More

Representation theory, topological field theory, and the Andrews-Curtis conjectureFeb 13 1992Feb 14 1992We pose a representation-theoretic question motivated by an attempt to resolve the Andrews-Curtis conjecture. Roughly, is there a triangular Hopf algebra with a collection of self-dual irreducible representations $V_i$ so that the product of any two decomposes ... More

Controlled K-theory I: Basic theoryFeb 24 2004Sep 19 2005This paper provides a full controlled version of algebraic $K$-theory. This includes a rich array of assembly maps; the controlled assembly isomorphism theorem identifying the controlled group with homology; and the stability theorem describing the behavior ... More

The triangulation of manifoldsOct 28 2013Nov 12 2013A mostly expository account of old questions about the relationship between polyhedra and topological manifolds. Topics are old topological results, new gauge theory results (with speculations about next directions), and history of the questions.

Derivation of Delay Equation Climate Models Using the Mori-Zwanzig FormalismFeb 08 2019Models incorporating delay have been frequently used to understand climate variability phenomena, but often the delay is introduced through an ad-hoc physical reasoning, such as the propagation time of waves. In this paper, the Mori-Zwanzig formalism ... More

Dual 2-complexes in 4-manifoldsSep 27 2000Concerns decompositions of smooth 4-manifolds as the union of two handlebodies, each with handles of index <=2 (``Heegard'' decompositions).Sample result: Two 2-complexes are (up to 2-deformation) dual spines of a Heegard decomposition of the 4-sphere ... More

Fractions in elementary educationNov 10 2013This paper is one of a series in which elementary-education practice is analyzed by comparison with the history of mathematics, mathematical structure, modern practice, and (occasionally) cognitive neuroscience. The primary concerns are: Why do so many ... More

The CP Puzzle in the Strong InteractionsOct 03 2001This lecture, directed to an broad audience including non-specialists, presents a short review of the problem of strong CP symmetry maintenance. The problem is defined and the possible solutions briefly reviewed. I discuss the way in which Roberto Peccei ... More

The Mid-Pleistocene Transition induced by delayed feedback and bistabilityDec 20 2017The Mid-Pleistocene Transition, the shift from 41 kyr to 100 kyr glacial-interglacial cycles that occurred roughly 1 Myr ago, is often considered as a change in internal climate dynamics. Here we revisit the model of Quaternary climate dynamics that was ... More

Basin bifurcations, oscillatory instability and rate-induced thresholds for AMOC in a global oceanic box modelJan 29 2019The Atlantic Meridional Overturning Circulation (AMOC) transports substantial amounts of heat into the North Atlantic sector, and hence is of very high importance in regional climate projections. The AMOC has been observed to show multi-stability across ... More

Direct Imaging in Reflected Light: Characterization of Older, Temperate Exoplanets With 30-m TelescopesAug 29 2018Direct detection, also known as direct imaging, is a method for discovering and characterizing the atmospheres of planets at intermediate and wide separations. It is the only means of obtaining spectra of non-transiting exoplanets. Characterizing the ... More

A controlled-topology proof of the product structure theoremOct 03 2006The controlled end and h-cobrodism theorems (Ends of maps I, 1979) are used to give quick proofs of the Top/PL and PL/DIFF product structure theorems.

Group categories and their field theoriesNov 08 1998Nov 21 1999A group-category is an additively semisimple category with a monoidal product structure in which the simple objects are invertible. For example in the category of representations of a group, 1-dimensional representations are the invertible simple objects. ... More

B Physics and CP ViolationNov 14 2001These lectures provide a basic overview of topics related to the study of CP Violation in B decays. In the first lecture, I review the basics of discrete symmetries in field theories, the quantum mechanics of neutral but flavor-non-trivial mesons, and ... More

Dual decompositions of 4-manifolds II: linear invariantsSep 20 2001Mar 06 2004This paper continues the study of decompositions of a smooth 4-manifold into two handlebodies with handles of index $\leq2$. Part I gave existence results in terms of spines and chain complexes over the fundamental group of the ambient manifold. Here ... More

Studies of single top quark production at the TevatronJan 19 2011In this paper we present several measurements of single top quark production from the CDF and D0 experiments at the Tevatron. The various analyses utilize integrated luminosity ranging from 2.1 to 4.8 fb -1. The results include the observation of single ... More

Problems on homology manifoldsOct 17 2003Mar 18 2009A list of problems prepared for the proceedings of the Workshop on Exotic Homology Manifolds, Oberwolfach June 29-July 5 2003.

