Dresden 2006 – wissenschaftliches Programm

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DY: Dynamik und Statistische Physik

DY 27: Granular Matter and Contact Dynamics II

DY 27.4: Vortrag

Dienstag, 28. März 2006, 17:15–17:30, SCH 251

Sound propagation in granular matter — •Ioannis Tzavaras and Michael Schulz — Universität Ulm, Abteilung Theoretischer Physik, Albert-Einstein-Allee 11, 89069 Ulm

The aim of this contribution is to find a suitable mathematical description for the propagation of mechanical excitations as for example sound waves in granular matter. We determined numerically the frequency spectrum of a linear chain of particles (up to 5 particles under periodic boundary conditions). The calculations were based on equations of motion, that were derived from a potential that vanishes as long as the particles are not in contact and that is that of a harmonic oscillator, when the particles press on each other, in other words when the distance of next neighbours is smaller than 2R (R: radius of the particles). The shape of the numerical solutions of the equations of motion for a linear chain of N particles suggested that a short time after the excitation solitons occur. We tried to approximate the equations of motion by fitting the parameters to the Toda lattice equation, which shows an exponential interaction between nearest neighbour particles and possesses analytical solutions especially soliton solutions. We could show that the soliton solution of the Toda lattice equations fulfils the equation of motion of granular matter too, if the soliton has a very small velocity, amplitude and a large width. At present time the concern of our work is to transfer the equation of motion of granular matter into the Korteweg de Vries (KdV) equation by performing the continuum limit and some transformations that connect also the Toda equation with the KdV equation.