title: Dissipative solitary waves in granular crystals.
abstract: 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.
authors.affiliation: Department of Mathematics and Statistics, San Diego State University, San Diego, California 92182-7720, USA.
authors.forename: R
authors.initials: R
authors.lastname: Carretero-González
authors.forename: D
authors.initials: D
authors.lastname: Khatri
authors.forename: Mason A
authors.initials: MA
authors.lastname: Porter
authors.forename: P G
authors.initials: PG
authors.lastname: Kevrekidis
authors.forename: C
authors.initials: C
authors.lastname: Daraio
mesh_terms: D003300:Copper / Q000737:chemistry; D003460:Crystallization; D008956:Models, Chemical; D011138:Polytetrafluoroethylene / Q000737:chemistry; D013232:Steel / Q000737:chemistry; D015032:Zinc / Q000737:chemistry
chemical_list: D013232:Steel; C048399:brass; D003300:Copper; D011138:Polytetrafluoroethylene; D015032:Zinc