Results for "G. Laughlin"

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The Minimum-Mass Extrasolar Nebula: In-Situ Formation of Close-In Super-EarthsNov 07 2012Mar 06 2013Close-in super-Earths, with radii R = 2-5 R_Earth and orbital periods P < 100 days, orbit more than half, and perhaps nearly all Sun-like stars in the universe. We use this omnipresent population to construct the minimum-mass extrasolar nebula (MMEN), ... More
Combining Kepler and HARPS Occurrence Rates to Infer the Period-Mass-Radius Distribution of Super-Earths/Sub-NeptunesAug 30 2011The ongoing High Accuracy Radial velocity Planet Search (HARPS) has found that 30-50% of GK dwarfs in the solar neighborhood host planets with sub-Neptune masses in orbits of P < 50 days. At first glance, this overall occurrence rate seems inconsistent ... More
Evidence for Quasiparticle Decay in Photoemission from Underdoped CupratesAug 15 1996Feb 17 1998I argue that the ``gap'' recently observed at the Brillouin zone face of cuprate superconductors in photoemission by Marshall et al [Phys. Rev. Lett. 76, 4841 (1996)] and Ding et al [Nature 382, 54 (1996)] is evidence for the decay of the injected hole ... More
Hydrodynamic Simulations of Unevenly Irradiated Jovian PlanetsNov 14 2007We employ a two-dimensional grid-based hydrodynamic model to simulate upper atmospheric dynamics on extrasolar giant planets. Our model is well-suited to simulate the dynamics of the atmospheres of planets with high orbital eccentricity that are subject ... More
Gossamer SuperconductivitySep 11 2002An new superconducting hamiltonian is introduced for which the exact ground state is the Anderson resonating valence bond. It differs from the t-J and hubbard hamiltonians in possessing a powerful attractive force. Its superconducting state is characterized ... More
Magnetic Induction of d + i d Order in High-Tc SuperconductorsAug 31 1997I propose that the phase transition in Bi2Sr2CaCu2O8 recently observed by by Krishana et al [Science 277, 83 (1997)] is the development of a small d-xy superconducting order parameter phased by pi/2 with respect to the principal d-(x2-y2) one to produce ... More
Are Proxima and Alpha Centauri Gravitationally Bound?Jul 17 2006Using the most recent kinematic and radial velocity data in the literature, we calculate the binding energy of Proxima Centauri relative to the center of mass of the Alpha Centauri system. When we adopt the centroids of the observed data, we find that ... More
The Feasibility and Benefits of In Situ Exploration of `Oumuamua-like objectsMar 19 2018Apr 11 2018A rapid accumulation of observations and interpretation have followed in the wake of 1I `Oumuamua's passage through the inner Solar System. We briefly outline the consequences that this first detection of an interstellar asteroid implies for the planet-forming ... More
Possible Stellar Metallicity Enhancements from the Accretion of PlanetsOct 10 1997A number of recently discovered extrasolar planet candidates have surprisingly small orbits, which may indicate that considerable orbital migration takes place in protoplanetary systems. A natural consequence of orbital migration is for a series of planets ... More
A Dying Universe: The Long Term Fate and Evolution of Astrophysical ObjectsJan 18 1997This paper outlines astrophysical issues related to the long term fate of the universe. We consider the evolution of planets, stars, stellar populations, galaxies, and the universe itself over time scales which greatly exceed the current age of the universe. ... More
Relativistic Effects in Extrasolar Planetary SystemsNov 28 2006This paper considers general relativistic (GR) effects in currently observed extrasolar planetary systems. Although GR corrections are small, they can compete with secular interactions in these systems and thereby play an important role. Specifically, ... More
Implications of White Dwarf Galactic HalosFeb 01 1996Motivated by recent measurements which suggest that roughly half the mass of the galactic halo may be in the form of white dwarfs, we study the implications of such a halo. We first use current limits on the infrared background light and the galactic ... More
