Louis F. Rossi

Recent Items

1. Swarm Interpolation Using an Approximate Chebyshev Distribution.
   Work with Joshua Kirby, Marco A. Montes de Oca, Steven Senger, and Chien-Chung Shen. We propose a new way of remotely sensing fields with autonomous wireless robots by finessing swarming rules to obtain an approximate Chebyshev distribution.
2. The Role of Memory in Stabilizing Swarms.
   Work with Jen Miller, Hao Luan and Chien-Chung Shen. In wireless robotic applications, communication, not memory or CPU, is the limiting commodity. In this paper, we connect the stability of swarms to essential topics in numerical ODEs. We show that we can design stable swarming algorithms that require less frequent updating.
3. Quantifying and Tracing Information Cascades in Swarms.
   Work with Rose Wang, Jen Miller, Joe Lizier and Mikhail Prokopenko in PLoS ONE measuring theoretical information transfer in swarms. We provide the first direct information-theoretic evidence for the long-held conjecture that the information cascades occur in waves rippling through the swarm.

Activities

Research

I am interested in a solving a variety of problems that arise in fluid dynamics, computational methods, swarming and wireless networks. On the surface, it may look like these problems have nothing to do with one another, but mathematically, they are all connected. In the broad sense, the mathematical problems that interest me involve the deep connections between discrete and continuous mathematical structures. For instance, I like to solve partial differential equations that describe fluid motion using particle methods. The fluid motion is described by continuous equations. My numerical methods capture this behavior with discrete particles.

Teaching

Spring 2012: Math 612: Introduction to Numerical Discretization

Spring 2012 office hours: Mon 1430-1530, Tue 0900-1000 and Fri 0900-1000.

Special for Spring 2013: OCCAM 5th UK Graduate Modelling Camp 2013

Students

Current Doctoral Students

Rui Fang: Modeling and analysis of ant-based wireless protocols.
Zhenyu He: Numerical analysis of particle methods.
Yu Sun: PDE modeling and analysis of swarms with leadership.

Recent PhD's

Jennifer Miller: PDE modeling and analysis of swarms. Dr. Miller is now a Visiting Assistant Professor at
Claudio Torres: High performance computing with particles. Numerical PDEs. Dr. Torres is now a postdoctoral fellow in Prof. Emelianenko's group at George Mason University.