Newhall, Katherine A
Applied Mathematics, Stochastic Differential Equations, Dynamical Systems
B.S. in Applied Physics and Applied Mathematics from Rensselaer Polytechnic Institute, 2004; M.S. in Aeronautical Engineering from Rensselaer Polytechnic Institute, 2006; Ph.D. in Mathematics from Rensselaer Polytechnic Institute, 2011; Courant Instructor/Assistant Research Professor at the Courant Institute for Mathematical Sciences, New York University 2011-2014;
I develop new tools for analyzing large and infinite dimensional stochastic systems in order to understand large-scale and long-time dynamics of physical and biological systems. Stochastic models are becoming more prevalent in all fields of science, with successful analysis often being based on Fokker-Planck type formulations.
As these Stochastic models increase in dimension and complexity, the standard Fokker-Planck based tools become intractable to use both computationally and analytically. Rather, my work builds on concepts of statistical mechanics, creating macroscopic or population level descriptions from the statistics of individual units, and extending the usefulness of an energy landscape even in the case of non-gradient systems. By advancing these tools for stochastic systems, I have been able to explain experimentally observable phenomena while exposing the fundamental mechanism responsible for the system's behavior.
Nonlocal Stochastic-Partial-Differential-Equation Limits of Spatially Correlated Noise-Driven Spin Systems Derived to Sample a Canonical Distribution
Y. Gau, J. L. Marzuola, J. Mattingly, K. A. Newhall,
Physical Review E, 102, 052112, 2020
Metastability of the Nonlinear Wave Equation: insights From Transition State theory
K. A. Newhall & E. Vanden-Eijnden,
Journal of Nonlinear Science, 27, 007-1042, 2017
Size-Topology Relations in Packings of Grains, Emulsions, Foams, and Biological Cells
K. A. Newhall, L. L. Pontani, I. Jorjadze, S. Hilgenfeldt, and J. Brujic,
Physical Review Letters, 108, 268001, 2012