Analysis of stresses in two-dimensional isostatic granular systems

We analyze a recently proposed continuous model for stress fields that develop in two-dimensional purely isostatic granular systems. We present a reformulation of the field equations, as a linear first-order hyperbolic system, and show that it is very convenient both for analysis and for numerical computations. Our analysis allows us to predict quantitatively the formation and directions of stress paths and, from these, trajectories and magnitudes of force chains, given the structure in terms of a particular fabric tensor. We further predict quantitatively changes of stresses along the paths, as well as leakage and branching of stress from the main paths into the cones that they make in terms of the fabric tensor. Numerical computations in both Cartesian and cylindrical coordinates verify the analytic results and illustrate the rich behavior discovered. All the phenomena predicted by our solutions have been observed experimentally, suggesting that stresses in isostatic systems can form a base model for a more developed stress theory in granular materials.     

Stress chain solutions in two-dimensional isostatic granular systems: fabric-dependent paths, leakage, and branching

The stress field equations for two-dimensional disordered isostatic granular materials are reformulated, giving new results beyond the commonly accepted force chains. Localized loads give rise to exactly determinable cones of influence, bounded by stress chains. Disorder couples same-source chains, attenuates stresses along chains, causes stress leakage from chains into the cone, and gives rise to branching. Chains from spatially separate sources do not interact. The formulation is convenient for computation, and several numerical solutions are presented.     

Formant frequency tuning in singing

It is sometimes claimed that some singers tune their two lowest formant frequencies to harmonic partials in order to increase the audibility of the voice. Voice acoustics predicts that such tuning of formants should cause vowel quality to change. Using a newly constructed digital singing machine, the authors have explored the perceptual consequences of such tuning. Four different cases were represented, in which the two lowest formant frequencies were either constant or adapted to the fundamental frequency according to either of three different strategies. The resulting voice timbres were judged by an expert panel of singing teachers in a listening test consisting of descending chromatic scales. Constant formant frequencies were clearly preferred, presumably because formant tuning entails formant frequency shifts between adjacent tones so substantial that salient vowel quality shifts occur.     

Convergence to steady state of solutions of the euler equations,I

In this paper we analyze the convergence to steady state of solutions of the compressible and the incompressible isentropic Euler equations in two space dimensions. In the compressible case, the original equations do not converge. We replace the equation of continuity with an elliptic equation for the density, obtaining a new set of equations, which have the same steady solution. In the incompressible case, the equation of continuity is replaced by a Poisson equation for the pressure. In both cases, we linearize the equations around a steady solution and show that the unsteady solution of the linearized equations converges to the steady solution, if the steady solution is sufficiently smooth. In the proof we consider how the energy of the time dependent part developes with time, and find that it decrease exponentially.     

Excitation lines and multiple ionization in Auger spectra

Satellite lines of a new type and excessively large continuous distributions of energy degraded electrons are observed in theKLL Auger spectra of potassium, chlorine, and sulfur. The lines are tentatively interpreted as due to a process that is characteristic of the atom more than of the entire solid and the excessive number of electrons in the continuous distributions is interpreted as due to multiple ionization.