PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Hope Shaffer, Chun Liu, Fei Wang.

Title:Chemistry and Biology Need Variational Models
Seminar:Computational and Applied Mathematics Colloquium
Speaker:Bob Eisenberg, Rush Medical Center (Host: J Xu)
Abstract:
Mathematics is responsible for most of our standard of living, but no one seems to know that. The quantitatively reliable calculations of structural mechanics makes tall buildings possible; the quantitatively reliable calculations of fluid mechanics makes airplanes possible (as well as plumbing); most importantly the quantitatively reliable calculations of electronics makes our semiconductor technology possible, and that has remade our lives. Our computer technology is one billion times more capable than when I was a graduate student! Without PNP (called drift diffusion in computational electronics), semiconductor technology would be crippled. Indeed, it would not exist. Mathematics has been a much less reliable guide in chemistry and biology. Biological sciences are almost entirely sophisticated trial and error. Chemical sciences use mathematics more to interpret than design. Chemical models must change parameters in ways that cannot be predicted as conditions change. Chemical models are rarely “transferrable” to use their language. The ‘law of mass action’ is the foundation of most chemical and biological theory, because it seems a simple statement of conservation of mass. The law of mass action leads to models that cannot be used in more than one set of conditions, in most cases. The law of mass action is incompatible with the laws of electricity. It does not conserve charge movement because it does not deal with charge at all. Models built ONLY on the law of mass action are local. Electrical behavior and its laws are global. Very specifically, everyone knows that “current flows in loops”. Everyone knows that interruptions in current flow anywhere in a series of reactions interrupts the flow everywhere. Schemes built only from the law of mass action (conservation of matter as used in chemical theory) do not have this property. Variational methods can deal with global interacting systems like these. Variational methods can combine conservation laws for mass and electric current. But those methods have not been available for dissipative systems. Mathematics of chemistry and biology must deal with dissipation, because friction is everywhere in condensed phases. There is no empty space in condensed phases, so when something moves, it collides and dissipates energy into the randomized motion we call heat. Variational methods have now been extended to include dissipative systems, like those found throughout biology and chemistry, thanks to Chun Liu, more than anyone else. I will show in detail how current flow in a wide variety of systems needs such mathematics. I will show our variational model of ions in solutions and in biological molecules called ion channels. I will seek help in solving these models and converting them into specific predictions of experiments. Mathematics in chemistry and biology promises to make models as reliable as those of semiconductors. Technological progress will vastly accelerate in biology and nanosciences, include chemistry, when trial and error experimentation can be catalyzed by models that are quantitatively reliable.

Room Reservation Information

Room Number:MB106
Date:02 / 02 / 2015
Time:02:30pm - 03:30pm