Bjorn Sandstede Professor of Applied Mathematics, Chair of Applied Mathematics

Bjorn Sandstede received his PhD in Mathematics from the University of Stuttgart in 1993. After holding postdoctoral positions at the Weierstrass Institute and at Brown University, he joined the faculty at the Ohio State University in 1997, before moving to the University of Surrey in 2004. In 2008, Sandstede became a faculty member at Brown University, where he currently serves as the Chair of the Division of Applied Mathematics and as an Associate Director of ICERM.

Brown Affiliations

Research Areas

scholarly work

A complete list of my publications is available on my personal homepage .

research overview

The theoretical part of my research focuses on the formation and the dynamics of patterns and nonlinear waves: recent projects include the nonlinear stability of coherent structures, and I usually employ a range of analytical techniques, supplemented by numerical computations. I also work on applications in biology, climate, data assimilation, and traffic flow.
 

research statement

Most of my past and current research projects are concerned with understanding the formation of patterns and the dynamics of nonlinear waves in spatially extended systems. Extended systems are typically modelled by partial differential equations on unbounded domains. Nonlinear waves correspond to interfaces, or defects, that are formed between co-existing patterns. These patterns, as well as the defects and interfaces formed between them, are found in many biological, chemical, and physical applications. Examples are the transmission of signals in optical fibers, the formation of hexagonal and stripe patterns in fluid convection, and the generation of spiral waves in catalytic chemical reactions. Motivated by experiments and numerical simulations, I aim to understand when and how patterns and defects are formed, how they behave under small perturbations, what other patterns or waves with a more complicated spatio-temporal behaviour can bifurcate from them, and how they interact with each other or with domain boundaries. To answer these questions, I use a mixture of analytical and geometric dynamical-systems techniques, and I have also developed numerical algorithms for the computation of waves and their bifurcations.

funded research

Recent grants include

  • Institute for Computational and Experimental Research in Mathematics (Co-PI: $15M, 2010-2015, $17.5M  2015-2020)
  • Research Training Group: Integrating Dynamics and Stochastics (PI: $2.1M, 2012-2017)
  • NSF "Dynamics near coherent structures" (PI: $600k, 2009-2014)