GAMer 2: A System for 3D Mesh Processing of Cellular Electron MicrographsJan 29 2019Jul 23 2019Recent advances in electron microscopy have, for the first time, enabled imaging of single cells in 3D at a nanometer length scale resolution. An uncharted frontier for in silico biology is the ability to simulate cellular processes using these observed ... More
Branch, Spur, and Feather Formation in Spiral GalaxiesJun 23 2003We use hydrodynamical simulations to investigate the response of geometrically thin, self-gravitating, singular isothermal disks of gas to imposed rigidly rotating spiral potentials. By minimizing reflection-induced feedback from boundaries, and by restricting ... More
Core-Accretion Model Predicts Few Jovian-Mass Planets Orbiting Red DwarfsJul 15 2004The favored theoretical explanation for giant planet formation -- in both our solar system and others -- is the core accretion model (although it still has some serious difficulties). In this scenario, planetesimals accumulate to build up planetary cores, ... More
Evidence for composite nature of quasiparticles in the 2D t-J modelMay 19 1995It is shown that the dynamics of a single hole in a quantum antiferromagnet (described by the t--J model) can be simply understood in terms of a composite quasiparticle. This description provides naturally two different energy scales t and J corresponding ... More
Differential light scattering: probing the sonoluminescence collapseDec 09 1999We have developed a light scattering technique based on differential measurement and polarization (differential light scattering, DLS) capable in principle of retrieving timing information with picosecond resolution without the need for fast electronics. ... More
On the Formation of Brown DwarfsOct 27 2006The observational properties of brown dwarfs pose challenges to the theory of star formation. Because their mass is much smaller than the typical Jeans mass of interstellar clouds, brown dwarfs are most likely formed through secondary fragmentation processes, ... More
On the Anomalous Acceleration of 1I/2017 U1 `OumuamuaMar 12 2019We show that the $P\sim8\,{\rm h}$ photometric period and the astrometrically measured $A_{\rm ng}\sim2.5\times10^{-4}\,{\rm cm\,s^{-2}}$ non-gravitational acceleration (at $r\sim1.4\,{\rm AU}$) of the interstellar object 1I/2017 (`Oumuamua) can be explained ... More
Quantum Phase Transitions and the Breakdown of Classical General RelativityDec 25 2000It is proposed that the event horizon of a black hole is a quantum phase transition of the vacuum of space-time analogous to the liquid-vapor critical point of a bose fluid. The equations of classical general relativity remain valid arbitrarily close ... More
Singular Isothermal Disks and the Formation of Multiple StarsDec 01 2000A crucial missing ingredient in previous theoretical studies of fragmentation is the inclusion of dynamically important levels of magnetic fields. As a minimal model for a candidate presursor to the formation of binary and multiple stars, we therefore ... More
Shear-Induced Nitric Oxide Production by Endothelial CellsMay 19 2016We present a biochemical model of the wall shear stress (WSS)-induced activation of endothelial nitric oxide synthase (eNOS) in an endothelial cell (EC). The model includes three key mechanotransducers: mechanosensing ion channels, integrins and G-protein-coupled ... More
Astronomical engineering: a strategy for modifying planetary orbitsFeb 07 2001The Sun's gradual brightening will seriously compromise the Earth's biosphere within ~ 1E9 years. If Earth's orbit migrates outward, however, the biosphere could remain intact over the entire main-sequence lifetime of the Sun. In this paper, we explore ... More
On the Radii of Extrasolar Giant PlanetsMar 24 2003We have computed evolutionary models for extrasolar planets which range in mass from 0.1 to 3.0 Jovian Masses, and which range in equilibrium temperature from 113 K to 2000 K. We present four sequences of models, designed to show the structural effects ... More
One-loop Quantum Gravity in Schwarzschild SpacetimeDec 23 1994The quantum theory of linearized perturbations of the gravitational field of a Schwarzschild black hole is presented. The fundamental operators are seen to be the perturbed Weyl scalars $\dot\Psi_0$ and $\dot\Psi_4$ associated with the Newman-Penrose ... More
