Open Access. Powered by Scholars. Published by Universities.®
Partial Differential Equations Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Discipline
-
- Numerical Analysis and Computation (5)
- Engineering (3)
- Mechanical Engineering (3)
- Other Applied Mathematics (3)
- Physics (3)
-
- Chemical Engineering (2)
- Energy Systems (2)
- Heat Transfer, Combustion (2)
- Other Mechanical Engineering (2)
- Thermodynamics (2)
- Transport Phenomena (2)
- Analysis (1)
- Applied Mechanics (1)
- Atomic, Molecular and Optical Physics (1)
- Civil Engineering (1)
- Civil and Environmental Engineering (1)
- Computational Engineering (1)
- Computer Sciences (1)
- Condensed Matter Physics (1)
- Data Science (1)
- Earth Sciences (1)
- Engineering Mechanics (1)
- Engineering Physics (1)
- Engineering Science and Materials (1)
- Environmental Sciences (1)
- Geological Engineering (1)
- Geology (1)
- Keyword
-
- Bose-Einstein Condensate (3)
- Anisotropic (1)
- Atom Interferometry (1)
- Bender Element (1)
- Bessel functions (1)
-
- Black-Scholes (1)
- Blowup Solution (1)
- Contact resistance (1)
- Darcy’s velocity (1)
- Discrete Element Method (1)
- Finance (1)
- Financial Mathematics (1)
- Finite volume method (1)
- Granular Material (1)
- Gravitational Constant (1)
- Gross-Pitaevskii Equation (1)
- GroundState Solution (1)
- Hankel transform (1)
- Heat Equation (1)
- Heat and mass transfer (1)
- Heat transfer (1)
- Hydrogen storage (1)
- Lagrangian Variational Method (1)
- Lithium-ion batteries (1)
- Mathematical modeling (1)
- Metal hydrides (1)
- Nonlinear Schrodinger equation (1)
- Numerical modeling (1)
- Numerical Model (1)
- Reactive porous media (1)
Articles 1 - 9 of 9
Full-Text Articles in Partial Differential Equations
Applying The Lagrangian Variational Method To Atom Interferometry, Jeffrey W. Heward
Applying The Lagrangian Variational Method To Atom Interferometry, Jeffrey W. Heward
College of Graduate Studies: Theses & Dissertations
Atom interferometry in Bose-Einstein condensate systems has emerged as a promising technique for precision metrology. The dynamics of these systems are well-described by the Gross-Pitaevskii equation (GPE), but direct numerical solution of this equation is infeasible for realistic systems. We use the Lagrangian Variational Method (LVM) to approximate solutions of the GPE in 1D and 3D, and we compare the LVM results to the exact solutions. We also present 3D LVM results for a case where numerical solution of the GPE is infeasible.
Mathematical Modeling Of Coupled Heat And Mass Transfer In Metal-Hydride Hydrogen Storage Systems, Muhammad Hasnain
Mathematical Modeling Of Coupled Heat And Mass Transfer In Metal-Hydride Hydrogen Storage Systems, Muhammad Hasnain
College of Graduate Studies: Theses & Dissertations
As a promising clean energy carrier hydrogen has recently gained significant interest, but its efficient and safe storage is a major challenge. Compared to the gaseous state and liquid state, metal hydrides (MH) offer a potentially more effective storage approach for hydrogen. However, the main challenge in this approach is the low thermal conductivity of the MH bed that leads to low heat transfer and ultimately to higher charging and discharging times. The purpose of this work is to develop an in-house comprehensive heat and mass transfer model for hydrogen sorption in MH reactors to simulate the dynamic behavior of …
Numerical Modeling Of Thermal Runaway In Lithium-Ion Batteries Using Decomposition Kinetics And Inter-Cell Contact Resistance, Shehzad Khan
Numerical Modeling Of Thermal Runaway In Lithium-Ion Batteries Using Decomposition Kinetics And Inter-Cell Contact Resistance, Shehzad Khan
College of Graduate Studies: Theses & Dissertations
Lithium-ion batteries (LIBs) are central in numerous high-demand applications due to their high energy density and prolonged cycle life. Despite these advantages, their susceptibility to thermal runaway (TR) poses a significant safety risk, with the potential for catastrophic failures. This study focuses on the thermal behavior of prismatic lithium-ion cells, using a finite volume-based partial differential equation (PDE) solver developed in MATLAB and JULIA to model TR behavior. This solver accurately simulates transient behaviors, convection, diffusion, and source terms across various coordinate systems. By engaging in a series of increasing complex case studies, this research aims to identify the critical …
