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Full-Text Articles in Chemistry
Stiefel And Grassmann Manifolds In Quantum Chemistry, Eduardo Chiumiento, Michael Melgaard
Stiefel And Grassmann Manifolds In Quantum Chemistry, Eduardo Chiumiento, Michael Melgaard
Articles
We establish geometric properties of Stiefel and Grassmann manifolds which arise in relation to Slatertype variational spaces in many-particle Hartree-Fock theory and beyond. In particular, we prove thatthey are analytic homogeneous spaces and submanifolds of the space of bounded operators on the single-particle Hilbert space. As a by-product we obtain that they are complete Finsler manifolds. These geometric properties underpin state-of-the-art results on existence of solutions to Hartree-Fock type equations.
Optimising Design Parameters Of Enzyme-Channelling Biosensors, Dana Mackey, Tony Killard
Optimising Design Parameters Of Enzyme-Channelling Biosensors, Dana Mackey, Tony Killard
Conference Papers
Two mathematical models for an electrochemical biosensor are proposed and compared with a view to determining the ratio of two immobilized enzymes which maximizes the amperometric signal amplitude.
Simulation Of Dynamic Electrochemical Processes, John Cassidy
Simulation Of Dynamic Electrochemical Processes, John Cassidy
Articles
This work is designed to introduce electrochemists in a tutorial manner to the basics of modeling of electrochemical systems based primarily on diffusion equations. There is an introduction to analytical and numerical methods with examples taken from typical electrochemical experiments. The Laplace transform is used to derive the Cottrell equation and chronopotentiometry. The response of an electrode to a Gaussian concentration profile is detailed. Laplace’s equation is solved for a simple cell to determine the potential distribution. Discrete methods are employed to calculate the current time behavior following a potential step using the explicit finite difference method. Cyclic voltammetry is …