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You searched for +publisher:"Texas State University – San Marcos" +contributor:("Treinen, Ray"). Showing records 1 – 3 of 3 total matches.

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Texas State University – San Marcos

1. King, Haley R. The Double Sessile Drop.

Degree: MS, Mathematics, 2017, Texas State University – San Marcos

We consider the double sessile drop, which is formed of two connected drops of liquid with prescribed volumes V1 and V2 resting in equilibrium on a horizontal plane P in a vertical gravity field directed toward P. We suppose that the plane is made of homogeneous material so that contact angles are constant. The size and shape of each drop for any liquid is determined by the prescribed volume and the solutions for the curves that enclose the liquid. Advisors/Committee Members: Treinen, Ray (advisor), Dix, Julio (committee member), Passty, Gregory (committee member).

Subjects/Keywords: Capillarity; Fluids; Surface chemistry; Capillarity

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APA (6th Edition):

King, H. R. (2017). The Double Sessile Drop. (Masters Thesis). Texas State University – San Marcos. Retrieved from https://digital.library.txstate.edu/handle/10877/6760

Chicago Manual of Style (16th Edition):

King, Haley R. “The Double Sessile Drop.” 2017. Masters Thesis, Texas State University – San Marcos. Accessed August 17, 2019. https://digital.library.txstate.edu/handle/10877/6760.

MLA Handbook (7th Edition):

King, Haley R. “The Double Sessile Drop.” 2017. Web. 17 Aug 2019.

Vancouver:

King HR. The Double Sessile Drop. [Internet] [Masters thesis]. Texas State University – San Marcos; 2017. [cited 2019 Aug 17]. Available from: https://digital.library.txstate.edu/handle/10877/6760.

Council of Science Editors:

King HR. The Double Sessile Drop. [Masters Thesis]. Texas State University – San Marcos; 2017. Available from: https://digital.library.txstate.edu/handle/10877/6760


Texas State University – San Marcos

2. Clancy, Richard J. Numerical Solutions to Poisson's Equation Over Non-Uniform Discretizations with Associated Fast Solvers.

Degree: MS, Applied Mathematics, 2017, Texas State University – San Marcos

Partial differential equations (PDE's) lay the foundation for the physical sciences and many engineering disciplines. Unfortunately, most PDE's can't be solved analytically. This limitation necessitates approximate solutions to these systems. This thesis focuses on a particular formulation for solving differential equations numerically known as the finite difference method (FDM). Traditional FDM calls for a uniform discretization of the domain over which the PDE is defined. In certain cases, the behavior of a PDE's solution is interesting in a particular region that we would like to better understand. Uniform discretization fails to increase resolution where desired. This manuscript investigates the approximation error of non-uniform discretizations and outlines attempts made at developing a fast-solver for efficiently handling the resultant non-symmetric system of linear equations. Advisors/Committee Members: Lee, Young Ju (advisor), Passty, Gregory (committee member), Treinen, Ray (committee member).

Subjects/Keywords: Numerical PDE; Shortley-Weller; Differential equations, Partial; Numerical analysis

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Clancy, R. J. (2017). Numerical Solutions to Poisson's Equation Over Non-Uniform Discretizations with Associated Fast Solvers. (Masters Thesis). Texas State University – San Marcos. Retrieved from https://digital.library.txstate.edu/handle/10877/6613

Chicago Manual of Style (16th Edition):

Clancy, Richard J. “Numerical Solutions to Poisson's Equation Over Non-Uniform Discretizations with Associated Fast Solvers.” 2017. Masters Thesis, Texas State University – San Marcos. Accessed August 17, 2019. https://digital.library.txstate.edu/handle/10877/6613.

MLA Handbook (7th Edition):

Clancy, Richard J. “Numerical Solutions to Poisson's Equation Over Non-Uniform Discretizations with Associated Fast Solvers.” 2017. Web. 17 Aug 2019.

Vancouver:

Clancy RJ. Numerical Solutions to Poisson's Equation Over Non-Uniform Discretizations with Associated Fast Solvers. [Internet] [Masters thesis]. Texas State University – San Marcos; 2017. [cited 2019 Aug 17]. Available from: https://digital.library.txstate.edu/handle/10877/6613.

Council of Science Editors:

Clancy RJ. Numerical Solutions to Poisson's Equation Over Non-Uniform Discretizations with Associated Fast Solvers. [Masters Thesis]. Texas State University – San Marcos; 2017. Available from: https://digital.library.txstate.edu/handle/10877/6613


Texas State University – San Marcos

3. Gallo, Erika. Numerical Approach to Energy Minimization of Fluid Configurations Using Phase-Field Models.

Degree: MS, Applied Mathematics, 2018, Texas State University – San Marcos

We consider a fluid, under isothermal conditions and confined to a bounded container of homogeneous makeup, whose Gibbs free energy, per unit volume, is a prescribed function of its density distribution. Based on the Van der Waals-Cahn-Hilliard Theory of phase transitions, we minimize our functional, whose phase field formulation is obtained by considering an energy of the type EE(u) = {Ω (E|∇u| + a u (1 − u) + uG(x) + λu dx, where u is the phase function, G is a potential energy, and λ represents volume constraint. We know that these minimizers, EE, as E goes to 0, will Γ−converge to the minimizer of the capillary energy functional. Although numerical approaches to this minimization exists, current approaches are unable to distinguish between local and global minimizers of the functional. I propose a mesh-grid-based optimization approach, with Dirichlet boundary conditions. Assuming convexity of our system, we utilize a logarithmic barrier optimization scheme in hopes to guarantee convergence to the global minimum of our energy functional. Advisors/Committee Members: Treinen, Ray (advisor), Lee, Young Ju (committee member), Wang, Chunmei (committee member).

Subjects/Keywords: Phase Field; Fluid Configurations; Capillarity; Optimization; Energy Minimization; Multiphase flow – Mathematical models; Fluid dynamics

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Gallo, E. (2018). Numerical Approach to Energy Minimization of Fluid Configurations Using Phase-Field Models. (Masters Thesis). Texas State University – San Marcos. Retrieved from https://digital.library.txstate.edu/handle/10877/7367

Chicago Manual of Style (16th Edition):

Gallo, Erika. “Numerical Approach to Energy Minimization of Fluid Configurations Using Phase-Field Models.” 2018. Masters Thesis, Texas State University – San Marcos. Accessed August 17, 2019. https://digital.library.txstate.edu/handle/10877/7367.

MLA Handbook (7th Edition):

Gallo, Erika. “Numerical Approach to Energy Minimization of Fluid Configurations Using Phase-Field Models.” 2018. Web. 17 Aug 2019.

Vancouver:

Gallo E. Numerical Approach to Energy Minimization of Fluid Configurations Using Phase-Field Models. [Internet] [Masters thesis]. Texas State University – San Marcos; 2018. [cited 2019 Aug 17]. Available from: https://digital.library.txstate.edu/handle/10877/7367.

Council of Science Editors:

Gallo E. Numerical Approach to Energy Minimization of Fluid Configurations Using Phase-Field Models. [Masters Thesis]. Texas State University – San Marcos; 2018. Available from: https://digital.library.txstate.edu/handle/10877/7367

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