Applied Mathematics Commons^™

Effects Of Topography On Tornado Paths Using Navier Stokes Equations, Kayleigh Smith

Mathematics Senior Capstone Papers

Tornadoes are relatively common in Louisiana with an average of 55 tornadoes per year. Predicting tornado paths has been extremely challenging due to the many factors that play into the formation of a tornado. According to NASA/ADS topography can have significant influence on tornado direction. The main goal of this research is to analyze tornado patterns and to determine if local topography has an effect on tornadic activity. Navier-Stokes partial differential equations will be used to model the data that is collected from the national weather service and a finite difference method will be used to solve the equations. Data …

Integrable Systems On Symmetric Spaces From A Quadratic Pencil Of Lax Operators, Rossen Ivanov

Conference papers

The article surveys the recent results on integrable systems arising from quadratic pencil of Lax operator L, with values in a Hermitian symmetric space. The counterpart operator M in the Lax pair defines positive, negative and rational flows. The results are illustrated with examples from the A.III symmetric space. The modeling aspect of the arising higher order nonlinear Schrödinger equations is briefly discussed.

Modeling Self-Diffusiophoretic Janus Particles In Fluid, Kausik Das

HMC Senior Theses

We explore spherical Janus particles in which a chemical reaction occurs on one face, depleting a substrate in the suspending fluid, while no reaction occurs on the other face. The steady state concentration field is governed by Laplace’s equation with mixed boundary conditions. We use the collocation method to obtain numerical solutions to the equation in spherical coordinates. The asymmetry of the reaction gives rise to a slip velocity that causes the particle to move spontaneously in the fluid through a process known as self-diffusiophoresis. Using the Lorentz reciprocal theorem, we obtain the swimming velocity of the particle. We extend …

Foundations Of Wave Phenomena: Complete Version, Charles G. Torre

Foundations of Wave Phenomena

This is the complete version of Foundations of Wave Phenomena. Version 8.3.1.

Please click here to explore the components of this work.

Solitons And Their Applications In Physics, B. A. Yount

EWU Masters Thesis Collection

No abstract provided.

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.

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 …

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 …

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 …

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 …

(R1885) Analytical And Numerical Solutions Of A Fractional-Order Mathematical Model Of Tumor Growth For Variable Killing Rate, N. Singha, C. Nahak

Applications and Applied Mathematics: An International Journal (AAM)

This work intends to analyze the dynamics of the most aggressive form of brain tumor, glioblastomas, by following a fractional calculus approach. In describing memory preserving models, the non-local fractional derivatives not only deliver enhanced results but also acknowledge new avenues to be further explored. We suggest a mathematical model of fractional-order Burgess equation for new research perspectives of gliomas, which shall be interesting for biomedical and mathematical researchers. We replace the classical derivative with a non-integer derivative and attempt to retrieve the classical solution as a particular case. The prime motive is to acquire both analytical and numerical solutions …

(R1894) Invariant Solution For Two-Dimensional And Axisymmetric Jet Of Power-Law Fluids, Bhavixa Bhagat, M. G. Timol

Applications and Applied Mathematics: An International Journal (AAM)

An invariant solution is derived using the Lie symmetry technique for steady laminar two-dimensional and axisymmetric boundary layer jet flow of incompressible power-law fluids with appropriate boundary conditions. Using symmetry, the nonlinear partial differential equation of the jet flow problem is transformed into a nonlinear ordinary differential equation. The resultant nonlinear ordinary differential equation with boundary conditions is converted to an initial value problem using the Lie symmetry technique. A numerical solution for the resulting initial value problem is derived using Fehlberg’s fourth-fifth order Runge-Kutta method through Maple software. The graphical representation of the characteristics of the velocity field for …

(R2020) Dynamical Study And Optimal Harvesting Of A Two-Species Amensalism Model Incorporating Nonlinear Harvesting, Manoj Kumar Singh, Poonam .

Applications and Applied Mathematics: An International Journal (AAM)

This study proposes a two-species amensalism model with a cover to protect the first species from the second species, with the assumption that the growth of the second species is governed by nonlinear harvesting. Analytical and numerical analyses have both been done on this suggested ecological model. Boundedness and positivity of the solutions of the model are examined. The existence of feasible equilibrium points and their local stability have been discussed. In addition, the parametric conditions under which the proposed system is globally stable have been determined. It has also been shown, using the Sotomayor theorem, that under certain parametric …

(R1969) On The Approximation Of Eventual Periodicity Of Linearized Kdv Type Equations Using Rbf-Ps Method, Hameed Ullah Jan, Marjan Uddin, Asma Norin, Tamheeda .

