# American Institute of Mathematical Sciences

February  2011, 4(1): 223-237. doi: 10.3934/dcdss.2011.4.223

## Best design for a fastest cells selecting process

 1 IRMAR, ENS Cachan Bretagne, CNRS, UEB, av Robert Schuman F-35170 Bruz, France, France

Received  May 2009 Revised  September 2009 Published  October 2010

We consider a cell sorting process based on negative dielectrophoresis. The goal is to optimize the shape of an electrode network to speed up the positioning. We first show that the best electric field to impose has to be radial in order to minimize the average time for a group of particles. We can get an explicit formula in the specific case of a uniform distribution of initial positions, through the resolution of the Abel integral equation. Next,we use a least-square numerical procedure to design the electrode's shape.
Citation: Michel Pierre, Grégory Vial. Best design for a fastest cells selecting process. Discrete & Continuous Dynamical Systems - S, 2011, 4 (1) : 223-237. doi: 10.3934/dcdss.2011.4.223
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