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- Andrew J. Bernoff, Chad M. Topaz
- SIAM J. Applied Dynamical Systems
- 2011

We study equilibrium configurations of swarming biological organisms subject to exogenous and pairwise endogenous forces. Beginning with a discrete dynamical model, we derive a variationalâ€¦ (More)

- Andrew J. Leverentz, Chad M. Topaz, Andrew J. Bernoff
- SIAM J. Applied Dynamical Systems
- 2009

We classify and predict the asymptotic dynamics of a class of swarming models. The model consists of a conservation equation in one dimension describing the movement of a population density field.â€¦ (More)

We study the dynamics of dissipation and blow-up in a critical-case unstable thin film equation. The governing equation is a nonlinear fourth-order degenerate parabolic PDE derived from a generalizedâ€¦ (More)

We construct an individual-based kinematic model of rolling migratory locust swarms. The model incorporates social interactions, gravity, wind, and the effect of the impenetrable boundary formed byâ€¦ (More)

- Alan E. Lindsay, Andrew J. Bernoff, Michael J. Ward
- Multiscale Modeling & Simulation
- 2017

We study the first passage time problem for a diffusing molecule in an enclosed region to hit a small spherical target whose surface contains many small absorbing traps. This study is motivated byâ€¦ (More)

Onset of superconductivity in decreasing fields for general domains. Ginzburgâ€“Landau theory has provided an effective method for understanding the onset of superconductivity in the presence of anâ€¦ (More)

- Andrew J. Bernoff, Chad M. Topaz
- SIAM Review
- 2013

Biological aggregations such as fish schools, bird flocks, bacterial colonies, and insect swarms have characteristic morphologies governed by the group membersâ€™ intrinsic social interactions withâ€¦ (More)

We explore the behavior of an integrodifferential equation used to model one-dimensional biological swarms. In this model, we assume the motion of the swarm is determined by pairwise interactions,â€¦ (More)

We discuss a methodology for studying the linear stability of self-similar solutions. We will illustrate these fundamental ideas on three prototype problems: a simple ODE with finite-time blowup, aâ€¦ (More)

By JAMES C. ALEXANDER, ANDREW J. BERNOFF, ELIZABETH K. MANN, J. ADIN MANN Jr, JACOB R. WINTERSMITH AND LU ZOU Department of Mathematics, Case Western Reserve University, Cleveland, OH 44106, USAâ€¦ (More)