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MSCA Expressions of Interest 2017

Ana Carpio
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Mathematics applied to biological and physical systems
Applied Mathematics
Faculty of Mathematical Science
The Group works in a variety of modelling, analysis, numerical and computational issues arising in the study of biomedical and physical problems of current interest.

Publications and projects cover a wide range of topics:

1) Modeling and simulation:
-Biomedicine: hybrid models for cellular aggregates including cellular activity and macroscopic responses, development of biofilm patterns on surfaces and in flows, folding and unfolding of proteins, transmission of nerve impulses along myelinated nerves…
-Materials: defects in hexagonal graphene lattices, curvature effects and interaction with ripples adapting Von-Karman plate theory to graphene sheets, discrete periodized elasticity for dislocations in crystals...

2) Variational methods for imaging:
- Methods based on the topological derivative of error functionals to predict the material properties and structure of objects buried in a medium.
- Applications to tomography, acoustics, phototermia, digital holography.

3) Analysis of differential models in physics and biology:
-Well posedness and long time behavior in kinetic equations of Fokker-Plank type for angiogenesis, Boltzmann equations for semiconductors, Navier-Stokes and vorticity equations.
-Discrete waves: Pinning and depinning of travelling waves in nonlinear lattice models, nonreflecting numerical schemes for the approximation of waves.

The group interacts with researchers in top Universities: Oxford, Stanford, Harvard, UC Santa Barbara, Duke, Paris VI, Milan...
Mathematical models for the treatment of depressive disorders.
- New line to study the influence of biochemical and sociological factors on this type of disorders in collaboration with the biomedical sector.

Multiscale modeling and simulation of biofilms
- Developing descriptions of cellular aggregates such as baterial biofilms requires the study of mechanisms at the microcospic and macroscopic level as well as their interaction. Mathematical approaches for cell behavior often have a stochastic basis, informed by the dynamics of continuum variables (concentrations, flows...).
Describing the macroscopic responses of the cellular aggregate involves continuum models: 3D elasticity, plate and rod approximations, fluid transport in porous media, poroelasticity, interaction fluid/structure... Strategies to transfer key information between the microscopic and macroscopic submodels must be devised. Efficient simulation environments for the variety of equations in volved must be developed.

Long time behavior and perturbation methods in partial differential equations
- Recent angiogenesis models describe the dynamics of the vessel tip density through Fokker-Planck type equations with measure valued coefficients coupled to reaction-diffusion systems. Well posedness results, numerical schemes and long time dynamics are the subject of current research.

Variational methods for imaging
- Topological sensitivity based techniques have arisen as a powerful tool to reconstruct the geometry and properties of objects buried in a medium by scattering of electromagnetic, acoustic or thermal waves, without a priori knowledge on the objects. Applications to noninvasive imaging of biological and soft matter samples in digital holography settings at the nano and microscales are in progress.
Life Sciences (LIF), Mathematics (MAT), Physics (PHY)
Curriculum vitae: education, career/employment, honours, awards, fellowships, publicactions, conferences, research grants, student training, computing skills, other academic activities, non academic activities
Presentation letter detailing overall research interests and the motivation to join our group
Recommendation/reference letters
Relevant publications
2017-07-15 00:00:00
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