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The spin asymmetry in deep inelastic scattering of longitudinally polarised muons by longitudinally polarised protons has been measured over a large x range (0.01<x<0.7). The spin-dependent structure function g1(x) for the proton has been determined and its integral over x found to be 0.114±0.012±0.026, in disagreement with the Ellis-Jaffe sum rule. Assuming the validity of the Bjorken sum rule, this result implies a significant negative value for the integral of g1 for the neutron. These values for the integrals of g1 lead to the conclusion that the total quark spin constitutes a rather small fraction of the spin of the nucleon.
Dynamics of Granular Material Avalanches and Numerical Approximations of Savage-Hutter Models
(2004)
Höhere Mathematik kompakt
(2013)
This paper examines the positive and negative aspects of a range of interpretations of nearest-neighbours models. Measures-oriented and distributionoriented verification methods are applied to categorial, probabilistic and descriptive interpretations of nearest neighbours used operationally in avalanche forecasting in Scotland and Switzerland. The dependence of skill and accuracy measures on base rate is illustrated. The purpose of the forecast and the definition of events are important variables in determining the quality of the forecast. A discussion of the application of different interpretations in operational avalanche forecasting is presented.
Using results from an 8 m2 instrumented force plate we describe field measurements of normal and shear stresses, and fluid pore pressure for a debris flow. The flow depth increased from 0.1 to 1 m within the first 12 s of flow front arrival, remained relatively constant until 100 s, and then gradually decreased to 0.5 m by 600 s. Normal and shear stresses and pore fluid pressure varied in-phase with the flow depth. Calculated bulk densities are ρb = 2000–2250 kg m−3 for the bulk flow and ρf = 1600–1750 kg m−3 for the fluid phase. The ratio of effective normal stress to shear stress yields a Coulomb basal friction angle of ϕ = 26° at the flow front. We did not find a strong correlation between the degree of agitation in the flow, estimated using the signal from a geophone on the force plate, and an assumed dynamic pore fluid pressure. Our data support the idea that excess pore-fluid pressures are long lived in debris flows and therefore contribute to their unusual mobility.
Numerical models have become an essential part of snow avalanche engineering. Recent
advances in understanding the rheology of flowing snow and the mechanics of entrainment and
deposition have made numerical models more reliable. Coupled with field observations and historical
records, they are especially helpful in understanding avalanche flow in complex terrain. However, the
application of numerical models poses several new challenges to avalanche engineers. A detailed
understanding of the avalanche phenomena is required to specify initial conditions (release zone
dimensions and snowcover entrainment rates) as well as the friction parameters, which are no longer
based on empirical back-calculations, rather terrain roughness, vegetation and snow properties. In this
paper we discuss these problems by presenting the computer model RAMMS, which was specially
designed by the SLF as a practical tool for avalanche engineers. RAMMS solves the depth-averaged
equations governing avalanche flow with first and second-order numerical solution schemes. A
tremendous effort has been invested in the implementation of advanced input and output features.
Simulation results are therefore clearly and easily visualized to simplify their interpretation. More
importantly, RAMMS has been applied to a series of well-documented avalanches to gauge model
performance. In this paper we present the governing differential equations, highlight some of the input
and output features of RAMMS and then discuss the simulation of the Gatschiefer avalanche that
occurred in April 2008, near Klosters/Monbiel, Switzerland.