'Finding Order in the Apparent Chaos of Currents', New York Times
'Lagrangian coherent structures rule the world', The Economist

Attracting Lagrangian Coherent Structures (LCS) inside an urban street canyon for finite-size inertial particles. The LCS are computed from the slow manifoid velocity derived from simulation data. The forward-time motion shows that an inertial particles is attracted to the local maxima of the Direct Lyapunov Exponent field. The backward-time motion shows the results for inversion of the finite-size particle using different schemes.

Reference: Locating an atmospheric contamination source using slow manifolds (2009), Tang, W., Haller, G., Baik, J.-J. & Ryu, Y.-H., Phys. Fluids, 21, 043302.

Comparison between the repelling LCS generated from model data and atmospheric characteristics estimated by weather balloon measurements. Color contour is the Forward-time DLE. Black line originating from the big island is the balloon trajectory, green curve is refractive index structure constant Cn2 and blue curve is the dissipation rate.

Reference: Lagrangian Coherent Structures Near a Subtropical Jet Stream (2010), Tang, W., Mathur, M., Haller, G., Hahn, D.C. & Ruggiero, F.H., J. Atmos. Sci., 67, 7, 2307-2319.

Evolution of radial velocity detected by LIDAR along with backward-time FDFTLE extracted from the retrieved 2D velocity field. Also shown are Hovmoller diagrams at various ranges indicated by the dotted lines in the movies. First movie: recirculation bubble detachment and regeneration next to a mountain peak. Second movie: a persistent ridge of updraft originated inside a mountain gap.

Reference: Lagrangian Coherent Structure analysis of terminal winds detected by LIDAR. Part II: structure evolution and flight data analyses (2011). Tang, W. Haller, G. & Chan, P.W., J. Appl. Meteorol. Clim., 50, 2167-2183

This workshop is aimed at engaging high-achieving high school students with continued motivation for further mathematical studies. Mathematical models are introduced along with development of physical concepts so the students will learn both simultaneously. Various types of ODE models for natural systems are formed and the concept of dynamics is developed through discussions of the meaning of the models. Students in this workshop get hands-on experience in applying mathematical tools to analyze the dynamical behaviors of the models. Topics such as the Taylor series expansion, vector calculus, linear algebra, differential equations and phase portraits, suitable to the problems presented, are connected so they will not be perceived as disjointed math subjects in future studies.

High school students in this workshop also get the opportunity to visit the ASU campus and collaborate with successful undergraduate students in applied mathematics on problems discussed in workshop. Interactions with college students and faculty help the participating students learn from role models and be informed with career opportunities in STEM fields.

A presentation on applied dynamics can be located here.

Workshop notes can be located here.

High school students can also participate in research activities at our lab. Throughout the course of the internship the students will be exposed to different mathematical concepts linked to solve applied problems in different disciplines. Concept based learning of mathematical topics is further solidified through hands on research questions.

Currently students from BioSciences High School, Phoenix have benefitted from participating in this internship.