Dissipative solitary waves in granular crystals.
We provide a quantitative characterization of dissipative effects in one-dimensional granular crystals. We use the propagation of highly nonlinear solitary waves as a diagnostic tool and develop optimization schemes that allow one to compute the relevant exponents and prefactors of the dissipative terms in the equations of motion. We thereby propose a quantitatively accurate extension of the Hertzian model that encompasses dissipative effects via a discrete Laplacian of the velocities. Experiments and computations with steel, brass, and polytetrafluoroethylene reveal a common dissipation exponent with a material-dependent prefactor.
Carretero-González
R
R
Department of Mathematics and Statistics, San Diego State University, San Diego, California 92182-7720, USA.
Khatri
D
D
Porter
Mason A
MA
Kevrekidis
P G
PG
Daraio
C
C
D003300:Copper / Q000737:chemistry; D003460:Crystallization; D008956:Models, Chemical; D011138:Polytetrafluoroethylene / Q000737:chemistry; D013232:Steel / Q000737:chemistry; D015032:Zinc / Q000737:chemistry
D013232:Steel; C048399:brass; D003300:Copper; D011138:Polytetrafluoroethylene; D015032:Zinc