Simulation Of Wave Propagation In Granular Particles Using A Discrete Element Model, Syed Tahmid Hussan
Simulation Of Wave Propagation In Granular Particles Using A Discrete Element Model, Syed Tahmid Hussan
College of Graduate Studies: Theses & Dissertations
The understanding of Bender Element mechanism and utilization of Particle Flow Code (PFC) to simulate the seismic wave behavior is important to test the dynamic behavior of soil particles. Both discrete and finite element methods can be used to simulate wave behavior. However, Discrete Element Method (DEM) is mostly suitable, as the micro scaled soil particle cannot be fully considered as continuous specimen like a piece of rod or aluminum. Recently DEM has been widely used to study mechanical properties of soils at particle level considering the particles as balls. This study represents a comparative analysis of Voigt and Best …
Analysis On Sharp And Smooth Interface, Elizabeth V. Hawkins
Analysis On Sharp And Smooth Interface, Elizabeth V. Hawkins
College of Graduate Studies: Theses & Dissertations
In biology, minimizing a free energy functional gives an equilibrium shape that is the most stable in nature. The formulation of these functionals can vary in many ways, in particular they can have either a smooth or sharp interface. Minimizing a functional can be done through variational calculus or can be proved to exist using various analysis techniques. The functionals investigated here have a smooth and sharp interface and are analyzed using analysis and variational calculus respectively. From the former we find the condition for extremum and its second variation. The second variation is commonly used to analyze stability of …
Blow Up Solution Of Bose-Einstein Condensates With Anisotropic Trapping Potential And Rotation, Christopher Leonard
Blow Up Solution Of Bose-Einstein Condensates With Anisotropic Trapping Potential And Rotation, Christopher Leonard
College of Graduate Studies: Theses & Dissertations
In this paper we will analyze a nonlinear Schrodinger equation with quadratic anisotropic trapping potential used to describe a Bose-Einstein condensate. We will find sufficient condition for the global existence of the solution and for the blow up result using physical properties associated to the equation such as the mass, energy, and angular momentum along with some other identities related to the equation. We will finish the thesis with showing some graphical representations describing the solution of the equation.
The Bessel Function, The Hankel Transform And An Application To Differential Equations, Isaac C. Voegtle
The Bessel Function, The Hankel Transform And An Application To Differential Equations, Isaac C. Voegtle
College of Graduate Studies: Theses & Dissertations
In this thesis we explore the properties of Bessel functions. Of interest is how they can be applied to partial differential equations using the Hankel transform. We use an example in two dimensions to demonstrate the properties at work as well as formulate thoughts on how to take the results further.
Black-Scholes Equation And Heat Equation, Charles D. Joyner
Black-Scholes Equation And Heat Equation, Charles D. Joyner
Honors College Theses
First, we present and define the Black-Scholes equation which is used to model assets on the stock market. After that, we derive the heat equation that describes how the temperature increases through a homogeneous material. Finally, we detail how the two equations are related. We introduce and relate the Black-Scholes equation and Heat Equation.
Stereographic Visualization Of Bose-Einstein Condensate Clouds To Measure The Gravitational Constant, Ed Wesley Wells
Stereographic Visualization Of Bose-Einstein Condensate Clouds To Measure The Gravitational Constant, Ed Wesley Wells
College of Graduate Studies: Theses & Dissertations
This thesis describes a set of tools that can be used for the rapid design of atom interferometer schemes suitable for measuring Newton's Universal Gravitation constant also known as "Big G". This tool set is especially applicable to Bose--Einstein--condensed systems present in NASA's Cold Atom Laboratory experiment to be deployed to the International Space Station in 2017. These tools include a method of approximating the solutions of the nonlinear Schrödinger or Gross--Pitaevskii equation (GPE) using the Lagrangian Variational Method. They also include a set of software tools for translating the approximate solutions of the GPE into images of the optical …