Seminar Event Detail

Applied Interdisciplinary Mathematics (AIM)

Date:  Friday, March 11, 2016
Location:  1084 East Hall (3:00 PM to 4:00 PM)

Title:  Collective dynamics: from emergence of consensus to social hydrodynamics

Abstract:   We discuss the collective dynamics of systems driven by "social engagement" of agents with their local neighbors. Prototypical examples which involve environmental averaging include alignment-based models in opinion dynamics, flocking, self-organization of biological organisms, and rendezvous in mobile networks.
We address two natural questions which arise in this context. First, how different rules of engagement influence the formation of large time, large scale patterns such as clusters, and in particular, the emergence of "consensus". We propose an alternative paradigm based on the tendency of agents "to move ahead" which leads to the emergence of leaders. Second, the group behavior of systems which involve a large number of agents lend themselves to kinetic and hydrodynamic descriptions. It is known that if smooth solutions of "social hydrodynamics" exist, then they must flock. Do such smooth solutions exist? Alignment-based models reflect the competition on resources, and left unchecked, may lead to finite-time singularities. We discuss the global regularity of social hydrodynamics for sub-critical initial configurations.


Speaker:  Eitan Tadmor
Institution:  University of Maryland, College Park

Event Organizer:   Peter Smereka


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