Self-similar champagne flows in HII regionsSep 02 2002(Abridged) We consider the expansion of an initially self-gravitating, static, singular, isothermal cloud core. For t>0, the gas is ionized and heated to a higher uniform temperature by the formation of a luminous, but massless, star in its center. The ... More
On the Formation of Brown DwarfsSep 19 2003The observational properties of brown dwarfs pose challenges to the theory of star formation. Because their mass is much smaller than the typical Jeans mass of interstellar clouds, brown dwarfs are most likely formed through secondary fragmentation processes, ... More
Photoevaporation of Circumstellar Disks due to External FUV Radiation in Stellar AggregatesApr 20 2004When stars form in small groups (N = 100 - 500 members), their circumstellar disks are exposed to little EUV radiation but a great deal of FUV radiation from massive stars in the group. This paper calculates mass loss rates for circumstellar disks exposed ... More
Magnetic Instability in Strongly Correlated SuperconductorsMar 03 2003Recently a new phenomenological Hamiltonian has been proposed to describe the superconducting cuprates. This so-called Gossamer Hamiltonian is an apt model for a superconductor with strong on-site Coulomb repulsion betweenthe electrons. It is shown that ... More
Mining the Metal-Rich Stars for PlanetsAug 15 2000We examine the correlation between stellar metallicity and short period planets. It appears that approximately 1% of dwarf stars in the solar neighborhood harbor short-period planets characterized by near-circular orbits and orbital periods P<20 days. ... More
Darwin Tames an Andromeda Dwarf: Unraveling the Orbit of NGC 205 Using a Genetic AlgorithmApr 04 2008NGC 205, a close satellite of the M31 galaxy, is our nearest example of a dwarf elliptical galaxy. Photometric and kinematic observations suggest that NGC 205 is undergoing tidal distortion from its interaction with M31. Despite earlier attempts, the ... More
The GJ 876 Planetary System -- A Progress ReportJul 21 2004We present an updated analysis of the GJ 876 planetary system based on an augmented data set that incorporates 65 new high-precision radial velocities obtained with the Keck telescope from 2001 to 2004. These new radial velocities permit a more accurate ... More
Extrasolar Trojans: The Viability and Detectability of Planets in the 1:1 ResonanceApr 04 2002We explore the possibility that extrasolar planets might be found in the 1:1 mean-motion resonance. There are a variety of stable co-orbtial configurations, and we specifically examine three different versions of the 1:1 resonance. These include tadpole ... More
Obliquity Tides May Drive WASP-12b's Rapid Orbital DecayDec 04 2018Dec 10 2018Recent analyses have revealed a mystery. The orbital period of the highly inflated hot Jupiter, WASP-12b, is decreasing rapidly. The rate of inspiral, however, is too fast to be explained by either eccentricity tides or equilibrium stellar tides. While ... More
Polynomial Solutions to Pell's Equation and Fundamental Units in Real Quadratic FieldsDec 27 2018Finding polynomial solutions to Pell's equation is of interest as such solutions sometimes allow the fundamental units to be determined in an infinite class of real quadratic fields. In this paper, for each triple of positive integers $(c,h,f)$ satisfying ... More
On the Consequences of the Detection of an Interstellar AsteroidNov 07 2017The arrival of the robustly hyperbolic asteroid A/2017 U1 has potentially interesting ramifications for the planet-formation process. Although extrapolations from a sample size of one are necessarily uncertain, order-of-magnitude estimates suggest that ... More
Multi-variable Polynomial Solutions to Pell's Equation and Fundamental Units in Real Quadratic FieldsJan 31 2000Jan 01 2019For each positive integer $n$ it is shown how to construct a finite collection of multivariable polynomials $\{F_{i}:=F_{i}(t,X_{1},..., X_{\lfloor \frac{n+1}{2} \rfloor})\}$ such that each positive integer whose squareroot has a continued fraction expansion ... More
Some Observations on Lambert series, vanishing coefficients and dissections of infinite products and seriesJun 27 2019Andrews and Bressoud, Alladi and Gordon, and others, have proven, in a number of papers, that the coefficients in various arithmetic progressions in the series expansions of certain infinite $q$-products vanish. In the present paper it is shown that these ... More
