THE MALLAT FAMILY FUND FOR RESEARCH IN MATHEMATICS
invites you to a
SPECIAL LECTURE SERIES
to be presented by
The lectures will be held in
Technion - Israel Institute of Technology
Diffusion mediated transport with a look at motor proteins
Motion in small live systems has many challenges. Prominent environmental conditions are high viscosity and warmth. Not only is it difficult to move, but maintaining a course is rendered difficult by immersion in a highly fluctuating bath. This holds especially for the motor proteins responsible for much of eukaryotic cellular traffic. The situation falls under the rubric of diffusion mediated transport. We give some brief historical notes, the work of many distinguished scientists, and then turn to an approach based on the Monge transport problem (1787) and its modern version, Monge- Kantorovich Theory, which offers us a means of studying these systems with analysis. We arrive at a precipice: does this help? Can we say anything about the behavior of the cellular process? An exciting venue for math in the natural world!
Analysis of the multistate transport system
The multistate Brownian motors or molecular rachet mechanisms introduced in the first talk result in weakly coupled systems of evolution equations, generally speaking. Their stationary solutions are not in equilibrium and detailed balance conditions fail to hold. But out of equilibrium status is not sufficient for reliable transport. We examine this question
Making sense of microstructure
Most technologically useful materials are polycrystalline, comprised of many small grains separated by interfaces, called grain boundaries. The energetics and connectivity of this network of interfaces plays a role in many material properties and across many scales of use. Preparing arrangements of grains and boundaries, a texture, suitable for a given purpose is a central problem in materials science: it is the problem of microstructure. Recent years have witnessed a changing paradigm in experimental science: automated data acquisition technologies, now practiced in disciplines as varied as materials science and molecular biology, allow vast interrogation at certain scales. Typically most interesting are those mesoscales rich in information. The yield has been huge amounts of data, demanding novel approaches for interpretation. These advances pose new challenges for our understanding of such systems through mathematical modeling, simulation, and analysis.