Professor Keith Promislow

PhD Students

Graduate Students Ph.D Progression Thesis Description
Noa Kraitzman
Noa Kraitzman
June 2015 Postdoc: Univ. of Utah Noa has developed analytic characterizations of the pearling bifurcation for general bilayer morphologies under the strong functionalization regime of the FCH free energy. She is extending this to pore morphologies (co-dimension two), and will examine the competive geometric evolution of pore and bilayer morphologies and its impact on the pearling bifuraction.
Hana Cho
Hana Cho
Current Ph.D student at MSU Under the primary supervision of Andrew Christlieb, Hana is developing numerical alogrithms for the Cahn-Hilliard and Functionalized Cahn-Hilliard gradient flows based upon an exponential time differencing approach that exploits higher-order truncations of resolvent expansions for the associated semi-group. Her goal is to develop higher-order numerical methods whose time-stepping is limited by accuracy and not stability and are applicatble to wide ranges of boundary conditions.
Jaylan Jones
Jaylan Jones (left) FCH (right)
2013 Current: Raytheon Corporation Under the primary supervision of Andrew Christlieb, Jaylan developed numerical algorithms for the Functionalized Cahn-Hilliard gradient flow in three space dimensions+time. In particular he adapted Eyre type concave-convex splitting ideas as well as exponential time integrators to run on GPGPU machines, see publications [53] and [58].
Yang Li
Li Yang (right)
2013 Postdoc: INRIA, Sophia-Antipolis, France Li investigated the bifurcation of bilayer morphologies from single layers as a singular limit in the equal to unequal depth well transition within the FCH free energy. He combined dynamical systems and functional analysis techniques, removing the singularity via a delicate projection off a particular component of a Jordon block subspace that unfolds during the transtion. See publication [57].
Gurgen (Greg) Hayrapetyan
Gurgen (Greg) Hayrapetyan (right)
2011 Postdoc: Carnegie Mellon Univ.

Asst. Prof.: University of Ohio
Greg pursued a rigorous analysis of geometric evolution of bilayers under the gradient flow of the Functioanlized Cahn-Hilliard (FCH) free energy. He analyzed the structure of the second variational derivative of the FCH about bilayers, showing that the only possible instabilities arise from the meander instability via curvature driven flow or through pearling instabilities. For related work see publications [47], [59], and [61]. Greg completed a postdoctoral fellowship at Carnegie Mellon University in 2014.
Tom Bellsky
Tom Bellsky
2011 Postdoc: Arizona State Univ.

Asst. Prof.: University of Maine
Tom extended renormalization group techniques to analyze semi-strong multipulse interaction within a singularly-perturbed reaction diffusion system. In particular Tom addressed the limit in which the essential spectrum is asymptotically close to the origin, and the multipulse family loses a form of normal hyperbolicity. See publication [55] for details. Tom completed a postdoctoral fellowship at Arizona State University in 2014.
Mohar Guha
Mohar Guha
2007 Postdoc: Univ. Michigan

Current: Data Analyst in Bay Area
Mohar investigated the stability of traveling pulses in a non-smooth exhitable medium in a noisy enviroment. The key difficulty was the identification of function spaces strong enough to control the location of the front while weak enough to tolerate the discontinuity in the nonlinearity. The resulting rigorous analysis appeared in publication [44]. Mohar continued her studies as a postdoctoral fellow at the University of Michigan, and is currently employed as a data analyst in the Bay Area.
Paul Chang
Paul Chang
2002 Postdoc: Univ. British Columbia

Current:Microsoft Scientist
Paul analysed stability of multicomponent pulses in optical paramteric oscillators [38] and developed models of water transport within polymer electrolyte membranes. During his postdoctoral work he was affiliated with the MITACS group at Ballard Power systems. Currently Paul is a scientist in the Chief Economist's Office at Microsoft, contributing applied econometric analysis to high-impact projects including cloud pricing, search auctions, machine learning prediction, and market design.

Postdocs

Postdoc At MSU Now Research Activities
Qiliang Wu
Qiliang Wu
2013-2015 Current Qiliang has derived rigorous existence of pearled bilayer morphologies in the strong FCH free energy using spatial dynamics techniques, characterizing the reduction to the center manifold which leads to pearling as a degenerate 1:1 resonant normal form. The degeneracy illuminates the difficulties encountered with accurate numerical resolution of pearled states, see publication [63].
Shibin Dai
Shibin Dai
2011-2013 Asst. Prof.: New Mexico State Univ. Developed asymptotics for the coupled geometric evolution of co-dimension one bilayers and co-dimension two pores under the weak limit of the Functionalized Cahn-Hilliard free energy. See publications [56] and [62] for details.
Nir Gavish
Nir Gavish (left)
2011-2013 Asst. Prof.: Technion Institute Analyzed the geometric evolution of bilayer morphologies in the equal-depth-well regime of the weak FCH free energy. Developed expressions for free energy of multicomponent salt solutions and connections to differential capacitance data. See publications [47] and [51] for details.
Richard Moore
Richard Moore
2001-2003 Assoc. Prof.: New Jersey Inst. Technology Used renormalization group techniques to derive asymptotics for multipluse interactions in the semi-strong regime of singularly perturbed dispersive PDEs, see publications [28] and [41].
Ricardo Carretero
Ricardo Carretero (right)
1998-2000 Prof.: San Diego State University Investigated existence of breather solutions in Bose-Einstein condensates and stability of nonlinear optical standing waves in lattice potentials, see publications [17, 19, 22].