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Research Spending & Results

Award Detail

Doing Business As Name:CUNY City College
  • Jack T Hanson
  • (212) 650-5174
Award Date:01/10/2020
Estimated Total Award Amount: $ 156,142
Funds Obligated to Date: $ 156,142
  • FY 2020=$156,142
Start Date:08/01/2020
End Date:07/31/2023
Transaction Type:Grant
Awarding Agency Code:4900
Funding Agency Code:4900
CFDA Number:47.049
Primary Program Source:040100 NSF RESEARCH & RELATED ACTIVIT
Award Title or Description:Random Media in and Beyond Two Dimensions
Federal Award ID Number:1954257
DUNS ID:603503991
Parent DUNS ID:073268849
Program Officer:
  • Pawel Hitczenko
  • (703) 292-5330

Awardee Location

Street:Convent Ave at 138th St
City:New York
County:New York
Awardee Cong. District:13

Primary Place of Performance

Organization Name:CUNY City College
Street:Convent Ave at 138th St
City:New York
County:New York
Cong. District:13

Abstract at Time of Award

This project involves the study of mathematical models of real physical phenomena. Among these are so-called percolative models, which describe the flow of fluid in a porous medium, a growing bacterial infection, or a long polymer chain. Another model to be studied is the Bak-Tang-Wiesenfeld model, the classic model of self-organized criticality (SOC), where simple, local rules generate complex, large-scale patterns. SOC has been used to explain commonalities between such apparently dissimilar phenomena as solar flares and neuron firing. Many of the most successful approaches to problems in these areas are valid only in certain special cases; for instance, certain two-dimensional percolative models with particular symmetry properties. A main goal of the project is the development of robust mathematical techniques which explain the behavior of such systems -- for instance, how smooth is the surface of a spreading drop of fluid -- in a broad range of physically interesting cases. The specific research problems to be studied include the following. In critical Bernoulli percolation (where one randomly removes just enough edges to make an infinite graph finite), the PI will study scaling limits of graph components and give sharp asymptotics for graph distances and electrical resistances. In first-passage percolation (where one randomly perturbs edge lengths in a graph), the PI will study fluctuations of graph distances and the tortuosity of long geodesics. In the Bak-Tang-Wiesenfeld model (an interacting particle system), the PI will study the correlation between particle movements at different moments of time. Some related problems have previously seemed more tractable in special settings like certain "solvable" growth models or in certain dimensions. This project will employ robust methods – stochastic geometric techniques, concentration of measure methods, and others – which apply to the widest range of possible settings and which distill the general principles underlying phenomena of interest. 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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