Noa Kraitzman

MSI Fellow

I am an MSI fellow at the Australian National University. My research interests lie in applied mathematics at the intersection of asymptotic analysis of multiscale dynamical systems, nonlinear partial differential equations, and functional analysis. Currently, I am interested in mathematical climate models which involve heat convection, phase separation and solidification in sea ice. I focus on thermal conduction in sea ice in the presence of fluid flow, as an important example of an advection diffusion process in the polar marine environment. Using new Stieltjes integral representations for the effective diffusivity in turbulent transport, we have obtained a series of rigorous bounds on the effective diffusivity.

From 2015-2019 I was a research assistant professor / NSF Ed Lorenz Postdoctoral Fellow in the Mathematics of Climate at the University of Utah, in the department of mathematics.

    In 2015, I received my Ph.D. from the mathematics department at Michigan State University. The focus of my Ph.D. was on the development of network morphologies in amphiphilic polymer systems with applications to ion transport in electrolyte membranes and to network formation in lipid membrane.

      I have a B.Sc. in mathematics from Tel Aviv University.

        Research interests

        Composite Material and Sea Ice

        I am interested in mathematical models that can be used to describe climate phenomena that involve advection enhanced diffusion processes, phase separation and solidification. Using analysis of the heat equation, modification of the Stefan problem and Stieltjes integrals I was able to obtain analytic bounds on the thermal conductivity in the presence of fluid flow, analytic bounds on the trapping constant and a coupled system describing the evolution of the marginal ice zone involving the ice concentration and heat diffusion.

        September 2017, invited speaker, Multi-scale modelling of ice characteristics and behaviour, Isaac Newton Institute for Mathematical Sciences, Cambridge, UK.  See lecture here

         

        Functionalized Cahn-Hilliard

        The FCH is a higher-order free energy for blends of amphiphilic polymers and solvent which balances solvation energy of ionic groups against elastic energy of the underlying polymer backbone. Its gradient flows describe the formation of solvent network structures which are essential to ionic conduction in polymer membranes. The FCH possesses stable, coexisting network morphologies and we characterise their geometric evolution, bifurcation and competition through a center-stable manifold reduction which encompasses a broad class of coexisting network morphologies. The stability of the different networks is characterised by the meandering and pearling modes associated to the linearized system. For the H−1H−1 gradient flow of the FCH energy, using functional analysis and asymptotic methods, we drive a sharp-interface geometric motion which couples the flow of co-dimension 1 and 2 network morphologies, through the far-field chemical potential. In particular, we derive expressions for the pearling and meander eigenvalues for a class of far-from-self-intersection co-dimension 1 and 2 networks, and show that the linearization is uniformly elliptic off of the associated center stable space.

        May 2015, mini-symposium organiser, SIAM: Conference on Applications of Dynamical Systems, Snowbird, UT. See lecture here

        Groups

        Publications

        • N. Kraitzman & K. Promislow, (2014) An Overview of Network Bifurcations in the Functionalized Cahn-Hilliard Free Energy, editors: Jean Pierre Bourguignon, Rolf Jeltsch, Alberto Pinto, and Marcelo Viana, Mathematics of Energy and Climate Change: International Conference and Advanced School Planet Earth, Springer International Publishing, (pp. 191-214).
        • N. Kraitzman & K. Promislow, (2018) Pearling Bifurcations in the Strong Functionalized Cahn-Hilliard Free Energy, SIAM Journal on Mathematical Analysis), Volume 50, Issue 3, pp.3395-3426. DOI
        • A. Christlieb, N. Kraitzman & K. Promislow, (2019)  Competition and complexity in amphiphilic polymer morphology. Physica D: Nonlinear Phenomena. DOI

        Under Review

        • N. Kraitzman, E. Cherkaev & K. Golden, Advection Enhanced Diffusion in a Porous Medium, Submitted.

        Work in Progress

        • N. Kraitzman, R. Hardenbrook, B. Murphy, E. Cherkaev, J. Zhu & K.Golden, Bounds on the Effective Thermal Conductivity of Sea Ice in the Presence of Fluid Convection, In preparation.
        • N. Kraitzman, E. Cherkaev & K. Golden, Analytic Bounds on the Trapping Constant in Sea Ice, In preparation.