A Kinetic Flocking Model with Diffusion

By Renjun Duan, Massimo Fornasier, Giuseppe Toscani. 2010

145 citations recorded by the source corpus.

Subfields: Condensed Matter Physics, Modeling and Simulation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/9ae3be97960f9b750f7f34d552fd5d965f29453e

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In Condensed Matter Physics

In Modeling and Simulation

In Statistical and Nonlinear Physics

Citations in the corpus

Existence of piecewise weak solutions of a discrete Cucker-Smale's flocking model with a singular communication weight (2013, background): “for alignment models similar to C-S (both in continuous and discrete cases) were extensively studied, both from physical and biological point of view [13] -[16], [30], [33] - [35] and from more theoretical point of view [1, 2], [4] - [11], [17] - [25], [29, 31].”
Cucker-Smale model with normalized communication weights and time delay (2016, background): “studied in [10, 14], showing the existence of a unique global classical solution near Maxwellians and the convergence to them.”
On collision-avoiding initial configurations to Cucker-Smale type flocking models (2012, background): “Cucker-Smale’s flocking estimates were refined and generalized to the kinetic and fluid models in recent literature [1, 2, 4, 5, 6, 7, 8, 9, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 27, 31].”
Stochastic Mean-Field Limit: Non-Lipschitz Forces & Swarming (2010, background): “[20, 37] More precisely, they can depend on local in space-averaged quantities of the swarm, such as the averaged local density or velocity.”
Particle, kinetic, and hydrodynamic models of swarming (2010, background): “In [ 31, Theorem 1 ] it is shown that this steady pattern is locally stable.”
Emergent dynamics of the Cucker-Smale flocking model and its variants (2016, background): “17) with noises are treated in [36, 18] showing the global existence of classical solutions near the global Maxwellian and its largetime behavior.”