One-dimensional kinetic models of granular flows

By Giuseppe Toscani. 2000

138 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics, Ocean Engineering

View Paper: https://www.semanticscholar.org/paper/cec3e59843f050abd334c0e6d6f22b5e225882f1

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In Applied Mathematics

In Computational Mechanics

In Ocean Engineering

Citations in the corpus

Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates (2003, background): “Equations such as (1.1) appear in various contexts; our interest for them arose from their use in the modelling of granular flows: see the works of Benedetto, Caglioti, Carrillo, Pulvirenti, Toscani [3, 4, 31] and the references there for physical background and mathematical study (a short mathemati”
Blow-up in multidimensional aggregation equations with mildly singular interaction kernels (2009, unknown): “Mathematics Subject Classification: 35B40, 35L60, 92B05”
Long-Time Asymptotics of Kinetic Models of Granular Flows (2004, background): “Abstract We analyze the long-time asymptotics of certain one-dimensional kinetic models of granular flows, which have been recently introduced in [22] in connection with the quasi elastic limit of a model Boltzmann equation with dissipative collisions and variable coefficient of restitution.”
Geometry of minimizers for the interaction energy with mildly repulsive potentials (2016, background): “These equations describe the continuum behavior of agents interacting via the potential W , and are at the core of many applications ranging from mathematical biology to granular media and economics, see [16, 14, 11, 17, 4] and the references therein.”
Mathematical tools for kinetic equations (2004, background): “For instance recent interest has been to understand inelastic collisions, because such models arise in some regimes of granular flows; see Bobylev, Carillo and Gamba [22], Toscani [112], and Benedetto et al.”
On minimizers of interaction functionals with competing attractive and repulsive potentials (2015, background): “Model (3) appears in the study of many phenomena, including biological swarms [11,12], granular media [1,13], self-assembly of nanoparticles [7,8] and molecular dynamics simulations of matter [16].”
Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations (2011, methodology): “Simplified inelastic interaction models for granular media were considered in [4] [18] with W = |x| 3 /3 and [43] [28] with W = |x| α , α > 1.”
Contractions in the 2-Wasserstein Length Space and Thermalization of Granular Media (2006, background): “Let us also mention that Wasserstein contraction estimates have been obtained recently by Li & Toscani [37] for the family of one-dimensional granular media models introduced in [51].”
Boltzmann and Fokker–Planck equations modelling opinion formation in the presence of strong leaders (2009, unknown): “In particular, the non-local nature of the compromise process is analogous to the variable coefficient of restitution in inelastic collisions (Toscani 2000).”
Lp theory for the multidimensional aggregation equation (2011, background): “3) arises in a number of models for biological aggregation [11, 14, 15, 23, 28, 37, 36, 38, 39] as well as problems in materials science [24, 25] and granular media [3, 17, 18, 31, 40].”