An L1 Penalty Method for General Obstacle Problems

We construct an efficient numerical scheme for solving obstacle problems in divergence form. The numerical method is based on a reformulation of the obstacle in terms of an L1-like penalty on the variational problem. The reformulation is an exact regularizer in the sense that for large (but finite) penalty parameter, we recover the exact solution. Our formulation is applied to classical elliptic obstacle problems as well as some related free boundary problems, for example the two-phase membrane problem and the Hele-Shaw model. One advantage of the proposed method is that the free boundary inherent in the obstacle problem arises naturally in our energy minimization without any need for problem specific or complicated discretization. In addition, our scheme also works for nonlinear variational inequalities arising from convex minimization problems.Comment: 20 pages, 18 figure

Analysis of Shroud Options in Support of the Human Exploration of Mars

In support of the Mars Design Reference Architecture (DRA) 5.0, the NASA study team analyzed several shroud options for use on the Ares V launch vehicle.1,2 These shroud options included conventional "large encapsulation" shrouds with outer diameters ranging from 8.4 to 12.9 meters (m) and overall lengths of 22.0 to 54.3 meters, along with a "nosecone-only" shroud option used for Mars transfer vehicle component delivery. Also examined was a "multi-use" aerodynamic encapsulation shroud used for launch, Mars aerocapture, and entry, descent, and landing of the cargo and habitat landers. All conventional shroud options assessed for use on the Mars launch vehicles were the standard biconic design derived from the reference shroud utilized in the Constellation Program s lunar campaign. It is the purpose of this paper to discuss the technical details of each of these shroud options including material properties, structural mass, etc., while also discussing both the volume and mass of the various space transportation and surface system payload elements required to support a "minimum launch" Mars mission strategy, as well as the synergy, potential differences and upgrade paths that may be required between the Lunar and Mars mission shrouds

Entropic descriptor of a complex behaviour

We propose a new type of entropic descriptor that is able to quantify the statistical complexity (a measure of complex behaviour) by taking simultaneously into account the average departures of a system's entropy S from both its maximum possible value Smax and its minimum possible value Smin. When these two departures are similar to each other, the statistical complexity is maximal. We apply the new concept to the variability, over a range of length scales, of spatial or grey-level pattern arrangements in simple models. The pertinent results confirm the fact that a highly non-trivial, length-scale dependence of the entropic descriptor makes it an adequate complexity-measure, able to distinguish between structurally distinct configurational macrostates with the same degree of disorder.Comment: 14 pages, 7 figures, extended versio

Texture Coding in the Rat Whisker System: Slip-Stick Versus Differential Resonance

Rats discriminate surface textures using their whiskers (vibrissae), but how whiskers extract texture information, and how this information is encoded by the brain, are not known. In the resonance model, whisker motion across different textures excites mechanical resonance in distinct subsets of whiskers, due to variation across whiskers in resonance frequency, which varies with whisker length. Texture information is therefore encoded by the spatial pattern of activated whiskers. In the competing kinetic signature model, different textures excite resonance equally across whiskers, and instead, texture is encoded by characteristic, nonuniform temporal patterns of whisker motion. We tested these models by measuring whisker motion in awake, behaving rats whisking in air and onto sandpaper surfaces. Resonant motion was prominent during whisking in air, with fundamental frequencies ranging from approximately 35 Hz for the long Delta whisker to approximately 110 Hz for the shorter D3 whisker. Resonant vibrations also occurred while whisking against textures, but the amplitude of resonance within single whiskers was independent of texture, contradicting the resonance model. Rather, whiskers resonated transiently during discrete, high-velocity, and high-acceleration slip-stick events, which occurred prominently during whisking on surfaces. The rate and magnitude of slip-stick events varied systematically with texture. These results suggest that texture is encoded not by differential resonant motion across whiskers, but by the magnitude and temporal pattern of slip-stick motion. These findings predict a temporal code for texture in neural spike trains

Aligned electrospun nanofibers specify the direction of dorsal root ganglia neurite growth

Nerve injury, a significant cause of disability, may be treated more effectively using nerve guidance channels containing longitudinally aligned fibers. Aligned, electrospun nanofibers direct the neurite growth of immortalized neural stem cells, demonstrating potential for directing regenerating neurites. However, no study of neurite guidance on these fibers has yet been performed with primary neurons. Here, we examined neurites from dorsal root ganglia explants on electrospun poly- L -lactate nanofibers of high, intermediate, and random alignment. On aligned fibers, neurites grew radially outward from the ganglia and turned to follow the fibers upon contact. Neurite guidance was robust, with neurites never leaving the fibers to grow on the surrounding cover slip. To compare the alignment of neurites to that of the nanofiber substrates, Fourier methods were used to quantify the alignment. Neurite alignment, however striking, was inferior to fiber alignment on all but the randomly aligned fibers. Neurites on highly aligned substrates were 20 and 16% longer than neurites on random and intermediate fibers, respectively. Schwann cells on fibers assumed a very narrow morphology compared to those on the surrounding coverslip. The robust neurite guidance demonstrated here is a significant step toward the use of aligned, electrospun nanofibers for nerve regeneration. © 2007 Wiley Periodicals, Inc. J Biomed Mater Res, 2007Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/57401/1/31285_ftp.pd

Are the Japanese Unique? An Analysis of Consumption and Saving Behavior in Japan

In this paper, I conduct an analysis of consumption and saving behavior in Japan, looking both at trends over time and comparisons with the other industrialized countries. I find that some of the conventional wisdoms (that the Japanese are asset-rich and hold conservative portfolios) still hold but that others (that the Japanese are high savers and shun borrowing) no longer hold and that the Japanese are not unique, with the United States and the other Anglo-Saxon countries being the true exceptions in many respects

Judicial Review, Irrationality, and the Legitimacy of Merits-Review

The definition of the irrationality ground of judicial review recognises the constitutional principle of the separation of powers, in allowing for judicial control of the executive only very rarely. The author in a previous article in this study found that the courts, on occasions, had intervened in circumstances where administrative decisions arguably were not irrational. To this end, the purpose of this article is to assess the constitutionality of these seemingly low standards of irrationality. The author does so by reference either to the manner of review employed—the use of the proportionality principle, for example—or the context of the administrative decision under scrutiny, such as the infringement of the applicant’s fundamental rights. The author finds that the cases from the previous article where low standards of irrationality were arguably adopted were, in fact, legitimate according to these chosen methods of evaluation. However, this is an interim conclusion because, for reasons of word length, the author is unable to complete a full assessment here. It is therefore proposed that a subsequent article will continue to examine the constitutionality of these cases. Furthermore, the author will also try and establish a zone of executive decision-making, for reasons of democracy, where the courts are excluded from irrationality review. If the author is unsuccessful in this regard, the final conclusion of this study will inevitably be that low standards of judicial intervention exist without limit—a clear assault on the constitutional principle stated above