A Scientometric Prediction of the Discovery of the First Potentially Habitable Planet with a Mass Similar to EarthSep 12 2010The search for a habitable extrasolar planet has long interested scientists, but only recently have the tools become available to search for such planets. In the past decades, the number of known extrasolar planets has ballooned into the hundreds, and ... More
An Improved uvby-Metallicity Calibration for Metal-Rich StarsJul 01 2002We present an improved uvby-metallicity relation calibrated for F, G, and early K dwarfs, and an analogous uvby-T(eff) relation, both derived using a Levenberg-Marquardt minimization scheme. Our calibrations are based on 1533 stars which appear in both ... More
Supervised Learning Detection of Sixty Non-Transiting Hot Jupiter CandidatesJun 20 2017The optical, full-phase photometric variations of a short-period planet provide a unique view of the planet's atmospheric composition and dynamics. The number of planets with optical phase curve detections, however, is currently too small to study them ... More
Obliquity-Driven Sculpting of Exoplanetary SystemsMar 04 2019NASA's Kepler mission revealed that $\sim 30\%$ of Solar-type stars harbor planets with sizes between that of Earth and Neptune on nearly circular and co-planar orbits with periods less than 100 days. Such short-period compact systems are rarely found ... More
Combinatorial Identities Deriving From The $N$-th Power Of A $2\Times 2$ MatrixDec 28 2018In this paper we give a new formula for the $n$-th power of a $2\times2$ matrix. More precisely, we prove the following: Let $A= \left ( \begin{matrix} a & b \\ c & d \end{matrix} \right )$ be an arbitrary $2\times2$ matrix, $T=a+d$ its trace, $D= ad-bc$ ... More
Mock Theta Function Identities Deriving from Bilateral Basic Hypergeometric SeriesJun 27 2019The bilateral series corresponding to many of the third-, fifth-, sixth- and eighth order mock theta functions may be derived as special cases of $_2\psi_2$ series \[ \sum_{n=-\infty}^{\infty}\frac{(a,c;q)_n}{(b,d;q)_n}z^n. \] Three transformation formulae ... More
Symmetry and Specializability in the continued fraction expansions of some infinite productsFeb 27 2004Let $f(x) \in \mathbb{Z}[x]$. Set $f_{0}(x) = x$ and, for $n \geq 1$, define $f_{n}(x)$ $=$ $f(f_{n-1}(x))$. We describe several infinite families of polynomials for which the infinite product \prod_{n=0}^{\infty} (1 + \frac{1}{f_{n}(x)}) has a \emph{specializable} ... More
Parallels Between Quantum Antiferromagnetism and the Strong InteractionsFeb 17 1998I argue that there is a connection between quantum antiferromagnetism and the strong interactions. The underlying idea is that the t-J Hamiltonian and other models commonly studied in the context of cuprate superconductivity are near a quantum critical ... More
Hartree-Fock Computation of the High-Tc Cuprate Phase DiagramJun 22 2013Jan 18 2014A computation of the cuprate phase diagram is presented. Adiabatic deformability back to the density function band structure is assumed. Symmetry constraints lead to a fermi liquid theory with 5 interaction parameters. Two of these are forced to zero ... More
Tunneling Gap as Evidence for Time-Reversal Symmetry Breaking at Surfaces of High-Temperature SuperconductorsJul 31 1994It is argued that recent Josephson junction and point-contact tunneling experiments, interpreted as intended by their authors, indicate that time-reversal symmetry breaking occurs at surfaces of cuprate superconductors. The variation among experiments ... More
Systemic: A Testbed for Characterizing the Detection of Extrasolar Planets. II. Numerical approaches to the Transit Timing Inverse ProblemMay 28 2010Transit timing variations - deviations from strict periodicity between successive passages of a transiting planet - can be used to probe the structure and dynamics of multiple-planet systems. In this paper, we examine prospects for numerically solving ... More
