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Research Spending & Results

Award Detail

Awardee:BROWN UNIVERSITY IN PROVIDENCE IN THE STATE OF RHODE ISLAND AND PROVIDENCE PLANTATIONS
Doing Business As Name:Brown University
PD/PI:
  • Bjorn Sandstede
  • (401) 863-2815
  • Bjorn_Sandstede@brown.edu
Award Date:06/07/2021
Estimated Total Award Amount: $ 350,000
Funds Obligated to Date: $ 350,000
  • FY 2021=$350,000
Start Date:07/01/2021
End Date:06/30/2024
Transaction Type:Grant
Agency:NSF
Awarding Agency Code:4900
Funding Agency Code:4900
CFDA Number:47.049
Primary Program Source:040100 NSF RESEARCH & RELATED ACTIVIT
Award Title or Description:Spiral Waves and Target Patterns
Federal Award ID Number:2106566
DUNS ID:001785542
Parent DUNS ID:001785542
Program:APPLIED MATHEMATICS
Program Officer:
  • Victor Roytburd
  • (703) 292-8584
  • vroytbur@nsf.gov

Awardee Location

Street:BOX 1929
City:Providence
State:RI
ZIP:02912-9002
County:Providence
Country:US
Awardee Cong. District:01

Primary Place of Performance

Organization Name:Brown University
Street:182 George Street, Box F
City:Providence
State:RI
ZIP:02912-9023
County:Providence
Country:US
Cong. District:01

Abstract at Time of Award

Many biological, chemical, and physical processes exhibit spiral waves and target patterns. Spiral waves occur, for instance, in autocatalytic chemical reactions, during cellular signaling of amoebae, and in cardiac tissue where they are often the cause of cardiac arrhythmias and the precursor to ventricular fibrillation and cardiac arrest. Similarly, target patterns appear prominently in autocatalytic reactions and are also often found in systems with small spatial inhomogeneities. This project focuses on understanding when spiral waves and target patterns arise, under which conditions they can be observed, and what mechanisms cause them to change their shape or disappear. The investigator will develop analytical, computational, and geometric tools to answer these questions and apply the findings to models of autocatalytic chemical reactions and wave propagation in cardiac tissue. Graduate and undergraduate students will be engaged in these research activities. This project focuses on understanding existence, multiplicity, stability, and bifurcations of spiral waves and target patterns through the development of spatial-dynamics methodologies that can be applied to a broad range of reaction-diffusion systems. The investigator will establish multiplicity results for one-dimensional spiral waves and target patterns in reaction-diffusion systems using spatial dynamics and apply these results to the Brusselator model. The second project centers on transverse instabilities of spiral waves and target patterns. Transverse instabilities do not contribute to the spectra of planar structures, though they do cause linear instabilities. The aim is to investigate how these instabilities manifest themselves on large bounded disks. The third project focuses on making the numerical computation of spiral spectra more robust by developing preconditioners that rely on appropriate exponential weights to reduce the norm of the resolvent independently of the size of the domain. In the last project, singular perturbation methods will be developed to understand the limits of profiles and spectra of planar spiral waves and target patterns when some of the diffusion coefficients in the model approach zero. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

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