Size Gap for Zero Temperature Black Holes in Semiclassical GravityJun 16 1998We show that a gap exists in the allowed sizes of all zero temperature static spherically symmetric black holes in semiclassical gravity when only conformally invariant fields are present. The result holds for both charged and uncharged black holes. By ... More

Probing condensate order in deep optical latticesNov 17 2008May 02 2009We study interacting bosons in optical lattices in the weak-tunneling regime in systems that exhibit the coexistence of Mott-insulating and condensed phases. We discuss the nature of the condensed ground state in this regime and the validity of the mean-field ... More

The nonsmooth landscape of phase retrievalNov 09 2017Jan 07 2018We consider a popular nonsmooth formulation of the real phase retrieval problem. We show that under standard statistical assumptions, a simple subgradient method converges linearly when initialized within a constant relative distance of an optimal solution. ... More

Fast Bayesian Inference for Exoplanet Discovery in Radial Velocity DataJan 27 2015Inferring the number of planets $N$ in an exoplanetary system from radial velocity (RV) data is a challenging task. Recently, it has become clear that RV data can contain periodic signals due to stellar activity, which can be difficult to distinguish ... More

Constraints on the Geometries of Black Holes in Classical and Semiclassical GravityNov 20 1997Constraints on the geometries of static spherically symmetric black holes are obtained by requiring that the spacetime curvature be analytic at the event horizon. Further constraints are obtained by requiring that the semiclassical trace equation be satisfied ... More

Constraints on Black Holes in Classical and Semiclassical Theories of GravityJul 11 1997Constraints on the geometry of a static spherically symmetric black hole are obtained by requiring the spacetime curvature to be analytic at the event horizon. For a zero temperature black hole further constraints are obtained by also requiring that the ... More

Powder Lot Variations: A Case Study with Varget - Hodgdon ExtremeJan 27 2015Small arms propellant distributor Hodgdon claims that rifle powders in its Extreme line have small velocity variations with both temperature changes and lot number. This paper reports on the variations in average velocity of four different lots of Hodgdon ... More

Finite domination and Novikov rings. Iterative approachAug 15 2011Oct 12 2011Suppose C is a bounded chain complex of finitely generated free modules over the Laurent polynomial ring L = R[x,1/x]. Then C is R-finitely dominated, ie, homotopy equivalent over R to a bounded chain complex of finitely generated projective R-modules, ... More

A Statistical Examination of the Short Term Stability of the Upsilon Andromedae SystemJun 09 2000Because of the high eccentricities (~0.3) of two of the possible planets about the star Upsilon Andromeda, the stability of the system requires careful study. We present results of 1000 numerical simulations which explore the orbital parameter space as ... More

Experimental Tests of the Proportionality of Aerodynamic Drag to Air Density for Supersonic ProjectilesOct 26 2015Pure theory recognizes the dependence of supersonic drag coefficients on both Mach number and Reynolds number, which includes an implicit dependence of drag coefficient on air density. However, many modern approaches to computing trajectories for artillery ... More

Shock Tube Design for High Intensity Blast Waves for Laboratory Testing of Armor and Combat MaterielJan 30 2015Shock tubes create simulated blast waves which can be directed and measured to study blast wave effects under laboratory conditions. It is desirable to increase available peak pressure from ~1 MPa to ~5 MPa to simulate closer blast sources and facilitate ... More

Summary and Outlook for 9th International Symposium on Heavy Flavor PhysicsNov 14 2001This is the summary talk of a meeting held at the California Institute of Technology Sept 10-13, 2001. I do not attempt to summarize all the beautiful experimental results we have seen this week, nor to repeat the lively theoretical discussions that have ... More

``Theoretical mathematics'': Toward a cultural synthesis of mathematics and theoretical physicsJul 01 1993Is speculative mathematics dangerous? Recent interactions between physics and mathematics pose the question with some force: traditional mathematical norms discourage speculation, but it is the fabric of theoretical physics. In practice there can be benefits, ... More