On the Dynamical Stability of the Solar SystemApr 11 2008A long-term numerical integration of the classical Newtonian approximation to the planetary orbital motions of the full Solar System (sun + 8 planets), spanning 20 Gyr, was performed. The results showed no severe instability arising over this time interval. ... More
Parity considerations in the expansion of Fermat-Pell polynomialsJan 31 2000For each positive integer $n$ it is shown how to construct a finite collection of multivariable polynomials $\{F_{i}:=F_{i}(t,X_{1},..., X_{\lfloor \frac{n+1}{2} \rfloor})\}$ such that each positive integer whose squareroot has a continued fraction expansion ... More
Jupiter's Decisive Role in the Inner Solar System's Early EvolutionMar 24 2015Mar 31 2015The statistics of extrasolar planetary systems indicate that the default mode of planet formation generates planets with orbital periods shorter than 100 days, and masses substantially exceeding that of the Earth. When viewed in this context, the Solar ... More
Constraints on Planet Nine's Orbit and Sky Position within a Framework of Mean Motion ResonancesDec 22 2016A number of authors have proposed that the statistically significant orbital alignment of the most distant Kuiper Belt Objects (KBOs) is evidence of an as-yet undetected planet in the outer solar system, now referred to colloquially a "Planet Nine". Dynamical ... More
An Identity Motivated by an Amazing Identity of RamanujanJan 04 2019Ramanujan stated an identity to the effect that if three sequences $\{a_n\}$, $\{b_n\}$ and $\{c_n\}$ are defined by $r_1(x)=:\sum_{n=0}^{\infty}a_nx^n$, $r_2(x)=:\sum_{n=0}^{\infty}b_nx^n$ and $r_3(x)=:\sum_{n=0}^{\infty}c_nx^n$ (here each $r_i(x)$ is ... More
Some new Families of Tasoevian- and Hurwitzian Continued FractionsJan 04 2019We derive closed-form expressions for several new classes of Hurwitzian- and Tasoevian continued fractions, including $[0;\overline{p-1,1,u(a+2nb)-1,p-1,1,v(a+(2n+1)b)-1 }\,\,]_{n=0}^\infty$, $[0; \overline{c + d m^{n}}]_{n=1}^{\infty}$ and $[0; \overline{e ... More
An Open Source Mesh Generation Platform for Biophysical Modeling Using Realistic Cellular GeometriesSep 10 2019Advances in imaging methods such as electron microscopy, tomography and other modalities are enabling high-resolution reconstructions of cellular and organelle geometries. Such advances pave the way for using these geometries for biophysical and mathematical ... More
Critical Waves and the Length Problem of BiologyApr 17 2015It is pointed out that the mystery of how biological systems measure their lengths vanishes away if one premises that they have discovered a way to generate linear waves analogous to compressional sound. These can be used to detect length at either large ... More
Hiawatha's Valence BondingAug 14 2004There is increasing circumstantial evidence that the cuprate superconductors, and correlated-electron materials generally, defy simple materials categorization because of their proximity to one or more continuous zero-temperature phase transitions. This ... More
Emergent RelativityFeb 09 2003Feb 27 2003A possible resolution of the incompatibility of quantum mechanics and general relativity is that the relativity principle is emergent. I show that the central paradox of black holes also occurs at a liquid-vapor critical surface of a bose condensate but ... More
Observational Consequences of Hydrodynamic Flows on Hot JupitersFeb 27 2007We use a grid-based shallow water model to simulate the atmospheric dynamics of the transiting hot Jupiter HD 209458b. Under the usual assumption that the planet is in synchronous rotation with zero obliquity, a steady state is reached with a well-localized ... More
The Case for a Large-Scale Occultation NetworkMay 15 2019We discuss the feasibility of and present initial designs and approximate cost estimates for a large ($N\sim2000$) network of small photometric telescopes that is purpose-built to monitor $V \lesssim 15$ Gaia Mission program stars for occultations by ... More
A Vorticity-Preserving Hydrodynamical Scheme for Modeling Accretion Disk FlowsSep 20 2017Vortices, turbulence, and unsteady non-laminar flows are likely both prominent and dynamically important features of astrophysical disks. Such strongly nonlinear phenomena are often difficult, however, to simulate accurately, and are generally amenable ... More
