More than 120 mathematicians from around the world descended last month upon New Jersey Institute of Technology (NJIT) for news of the foremost advances in mathematical fluid dynamics at the university’s annual conference on applied and computational mathematics. Plenary speakers included mathematician Charles S. Peskin, PhD, of the Courant Institute of Mathematical Sciences at New York University, well known for his research on mathematical models of the beating heart.
Other speakers included John Hinch, PhD, department of applied mathematics and theoretical physics at Cambridge University, England and a Fellow of the Royal Society; Grigory Barenblatt, PhD, a renowned applied mathematician from the University of California at Berkeley who studies the flow of fluids, and Tom Hou, PhD, a professor at California Institute of Technology, also famous for his work on the flow of fluids.
Today mathematicians, thanks to the ability of supercomputers, employ mathematical modeling to create remarkably accurate scenarios of unexplained phenomena in the physical and natural sciences. “In turn,” said Robert Miura, PhD, acting chair, of the department of mathematical sciences at NJIT, “scientific researchers find themselves teaming up with mathematicians to learn of better ways to eliminate or control the damage from natural disasters and other crises.”
Barenblatt’s research attracts the attention of not only mathematicians, but engineers and physicists. Using mathematics, he studies the flow of fluids, said Michael Siegel, PhD, professor in the department of mathematical sciences at NJIT. When gases and liquids, such as air and water, do not follow a uniform motion and become chaotic-- the behavior of physical systems become unpredictable. Barenblatt understands the mathematics behind these turbulent chaotic fluid motions.
“We have many mathematicians who wanted to hear Barenblatt,” said Siegel. “His theories may be useful in understanding why materials like metals crack, how flame waves move and the mechanics of explosions.”
Barenblatt’s presentation, “Incomplete Similarity in Continuum Mechanics,” focused on the chaotic or whirling motions of fluids (also known as turbulence), special similarity solutions and scaling laws in fluid dynamics.
Peskin is famous for his mathematical models using a computer representation of a beating heart. “This is very impressive stuff,” said Siegel. For example, Peskin might be able to work out for heart surgeons precise worst-case scenarios showing what happens next to the blood flow if, say, a heart were to develop an atrial fibrillation.
Siegel said that Peskin creates a mathematical model of the human heart, modeled as an elastic object embedded in a fluid. The difficulty of what he does is to link the fluid flow to the heart’s elastic motion. Peskin has been working on this research for more than 20 years. The new element, which he discussed at the meeting, was mathematically incorporating electric signals into his models.
Signals are important because they govern the coordination and control of the heartbeat, said Siegel. The electric signal tells the heart when to contract and when to relax. Peskin’s talk was entitled “Cardiac Mechanics and Electrophysiology by the Immersed Boundary Method.”
Hinch’s presentation analyzed the collapse of a column of grains. His research is motivated by the desire to understand landslides, explained Siegel. Hinch is well known for his work on the dynamics of drops and bubbles in fluids and for his work on suspensions. Hinch showed mathematically how the column of grains collapsed onto a horizontal, flat plain. Such an experiment offers researchers a better understanding of the distance the grains run out.
His research is really important because his model imitates the motion of particles in a landslide, Siegel explained. The model leads to simple rules concerning the distance the grains run out, which is in agreement with experimental and numerical simulations.
Hou presented recent work on what is considered an outstanding open problem in mathematical fluid dynamics. He asked and answered the question: Do the equations that govern the motion of frictionless fluids have reasonable solutions? The title of the presentation was: “The Interplay Between Local Geometric Properties and the Global Regularity of the 3-D Incompressible Euler Equations.”
To learn more about the conference or the department of mathematical sciences at NJIT, contact Susan Sutton at 973-596-3235.