Conway's subprime Fibonacci sequences

It's the age-old recurrence with a twist: sum the last two terms and if the result is composite, divide by its smallest prime divisor to get the next term (e.g., 0, 1, 1, 2, 3, 5, 4, 3, 7, ...). These sequences exhibit pseudo-random behaviour and generally terminate in a handful of cycles, properties reminiscent of 3x+1 and related sequences. We examine the elementary properties of these 'subprime' Fibonacci sequences.Comment: 18 pages, 5 figure

A method to predict the soil susceptibility to compaction of surface layers as a function of water content and bulk density

International audienceIdentifying the vulnerability of soils to compaction damage becomes an increasingly important issue in the planning and execution of farming operations. Soil compaction models are efficient tools for predicting soil compaction due to agricultural field traffic. Most of these models require the knowledge of the stress/strain relationship, as well as the mechanical parameters and their variation with different soil physical properties. Because the soil compaction depends on its water content, bulk density and texture, a good understanding of the relation between them is essential for defining suitable farming strategies according to climatic changes. In this work we propose a new pedotransfer function for 10 French representative soils collected from cultivated fields, a vineyard and forests. We investigate the relationship between soil mechanical properties and easily measurable soil properties as well as water content and bulk density. Confined compression tests were performed on remoulded soils of a large range of textures at different initial bulk densities and water contents. The use of remoulded samples allowed us examining a large range of initial conditions with low variability of measurement. A good linear regression was obtained between soil precompression stress, compression index, initial water content, initial bulk density and soil texture. The higher the clay content, the higher the soil capacity to bear higher stresses at higher initial water content without reaching severe compaction state. The initial water content played an important role in clayey and loamy soils. In contrast, for sandy soils, the mechanical parameters were less dependent of initial water content but more related to the initial bulk density. These pedotransfer functions are expected to hold for soils of surface layers with tillage but further measurements on intact samples are needed to tests their validity

Armor or Withdraw? Likely Litigation and Potential Adjudication of Shoreland Conflicts Along Michigan\u27s Shifting Great Lake Coasts

Michigan enjoys along its inland seas, the Laurentian Great Lakes, one of the longest coastlines in the U.S. Much of that shoreline is privately owned. Because of a confluence of development pressures and irrepressible physical dynamics, growing numbers of Great Lakes shoreland properties, built on shifting sandy shores, are at heightened risk of loss from coastal storm surge, inundation, erosion, and shoreline recession. In response, property owners are installing extensive hardened shoreline armoring structures like seawalls and revetments to arrest those erosional processes. Those structures, however, will substantially impair, if not ultimately destroy, the state’s natural coastal beaches and other shoreland resources, as well as accelerate erosion of neighboring shoreland properties. The clash of imperatives to protect shoreland properties versus conserve coastal resources signifies a wicked dilemma the State cannot avoid: armor or withdraw? More precisely, should we allow the armoring of Michigan’s Great Lakes shorelines in an attempt to fix in place shoreland properties, at great and ongoing private and public expense, and ultimately risk the loss of public trust resources? Or should we allow—and should we compel shoreland property owners to allow—natural processes to proceed, even though doing so will increase the rate at which privately owned shorelands naturally convert into state-owned submerged bottomlands? We cannot hope to simultaneously protect both the beach and the beach house along naturally receding Great Lakes shorelines; we must choose which interest to prioritize first, recognizing the cost of doing so by losing the other. In addition to the complex physical dynamics at play along Michigan’s Great Lakes coasts, there are evolving legal complexities as well. The State, as sovereign, enjoys police power authorities that encompass coastal shoreland management. The State has also long recognized the applicability of the public trust doctrine to its Great Lakes shores, and its constitution mandates the protection of natural resources. This article first analyzes current Michigan law to determine how those doctrines and mandates apply to Great Lakes shoreline armoring, particularly in terms of what to prioritize. Based on that assessment, we conclude that Michigan’s courts, legislature, and people have consistently and clearly prioritized protecting and conserving Great Lakes natural coastal resources above developing or impairing them for private use, except when such development truly serves larger public trust interests. In contrast, the administrative rules now used to execute those protections prioritize protecting the private beach house first, even at the expense of destroying the natural beach and impairing other public trust interests. This administrative approach was not inevitable— indeed it may be unlawful—and it has created strong expectations on the part of shoreland property owners, heightening the likelihood of litigation. The article then analyzes current Michigan law to determine how the courts might resolve disputes between property owners hoping to armor the shore and State or local constraints on such armoring. Here we find that while the Michigan courts have resolved a number of key questions regarding coastal shorelands, there is no caselaw addressing directly the lawfulness of shoreline armoring. Based on our review of relevant caselaw, we conclude the courts are not likely to find that the State lacks authority to regulate—or prohibit altogether—shoreline armoring to protect coastal resources. There is conflicting caselaw, however, upon which the courts could rely to find either that the current regulatory regime provides adequate protection of coastal resources, or alternatively that it is deficient. Finally, beyond questions of regulatory authority, the courts are not likely to find that reinvigorated regulatory efforts to prevent the destruction and impairment of public trust coastal resources from armoring—even those resulting in the accelerated loss of private properties—violate constitutional protections, especially if State reforms are undertaken with deliberation and care. If the courts conclude that current regulatory efforts are lawful and require no greater protection, then Michigan will likely see much of its Great Lakes shorelines armored and its natural coastal beaches destroyed. If they conclude that current regulatory efforts are deficient (or if they approve of reinvigorated protection efforts), however, then private shoreland properties may be lost to the lakes. Such losses cannot be avoided forever, especially along naturally receding shorelines, but they might occur sooner than would happen absent attempts to arrest shoreline erosion with armoring. As with most wicked policy dilemmas, the best response may not be at either extreme—always armor or always withdraw—but somewhere in between. Crafting that hybrid approach, and the appropriate rules for applying it, will be the most challenging course to navigate

