Detecting the Dusty Debris of Terrestrial Planet Formation

We use a multiannulus accretion code to investigate debris disks in the terrestrial zone, at 0.7-1.3 AU around a 1 solar mass star. Terrestrial planet formation produces a bright dusty ring of debris with a lifetime of at least 1 Myr. The early phases of terrestrial planet formation are observable with current facilities; the late stages require more advanced instruments with adaptive optics.Comment: 11 pages of text, 3 figures, accepted for ApJ Letters, additional info at http://cfa-www.harvard.edu/~kenyon/pf/terra/td

A note on dimer models and McKay quivers

We give one formulation of an algorithm of Hanany and Vegh which takes a lattice polygon as an input and produces a set of isoradial dimer models. We study the case of lattice triangles in detail and discuss the relation with coamoebas following Feng, He, Kennaway and Vafa.Comment: 25 pages, 35 figures. v3:completely rewritte

Tighter Relations Between Sensitivity and Other Complexity Measures

Sensitivity conjecture is a longstanding and fundamental open problem in the area of complexity measures of Boolean functions and decision tree complexity. The conjecture postulates that the maximum sensitivity of a Boolean function is polynomially related to other major complexity measures. Despite much attention to the problem and major advances in analysis of Boolean functions in the past decade, the problem remains wide open with no positive result toward the conjecture since the work of Kenyon and Kutin from 2004. In this work, we present new upper bounds for various complexity measures in terms of sensitivity improving the bounds provided by Kenyon and Kutin. Specifically, we show that deg(f)^{1-o(1)}=O(2^{s(f)}) and C(f) < 2^{s(f)-1} s(f); these in turn imply various corollaries regarding the relation between sensitivity and other complexity measures, such as block sensitivity, via known results. The gap between sensitivity and other complexity measures remains exponential but these results are the first improvement for this difficult problem that has been achieved in a decade.Comment: This is the merged form of arXiv submission 1306.4466 with another work. Appeared in ICALP 2014, 14 page

Discrete complex analysis on planar quad-graphs

We develop a linear theory of discrete complex analysis on general quad-graphs, continuing and extending previous work of Duffin, Mercat, Kenyon, Chelkak and Smirnov on discrete complex analysis on rhombic quad-graphs. Our approach based on the medial graph yields more instructive proofs of discrete analogs of several classical theorems and even new results. We provide discrete counterparts of fundamental concepts in complex analysis such as holomorphic functions, derivatives, the Laplacian, and exterior calculus. Also, we discuss discrete versions of important basic theorems such as Green's identities and Cauchy's integral formulae. For the first time, we discretize Green's first identity and Cauchy's integral formula for the derivative of a holomorphic function. In this paper, we focus on planar quad-graphs, but we would like to mention that many notions and theorems can be adapted to discrete Riemann surfaces in a straightforward way. In the case of planar parallelogram-graphs with bounded interior angles and bounded ratio of side lengths, we construct a discrete Green's function and discrete Cauchy's kernels with asymptotics comparable to the smooth case. Further restricting to the integer lattice of a two-dimensional skew coordinate system yields appropriate discrete Cauchy's integral formulae for higher order derivatives.Comment: 49 pages, 8 figure

Correlated radial velocity and X-ray variations in HD 154791/4U 1700+24

We present evidence for approximately 400-d variations in the radial velocity of HD 154791 (V934 Her), the suggested optical counterpart of 4U 1700+24. The variations are correlated with the previously reported approximately 400 d variations in the X-ray flux of 4U 1700+24, which supports the association of these two objects, as well as the identification of this system as the second known X-ray binary in which a neutron star accretes from the wind of a red giant. The HD 154791 radial velocity variations can be fit with an eccentric orbit with period 404 +/- 3 d, amplitude K=0.75 +/- 0.12 km/s and eccentricity e=0.26 +/- 0.15. There are also indications of variations on longer time scales >~ 2000 d. We have re-examined all available ASM data following an unusually large X-ray outburst in 1997-98, and confirm that the 1-d averaged 2-10 keV X-ray flux from 4U 1700+24 is modulated with a period of 400 +/- 20 d. The mean profile of the persistent X-ray variations was approximately sinusoidal, with an amplitude of 0.108 +/- 0.012 ASM count/s (corresponding to 31% rms). The epoch of X-ray maximum was approximately 40 d after the time of periastron according to the eccentric orbital fit. If the 400 d oscillations from HD 154791/4U 1700+24 are due to orbital motion, then the system parameters are probably close to those of the only other neutron-star symbiotic-like binary, GX 1+4. We discuss the similarities and differences between these two systems.Comment: 6 pages, 2 figures; accepted by Ap

