Jamming Criticality Revealed by Removing Localized Buckling Excitations

Recent theoretical advances offer an exact, first-principle theory of jamming criticality in infinite dimension as well as universal scaling relations between critical exponents in all dimensions. For packings of frictionless spheres near the jamming transition, these advances predict that nontrivial power-law exponents characterize the critical distribution of (i) small inter-particle gaps and (ii) weak contact forces, both of which are crucial for mechanical stability. The scaling of the inter-particle gaps is known to be constant in all spatial dimensions $d$ -- including the physically relevant $d=2$ and 3, but the value of the weak force exponent remains the object of debate and confusion. Here, we resolve this ambiguity by numerical simulations. We construct isostatic jammed packings with extremely high accuracy, and introduce a simple criterion to separate the contribution of particles that give rise to localized buckling excitations, i.e., bucklers, from the others. This analysis reveals the remarkable dimensional robustness of mean-field marginality and its associated criticality.Comment: 12 pages, 4 figure

Weak Convergence in the Prokhorov Metric of Methods for Stochastic Differential Equations

We consider the weak convergence of numerical methods for stochastic differential equations (SDEs). Weak convergence is usually expressed in terms of the convergence of expected values of test functions of the trajectories. Here we present an alternative formulation of weak convergence in terms of the well-known Prokhorov metric on spaces of random variables. For a general class of methods, we establish bounds on the rates of convergence in terms of the Prokhorov metric. In doing so, we revisit the original proofs of weak convergence and show explicitly how the bounds on the error depend on the smoothness of the test functions. As an application of our result, we use the Strassen - Dudley theorem to show that the numerical approximation and the true solution to the system of SDEs can be re-embedded in a probability space in such a way that the method converges there in a strong sense. One corollary of this last result is that the method converges in the Wasserstein distance, another metric on spaces of random variables. Another corollary establishes rates of convergence for expected values of test functions assuming only local Lipschitz continuity. We conclude with a review of the existing results for pathwise convergence of weakly converging methods and the corresponding strong results available under re-embedding.Comment: 12 pages, 2nd revision for IMA J Numerical Analysis. Further minor errors correcte

Out-of-equilibrium dynamical fluctuations in glassy systems

In this paper we extend the earlier treatment of out-of-equilibrium mesoscopic fluctuations in glassy systems in several significant ways. First, via extensive simulations, we demonstrate that models of glassy behavior without quenched disorder display scalings of the probability of local two-time correlators that are qualitatively similar to that of models with short-ranged quenched interactions. The key ingredient for such scaling properties is shown to be the development of a critical-like dynamical correlation length, and not other microscopic details. This robust data collapse may be described in terms of a time-evolving Gumbel-like distribution. We develop a theory to describe both the form and evolution of these distributions based on a effective sigma-model approach.Comment: 20 pages, RevTex, 9 figure

Assembly of hard spheres in a cylinder: a computational and experimental study

Hard spheres are an important benchmark of our understanding of natural and synthetic systems. In this work, colloidal experiments and Monte Carlo simulations examine the equilibrium and out-of-equilibrium assembly of hard spheres of diameter $\sigma$ within cylinders of diameter $\sigma\leq D\leq 2.82\sigma$. Although in such a system phase transitions formally do not exist, marked structural crossovers are observed. In simulations, we find that the resulting pressure-diameter structural diagram echoes the densest packing sequence obtained at infinite pressure in this range of $D$. We also observe that the out-of-equilibrium self-assembly depends on the compression rate. Slow compression approximates equilibrium results, while fast compression can skip intermediate structures. Crossovers for which no continuous line-slip exists are found to be dynamically unfavorable, which is the source of this difference. Results from colloidal sedimentation experiments at high P\'eclet number are found to be consistent with the results of fast compressions, as long as appropriate boundary conditions are used. The similitude between compression and sedimentation results suggests that the assembly pathway does not here sensitively depend on the nature of the out-of-equilibrium dynamics.Comment: 11 pages, 8 figures and 63 reference

The ABC\u27s of Building Information Partnerships: Factors for Success in Building Active and Engaged Partnerships

Building strong information partnerships is an essential first step to effective information literacy programs and services. The overall goal of this paper is to highlight several factors that are especially useful for establishing productive relationships with a range of potential partners including students, faculty, and other campus or community partners. Five key factors for success will be discussed to help guide the development of active and engaged partnerships

Hubble Space Telescope times-series photometry of the planetary transit of HD189733: no moon, no rings, starspots

