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- W3035386475 abstract "We introduce a new class of models for emergent dynamics. It is based on a new communication protocol which incorporates two main features: short-range kernels which restrict the communication to local geometric balls, and anisotropic communication kernels, adapted to the local density in these balls, which form topological neighborhoods. We prove flocking behavior -- the emergence of global alignment for regular, non-vacuous solutions of the $n$-dimensional models based on short-range topological communication. Moreover, global regularity (and hence unconditional flocking) of the one-dimensional model is proved via an application of a De Giorgi-type method. To handle the non-symmetric singular kernels that arise with our topological communication, we develop a new analysis for local fractional elliptic operators, interesting for its own sake, encountered in the construction of our class of models." @default.
- W3035386475 created "2020-06-19" @default.
- W3035386475 creator A5072355478 @default.
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- W3035386475 date "2018-06-04" @default.
- W3035386475 modified "2023-09-27" @default.
- W3035386475 title "Topologically-based fractional diffusion and emergent dynamics with short-range interactions" @default.
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