The Case for a Large-Scale Occultation NetworkMay 15 2019May 17 2019We discuss the feasibility of and present initial designs and approximate cost estimates for a large ($N\sim2000$) network of small photometric telescopes that is purpose-built to monitor $V \lesssim 15$ Gaia Mission program stars for occultations by ... More
Refinements of Some Partition InequalitiesJan 06 2019In the present paper we initiate the study of a certain kind of partition inequality, by showing, for example, that if $M\geq 5$ is an integer and the integers $a$ and $b$ are relatively prime to $M$ and satisfy $1\leq a<b<M/2$, and the $c(m,n)$ are defined ... More
Small Prime Powers in the Fibonacci SequenceOct 15 2001Feb 16 2002It is shown that there are no non-trivial fifth-, seventh-, eleventh-, thirteenth- or seventeenth powers in the Fibonacci sequence. For eleventh, thirteenth- and seventeenth powers an alternative (to the usual exhaustive check of products of powers of ... More
The N2K Consortium. VII. Atmospheric Parameters of 1907 Metal-Rich Stars: Finding Planet-Search TargetsJan 22 2007We report high-precision atmospheric parameters for 1907 stars in the N2K low-resolution spectroscopic survey, designed to identify metal-rich FGK dwarfs likely to harbor detectable planets. 284 of these stars are in the ideal temperature range for planet ... More
A Critique of Two MetalsSep 17 1997Feb 08 1998I argue that the conflict between the fermi-liquid and non-fermi-liquid metallic states viewed by Anderson as the central intellectual issue of cuprate superconductivity, and which motivates the recent criticism by Baskaran and Anderson [cond-mat/9706076] ... More
Resolving the Sin(I) degeneracy in Low-Mass Multi-Planet SystemsFeb 01 2011Long-term orbital evolution of multi-planet systems under tidal dissipation often converges to a stationary state, known as the tidal fixed point. The fixed point is characterized by a lack of oscillations in the eccentricities and apsidal alignment among ... More
A New Atmospheric Model for HD 189733 bAug 22 2008We have developed a new two-dimensional hydrostatically-balanced isobaric hydrodynamic model for use in simulation of exoplanetary atmospheres. We apply this model to the infrared photosphere of the hot Jupiter HD 189733 b, for which an excellent 8-micron ... More
The potential impact of groove modes on Type II planetary migrationApr 22 2008In this letter, we briefly describe the evolution of a variety of self-gravitating protoplanetary disk models that contain annular grooves (e.g. gaps) in their surface density. These grooves are inspired by the density gaps that are presumed to open in ... More
Formation and Detection of Earth Mass Planets around Low Mass StarsMar 13 2009We investigate an in-situ formation scenario for Earth-mass terrestrial planets in short-period, potentially habitable orbits around low-mass stars (M_star < 0.3 M_sun). We then investigate the feasibility of detecting these Earth-sized planets. Our simulations ... More
Some new Transformations for Bailey pairs and WP-Bailey PairsJan 05 2019We derive several new transformations relating WP-Bailey pairs. We also consider the corresponding transformations relating standard Bailey pairs, and as a consequence, derive some quite general expansions for products of theta functions which can also ... More
General Multi-sum Transformations and Some ImplicationsJan 06 2019We give two general transformations that allows certain quite general basic hypergeometric multi-sums of arbitrary depth (sums that involve an arbitrary sequence $\{g(k)\}$), to be reduced to an infinite $q$-product times a single basic hypergeometric ... More
Further Results on Vanishing Coefficients in Infinite Product ExpansionsJan 06 2019We extend results of Andrews and Bressoud on the vanishing of coefficients in the series expansions of certain infinite products. These results have the form that if \begin{equation*} \frac{(q^{r-tk}, q^{mk-(r-tk)}; q^{mk})_\infty}{(q^r,q^{mk-r}; q^{mk})_\infty} ... More
A New Summation Formula for WP-Bailey PairsJan 05 2019Let $(\alpha_n(a,k),\beta_n(a,k))$ be a WP-Bailey pair. Assuming the limits exist, let \[ (\alpha_n^*(a),\beta_n^*(a))_{n\geq 1} = \lim_{k \to 1}\left(\alpha_n(a,k),\frac{\beta_n(a,k)}{1-k}\right)_{n\geq 1} \] be the \emph{derived} WP-Bailey pair. By ... More
