Skip Navigation Links

Project Information

COLLABORATIVE RESEARCH: REVEALING THE GEOMETRY OF SPATIO-TEMPORAL CHAOS WITH COMPUTATIONAL TOPOLOGY: THEORY, NUMERICS AND EXPERIMENT

Agency:
NSF

National Science Foundation

Project Number:
1622401
Contact PI / Project Leader:
MISCHAIKOW, KONSTANTIN M
Awardee Organization:
RUTGERS THE ST UNIV OF NJ NEW BRUNSWICK

Description

Abstract Text:
The weather we experience is driven by convection, sunlight warms the earth which heats the atmosphere which is cooled by the cold temperatures of outer space. Most people are not interested in microscopic behavior, for example the behavior of the individual molecules in the air, nor macroscopic behavior, such as worldwide average temperature. What is of interest are mesoscopic patterns, for example weather fronts which result in local changes in temperature. This interest in mesoscopic, as opposed to micro- or macroscopic features, of large scale systems occurs in a wide variety of complex large scale physical phenomena such as combustion in engines, dynamics of biomass in the oceans, ventricle fibrillation in a human heart, etc. These mesoscopic patterns take on many different shapes and sizes and change with time, sometimes slowly and sometimes rapidly. The form of these patterns and how they evolve in time is often very dependent on parameters. New technologies are greatly increasing our abilities to measure and simulate these physical phenomena, resulting in enormous data sets, but our ability to extract and quantify this information in a way that leads to understanding, predictability, and control of these systems is not keeping pace. We will explore the use of new mathematical tools to address this problem. The spatial and temporal complexity of Rayleigh-B?nard convection produces high dimensional time series data. A relatively new algebraic topological tool called Persistent Homology will be used to provide new tools for nonlinear dimension reduction. To ensure the applicability of these methods and that physically important mesoscopic features of the dynamics are preserved they will be developed in conjunction with the further development of carefully controlled high precision convection experiments and state-of-the-art, large scale, high-resolution numerical simulations of the Boussinesq equations. This includes the analysis of the geometry of covariant Lyapunov exponents. The new computational tools developed in this work should find broad application in a wide variety of problems involving complex nonequilibrium systems in nature (oceanic and atmospheric flows, climate and weather forecasting) and in technology (nonlinear optical systems, combustion and chemical reactions) where understanding and prediction of complex behavior is desired.
Project Terms:
Address; Air; Arts; Behavior; Biomass; chemical reaction; Climate; cold temperature; Complex; computerized tools; Convection; Data; Data Set; Development; Dimensions; Ensure; Equation; experience; Geometry; Heart; Heating; Human; Individual; interest; Measures; Methods; Microscopic; Nature; new technology; Oceans; Optics; outer space; Pattern; planetary Atmosphere; Research; research study; Resolution; Series; Shapes; simulation; Sunlight; System; Technology; Temperature; theories; Time; tool; Weather; Work

Details

Contact PI / Project Leader Information:
Name:  MISCHAIKOW, KONSTANTIN M
Other PI Information:
Not Applicable
Awardee Organization:
Name:  RUTGERS THE ST UNIV OF NJ NEW BRUNSWICK
City:  PISCATAWAY    
Country:  UNITED STATES
Congressional District:
State Code:  NJ
District:  06
Other Information:
Fiscal Year: 2016
Award Notice Date: 23-Jun-2016
DUNS Number: 001912864
Project Start Date: 01-Aug-2016
Budget Start Date:
CFDA Code: 47.049
Project End Date: 31-Jul-2019
Budget End Date:
Agency: ?

Agency: The entity responsible for the administering of a research grant, project, or contract. This may represent a federal department, agency, or sub-agency (institute or center). Details on agencies in Federal RePORTER can be found in the FAQ page.

National Science Foundation
Project Funding Information for 2016:
Year Agency

Agency: The entity responsible for the administering of a research grant, project, or contract. This may represent a federal department, agency, or sub-agency (institute or center). Details on agencies in Federal RePORTER can be found in the FAQ page.

FY Total Cost
2016 NSF

National Science Foundation

$120,000

Results

i

It is important to recognize, and consider in any interpretation of Federal RePORTER data, that the publication and patent information cannot be associated with any particular year of a research project. The lag between research being conducted and the availability of its results in a publication or patent award varies substantially. For that reason, it's difficult, if not impossible, to associate a publication or patent with any specific year of the project. Likewise, it is not possible to associate a publication or patent with any particular supplement to a research project or a particular subproject of a multi-project grant.

ABOUT FEDERAL REPORTER RESULTS

Publications: i

Click on the column header to sort the results

PubMed = PubMed PubMed Central = PubMed Central Google Scholar = Google Scholar

Patents: i

Click on the column header to sort the results

Similar Projects

Download Adobe Acrobat Reader:Adobe Acrobat VERSION: 3.41.0 Release Notes
Back to Top