A sharper threshold for bootstrap percolation in two dimensions

Two-dimensional bootstrap percolation is a cellular automaton in which sites become 'infected' by contact with two or more already infected nearest neighbors. We consider these dynamics, which can be interpreted as a monotone version of the Ising model, on an n x n square, with sites initially infected independently with probability p. The critical probability p_c is the smallest p for which the probability that the entire square is eventually infected exceeds 1/2. Holroyd determined the sharp first-order approximation: p_c \sim \pi^2/(18 log n) as n \to \infty. Here we sharpen this result, proving that the second term in the expansion is -(log n)^{-3/2+ o(1)}, and moreover determining it up to a poly(log log n)-factor. The exponent -3/2 corrects numerical predictions from the physics literature.Comment: 21 page

Swashplate feedback control for tilt-rotor aircraft

Changes in angle of attack in system were sensed indirectly by gages which responded to strains induced in wing structure. Output signals were amplified, filtered, and used to activate swashplate actuators. System provided significant reduction in blade loads and desirable changes in hub forces and moments

Collective diffusion in sheared colloidal suspensions

Collective diffusivity in a suspension of rigid particles in steady linear viscous flows is evaluated by investigating the dynamics of the time correlation of long-wavelength density fluctuations. In the absence of hydrodynamic interactions between suspended particles in a dilute suspension of identical hard spheres, closed-form asymptotic expressions for the collective diffusivity are derived in the limits of low and high Péclet numbers, where the Péclet number Pe = gamma-dot a^2/D0 with gamma-dot being the shear rate and D0 = kB T/6πη a is the Stokes–Einstein diffusion coefficient of an isolated sphere of radius a in a fluid of viscosity η. The effect of hydrodynamic interactions is studied in the analytically tractable case of weakly sheared (Pe « 1) suspensions. For strongly sheared suspensions, i.e. at high Pe, in the absence of hydrodynamics the collective diffusivity Dc = 6 Ds∞, where Ds∞ is the long-time self-diffusivity and both scale as φ gamma-dot a^2$, where φ is the particle volume fraction. For weakly sheared suspensions it is shown that the leading dependence of collective diffusivity on the imposed flow is proportional to D0 φPe Ê, where Ê is the rate-of-strain tensor scaled by gamma-dot, regardless of whether particles interact hydrodynamically. When hydrodynamic interactions are considered, however, correlations of hydrodynamic velocity fluctuations yield a weakly singular logarithmic dependence of the cross-gradient-diffusivity on k at leading order as ak → 0 with k being the wavenumber of the density fluctuation. The diagonal components of the collective diffusivity tensor, both with and without hydrodynamic interactions, are of O(φPe2), quadratic in the imposed flow, and finite at k = 0. At moderate particle volume fractions, 0.10 ≤ φ ≤ 0.35, Brownian Dynamics (BD) numerical simulations in which there are no hydrodynamic interactions are performed and the transverse collective diffusivity in simple shear flow is determined via time evolution of the dynamic structure factor. The BD simulation results compare well with the derived asymptotic estimates. A comparison of the high-Pe BD simulation results with available experimental data on collective diffusivity in non-Brownian sheared suspensions shows a good qualitative agreement, though hydrodynamic interactions prove to be important at moderate concentrations

Length of Marriage as a Factor in Marital Satisfaction, Communication, and Performance on the Prisoner\u27s Dilemma Game

[No abstract provided.

Fuel for Wildfire: Controls on the Distribution of Wildfire in the Southeastern United States

Ecologists and wildlife managers alike have explored the role of fire as an ecosystem disturbance for decades and, yet, the role of scale remains poorly understood in pyrogeography. Understanding how wildfire occurs on the landscape and, furthermore, how these trends will change in the future provides an enhanced understanding of vegetative patterns, successional changes and biome distributions. As scientific research begins to account for the effects of climate change, predictive modeling will remain one of the foremost tools in understanding how present-day trends will begin to change. This study employs a series of spatial modeling techniques to examine which factors are most influential on the presence of wildfire hotspots on the landscape and which factors may be influential on areas devoid of wildfire occurrence entirely. Clustering algorithms were used to identify wildfire hotspots across the study area and targeted pseudo-absence points were created outside the bounds of these clusters. The resulting presence/absence points were analyzed within physiographic regions and a predictive model was fit to the data. Analysis of common covariates, such as climatic variables, land use, and topography allowed this study to not just fit a model to wildfire distribution, but inform comparable studies conducted anywhere similar data are available. As different aspects of climate change begin to exert influence on ecosystems globally, this study sheds light on how fire regimes may change with it