Cusp shapes of Hilbert-Blumenthal surfaces and floor simplicityNov 07 2017Apr 20 2018We introduce a new fundamental domain for the cusp stabilizer of a Hilbert modular group over a real quadratic field K=Q(sqrt n) of class number 1, computed using a Dirichlet domain for the maximal unipotent subgroup. This region is the product of R^+ ... More

Homogeneous BandsNov 29 2016A countable band $B$ is called homogeneous if every isomorphism between finitely generated subbands extends to an automorphism of $B$. In this paper we give a complete classification of all the homogeneous bands. We prove that a homogeneous band belongs ... More

Early Results from APOKASCSep 08 2014Asteroseismology and spectroscopy provide complementary constraints on the fundamental and chemical properties of stars. I describe the first results from APOKASC, a collaboration between the Kepler asteroseismic science consortium (KASC) and the SDSS-III ... More

Critical Pebbling Numbers of GraphsJan 17 2015We define three new pebbling parameters of a connected graph $G$, the $r$-, $g$-, and $u$-critical pebbling numbers. Together with the pebbling number, the optimal pebbling number, the number of vertices $n$ and the diameter $d$ of the graph, this yields ... More

Excited states in Bethe ansatz solvable models and the dressing of spin and chargeNov 23 2012Jun 21 2013A general formalism for the study of excitations above equilibrium in Bethe ansatz solvable models is presented. Nonzero temperature expressions for dressed energy, momentum, spin and charge are obtained, and it is found that the dressed spin and charge ... More

Fragmentation of protoplanetary disks around M-dwarfsJul 23 2016We investigate the conditions required for planet formation via gravitational instability (GI) and protoplanetary disk (PPD) fragmentation around M-dwarfs. Using a suite of 64 SPH simulations with $10^6$ particles, the parameter space of disk mass, temperature, ... More

Homogeneity of Inverse SemigroupsJun 03 2017Aug 11 2017An inverse semigroup $S$ is a semigroup in which every element has a unique inverse in the sense of semigroup theory, that is, if $a \in S$ then there exists a unique $b\in S$ such that $a = aba$ and $b = bab$. We say that an inverse semigroup $S$ is ... More

Comparing Measured Fluorocarbon Leader Breaking Strength with Manufacturer ClaimsFeb 23 2012The experiment reported in this article addresses manufacturer claims of fluorocarbon leader material strength versus experimental tests of leaders strength. Breaking strength of fishing line is the most common specification when marketing fishing line. ... More

Counting odd numbers in truncations of Pascal's triangleJul 21 2018Jul 26 2018A "truncation" of Pascal's triangle is a triangular array of numbers that satisfies the usual Pascal recurrence but with a boundary condition that declares some terminal set of numbers along each row of the array to be zero. Presented here is a family ... More

Subgradient methods for sharp weakly convex functionsMar 06 2018Subgradient methods converge linearly on a convex function that grows sharply away from its solution set. In this work, we show that the same is true for sharp functions that are only weakly convex, provided that the subgradient methods are initialized ... More

Methods for Accurate Free Flight Measurement of Drag CoefficientsMar 18 2015This paper describes experimental methods for free flight measurement of drag coefficients to an accuracy of approximately 1%. There are two main methods of determining free flight drag coefficients, or equivalent ballistic coefficients: 1) measuring ... More

A $55 Shock Tube for Simulated Blast WavesFeb 21 2015Shock tubes are commonly employed to test candidate armor materials, validate numerical models, and conduct simulated blast experiments in animal models. As DoD interests desire to field wearable sensors as blast dosimeters, shock tubes may also serve ... More

Permutation Group Symmetry and CorrelationsJun 11 2013Correlation factors are constructed that are consistent with the permutation symmetry group of N Fermions at given value of the filling factor.

Into the third dimension: stochastic measurements of Stokes parameters within the Poincaré sphereOct 05 2014Inspired by recent use of polarimetry to study the Cosmic Microwave Background and extragalatic supernovae, a foray into the statistical properties of Stokes parameters expressed in spherical coordinates is began, allowing circular polarization and linear ... More

Triple cascade behaviour in QG and drift turbulence and generation of zonal jetsMay 08 2009We study quasi-geostrophic turbulence and plasma drift turbulence within the Charney-Hasegawa-Mima (CHM) model. We focus, theoretically and using numerical simulations, on conservation of {\em zonostrophy} and on its role in the formation of the zonal ... More

