The geometry of manifolds and the perception of space

This essay discusses the development of key geometric ideas in the 19th century which led to the formulation of the concept of an abstract manifold (which was not necessarily tied to an ambient Euclidean space) by Hermann Weyl in 1913. This notion of manifold and the geometric ideas which could be formulated and utilized in such a setting (measuring a distance between points, curvature and other geometric concepts) was an essential ingredient in Einstein's gravitational theory of space-time from 1916 and has played important roles in numerous other theories of nature ever since.Comment: arXiv admin note: substantial text overlap with arXiv:1301.064

Dissolution kinetics: The nature of the particle attack of layered silicates in HF

The dissolution of layered silicates by hydrofluoric acid was studied with the aid of a slurry reactor. The nature of particle dissolution was delineat by measurements of reaction rates and by the examination of partially dissolved particles using a scanning electron microscope. The rates of particle d per unit mass were modeled as a function of the fraction x dissolved by an equation of the form [-r(x)]/[-r(x = 0)] = (1 - x) n-1. For the three layer silicates the parameter n takes on a value of 1/2, reflecting radial attack at the unit cell edges. The reactive edge surface area is considerably smaller than the total wetted particle surface area. In contrast, the two layer kaolinite structure dissolves at both the layer edges and the planar faces, and the parameter n varies from 0 to 1 as the particle dissolution proceeds to completion. Comparison of the rates of dissolution on the basis of the actual reactive surface areas show that layered silicates having the same octahedral sheet dissolve at the same rate. It is concluded that attack is preferential at surfaces where the octahedral sheets are exposed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/24574/1/0000857.pd

Compressible flow structures interaction with a two-dimensional ejector: a cold-flow study

An experimental study has been conducted to examine the interaction of compressible flow structures such as shocks and vortices with a two-dimensional ejector geometry using a shock-tube facility. Three diaphragm pressure ratios ofP4 =P1 = 4, 8, and 12 have been employed, whereP4 is the driver gas pressure andP1 is the pressure within the driven compartment of the shock tube. These lead to incident shock Mach numbers of Ms = 1:34, 1.54, and 1.66, respectively. The length of the driver section of the shock tube was 700 mm. Air was used for both the driver and driven gases. High-speed shadowgraphy was employed to visualize the induced flowfield. Pressure measurements were taken at different locations along the test section to study theflow quantitatively. The induced flow is unsteady and dependent on the degree of compressibility of the initial shock wave generated by the rupture of the diaphragm

Shoot growth of woody trees and shrubs is predicted by maximum plant height and associated traits

1. The rate of elongation and thickening of individual branches (shoots) varies across plant species. This variation is important for the outcome of competition and other plant-plant interactions. Here we compared rates of shoot growth across 44 species from tropical, warm temperate, and cool temperate forests of eastern Australia.2. Shoot growth rate was found to correlate with a suite of traits including the potential height of the species, xylem-specific conductivity, leaf size, leaf area per xylem cross-section, twig diameter (at 40 cm length), wood density and modulus of elasticity.3. Within this suite of traits, maximum plant height was the clearest correlate of growth rates, explaining 50 to 67% of the variation in growth overall (p p 4. Growth rates were not strongly correlated with leaf nitrogen or leaf mass per unit leaf area.5. Correlations between growth and maximum height arose both across latitude (47%, p p p p < 0.0001), reflecting intrinsic differences across species and sites

How much laser power can propagate through fusion plasma?

Propagation of intense laser beams is crucial for inertial confinement fusion, which requires precise beam control to achieve the compression and heating necessary to ignite the fusion reaction. The National Ignition Facility (NIF), where fusion will be attempted, is now under construction. Control of intense beam propagation may be ruined by laser beam self-focusing. We have identified the maximum laser beam power that can propagate through fusion plasma without significant self-focusing and have found excellent agreement with recent experimental data, and suggest a way to increase that maximum by appropriate choice of plasma composition with implication for NIF designs. Our theory also leads to the prediction of anti-correlation between beam spray and backscatter and suggests the indirect control of backscatter through manipulation of plasma ionization state or acoustic damping.Comment: 15 pages, 4 figures, submitted to Plasma Physics and Controlled Fusio

Denying humanness to victims: How gang members justify violent behavior

The high prevalence of violent offending amongst gang-involved youth has been established in the literature. Yet the underlying psychological mechanisms that enable youth to engage in such acts of violence remain unclear. 189 young people were recruited from areas in London, UK, known for their gang activity. We found that gang members, in comparison to non-gang youth, described the groups they belong to as having recognized leaders, specific rules and codes, initiation rituals, and special clothing. Gang members were also more likely than non-gang youth to engage in violent behavior and endorse moral disengagement strategies (i.e., moral justification, euphemistic language, advantageous comparison, displacement of responsibility, attribution of blame, and dehumanization). Finally, we found that dehumanizing victims partially mediated the relationship between gang membership and violent behavior. These findings highlight the effects of groups at the individual level and an underlying psychological mechanism that explains, in part, how gang members engage in violence

Psychophysiological processes of stress in chronic physical illness: a theoretical perspective

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/75576/1/j.1365-2648.1990.tb01843.x.pd