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Partial Differential Equations Commons™

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2023

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Articles 31 - 35 of 35

Full-Text Articles in Partial Differential Equations

Beginner's Analysis Of Financial Stochastic Process Models, David Garcia Jan 2023

Beginner's Analysis Of Financial Stochastic Process Models, David Garcia

HMC Senior Theses

This thesis explores the use of geometric Brownian motion (GBM) as a financial model for predicting stock prices. The model is first introduced and its assumptions and limitations are discussed. Then, it is shown how to simulate GBM in order to predict stock price values. The performance of the GBM model is then evaluated in two different periods of time to determine whether it's accuracy has changed before and after March 23, 2020.

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The Lagrangian Formulation For Wave Motion With A Shear Current And Surface Tension, Conor Curtin, Rossen Ivanov Jan 2023

The Lagrangian Formulation For Wave Motion With A Shear Current And Surface Tension, Conor Curtin, Rossen Ivanov

Articles

The Lagrangian formulation for the irrotational wave motion is straightforward and follows from a Lagrangian functional which is the difference between the kinetic and the potential energy of the system. In the case of fluid with constant vorticity, which arises for example when a shear current is present, the separation of the energy into kinetic and potential is not at all obvious and neither is the Lagrangian formulation of the problem. Nevertheless, we use the known Hamiltonian formulation of the problem in this case to obtain the Lagrangian density function, and utilising the Euler-Lagrange equations we proceed to derive some …

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Using Modflow To Assess Groundwater Storage Enhancement Via A Floodplain Infiltration Basin, Lindsay Henning Jan 2023

Using Modflow To Assess Groundwater Storage Enhancement Via A Floodplain Infiltration Basin, Lindsay Henning

All Master's Theses

Delaying groundwater discharge into rivers until it is critically needed during baseflow conditions provides promise for lowering elevated stream temperatures and improving habitat for aquatic species. Increasing groundwater storage may accomplish this in locations where excess spring runoff can be captured and allowed to infiltrate into the subsurface for later beneficial use, a process known as Managed Aquifer Recharge (MAR). Here, MAR via an infiltration basin is considered at a site along the Teanaway River in central Washington State. The effects of simulated ephemeral ponds of sizes varying from 554 m3 to 2430 m3 (0.449 acre-feet to 1.97 …

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Novel Approaches To Compute Manifold Operators With The Radial Basis Functions Method, Jacob James Blazejewski Jan 2023

Novel Approaches To Compute Manifold Operators With The Radial Basis Functions Method, Jacob James Blazejewski

Dissertations, Master's Theses and Master's Reports

The bulk of this dissertation is mainly composed of four chapters, which are organized as follows: Chapter 1 provides an introduction to the Radial Basis Functions (RBF) method by briefly outlining its historical developments and reviewing the RBF interpolation and the RBF-Finite Difference (FD) methodologies, and their advantages/disadvantages. Chapter 2 describes the Orthogonal Gradients (OGr) method and the Fast OGr method and how these can be used to compute differential operators restricted to hypersurfaces and space curves ($\Gamma$) embedded in R3. We will highlight a challenge of pairing Fast OGr with RBF-FD on nearly flat local clusters and how to …

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Effects Of Slip On Highly Viscous Thin-Film Flows Inside Vertical Tubes (Constant Radius, Constricted And Flexible), Mark S. Schwitzerlett Jan 2023

Effects Of Slip On Highly Viscous Thin-Film Flows Inside Vertical Tubes (Constant Radius, Constricted And Flexible), Mark S. Schwitzerlett

Theses and Dissertations

Viscous liquid film flows in a tube arise in numerous industrial and biological applications, including the transport of mucus in human airways. Previous modeling studies have typically used no-slip boundary conditions, but in some applications the effects of slip at the boundary may not be negligible. We derive a long-wave model based on lubrication theory which allows for slippage along the boundary. Linear stability analysis verifies the impact of slip-length on the speed, growth rate, and wavelength of the most unstable mode. Nonlinear simulations demonstrate the impact of slip-length on plug formation and wave dynamics. These simulations are conducted for …

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