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Full-Text Articles in Physical Sciences and Mathematics
Mathematically Modeling Pcr: An Asymptotic Approximation With Potential For Optimization, Martha J. Garlick
Mathematically Modeling Pcr: An Asymptotic Approximation With Potential For Optimization, Martha J. Garlick
All Graduate Plan B and other Reports, Spring 1920 to Spring 2023
A mathematical model for PCR (Polymerase Chain Reaction) is developed using the law of mass action. Differential equations are written from the chemical equations, preserving the detail of the complementary DNA single strand being extended one bas e pair at a time. The equations for the annealing stage are solved analytically. The method of multiple scales is used to approximate solutions for the extension stage. A map is then developed from the solutions to simulate PCR. The advantage of this model is the ability to use the map to optimize the process. Our results suggest that dynamically optimizing the extension …
Modeling The Permittivity Of Two-Phase Media Containing Monodisperse Spheres: Effects Of Microstructure And Multiple Scattering, Timothy E. Doyle, David A. Robinson, Scott B. Jones, Keith H. Warnick, Brent L. Carruth
Modeling The Permittivity Of Two-Phase Media Containing Monodisperse Spheres: Effects Of Microstructure And Multiple Scattering, Timothy E. Doyle, David A. Robinson, Scott B. Jones, Keith H. Warnick, Brent L. Carruth
Plants, Soils, and Climate Faculty Publications
A numerical modeling approach was developed to predict the dielectric properties of heterogeneous particulate materials with arbitrary microstructures. To test the method, simulation and experimental data were acquired for the effective permittivities of various glass sphere suspensions. Both ordered lattices and random microstructures of up to 3600 spheres were modeled for volume fractions of 0.025–0.60. The electric fields in the suspensions were computed using an iterative multipole method that included multiple-scattering effects. The effective permittivities were obtained by averaging the electric field and electric displacement over a representative volume. Frequency spectra, electric field images, and single-scattering results (i.e., no particle-particle …