External potential deep well

Due to the ubiquitous nature of Brownian motion in microfluidics, the ability to constrain it has wide-ranging applications in sensing and directed assembly. The constraint is provided by imposing an appropriately shaped external potential on the particle s motion. For example, if the purpose is to trap a colloidal particle positionally, then the potential well should be deep enough so that the particle cannot escape the well due to the random Brownian perturbations experienced by it. Such potentials typically employ forces that depend on the particle s material properties, for example, optical and electrical. An alternate approach that does not rely on the particle s material properties but instead involves shaping the potential well by altering the flow surrounding... 

The reason for such problems is contained in the following quotation from Pulay [7] Nuclear coordinates as perturbation parameters are different from other common perturbations, e.g. weak external fields. The reason for this is the deep and singular potential well at the nucleus which leads to large charge density near the nucleus . The key is suggested by a further quotation from the same source ... the... 

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