Modeling Analysis and Novel Computational Algorithms for Nonlinear Convection and Self-Organized Dynamics
Abstract
The overall goal of this proposal is to investigate two new recent paradigms for nonlinear convection and for self-organized dynamics. We plan to follow up on the recently introduced notion of entropy measure valued solutions as an effective description to capture the nonuniqueness of multi-dimensional systems of conservation laws, most notably, compressible Euler and shallow-water equations. In this context of nonlinear conservation laws, physically relevant solution are singled out by their probability distribution functions (pdfs); our preliminary study, based on carefully tested entropy stable schemes validate the convergence of pdfs despite the lack of uniqueness. In a second line of research we plan to study a new, more realistic class of self-organized dynamics, in which the agent-based dynamics takes into account the two essential aspects of (i) tendencies and (ii) synchronization, as an extension to the exiting class of agent-based dynamics based on alignment; our preliminary numerical studies indicate the emergence of leaders and coherent cycles. We plan to analyze and simulate such models, From their agents-based to the hydrodynamic description in terms of nonlinear convection, which provide more realistic scenarios beyond the emergence of consensus in alignment-based models. We propose to construct new models, analyze their large time behavior and complement our study with accurate and ``faithful" numerical simulations to gain insight into these new paradigms.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Aug 12, 2016
- Source ID
- N000141512094
Entities
People
- Eitan Tadmor
Organizations
- Office of Naval Research
- United States Navy
- University of Maryland