Analysis of Spin Polarized Transfer and of Micro-Macro Theories for Polymers and Liquid Crystals

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The investigator takes up three projects. In the firstproject, the emphasis is the analysis and the design of efficientnumerical methods for the simulation of recent models proposed forthe dynamics of the magnetization coupled to the spin accumulationin multilayers when a current perpendicular to the plane of thelayers is applied. The dynamical equation for the spin is adiffusion equation with discontinuous coefficients, and themagnetization dynamics is described by the Landau-Lifshitzequation from ferromagnetism. In the second project, theinvestigator studies a new model for liquid crystals based onInhomogeneous Density Functional Theory. The model can describethe isotropic, nematic, smectic A, and crystalline phases. Finally, in the third project, the investigator studies theformation of aggregates in polymer mixtures. Ferromagnetic materials are widely used in the magneticrecording industry, which continues to be the dominant technologyfor the storage of digital data. The project addresses some ofthe technological difficulties found in the design of magneticdevices such as magnetic memories (MRAMs). Liquid crystals have awide range of applications. Their optical properties are highlysensitive to electric and magnetic fields, which has made liquidcrystals ideal candidates for optical-switching devices, such asvideo displays and optical memories. They are very sensitive totemperature changes as well, which makes them useful inapplications involving sensors. More generally, polymers appearin most aspects of our life, from the amniotic fluid insidebiological cells, to plastics and shampoos used on a daily basis. Understanding the dynamics of biological membranes and transportthrough them is of fundamental importance in the development ofefficient methods for the delivery of medicines. Understandingthe process of aggregation in polymer mixtures can have asignificant impact in the design of new products. This study ofpolymers and liquid crystals addresses some of these technologicaland biological issues.