Fuel for Wildfire: Controls on the Distribution of Wildfire in the Southeastern United States

Ecologists and wildlife managers alike have explored the role of fire as an ecosystem disturbance for decades and, yet, the role of scale remains poorly understood in pyrogeography. Understanding how wildfire occurs on the landscape and, furthermore, how these trends will change in the future provides an enhanced understanding of vegetative patterns, successional changes and biome distributions. As scientific research begins to account for the effects of climate change, predictive modeling will remain one of the foremost tools in understanding how present-day trends will begin to change. This study employs a series of spatial modeling techniques to examine which factors are most influential on the presence of wildfire hotspots on the landscape and which factors may be influential on areas devoid of wildfire occurrence entirely. Clustering algorithms were used to identify wildfire hotspots across the study area and targeted pseudo-absence points were created outside the bounds of these clusters. The resulting presence/absence points were analyzed within physiographic regions and a predictive model was fit to the data. Analysis of common covariates, such as climatic variables, land use, and topography allowed this study to not just fit a model to wildfire distribution, but inform comparable studies conducted anywhere similar data are available. As different aspects of climate change begin to exert influence on ecosystems globally, this study sheds light on how fire regimes may change with it

Design and Preliminary Testing of Demand-Responsive Transverse Rumble Strips

Transverse rumble strips are common practice to alert drivers by engaging their auditory and tactile senses in addition to visual senses by traffic signals. However, continuous exposure to noise and vibration by transverse rumble strips often results in diminished effectiveness and erratic behaviors, leading to additional safety challenges. In response, demand-responsive transverse rumble strips were developed as traffic safety countermeasures that reduce unnecessary noise and vibration associated with transverse rumble strips by incorporating active control of the rumble strips. Rather than staying static, demand-responsive transverse rumble strips are activated based on the presence of pedestrians, at predesignated times, or in response to abrupt changes in traffic flow. To evaluate the effectiveness of demand-responsive transverse rumble strips, the research team assessed noise and vibration data, both inside the vehicles and on the roadside, for various types of vehicles traveling at different speeds. The test data indicate that demand-responsive transverse rumble strips produced noticeable in-vehicle noise and vibration that could alert drivers to downstream events. Furthermore, demand-responsive transverse rumble strips generated sufficient noise to alert roadside pedestrians to vehicle presence but at low enough level to be considered as acceptable for a residential neighborhood use. Accordingly, demand-responsive transverse rumble strips could address the challenges that static transverse rumble strips face, by providing a design with relatively limited noise while enhancing safety

Full Three Dimensional Orbits For Multiple Stars on Close Approaches to the Central Supermassive Black Hole

With the advent of adaptive optics on the W. M. Keck 10 m telescope, two significant steps forward have been taken in building the case for a supermassive black hole at the center of the Milky Way and understanding the black hole's effect on its environment. Using adaptive optics and speckle imaging to study the motions of stars in the plane of sky with +-~2 mas precision over the past 7 years, we have obtained the first simultaneous orbital solution for multiple stars. Among the included stars, three are newly identified (S0-16, S0-19, S0-20). The most dramatic orbit is that of the newly identified star S0-16, which passed a mere 60 AU from the central dark mass at a velocity of 9,000 km/s in 1999. The orbital analysis results in a new central dark mass estimate of 3.6(+-0.4)x10^6(D/8kpc)^3 Mo. This dramatically strengthens the case for a black hole at the center of our Galaxy, by confining the dark matter to within a radius of 0.0003 pc or 1,000 Rsh and thereby increasing the inferred dark mass density by four orders of magnitude compared to earlier estimates. With the introduction of an adaptive-optics-fed spectrometer, we have obtained the spectra of these high-velocity stars, which suggest that they are massive (~15 Mo), young (<10 Myr) main sequence stars. This presents a major challenge to star formation theories, given the strong tidal forces that prevail over all distances reached by these stars in their current orbits and the difficulty in migrating these stars inward during their lifetime from further out where tidal forces should no longer preclude star formation.Comment: 7 pages, 5 figures (abridged abstract