Index Catalog // ScholarsArchive@OSU

On existence and uniqueness of weak solutions to the Navier-Stokes equations in R3

Creator:: Peterson, Samuel H.
Abstract:: This thesis is on the existence and uniqueness of weak solutions to the Navier-Stokes equations in R3 which govern the velocity of incompressible fluid with viscosity ν. The solution is obtained in the space of tempered distributions on R3 given an initial condition and forcing data which are dominated by...
Resource Type:: Masters Thesis
Full Text:: : _______________________________________________ Mina E. Ossiander This thesis is on the existence and uniqueness of weak solutions

Interpolation Schemes for Two Dimensional Flow with Applications

Creator:: Umhoefer, Joseph G.
Abstract:: In this thesis we study a numerical analysis problem motivated by the need to simulate an event such as an oil spill in a deep water environment. Numerical simulation can help to mitigate the disastrous effects of such events by aiding the management of risk assessment and recovery efforts. However,...
Resource Type:: Masters Thesis

Stochastic analysis of flow and transport in porous media

Creator:: Vasylkivska, Veronika S.
Abstract:: Random fields are frequently used in computational simulations of real-life processes. In particular, in this work they are used in modeling of flow and transport in porous media. Porous media as they arise in geological formations are intrinsically deterministic but there is significant uncertainty involved in determination of their properties...
Resource Type:: Dissertation
Full Text:: discuss without her enthusiastic attitude toward research. Second, I would like to thank Dr. Ralph E

An investigation of transition from penetration to deflection in the fracture of bi-material interfaces

Creator:: Strom, Joshua L.
Abstract:: The problem of determining whether a crack impinging on an interface will penetrate into the substrate or deflect along the interface is vital to the effective design of layered and composite material systems. Of particular interest is the transition between crack propagation by penetration through an interface and deflection along...
Resource Type:: Masters Thesis
Full Text:: . 0.0 0.5 1.0 1.5 2.0 2.5 1 10 100 N o rm al iz e d F ra ct u re L o ad

3D cone beam reconstruction formulas for the transverse-ray transform with source points on a curve

Creator:: Wongsason, Patcharee
Abstract:: 3D vector tomography has been explored and results have been achieved in the last few decades. Among these was a reconstruction formula for the solenoidal part of a vector field from its Doppler transform with sources on a curve. The Doppler transform of a vector field is the line integral...
Resource Type:: Dissertation
Full Text:: T f(a, θ) = ∫ ∞ 0 (θ × f)(a+ tθ)dt. (1.3) This transform has the property: T f(a, θ)× θ = Eθ

Mathematical treatment and simulation of methane hydrates and adsorption models

Creator:: Medina, Francis Patricia
Abstract:: In this dissertation we develop mathematical treatment for two important applications: (i) evolution of methane in coalbeds with the associated phenomena of adsorption, and (ii) formation of methane hydrates in seabed. We use simplified models for (i) and (ii) since we are more interested in qualitative properties of the solutions...
Resource Type:: Dissertation
Full Text:: Peszynska and Dr. Ralph Showalter for sharing their expertise with me while working in the project related

The Stokes problem of fluid mechanics, Riesz transform, and the Helmholtz-Hodge decomposition : probabilistic methods and their representations

Creator:: Kim, HoeWoon
Abstract:: The flow of incompressible, viscous fluids in R³ is governed by the non-linear Navier-Stokes equations. Two common linearizations of the Navier-Stokes equations, the Stokes equations and the Oseen equations, are studied in this thesis using probabilistic methods. The incompressibility condition presents new challenges for the well known theory relating partial...
Resource Type:: Dissertation
Full Text:: committee members, Ed Waymire, Donald Solmon, Ralph Showalter, and Glenn Evans. Personal I wish to thank

Nonlinear finite difference schemes for the Klausmeier system

Creator:: McClellan, Natalia A.
Abstract:: In this work we consider a model for pattern-producing vegetation in semi-arid regions of the world proposed by Klausmeier. It is a coupled nonlinear diffusion-advection evolutionary PDE system describing the vegetation density and water amount. The model was studied extensively by J.Sherratt who took into consideration the field data for...
Resource Type:: Masters Thesis
Full Text:: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.3.1 Equilibrium E = (0,A

Analysis of domain decomposition methods for the simulation of charge transport in semiconductor structures with heterojunctions

Creator:: Costa, Timothy B.
Abstract:: Charge transport in a semiconductor structure with heterojunction is described by a multiscale partial differential equation model. This model can be used, e.g., for the design of more efficient solar cells. Phenomena at the heterojunction must be resolved at the angstrom scale while the size of the device is that...
Resource Type:: Masters Thesis
Full Text:: Emission Model in Slotboom variables is [ψ]Γ = ψ4, (2.19)[ � ∂ψ ∂ν ] Γ = 0, (2.20) JΓn = a n 2 (e ψu

Some results in probability from the functional analytic viewpoint

Creator:: Gelbaum, Zachary A.
Abstract:: This dissertation presents some results from various areas of probability theory, the unifying theme being the use of functional analytic intuition and techniques. We first give a result regarding the existence of certain stochastic integral representations for Banach space valued Gaussian random variables. Next we give a spectral geometric construction...
Resource Type:: Dissertation
Full Text:: elsewhere that deserve thanks. Ralph Showalter had the largest impact on me mathematically; aside from my

ScholarsArchive@OSU

On existence and uniqueness of weak solutions to the Navier-Stokes equations in R3

Interpolation Schemes for Two Dimensional Flow with Applications

Stochastic analysis of flow and transport in porous media

An investigation of transition from penetration to deflection in the fracture of bi-material interfaces

3D cone beam reconstruction formulas for the transverse-ray transform with source points on a curve

Mathematical treatment and simulation of methane hydrates and adsorption models

The Stokes problem of fluid mechanics, Riesz transform, and the Helmholtz-Hodge decomposition : probabilistic methods and their representations

Nonlinear finite difference schemes for the Klausmeier system

Analysis of domain decomposition methods for the simulation of charge transport in semiconductor structures with heterojunctions

Some results in probability from the functional analytic viewpoint

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