Physics – Condensed Matter – Soft Condensed Matter
Scientific paper
2001-07-25
Physics
Condensed Matter
Soft Condensed Matter
Scientific paper
10.1103/PhysRevE.65.021307
We study the dependence on the external pressure $P$ of the velocities $v_{L,T}$ of long wavelength sound waves in a confined 2D h.c.p. lattice of 3D elastic frictional balls interacting via one-sided Hertz-Mindlin contact forces, whose diameters exhibit mild dispersion. The presence of an underlying long range order enables us to build an effective medium description which incorporates the radial fluctuations of the contact forces acting on a single site. Due to the non linearity of Hertz elasticity, self-consistency results in a highly non-linear differential equation for the "equation of state" linking the effective stiffness of the array with the applied pressure, from which sound velocities are then obtained. The results are in excellent agreement with existing experimental results and simulations in the high and intermediate pressure regimes. It emerges from the analysis that the departure of $v_{L}(P)$ from the ideal $P^{1/6}$ Hertz behavior must be attributed primarily to the fluctuations of the stress field, rather than to the pressure dependence of the number of contacts.
Caroli Christiane
Velický B.
No associations
LandOfFree
Pressure dependence of the sound velocity in a 2D lattice of Hertz-Mindlin balls: a mean field description does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Pressure dependence of the sound velocity in a 2D lattice of Hertz-Mindlin balls: a mean field description, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Pressure dependence of the sound velocity in a 2D lattice of Hertz-Mindlin balls: a mean field description will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-288233