In engineering, a dynamical system has a multitude of meanings. Fluid flow in the human body is considered to be such a system, as well as pollution and pathogens that travel through the air. In fact, atmospheric and aquatic environments provide a dynamical system for a plethora of biological activities. Even the motions of a basketball team or the shuffle of dollars through the economy constitute a dynamical system.
For the past eight years, since receiving his Ph.D. from the California Institute of Technology, Shane Ross, now an assistant professor of engineering science and mechanics at Virginia Tech, has focused his career on determining these various types of behavior and how to more successfully predict what many once believed to simply be chaotic motion.
Based on his activities and ideas, the National Science Foundation has awarded Ross one of its coveted 2012 CAREER Awards, valued at $420,000 over the next five years, to determine how to develop better engineering tools to understand and predict fluid motions.
What often appears to be a random flow of particles can be characterized more effectively, allowing scientists and engineers to have a better understanding and control over areas such as airborne spread of disease agents, Ross said about his motivation for the proposed work. "Many fluid flows have a transport network that may not be obvious. By elucidating this network using mathematical tools we can reveal previously hidden patterns of complex motion in flows," Ross said.
As part of an effort to integrate research and education, Ross plans to develop an unusual project-based graduate course, designed to broaden the application of concepts from dynamical systems theory to practical problems, which will bring together engineering students, non-engineering students, and faculty from varied disciplines across Virginia Tech for team-based projects.
One of the possible projects Ross has identified includes the transport process in drug delivery conducted by Rafael Davalos, a biomedical engineer who is also a CAREER Award recipient. One of Davalos' research areas is in microfluidics, the behavior of fluids at the microscale level. He is investigating the detection of cancer cells by injecting a blood or saliva sample into a specific microfluidic chip to screen for cancer, based on the cancer cells' electrical responses.
Ross also hopes to assemble a team working with Pavlos Vlachos, professor of mechanical engineering and another CAREER award winner, who has been advancing the understanding of cardiovascular flows in order to improve the diagnosis and treatment of heart disease. The physics of blood flow through the human body is still not well understood, and Ross believes an interdisciplinary effort with Vlachos might add to the medical knowledge.
A different type of example of dynamic flow is the oil spill in the Gulf of Mexico in 2010. If mathematical models could correctly show how the polluted particles might be dragged into the Gulf of Mexico's Loop Current, then the people charged with the clean-up task would have known exactly where and how to concentrate their efforts. Ross' findings on pollution dispersion and pathogen transport have been the subject of articles in the physics journal Chaos.
Using the CAREER Award, Ross will also reach out to high school students. He will be working with undergraduates and teaming with a Roanoke Valley Governor's School science teacher, Cynthia Bohland. Together they will design age-appropriate class lessons that address dynamical systems in biology. Bohland teaches a specialized high school elective course called Biotechnology and Bioinformatics. Ross hopes to see the developed resources disseminated through the Virginia Association of Science Teachers.
"Dr. Ross' work is an attempt to expand the applicability of dynamical systems methods to real world data, particularly in the context of fluid flows. His project will provide a new and fruitful approach for conceptualization, visualization, and extraction of information regarding the possible behaviors of such systems. The methods have applicability beyond fluid mechanics, for example, to the boundaries and transitions between qualitatively different kinds of behavior in data sets obtained from meteorological, financial, psychological, or population observations," said Ishwar Puri, professor and head of the engineering science and mechanics department.