Applications and Applied Mathematics: An International Journal (AAM)

Water wave propagation phenomena still attract the interest of researchers from many areas and with various objectives. The dispersive equations, including a large body of classes, are widely used models for a great number of problems in the fields of physics, chemistry and biology. For instance, the Korteweg-de Vries (KdV) equation is one of the famous dispersive wave equation appeared in the theories of shallow water waves with the assumption of small wave-amplitude and large wave length, also its various modifications serve as the modeling equations in several physical problems. Another interesting qualitative characteristic of solutions of some dispersive wave …

Modeling Of Population Dynamics In Spatially Continuous And Heterogeneous Environments Using Partial Differential Equations, Ryan T. St. Clair

Masters Theses & Specialist Projects

This thesis provides an expansion of existing reaction diffusion population ecology models into patchy landscapes with greater spatial heterogeneity. The Sturm-Loiville eigenvalue problem for a heterogeneous 3 patch landscape is solved implicitly and the population growth rate and migration dynamics on such a landscape are thoroughly discussed. In addition a system of interface equations is found whose greatest solution is the dominant eigenvalue of an N-patch landscape. The results of this model agree well with previously published results and show the mathematical equivalence of two published approaches for incorporating organism behavior at habitat interfaces. Increased modeling capabilities in heterogeneous environments …

(R1992) Rbf-Ps Method For Eventual Periodicity Of Generalized Kawahara Equation, Hameed Ullah Jan, Marjan Uddin, Arif Ullah, Naseeb Ullah

Applications and Applied Mathematics: An International Journal (AAM)

In engineering and mathematical physics, nonlinear evolutionary equations play an important role. Kawahara equation is one of the famous nonlinear evolution equation appeared in the theories of shallow water waves possessing surface tension, capillary-gravity waves and also magneto-acoustic waves in a plasma. Another specific subjective parts of arrangements for some of evolution equations evidenced by findings link belonging to their long-term actions named as eventual time periodicity discovered over solutions to IBVPs (initial-boundary-value problems). Here we investigate the solution’s eventual periodicity for generalized fifth order Kawahara equation (IBVP) on bounded domain in combination with periodic boundary conditions numerically exploiting mesh-free …

On Analysis Of Effectiveness Controlling Covid-19 With Quarantine And Vaccination Compartments In Indonesia, Prihantini Prihantini

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

(Si10-115) Controllability Results For Nonlinear Impulsive Functional Neutral Integrodifferential Equations In N-Dimensional Fuzzy Vector Space, Murugesan Nagarajan, Kumaran Karthik

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we concentrated to study the controllability of fuzzy solution for nonlinear impulsive functional neutral integrodifferential equations with nonlocal condition in n-dimensional vector space. Moreover, we obtained controllability of fuzzy result for the normal, convex, upper semi-continuous and compactly supported interval fuzzy number. Finally, an example was provided to reveal the application of the result.

(Si10-067) Numerical Study Of The Time Fractional Burgers’ Equation By Using Explicit And Implicit Schemes, Swapnali Doley, A. Vanav Kumar, L. Jino

Applications and Applied Mathematics: An International Journal (AAM)

The study discusses the numerical solution for a time fractional Burgers’ equation using explicit (scheme 1) and implicit scheme (scheme 2), respectively. The approximation of the differential equation is discretized using the finite difference method (FDM). A non-linear term present in the Burgers’ equation is approximated using the time-averaged values. The Von-Neumann analysis shows that the Scheme 1 is conditionally stable and Scheme 2 is unconditionally stable. The numerical solutions are compared with the exact solutions and are good in agreement. Also, the error is estimated between exact and numerical solutions.

Stochastic Modeling Of Flows In Membrane Pore Networks, Binan Gu

Dissertations

Membrane filters provide immediate solutions to many urgent problems such as water purification, and effective remedies to pressing environmental concerns such as waste and air treatment. The ubiquity of applications gives rise to a significant amount of research in membrane material selection and structural design to optimize filter efficiency. As physical experiments tend to be costly, numerical simulation and analysis of fluid flow, foulant transport and geometric evolution due to foulant deposition in complex geometries become particularly relevant. In this dissertation, several mathematical modeling and analytical aspects of the industrial membrane filtration process are investigated. A first-principles mathematical model for …

Mathematical Models Yield Insights Into Cnns: Applications In Natural Image Restoration And Population Genetics, Ryan Cecil

Electronic Theses and Dissertations

Due to a rise in computational power, machine learning (ML) methods have become the state-of-the-art in a variety of fields. Known to be black-box approaches, however, these methods are oftentimes not well understood. In this work, we utilize our understanding of model-based approaches to derive insights into Convolutional Neural Networks (CNNs). In the field of Natural Image Restoration, we focus on the image denoising problem. Recent work have demonstrated the potential of mathematically motivated CNN architectures that learn both `geometric' and nonlinear higher order features and corresponding regularizers. We extend this work by showing that not only can geometric features …