We monitored three transits of the giant gas planet around the nearby K dwarf HD 189733 with the ACS camera on the Hubble Space Telescope. The resulting very-high accuracy lightcurve (signal-to-noise ratio near 15000 on individual measurements, 35000 on 10-minute averages) allows a direct geometric measurement of the orbital inclination, radius ratio and scale of the system: i = 85.68 +- 0.04, Rpl/R*=0.1572 +- 0.0004, a/R*=8.92 +- 0.09. We derive improved values for the stellar and planetary radius, R*=0.755+- 0.011 Rsol, Rpl=1.154 +- 0.017 RJ, and the transit ephemerides, Ttr=2453931.12048 +- 0.00002 + n 2.218581 +- 0.000002$. The HST data also reveal clear evidence of the planet occulting spots on the surface of the star. At least one large spot complex (>80000 km) is required to explain the observed flux residuals and their colour evolution. This feature is compatible in amplitude and phase with the variability observed simultaneously from the ground. No evidence for satellites or rings around HD 189733b is seen in the HST lightcurve. This allows us to exlude with a high probability the presence of Earth-sized moons and Saturn-type debris rings around this planet. The timing of the three transits sampled is stable to the level of a few seconds, excluding a massive second planet in outer 2:1 resonance.Comment: revised version. Significant updates and new figures; to appear in Astronomy and Astrophysic

The Spitzer search for the transits of HARPS low-mass planets - I. No transit for the super-Earth HD 40307b

We have used Spitzer and its IRAC camera to search for the transit of the super-Earth HD 40307b. The transiting nature of the planet could not be firmly discarded from our first photometric monitoring of a transit window because of the uncertainty coming from the modeling of the photometric baseline. To obtain a firm result, two more transit windows were observed and a global Bayesian analysis of the three IRAC time series and the HARPS radial velocities was performed. Unfortunately, any transit of the planet during the observed phase window is firmly discarded, while the probability that the planet transits but that the eclipse was missed by our observations is nearly negligible (0.26%).Comment: Submitted to A&

Hard sphere crystallization gets rarer with increasing dimension

We recently found that crystallization of monodisperse hard spheres from the bulk fluid faces a much higher free energy barrier in four than in three dimensions at equivalent supersaturation, due to the increased geometrical frustration between the simplex-based fluid order and the crystal [J.A. van Meel, D. Frenkel, and P. Charbonneau, Phys. Rev. E 79, 030201(R) (2009)]. Here, we analyze the microscopic contributions to the fluid-crystal interfacial free energy to understand how the barrier to crystallization changes with dimension. We find the barrier to grow with dimension and we identify the role of polydispersity in preventing crystal formation. The increased fluid stability allows us to study the jamming behavior in four, five, and six dimensions and compare our observations with two recent theories [C. Song, P. Wang, and H. A. Makse, Nature 453, 629 (2008); G. Parisi and F. Zamponi, Rev. Mod. Phys, in press (2009)].Comment: 15 pages, 5 figure

Studying the atmosphere of the exoplanet HAT-P-7b via secondary eclipse measurements with EPOXI, Spitzer and Kepler

The highly irradiated transiting exoplanet, HAT-P-7b, currently provides one of the best opportunities for studying planetary emission in the optical and infrared wavelengths. We observe six near-consecutive secondary eclipses of HAT-P-7b at optical wavelengths with the EPOXI spacecraft. We place an upper limit on the relative eclipse depth of 0.055% (95% confidence). We also analyze Spitzer observations of the same target in the infrared, obtaining secondary eclipse depths of 0.098+/-0.017%, 0.159+/-0.022%, 0.245+/-0.031% and 0.225+/-0.052% in the 3.6, 4.5, 5.8 and 8.0 micron IRAC bands respectively. We combine these measurements with the recently published Kepler secondary eclipse measurement, and generate atmospheric models for the day-side of the planet that are consistent with both the optical and infrared measurements. The data are best fit by models with a temperature inversion, as expected from the high incident flux. The models predict a low optical albedo of ~< 0.13, with subsolar abundances of Na, K, TiO and VO. We also find that the best fitting models predict that 10% of the absorbed stellar flux is redistributed to the night side of the planet, which is qualitatively consistent with the inefficient day-night redistribution apparent in the Kepler phase curve. Models without thermal inversions fit the data only at the 1.25 sigma level, and also require an overabundance of methane, which is not expected in the very hot atmosphere of HAT-P-7b. We also analyze the eight transits of HAT-P-7b present in the EPOXI dataset and improve the constraints on the system parameters, finding a period of P = 2.2047308+/-0.0000025 days, a stellar radius of R* = 1.824+/-0.089Rsun, a planetary radius of Rp = 1.342+/-0.068RJup and an inclination of i = 85.7+3.5-2.2 deg.Comment: 21 pages, 8 figures, accepted by the Astrophysical Journa