A ~ 7.5 Earth-Mass Planet Orbiting the Nearby Star, GJ 876Oct 18 2005Oct 18 2005High precision, high cadence radial velocity monitoring over the past 8 years at the W. M. Keck Observatory reveals evidence for a third planet orbiting the nearby (4.69 pc) dM4 star GJ 876. The residuals of three-body Newtonian fits, which include GJ ... More
Planet Formation Around M-dwarfs: From Young Disks to PlanetsJan 10 2011Cool M dwarfs outnumber sun-like G stars by ten to one in the solar neighborhood. Due to their proximity, small size, and low mass, M-dwarf stars are becoming attractive targets for exoplanet searches via almost all current search methods. But what planetary ... More
HD 17156b: A Transiting Planet with a 21.2 Day Period and an Eccentric OrbitOct 03 2007Oct 20 2007We report the detection of transits by the 3.1 M_Jup companion to the V=8.17 G0V star HD 17156. The transit was observed by three independant observers on Sept. 9/10, 2007 (two in central Italy and one in the Canary Islands), who obtained detections at ... More
Long Term Evolution of Close Planets Including the Effects of Secular InteractionsJun 14 2006This paper studies the long term evolution of planetary systems containing short-period planets, including the effects of tidal circularization, secular excitation of eccentricity by companion planets, and stellar damping. For planetary systems subject ... More
Effects of Secular Interactions in Extrasolar Planetary SystemsJun 14 2006This paper studies the effects of dynamical interactions among the planets in observed extrasolar planetary systems, including hypothetical additional bodies, with a focus on secular perturbations. These interactions cause the eccentricities of the planets ... More
Migration and Dynamical Relaxation in Crowded Systems of Giant PlanetsJan 28 2003This paper explores the intermediate-time dynamics of newly formed solar systems with a focus on possible mechanisms for planetary migration. We consider two limiting corners of the available parameter space -- crowded systems containing N=10 giant planets ... More
Some more identities of the Rogers-Ramanujan typeJul 07 2006Jul 08 2006In this we paper we prove several new identities of the Rogers-Ramanujan type. These identities were found as the result of a computer search. The proofs involve a variety of techniques, including constant-term methods, a theorem of Watson on basic hypergeometric ... More
The Convergence and Divergence of $q$-Continued Fractions outside the Unit CircleDec 28 2018We consider two classes of $q$-continued fraction whose odd and even parts are limit 1-periodic for $|q|>1$, and give theorems which guarantee the convergence of the continued fraction, or of its odd- and even parts, at points outside the unit circle. ... More
A Physically-Motivated Photometric Calibration of M Dwarf MetallicityJun 14 2010The location of M dwarfs in the V-K_s--M_Ks color-magnitude diagram (CMD) has been shown to correlate with metallicity. We demonstrate that previous empirical photometric calibrations of M dwarf metallicity exploiting this correlation systematically underestimate ... More
Short-Term Dynamical Interactions Among Extrasolar PlanetsJan 23 2001Mar 27 2001We show that short-term perturbations among massive planets in multiple planet systems can result in radial velocity variations of the central star which differ substantially from velocity variations derived assuming the planets are executing independent ... More
Reassessing Exoplanet Light Curves with a Thermal ModelMay 10 2018We present a uniform assessment of existing near-infrared Spitzer Space Telescope observations of planet-bearing stars. Using a simple four-parameter blackbody thermal model, we analyze stars for which photometry in at least one of Spitzer's IRAC bands ... More
Some more Long Continued Fractions, IJan 03 2019In this paper we show how to construct several infinite families of polynomials $D(\bar{x},k)$, such that $\sqrt{D(\bar{x},k)}$ has a regular continued fraction expansion with arbitrarily long period, the length of this period being controlled by the ... More
Polynomial Continued FractionsDec 19 2018Continued fractions whose elements are polynomial sequences have been carefully studied mostly in the cases where the degree of the numerator polynomial is less than or equal to two and the degree of the denominator polynomial is less than or equal to ... More
