A mathematical model of a biosensor |
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| Authors: | S Jones B Jumarhon S McKee J A Scott |
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| Affiliation: | (1) Unilever Research, Colworth Laboratory, Colworth House, Sharnbrook, Bedford, U.K.;(2) School of Computing and Mathematical Sciences, Oxford Brookes University, OX3 0BP Oxford, U.K.;(3) Department of Mathematics, Strathclyde University, 26 Richmond Street, Glasgow, Scotland, U.K.;(4) Rutherford Appleton Laboratory, Didcot, Oxon, U.K. |
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| Abstract: | This paper is concerned with the modelling of the evolution of a chemical reaction within a small cell. Mathematically the problem consists of a heat equation with nonlinear boundary conditions. Through an integro-differential equation reformulation, an asymptotic result is derived, a perturbation solution is developed, and a modified product integration method is discussed. Finally, an alternative integral formulation is presented which acts as a check on the previous results and permits high accuracy numerical solutions. |
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