Collisional Cascades in Planetesimal Disks II. Embedded Planets

We use a multiannulus planetesimal accretion code to investigate the growth of icy planets in the outer regions of a planetesimal disk. In a quiescent minimum mass solar nebula, icy planets grow to sizes of 1000--3000 km on a timescale t = 15-20 Myr (a/30 AU)^3 where a is the distance from the central star. Planets form faster in more massive nebulae. Newly-formed planets stir up leftover planetesimals along their orbits and produce a collisional cascade where icy planetesimals are slowly ground to dust. The dusty debris of planet formation has physical characteristics similar to those observed in beta Pic, HR 4796A, and other debris disks. We derive dust masses for small particles, 1 mm and smaller, and large particles, 1 mm and larger, as a function of the initial conditions in the planetesimal disk. The dust luminosities derived from these masses are similar to those observed in Vega, HR 4796A, and other debris disks. The calculations produce bright rings and dark gaps. Bright rings occur where 1000 km and larger planets have recently formed. Dark gaps are regions where planets have cleared out dust or shadows where planets have yet to form.Comment: to be published in the Astronomical Journal, January 2004; 7 pages of text; 17 figures at http://cfa-www.harvard.edu/~kenyon/pf/emb-planet-figures.pdf; 2 animations at http://cfa-www.harvard.edu/~kenyon/pf/emb-planet-movies.htm

A Hybrid N-body--Coagulation Code for Planet Formation

We describe a hybrid algorithm to calculate the formation of planets from an initial ensemble of planetesimals. The algorithm uses a coagulation code to treat the growth of planetesimals into oligarchs and explicit N-body calculations to follow the evolution of oligarchs into planets. To validate the N-body portion of the algorithm, we use a battery of tests in planetary dynamics. Several complete calculations of terrestrial planet formation with the hybrid code yield good agreement with previously published calculations. These results demonstrate that the hybrid code provides an accurate treatment of the evolution of planetesimals into planets.Comment: Astronomical Journal, accepted; 33 pages + 11 figure

M.I.T./Canadian Vestibular Experiments on the Spacelab-1 Mission. Part 1: Sensory Adaptation to Weightlessness and Readaptation to One-G: An Overview

Experiments on human spatial orientation were conducted on four crewmembers of Space Shuttle Spacelab Mission 1. The conceptual background of the project, the relationship among the experiments, and their relevance to a 'sensory reinterpretation hypothesis' are presented. Detailed experiment procedures and results are presented in the accompanying papers in this series. The overall findings are discussed as they pertain to the following aspects of hypothesized sensory reinterpretation in weightlessness: (1) utricular otolith afferent signals are reinterpreted as indicating head translation rather than tilt, (2) sensitivity of reflex responses to footward acceleration is reduced, and (3) increased weighting is given to visual and tactile cues in orientation perception and posture control. Results suggest increased weighting of visual cues and reduced weighting of graviceptor signals in weightlessness

The statistics of the photometric accuracy based on MASS data and the evaluation of high-altitude wind

The effect of stellar scintillation on the accuracy of photometric measurements is analyzed. We obtain a convenient form of estimaton of this effect in the long exposure regime, when the turbulence shift produced by the wind is much larger than the aperture of the telescope. A simple method is proposed to determine index $S_3$ introduced by perture of the Kenyon et al. (2006), directly from the measurements with the Multi Aperture Scintillation Sensor (MASS) without information on vertical profile of the wind. The statistics $S_3$ resulting from our campaign of 2005 -- 2007 at Maidanak observatory is presented. It is shown that these data can be used to estimate high-altitude winds at pressure level 70 -- 100 mbar. Comparison with the wind speed retrieved from the NCEP/NCAR global models shows a good agreement. Some prospects for retrieval of the wind speed profile from the MASS measurements are outlined.Comment: 11 pages, 9 figures, accepted for publication in Astronomy Letter

Static deformation of heavy spring due to gravity and centrifugal force

The static equilibrium deformation of a heavy spring due to its own weight is calculated for two cases. First for a spring hanging in a constant gravitational field, then for a spring which is at rest in a rotating system where it is stretched by the centrifugal force. Two different models are considered. First a discrete model assuming a finite number of point masses connected by springs of negligible weight. Then the continuum limit of this model. In the second case the differential equation for the deformation is obtained by demanding that the potential energy is minimized. In this way a simple application of the variational calculus is obtained.Comment: 11 pages, 2 figure