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I will present how level set methods can be used to design and develop new algorithms for self-consistent field theory (SCFT) in polymer physics. I first present a computational framework, encoded on a forest of quad/oct trees in a parallel environment. I then introduce the concept of functional level-set derivative into SCFT which is then used to embed SCFT into a variable shape simulation. Finally an algorithm for the inverse geometric problem is presented: it finds a shape in order to obtain a desired structure.

Research Interests:

My research interests are but not limited to: computational and applied mathematics, soft matter, polymer field theory, fluid mechanics, shape optimization and high performance and parallel computing. During my master I developed a computational model to study the collective stochastic motion of biological cells during wound healing. In my PhD I developed algorithms for variable shape polymer field theory simulations using level set methods. Polymer field theory allow to find polymeric material properties and structure at thermodynamic equilibrium. Level set methods allow to vary the domain simulation in a simple way. When the geometry of the domain is a free variable of the polymeric material design, efficient algorithms are required to find the optimal shape. Currently during my postdoc I develop algorithms for massive parallelization of Stokesian dynamics to simulate large scale complex fluids where particles interact in a viscous fluid through hydrodynamic interactions.

In the future I intend to work on polymer field theory, fluid mechanics and numerical shape optimization methods. I am interested in electro active polymers which exhibit a change of shape and size when stimulated by an electric field. These are called artificial muscles and are used in soft robotics. I will develop a polymer theory which takes into account the electrical field, the mechanical stress and the change of shape. As well I will develop numerical methods and algorithms to solve the resulting equations. In fluid mechanics I am interested in soft robots with a continuous and transient shape immersed in a fluid. I am as well interested to develop numerical methods toward efficient shape optimization algorithms and applications. Indeed shape optimization methods have to rely on numerical shape derivatives which are highly complex objects and require special care either in finite difference or in finite element.

Teaching Interests:

My teaching interests are numerical methods, programming, finite element methods, mathematics, physics, solid mechanics, fluid mechanics, statistical mechanics and heat transfer. I enjoy teaching on the board, interact with students and answer questions.