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30 November 1998 Physics Letters A 249 (1998) 1911198

Summary: 30 November 1998
Physics Letters A 249 (1998) 1911198
A continuum model for the jumping sandbox
C.E. Garza-Hume a,1
, Pablo Padilla a,2
, H´ector D. Ceniceros b
a IIMAS, UNAM, Circuito Escolar, Cd. Universitaria, M´exico, D.F., Mexico
b Centro de Investigaci´on en Computaci´on, Instituto Polit´ecnico Nacional, Unidad Profesional Adolfo L´opez Mateos,
Zacatenco, M´exico, D.F. 07738, Mexico
Received 1 April 1998; revised manuscript received 1 September 1998; accepted for publication 1 September 1998
Communicated by C.R. Doering
We propose a continuum model for the motion of sand oscillating vertically. We derive a nonlinear parabolic equation
with a nonlinearity corresponding to a bistable potential multiplied by a switching function. This is obtained by modifying
the equation for a free surface and incorporating the thermodynamics of the interface. c 1998 Elsevier Science B.V.
Keywords: Granular material; Continuum model; Bistable potential; Capillarity; Free surface; Non-linear PDE
1. Introduction
Granular materials appear in many contexts and
applications, such as mining, agriculture, construc-
tion and the pharmaceutical industry (see for instance


Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara


Collections: Mathematics