Analysis of fluid dynamics data via persistent homology

• Grant number: 16/21032-6
• Support Opportunities: Scholarships abroad - Research
• Start date: February 01, 2017
• End date: January 31, 2018
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Marcio Fuzeto Gameiro
• Grantee: Marcio Fuzeto Gameiro
• Host Investigator: Konstantin Mischaikow
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Institution abroad: Rutgers The State University of New Jersey, New Brunswick, United States

Abstract

The goal of this project is to use topological data analysis techniques to analyze complex spatio-temporal data. One of the main tools in topological data analysis is persistent homology, which is essentially a non-linear reduction technique used to significantly reduce the dimension of high-dimensional data while still preserving its essential topological information. The main goal of this project is to apply these techniques to the analysis of fluid dynamics simulations and experimental data to understand its dynamics. This project will be carried out at Rutgers University in collaboration with the group of Konstantin Mischaikow, who is one of the leading scientist worldwide in the development and applications of techniques in topological data analysis. (AU)

Scientific publications

(5)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

GAMEIRO, MARCIO; SINGH, ABHINENDRA; KONDIC, LOU; MISCHAIKOW, KONSTANTIN; MORRIS, JEFFREY F.. Interaction network analysis in shear thickening suspensions. PHYSICAL REVIEW FLUIDS, v. 5, n. 3, MAR 23 2020. (16/08704-5, 16/21032-6)

CASTELLI, ROBERTO; GAMEIRO, MARCIO; LESSARD, JEAN-PHILIPPE. Rigorous Numerics for ill-posed PDEs: Periodic Orbits in the Boussinesq Equation. Archive for Rational Mechanics and Analysis, v. 228, n. 1, p. 129-157, APR 2018. (16/08704-5, 16/21032-6, 13/50382-7, 13/07460-7)

RODRIGUES, HILDEBRANDO M.; TEIXEIRA, MARCO A.; GAMEIRO, MARCIO. On Exponential Decay and the Markus-Yamabe Conjecture in Infinite Dimensions with Applications to the Cima System. Journal of Dynamics and Differential Equations, v. 30, n. 3, p. 1199-1219, SEP 2018. (13/07460-7, 16/21032-6, 12/18780-0, 16/08704-5, 15/19165-5)

RODRIGUES, HILDEBRANDO M.; WU, JIANHONG; GAMEIRO, MARCIO. SWITCHING SYNCHRONIZED CHAOTIC SYSTEMS APPLIED TO SECURE COMMUNICATION. JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, v. 8, n. 2, p. 413-426, APR 2018. (13/07460-7, 16/08704-5, 16/21032-6, 10/00875-9, 14/12277-0)

RODRIGUES, HILDEBRANDO M.; CARABALLO, TOMAS; GAMEIRO, MARCIO. DYNAMICS OF A CLASS OF ODES VIA WAVELETS. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, v. 16, n. 6, p. 2337-2355, NOV 2017. (13/07460-7, 16/21032-6, 16/08704-5, 15/19165-5)