Hubbard-Shastry lattice modelsNov 22 2011Feb 24 2012We consider two lattice models for strongly correlated electrons which are exactly-solvable in one dimension. Along with the Hubbard model and the su(2|2) spin chain, these are the only parity-invariant models that can be obtained from Shastry's R-matrix. ... More

Spin Observables in Antilambda-Lambda Production from Antiproton-Proton Annihilation with a Transverse Inital State PolarizationAug 04 2000The formalism describing the scattering of two spin-1/2 objects is reviewed for the case of antilambda-lambda production from antiproton-proton annihilation. It is shown that an experiment utilizing a transverse target polarization can, in principle, ... More

Bayesian analysis of polarization measurementsFeb 01 2012A detailed and formal account of polarization measurements using Bayesian analysis is given based on the assumption of gaussian error for the Stokes parameters. This analysis is crucial for the measurement of the polarization degree and angle at very ... More

Response to comments on ``Theoretical mathematics''Apr 01 1994The authors discuss various objections and rejoinders in the collected responses [math.HO/9404229,math.HO/9404236] to their original article on the relationship between mathematics and theoretical physics [math.HO/9307227].

Finite domination and Novikov rings. Laurent polynomial rings in two variablesNov 21 2012May 19 2013Let C be a bounded cochain complex of finitely generated free modules over the Laurent polynomial ring L = R[x,1/x,y,1/y]. The complex C is called R-finitely dominated if it is homotopy equivalent over R to a bounded complex of finitely generated projective ... More

Finite domination and Novikov rings. Laurent polynomial rings in several variablesOct 16 2014We present a homological characterisation of those chain complexes of modules over a Laurent polynomial ring in several indeterminates which are finitely dominated over the ground ring (that is, are a retract up to homotopy of a bounded complex of finitely ... More

The (In)Stability of Planetary SystemsJan 09 2004We present results of numerical simulations which examine the dynamical stability of known planetary systems, a star with two or more planets. First we vary the initial conditions of each system based on observational data. We then determine regions of ... More

A TESS Dress Rehearsal: Planetary Candidates and Variables from K2 Campaign 17Jun 08 2018We produce light curves for all ~34,000 targets observed with K2 in Campaign 17 (C17), identifying 34 planet candidates, 184 eclipsing binaries, and 222 other periodic variables. The location of the C17 field means follow-up can begin immediately now ... More

Errors in Length-weight Parameters at FishBase.orgApr 27 2011To investigate possible errors, length-weight parameters from FishBase.org were used to graph length-weight curves for six different species: channel catfish, black crappie, largemouth bass, rainbow trout, flathead catfish, and lake trout along with the ... More

Seasonal Variations in Relative Weight of Lake Trout (Salvelinus namaycush), Kokanee Salmon (Oncorhynchus nerka), Rainbow Trout (Onocorhynchus mykiss), and Brown Trout (Salmo trutta) in Blue Mesa Reservoir, ColoradoJun 15 2013Blue Mesa Reservoir is the largest body of water in Colorado and is located on the western slope of the Rocky Mountains at an elevation of 7520 feet. Blue Mesa Reservoir contains recreationally important populations of lake trout (Salvelinus namaycush), ... More

Orbispaces and their Mapping Spaces via Groupoids: A Categorical ApproachJan 20 2014In this paper, we give an accessible introduction to the theory of orbispaces via groupoids. We define a certain class of topological groupoids, which we call orbigroupoids. Each orbigroupoid represents an orbispace, but just as with orbifolds and Lie ... More

The cone of Betti diagrams over a hypersurface ring of low embedding dimensionSep 23 2011Feb 20 2012We give a complete description of the cone of Betti diagrams over a standard graded hypersurface ring of the form k[x,y]/<q>, where q is a homogeneous quadric. We also provide a finite algorithm for decomposing Betti diagrams, including diagrams of infinite ... More

Reassessing the Source of Long-Period CometsDec 09 2009We present numerical simulations to model the production of observable long-period comets (LPCs) from the Oort Cloud, a vast reservoir of icy bodies surrounding the Sun. We show that inner Oort Cloud objects can penetrate Jupiter's orbit via a largely ... More

Spin excitation spectra of integral and fractional quantum Hall systemsSep 28 2001Results are presented of detailed numerical calculations for the spin excitation spectra of a two-dimensional electron gas confined in a quantum well of finite width w, at magnetic fields corresponding to the fractional and integral fillings of the lowest ... More