2019 Ridgecrest Earthquake Reveals Areas of Los Angeles That Amplify Shaking of High-Rises

The populace of Los Angeles, California, was startled by shaking from the M 7.1 earthquake that struck the city of Ridgecrest located 200 km to the north on 6 July 2019. Although the earthquake did not cause damage in Los Angeles, the experience in high‐rise buildings was frightening in contrast to the shaking felt in short buildings. Observations from 560 ground‐level accelerometers reveal large variations in shaking in the Los Angeles basin that occurred for more than 2 min. The observations come from the spatially dense Community Seismic Network (CSN), combined with the sparser Southern California Seismic Network and California Strong Motion Instrumentation Program networks. Site amplification factors for periods of 1, 3, 6, and 8 s are computed as the ratio of each station’s response spectral values combined for the two horizontal directions, relative to the average of three bedrock sites. Spatially coherent behavior in site amplification emerges for periods ≥3  s⁠, and the maximum calculated site amplifications are the largest, by factors of 7, 10, and 8, respectively, for 3, 6, and 8 s periods. The dense CSN observations show that the long‐period amplification is clearly, but only partially, correlated with the depth to basement. Sites with the largest amplifications for the long periods (⁠≥3  s⁠) are not close to the deepest portion of the basin. At 6 and 8 s periods, the maximum amplifications occur in the western part of the Los Angeles basin and in the south‐central San Fernando Valley sedimentary basin. The observations suggest that the excitation of a hypothetical high‐rise located in an area characterized by the largest site amplifications could be four times larger than in a downtown Los Angeles location

Continuously Tunable 250 GHz Gyrotron with a Double Disk Window for DNP-NMR Spectroscopy

In this paper, we describe the design and experimental results from the rebuild of a 250 GHz gyrotron used for Dynamic Nuclear Polarization enhanced Nuclear Magnetic Resonance spectroscopy on a 380 MHz spectrometer. Tuning bandwidth of approximately 2 GHz is easily achieved at a fixed magnetic field of 9.24 T and a beam current of 95 mA producing an average output power of >10 W over the entire tuning band. This tube incorporates a double disk output sapphire window in order to maximize the transmission at 250.58 GHz. DNP Signal enhancement of >125 is achieved on a [superscript 13]C-Urea sample using this gyrotron.National Institutes of Health (U.S.) (Grant EB002804)National Institutes of Health (U.S.) (Grant EB003151)National Institutes of Health (U.S.) (Grant EB002026)National Institutes of Health (U.S.) (Grant EB001960)National Institutes of Health (U.S.) (Grant EB001035)National Institutes of Health (U.S.) (Grant EB001965)National Institutes of Health (U.S.) (Grant EB004866