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

The Formation of Zinc Ferrite from Zinc Sulfate and Ferric Oxide

Samples of zinc sulfate and ferric oxide were roasted for periods of one, two and three hours at temperatures between 750° and 1000°C. The per cent zinc oxide combined, as zinc ferrite, was determined by dissolving the soluble zinc in a ammonium-ammonia chloride solution. Six samples were roasted at 750°C to determine the degree of decomposition of zinc sulfate to zinc oxide and sulfur trioxide

Feature Films of World War II and Vietnam

My original topic was entitled «Feature Films of World War II and Vietnam,» but I noticed that most presentations and papers in this conference focus on World War II, so I will say justa few words about World War II, and place my emphasis on Vietnam

Operating characteristics of ground-water reservoirs occupying a trench

CER61MMS-75.Presented at the annual meeting of the American Association for the Advancement of Science, December 30, 1961, Denver, Colorado.Includes bibliographical references.Sediment filled valleys of intermittent streams can be used as underground reservoirs for storage of water. Water so stored is not subject to evaporation losses and the seepage losses may be small. Recharge and operational characteristics of such reservoirs are expressed in formula form. Some comments are made in regard to the problems of water quality maintenance

Preliminary Survey of Retrograde Velocities Required for Insertion Into Low-Altitude Lunar Orbits

Closed lunar orbits are envisaged in lunar mission programs. The study described herein was undertaken to obtain an appreciation of the relevant fuel consumption requirements. The retrograde impulses necessary for establishing the orbits were assumed to occur at the point of closest approach of the main earth-moon trajectory; this point, designated as the arrival position, was restricted to a lunar altitude of 5,000 nautical miles or less. The orientation of the arrival position vector relevant to any coplanar radius vector is not constrained, however, and similarly the scalar value of the arrival velocity is unrestrained. Since the arrival altitude is restricted to 5,000 nautical miles or less, the perturbing accelerations of the earth and sun are sufficiently small that the vehicle and moon essentially comprise an isolated two-body system; this is discussed in the report. Retrograde velocities are determined for any required pericynthion position. If the pericynthion orientation requirement is relaxed then a smaller retrograde velocity is in some cases possible. A comparison between minimum retrograde velocities and retrograde velocities necessary for stipulated pericynthion positions is given. Arrival velocities are correlated with feasible earth departure conditions. The equations developed for determining retrograde velocities for desired pericynthion positions are considered useful for estimating essential data for the preliminary planning of lunar missions. Some graphical representation is included herein for immediate familiarization with possible conditions

Biological treatment of the knee with platelet-rich plasma or bone marrow aspirate concentrates

ABSTRACT — Knee pathologies including focal cartilage injuries, osteoarthritis (OA), and ligament injuries are common. The poor regeneration and healing potential of cartilage has led to the search for other treatment modalities with improved healing capacity. Furthermore, with an increasing elderly population that desires to remain active, the burden of knee pathologies is expected to increase. Increased sports participation and the desire to return to activities faster is also demanding more effective and minimally invasive treatment options. Thus, the use of biologic agents in the treatment of knee pathologies has emerged as a potential option. Despite the increasing use of biologic agents for knee pathology, there are conflicting results on the efficacy of these products. Furthermore, strong data supporting the optimal preparation methods and composition for widely used biologic agents, such as platelet-rich plasma (PRP) and bone marrow aspirate concentrate (BMAC), largely remain absent from the literature. This review presents the literature on the most commonly employed biologic agents for the different knee pathologies

Zinc Department Anaconda Reduction Works

The electrolytic zinc department of the Anaconda Reduction Works consists of five divisions, each responsible for one phase in the preparation of electrolytic zinc. These divisions are: (1) The zinc concentrator which produces a high-zinc, low-lead concentrate for further treatment at Anaconda, and a low-zinc, high-lead concentrate which is shipped to East Helena for further treatment. (2) The roasting division wherein the concentrate is roasted to oxides and sulfates. (3) The leaching division which (a) leaches the roasted concentrate to dissolve the zinc, and (b) purifies the leached solution. (4) The electrolytic division which produces pure zinc cathodes by electrowinning from the leach solution, and (5) The casting division wherein the zinc cathodes are remelted and cast into commercial shapes for sale

Maine’s State Parks: Their Value to Visitors and Contribution to the State Economy

Maine’s state parks are important to the social and economic well-being of the state, and provide public access to a variety of outdoor activities. In the study reported here, the authors find that visitors have a high level of satisfaction in Maine’s day-use parks, campgrounds and historic sites. Moreover, the overall impact of visitor-related park spending exceeds $30 million in income and 1,449 jobs annually. Nonetheless, the majority of Maine’s state parks suffer from long-deferred maintenance and are in immediate need of major capital improvements if they are to continue their vital role in supporting tourism and outdoor recreation