Composite Fermions and the Fractional Quantum Hall Effect: Essential Role of the PseudopotentialMay 21 1999The mean field (MF) composite Fermion (CF) picture successfully predicts the band of low lying angular momentum multiplets of fractional quantum Hall systems for any value of the magnetic field. This success cannot be attributed to a cancellation between ... More

The Formation of the Oort Cloud in Open Cluster EnvironmentsJul 31 2007Apr 02 2008We study the influence of an open cluster environment on the formation and current structure of the Oort cloud. To do this, we have run 19 different simulations of the formation of the Oort Cloud for 4.5 Gyrs. In each simulation, the solar system spends ... More

Weighted norm inequalities of (1,q)-type for integral and fractional maximal operatorsJun 13 2016We study weighted norm inequalities of $(1,q)$- type for $0<q<1$, $\Vert \mathbf{G} \nu \Vert_{L^q(\Omega, d \sigma)} \le C \, \Vert \nu \Vert, \quad \text{for all positive measures $\nu$ in $\Omega$},$ along with their weak-type counterparts, where $\Vert ... More

Quasiparticle Interactions in Fractional Quantum Hall Systems: Justification of Different Hierarchy SchemesAug 21 1999The pseudopotentials describing the interactions of quasiparticles in fractional quantum Hall (FQH) states are studied. Rules for the identification of incompressible quantum fluid ground states are found, based upon the form of the pseudopotentials. ... More

Composite Fermions and the Fractional Quantum Hall EffectMay 18 1999The mean field (MF) composite Fermion (CF) picture successfully predicts low lying states of fractional quantum Hall systems. This success cannot be attributed to a cancellation between Coulomb and Chern-Simons interactions beyond the mean field and solely ... More

Landau level mixing in the nu=5/2 fractional quantum Hall stateSep 28 2006The nu=5/2 fractional quantum Hall state is studied numerically, directly including the effects of electron scattering between neighboring Landau levels. Significant reduction of the excitation gap caused by the LL mixing explains the discrepancy between ... More

Excitonic complexes in quantum Hall systemsAug 20 2003The formation and various possible decay processes of neutral and charged excitonic complexes in electronic integral and fractional quantum Hall systems are discussed. The excitonic complexes are bound states of a small number of the relevant negatively ... More

Hund's Rule for Monopole Harmonics, or Why the Composite Fermion Picture WorksOct 07 1998The success of the mean field composite Fermion (MFCF) picture in predicting the lowest energy band of angular momentum multiplets in fractional quantum Hall systems cannot be found in a cancellation between the Coulomb and Chern--Simons interactions ... More

Chern-Simons Theory with Finite Gauge GroupNov 03 1991Dec 18 1992These theories, which are surely some of the simplest possible quantum field theories, were introduced in a paper of Dijkgraaf and Witten. The path integral reduces to a finite sum, so it is quite amenable to direct mathematical study. Although the theory ... More

Three-body correlations and finite-size effects in the Moore--Read states on a sphereJul 16 2004Two- and three-body correlations in partially filled degenerate fermion shells are studied numerically for various interactions between the particles. Three distinct correlation regimes are defined, depending on the short-range behavior of the pair pseudopotential. ... More

Spin instabilities and quantum phase transitions in integral and fractional quantum Hall statesNov 28 2001The inter-Landau-level spin excitations of quantum Hall states at filling factors nu=2 and 4/3 are investigated by exact numerical diagonalization for the situation in which the cyclotron (hbar*omega_c) and Zeeman (E_Z) splittings are comparable. The ... More

Electron correlations in a partially filled first excited Landau levelJun 01 2001The form of electron correlations in a partially filled degenerate Landau level (LL) is related to the behavior of the anharmonic part of the interaction pseudopotential. Unlike in the lowest LL, the pseudopotential in the first excited LL is harmonic ... More

Novel excitonic states in quantum Hall systems: Bound states of spin waves and a valence band holeJun 21 2002If the Zeeman energy is small, the lowest energy excitations of a two dimensional electron gas at filling factor nu=1 are spin waves (spin flip excitations). At nu slightly larger (smaller) than unity, reversed spin electrons (spin holes) can form bound ... More