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ACCURATE AND EFFICIENT CALCULATION OF SINGULAR ELECTROSTATIC POTENTIALS IN CHARGE-DIELECTRIC SPHERICAL AND JANUS PARTICLE SYSTEMS
Title
ACCURATE AND EFFICIENT CALCULATION OF SINGULAR ELECTROSTATIC POTENTIALS IN CHARGE-DIELECTRIC SPHERICAL AND JANUS PARTICLE SYSTEMS
Author
Retz, Caylah
Date Created
2018
Subjects--Topical
Molecular biology, Mathematics, Physics
Description
We introduce an efficient and accurate boundary element method for computing the electrostatic potential in closely-packed dielectric spheres and Janus particles. Close physical proximity occurs in modeling molecular ion interactions or colloidal ...
High Order H(div) Discontinuous Galerkin Methods for MHD Equations
Title
High Order H(div) Discontinuous Galerkin Methods for MHD Equations
Author
Wu, Jian
Date Created
2016
Subjects--Topical
Mathematics
Description
In this dissertation, we investigate the divergence-free discontinuous Galerkin method using the $\mathcal{H}$(\textbf{div}) basis, to solve the nonlinear ideal magnetohydrodynamics (MHD) equations. This is a novel approach to ensure the divergenc...
Hybrid solvation models for electrostatic interactions in molecular dynamics simulations of ionic solvent
Title
Hybrid solvation models for electrostatic interactions in molecular dynamics simulations of ionic solvent
Author
Xiang, Ming
Date Created
2012
Subjects--Topical
Mathematics, Biochemistry, Biophysics
Description
In this dissertation, we mainly discuss the image approximation methods to the reaction field and their applications to electrostatic interactions in molecular dynamics simulations. The Poisson-Boltzman (PB) equation, a three-dimensional second or...
IMAGE CHARGE SOLVATION MODEL (ICSM) FOR SIMULATING BIOMOLECULES AND KCSA ION-CHANNELS
Title
IMAGE CHARGE SOLVATION MODEL (ICSM) FOR SIMULATING BIOMOLECULES AND KCSA ION-CHANNELS
Author
Baker, Katherine
Date Created
2014
Subjects--Topical
Mathematics
Description
We present an order N method for calculating electrostatic interactions that has been integrated into the molecular dynamics portion of the TINKER Molecular Modeling package. This method, termed the Image-Charge Solvation Model (ICSM), and introdu...
Path Integral Methods Using Feynman-Kac Formula and Reflecting Brownian Motions for Neumann and Robin Problems
Title
Path Integral Methods Using Feynman-Kac Formula and Reflecting Brownian Motions for Neumann and Robin Problems
Author
Zhou, Yijing
Date Created
2016
Subjects--Topical
Mathematics
Description
In this dissertation, we propose numerical methods for computing the boundary local time of reflecting Brownian motion (RBM) in 3d and its use in the probabilistic representation of the solution of the Laplace equation with the Neumann and Robin b...