Ocean Wave Prediction And Characterization For Intelligent Maritime Transportation, Pujan Pokhrel

LSU New Orleans Theses and Dissertations

The national Earth System Prediction (ESPC) initiative aims to develop the predictions
for the next generation predictions of atmosphere, ocean, and sea-ice interactions in the scale of days to decades. This dissertation seeks to demonstrate the methods we can use to improve the ESPC models, especially the ocean prediction model. In the application side of the weather forecasts, this dissertation explores imitation learning with constraints to solve combinatorial optimization problems, focusing on the weather routing of surface vessels. Prediction of ocean waves is essential for various purposes, including vessel routing, ocean energy harvesting, agriculture, etc. Since the machine learning approaches …

Navier-Stokes Equations In One And Two Dimensions, Jon Nerdal

LSU Master's Theses

The Navier-Stokes equations are an important tool in understanding and describing fluid flow. We investigate different formulations of the incompressible Navier-Stokes equations in the one-dimensional case along an axis and in the two-dimensional case in a circular pipe without swirl. For the one-dimensional case we show that the velocity approximations are remarkably accurate and we suggest that understanding this simple axial behaviour is an important starting point for further exploration in higher dimensions. The complexity of the boundary is then increased with the two-dimensional case of fluid flow through the cross section of a circular pipe, where we investigate two …

Bloch Spectra For High Contrast Elastic Media, Jayasinghage Ruchira Nirmali Perera

LSU Doctoral Dissertations

The primary goal of this dissertation is to develop analytic representation formulas and power series to describe the band structure inside periodic elastic crystals made from high contrast inclusions. We use source free modes associated with structural spectra to represent the solution operator of the Lame' system inside phononic crystals. Then we obtain convergent power series for the Bloch wave spectrum using the representation formulas. An explicit bound on the convergence radius is given through the structural spectra of the inclusion array and the Dirichlet spectra of the inclusions. Sufficient conditions for the separation of spectral branches of the dispersion …

Analytic Solution Of 1d Diffusion-Convection Equation With Varying Boundary Conditions, Małgorzata B. Glinowiecka-Cox

University Honors Theses

A diffusion-convection equation is a partial differential equation featuring two important physical processes. In this paper, we establish the theory of solving a 1D diffusion-convection equation, subject to homogeneous Dirichlet, Robin, or Neumann boundary conditions and a general initial condition. Firstly, we transform the diffusion-convection equation into a pure diffusion equation. Secondly, using a separation of variables technique, we obtain a general solution formula for each boundary type case, subject to transformed boundary and initial conditions. While eigenvalues in the cases of Dirichlet and Neumann boundary conditions can be constructed easily, the Robin boundary condition necessitates solving a transcendental algebraic …

Sparse Spectral-Tau Method For The Two-Dimensional Helmholtz Problem Posed On A Rectangular Domain, Gabriella M. Dalton

Mathematics & Statistics ETDs

Within recent decades, spectral methods have become an important technique in numerical computing for solving partial differential equations. This is due to their superior accuracy when compared to finite difference and finite element methods. For such spectral approximations, the convergence rate is solely dependent on the smoothness of the solution yielding the potential to achieve spectral accuracy. We present an iterative approach for solving the two-dimensional Helmholtz problem posed on a rectangular domain subject to Dirichlet boundary conditions that is well-conditioned, low in memory, and of sub-quadratic complexity. The proposed approach spectrally approximates the partial differential equation by means of …

A Bidirectional Formulation For Walk On Spheres, Yang Qi

Dartmouth College Master’s Theses

Poisson’s equations and Laplace’s equations are important linear partial differential equations (PDEs)
widely used in many applications. Conventional methods for solving PDEs numerically often need to
discretize the space first, making them less efficient for complex shapes. The random walk on spheres
method (WoS) is a grid-free Monte-Carlo method for solving PDEs that does not need to discrete the
space. We draw analogies between WoS and classical rendering algorithms, and find that the WoS
algorithm is conceptually identical to forward path tracing.
We show that solving the Poisson’s equation is equivalent to solving the Green’s function for every
pair of …

De-Coupling Cell-Autonomous And Non-Cell-Autonomous Fitness Effects Allows Solution Of The Fokker-Planck Equation For The Evolution Of Interacting Populations, Steph J. Owen

Biology and Medicine Through Mathematics Conference

No abstract provided.

Mathematical Modeling Of Brain Cancer Growth Using A Level-Set Method, Gbocho M. Terasaki

Biology and Medicine Through Mathematics Conference

No abstract provided.

Spatial Patterning Of Predator-Prey Distributions Arising From Prey Defense, Evan C. Haskell, Jonathan Bell

Biology and Medicine Through Mathematics Conference

No abstract provided.