Reclaiming our discipline

In this editorial we are taking the opportunity to set out our views on the current legal education and training reforms. In doing so we are perhaps taking a slightly unusual approach for an editorial but the issues currently facing us all as legal academics and educators are, we feel, too important for us to miss this opportunity

Light-cone behavior of the pion Bethe-Salpeter wave function in the ladder model

The Bethe-Salpeter wave function χ(q^ν+P^ν, q^ν) for two spin-½ quarks bound by the exchange of a scalar meson is examined in the ladder model. We seek the behavior of χ as the squared momentum, (q+P)^2, on one leg becomes infinite while the squared momentum, q^2, on the other leg remains fixed. This behavior is investigated by making a Wick rotation, expanding χ in partial-wave amplitudes χ^i_J(q^2) of the group O(4), and then looking for the rightmost poles of χ^i_J(q^2) in the complex J plane. Our results verify (in the ladder model) the useful hypothesis that the locations of these poles are independent of q^2 and can thus be computed in the q^2→∞ limit by using conformal invariance

Large-Q^2 behavior of the pion electromagnetic form factor

We study the large-Q^2 behavior of the electromagnetic form factor of the pion, which is viewed as a quark-antiquark bound state in a (nongauge) quantum field theory. When the pion's Bethe-Salpeter wave function is expanded in O(4) partial waves, it is found that the information needed about the partial-wave amplitudes is their scaling behavior at large momentum and the locations of their poles in the complex J plane. This information is determined by using the operator-product expansion, conformal invariance at short distances, and a regularity property that holds at least in the ladder model. The resulting behavior of the form factor is roughly F(Q^2)~(Q^2)^(-1), with corrections due to anomalous dimensions

Spatial and Temporal Evolution of the Volcanics and Sediments of the Kenya Rift

New volumetric and mass flux estimates have been calculated for the Kenya Rift. Spatial and temporal histories for volcanic eruptions, lacustrine deposition, and hominin fossil sites are presented, aided by the compilation of a new digital geologic map. Distribution of volcanism over time indicates several periods of southward expansion followed by relative positional stasis. Volcanism occurs throughout the activated rift length, with no obvious abandonment as the rift system migrated. The main exception is a period of volcanic concentration around 10 Ma, when activity was constrained within 2° of the equator. Volumes derived from seismic data indicate a total volume of c. 310,000 km3 (2.47 x 1010 kg/yr ), which is significantly more than the map-derived volumes found here or published previously. Map-based estimates are likely affected by a bias against recognizing small volume events in the older record. Such events are, however, the main driver of erupted volume over the last 5 Ma. A technique developed here to counter this bias results in convergence of the two volume estimation techniques. Relative erupted composition over time is variable. Overall, the erupted material has a mafic to silicic ratio of 0.9:1. Basalts are distinctly more common in the Turkana region, which previously experienced Mesozoic rifting. Despite the near equal ratio of mafic to silicic products, the Kenya Rift otherwise fits the definition of a SLIP. It is proposed that the compositions would better fit the published definition if the Turkana region was not twice-rifted. Lacustrine sedimentation post-dates initial volcanism by about 5 million years, and follows the same volcanic trends, showing south and eastward migration over time. This sedimentation delay is likely related to timing of fault displacements. Evidence of hominin habitation is distinctly abundant in the northern and southern sections of the Kenya Rift, but there is an observed gap in the equatorial rift between 4 and 0.5 million years ago. After 0.5 Ma, sites appear to progress towards the equator. The pattern and timing of hominid site distributions suggests that the equatorial gap in habitation may be the result of active volcanic avoidance

Evolution of the Southern Kenya Rift from Miocene to present with a focus on the Magadi area

