Reaction-diffusion theory in the presence of an attractive harmonic potential.
Problems involving the capture of a moving entity by a trap occur in a variety of physical situations, the moving entity being an electron, an excitation, an atom, a molecule, a biological object such as a receptor cluster, a cell, or even an animal such as a mouse carrying an epidemic. Theoretical considerations have almost always assumed that the particle motion is translationally invariant. We study here the case when that assumption is relaxed, in that the particle is additionally subjected to a harmonic potential. This tethering to a center modifies the reaction-diffusion phenomenon. Using a Smoluchowski equation to describe the system, we carry out a study which is explicit in one dimension but can be easily extended for arbitrary dimensions. Interesting features emerge depending on the relative location of the trap, the attractive center, and the initial placement of the diffusing particle.
BioFrontiers Center, University of Colorado at Colorado Springs, Colorado Springs, Colorado 80918, USA and Department of Physics and Energy Science, University of Colorado at Colorado Springs, Colorado Springs, Colorado 80918, USA.
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Spendier
Consortium of the Americas for Interdisciplinary Science, University of New Mexico, Albuquerque, New Mexico 87131, USA and Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131, USA.
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Sugaya
Consortium of the Americas for Interdisciplinary Science, University of New Mexico, Albuquerque, New Mexico 87131, USA and Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131, USA.
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Kenkre