A Reciprocity Relation for WP-Bailey PairsJan 06 2019We derive a new general transformation for WP-Bailey pairs by considering the a certain limiting case of a WP-Bailey chain previously found by the authors, and examine several consequences of this new transformation. These consequences include new summation ... More
Powers of a matrix and combinatorial identitiesDec 29 2018In this article we obtain a general polynomial identity in $k$ variables, where $k\geq 2$ is an arbitrary positive integer. We use this identity to give a closed-form expression for the entries of the powers of a $k \times k$ matrix. Finally, we use these ... More
Discovery and Characterization of Transiting SuperEarths Using an All-Sky Transit Survey and Follow-up by the James Webb Space TelescopeMar 27 2009Aug 03 2009Doppler and transit surveys are finding extrasolar planets of ever smaller mass and radius, and are now sampling the domain of superEarths (1-3 Earth radii). Recent results from the Doppler surveys suggest that discovery of a transiting superEarth in ... More
The Hunt for Planet Nine: Atmosphere, Spectra, Evolution, and DetectabilityApr 25 2016Jun 06 2016We investigate the physical characteristics of the Solar System's proposed Planet Nine using modeling tools with a heritage in studying Uranus and Neptune. For a range of plausible masses and interior structures, we find upper limits on the intrinsic ... More
Exoplanetary Geophysics -- An Emerging DisciplineJan 22 2015Thousands of extrasolar planets have been discovered, and it is clear that the galactic planetary census draws on a diversity greatly exceeding that exhibited by the solar system's planets. We review significant landmarks in the chronology of extrasolar ... More
A Hardy-Ramanujan-Rademacher-type formula for $(r,s)$-regular partitionsJan 05 2019Let $p_{r,s}(n)$ denote the number of partitions of a positive integer $n$ into parts containing no multiples of $r$ or $s$, where $r>1$ and $s>1$ are square-free, relatively prime integers. We use classical methods to derive a Hardy-Ramanujan-Rademacher-type ... More
Some properties of the distribution of the numbers of points on elliptic curves over a finite prime fieldJan 03 2019Let $p \geq 5$ be a prime and for $a, b \in \mathbb{F}_{p}$, let $E_{a,b}$ denote the elliptic curve over $\mathbb{F}_{p}$ with equation $y^2=x^3+a\,x + b$. As usual define the trace of Frobenius $a_{p,\,a,\,b}$ by \begin{equation*} \#E_{a,b}(\mathbb{F}_{p}) ... More
Asymptotics and Sequential Closures of Continued Fractions and GeneralizationsSep 12 2007Jan 09 2009Given a sequence of complex square matrices, $a_n$, consider the sequence of their partial products, defined by $p_n=p_{n-1}a_{n}$. What can be said about the asymptotics as $n\to\infty$ of the sequence $f(p_n)$, where $f$ is a continuous function? A ... More
Continued Fractions with Multiple LimitsMar 01 2004Apr 05 2004For integers $m \geq 2$, we study divergent continued fractions whose numerators and denominators in each of the $m$ arithmetic progressions modulo $m$ converge. Special cases give, among other things, an infinite sequence of divergence theorems, the ... More
On the Divergence in the General Sense of $q$-Continued Fraction on the Unit CircleDec 28 2018We show, for each $q$-continued fraction $G(q)$ in a certain class of continued fractions, that there is an uncountable set of points on the unit circle at which $G(q)$ diverges in the general sense. This class includes the Rogers-Ramanujan continued ... More
Some Observations on Khovanskii's Matrix Methods for extracting Roots of PolynomialsJan 03 2019In this article we apply a formula for the $n$-th power of a $3\times 3$ matrix (found previously by the authors) to investigate a procedure of Khovanskii's for finding the cube root of a positive integer. We show, for each positive integer $\alpha$, ... More
General WP-Bailey ChainsJan 05 2019Motivated by a recent paper of Liu and Ma, we describe a number of general WP-Bailey chains. We show that many of the existing WP-Bailey chains (or branches of the WP-Bailey tree), including chains found by Andrews, Warnaar and Liu and Ma, arise as special ... More