The Kenya (a.k.a., Gregory) Rift is a geologically active area located within the eastern branch of the larger East African Rift System (EARS). The study area is located in the southern Kenya Rift between 1° South and the Kenya-Tanzania border (covering approximately 1.5 square degrees, semi-centered on Lake Magadi) and is predominantly filled with extrusive igneous rocks (mostly basalts, phonolites and trachytes) of Miocene age or younger. Sediments are thin, less than 1.5Ma, and are confined to small grabens. The EARS can serve both as an analogue for ancient continental rifting and as a modern laboratory to observe the geologic processes responsible for rifting. This study demonstrates that vintage (as in older, quality maps published by the Kenya Geological Survey, that may be outdated based on newer findings) quarter-degree maps can be successfully combined with recently published data, and used to interpret satellite (mainly Landsat 7) images to produce versatile, updated digital maps. The study area has been remapped using this procedure and although it covers a large area, the mapping retains a quadrangle level of detail. Additionally, all geologic mapping elements (formations, faults, etc.) have been correlated across older map boundaries so that geologic units don\u27t end artificially at degree boundaries within the study area. These elements have also been saved as individual digital files to facilitate future analysis. A series of maps showing the evolution of the southern Kenya rift from the Miocene to the present was created by combining the updated geologic map with age dates for geologic formations and fault displacements. Over 200 age dates covering the entire length of the Kenya Rift have been compiled for this study, and 6 paleo-maps were constructed to demonstrate the evolution of the area, starting with the eruption of the Kishalduga and Lisudwa melanephelinites onto the metamorphic basement around 15Ma. These eruptions occurred before the initial rift faulting and were followed by a massive eruption of phonolites between 13-10 Ma that covered most of the Kenya dome. This was followed by a period of relative quiescence, until the initial faulting defined the western boundary of the rift around 7Ma. The resulting graben was asymmetrical until corresponding faults to the east developed around 3Ma. The rift valley was flooded by basalts and trachytes between 3Ma and 700ka, after which the volcanic activity slowed to a near halt. Since 700ka most of the deposition has been comprised of sediments, mainly from lakes occupying the various basins in the area. The main results of this study are, in addition to a detailed interpretation of the rift development, a new geologic map that correlates dozens of formations across old map boundaries and a compilation of over 300 age dates. Specific products include paleomaps, tables of fault timing and displacement, and volume estimates of volcanic formations. The study concludes with a generalization of the present environment at Magadi including discussions of lagoon chemistry, mantle gases in relation to the trona deposit, and biology of the hot springs. Several biologic samples were collected during the 2006 field season in an attempt to characterize the organisms that are commonly seen in the present Lake Magadi environment. Samples were selected to represent the different, distinctive forms that are found in the hotsprings. Each sample had it own distinctive growth habit, and analysis showed that each was formed by a different cyanobacterial. Actual algae was rare in the collected samples, and represented by a few scattered diatoms

Castles in the clouds: LiDAR for historical study and terrain analysis

Examples of castles and fortresses seen in publicly available LiDAR data by the national mapping agencies in Finland, the Netherlands, Norway, Slovenia, the United Kingdom, and United States demonstrate the value of LiDAR data for understanding military history. The data sets, which include derived grids and the original point clouds with densities from 2–24 points/m², always identify the ground points, generally include LiDAR return intensity values, and sometimes include point classifications that discriminate vegetation and buildings. Grids with 0,5- or onemetre resolution could be created from the highest density point clouds in this study, while grids with one- or two-metre resolution can be created from the lowest density clouds. The digital surface model, which includes everything seen by the sensor, notably ground, buildings, and vegetation, can be created with higher resolution than the bare earth grids. The surface model provides the best visual representation of the castle and its surroundings. Viewed in interactive 3D, the data allows familiarisation with the landscape. Optimal displays depend on the desired scale and the terrain characteristics, but hillshade or shaded reflectance maps, reverse greyscale slope maps, and openness maps all work effectively. Further analysis may include functions such as viewsheds, which enhance the understanding of key terrain

The American Religious Landscape and the 2004 Presidential Vote: Increased Polarization

Presents findings from a post-election survey conducted in November and December 2004. Explores the polarization between different religions, as well as within the major religious traditions

What can the observation of nonzero curvature tell us?

The eternally inflating multiverse provides a consistent framework to understand coincidences and fine-tuning in the universe. As such, it provides the possibility of finding another coincidence: if the amount of slow-roll inflation was only slightly more than the anthropic threshold, then spatial curvature might be measurable. We study this issue in detail, particularly focusing on the question: "If future observations reveal nonzero curvature, what can we conclude?" We find that whether an observable signal arises or not depends crucially on three issues: the cosmic history just before the observable inflation, the measure adopted to define probabilities, and the nature of the correlation between the tunneling and slow-roll parts of the potential. We find that if future measurements find positive curvature at \Omega_k < -10^-4, then the framework of the eternally inflating multiverse is excluded with high significance. If the measurements instead reveal negative curvature at \Omega_k > 10^-4, then we can conclude (1) diffusive (new or chaotic) eternal inflation did not occur in our immediate past; (2) our universe was born by a bubble nucleation; (3) the probability measure does not reward volume increase; and (4) the origin of the observed slow-roll inflation is an accidental feature of the potential, not due to a theoretical mechanism. Discovery of \Omega_k > 10^-4 would also give us nontrivial information about the correlation between tunneling and slow-roll; e.g. a strong correlation favoring large N would be excluded in certain measures. We also ask whether the current constraint on \Omega_k is consistent with multiverse expectations, finding that the answer is yes, except for certain cases. In the course of this work we were led to consider vacuum decay branching ratios, and found that it is more likely than one might guess that the decays are dominated by a single channel.Comment: 46 pages, 5 figures; reference updates and typo corrections arising from final Phys. Rev. D copy editin