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Articles 1 - 10 of 10
Full-Text Articles in Applied Mathematics
Solving Partial Differential Equations Using The Finite Difference Method And The Fourier Spectral Method, Jenna Siobhan Parkinson
Solving Partial Differential Equations Using The Finite Difference Method And The Fourier Spectral Method, Jenna Siobhan Parkinson
Undergraduate Student Research Internships Conference
This paper discusses the finite difference method and the Fourier spectral method for solving partial differential equations.
Lecture Note On Delay Differential Equation, Wenfeng Liu
Lecture Note On Delay Differential Equation, Wenfeng Liu
Undergraduate Student Research Internships Conference
Delay differential equation is an important field in applied mathematics since it concerns more situations than the ordinary differential equation. Moreover, it makes the equations more applicable to the object's movement in real life.
My project is the lecture note on the delay differential equation provides a basic introduction to the delay differential equation, its application in real life, improving the ordinary differential equation, the primary method and definition for solving the delay differential equation and the use of the way in the ordinary differential equation to estimate the periodic solution to the delay differential equation.
Simulating And Modelling Adaptive Walks With The Nk Model, Abigail K. Kushnir
Simulating And Modelling Adaptive Walks With The Nk Model, Abigail K. Kushnir
Undergraduate Student Research Internships Conference
This presentation outlines results obtained by simulating adaptive walks using the NK model. We were interested in how the mutation bias affects the distribution of fitness effects and how we could use our results to form theoretical equations to model the behaviour of a walk. Necessary biological background is also described.
A Kuramoto Model Approach To Predicting Chaotic Systems With Echo State Networks, Sophie Wu, Jackson Howe
A Kuramoto Model Approach To Predicting Chaotic Systems With Echo State Networks, Sophie Wu, Jackson Howe
Undergraduate Student Research Internships Conference
An Echo State Network (ESN) with an activation function based on the Kuramoto model (Kuramoto ESN) is implemented, which can successfully predict the logistic map for a non-trivial number of time steps. The reservoir in the prediction stage exhibits binary dynamics when a good prediction is made, but the oscillators in the reservoir display a larger variability in states as the ESN’s prediction becomes worse. Analytical approaches to quantify how the Kuramoto ESN’s dynamics relate to its prediction are explored, as well as how the dynamics of the Kuramoto ESN relate to another widely studied physical model, the Ising model.
Travelling Wave Solutions On A Cylindrical Geometry, Karnav R. Raval
Travelling Wave Solutions On A Cylindrical Geometry, Karnav R. Raval
Undergraduate Student Research Internships Conference
Fluid equations are generally quite difficult and computationally-expensive to solve. However, if one is primarily interested in how the surface of the fluid deforms, we can re-formulate the governing equations purely in terms of free surface variables. Reformulating equations in such a way drastically cuts down on computational cost, and may be useful in areas such as modelling blood flow. Here, we study one such free-boundary formulation on a cylindrical geometry.
Development Of A Low Field Mri-Based Approach For Observation Of Water Penetration Into Clay: Preliminary Results, Shivam Gupta
Development Of A Low Field Mri-Based Approach For Observation Of Water Penetration Into Clay: Preliminary Results, Shivam Gupta
Undergraduate Student Research Internships Conference
Magnetic resonance imaging (MRI) are considered one of the most efficient and non-invasive methods of observing water content in permeable substances. MRI can visualize and quantify the movement of water in real time. In this study, MRI was used to observe the water penetration through clay. Furthermore, MRI can acquire three-dimensional data due to its radio-frequency signals from any orientation. The contrast of the images produced by MRI is a display of the fluid concentration. As such, any change in the contrast intensity is interpreted as a regional change in the concentration of fluid. This report summarizes the preliminary results …
Ciculant Matrix And Fft, Thomas S. Devries
Ciculant Matrix And Fft, Thomas S. Devries
Undergraduate Student Research Internships Conference
The goal was to produce all the eigen values for a BOHEMIAN matrices using coefficient set {0, 1, -1, i, -i} of a size 15 vector. There are 5^15 eigen values so it was attempted to be done in parrallel for parts of the algorithm that permitted.
Using An Analytical Approach Of The Kuramoto Model To Stimulate 3d Neural Activity Of The Stomach, Morteza Al Rabya
Using An Analytical Approach Of The Kuramoto Model To Stimulate 3d Neural Activity Of The Stomach, Morteza Al Rabya
Undergraduate Student Research Internships Conference
No abstract provided.
Eigenvalue Problems On Atypical Domains - The Finite Element Method, Toufiic Ayoub
Eigenvalue Problems On Atypical Domains - The Finite Element Method, Toufiic Ayoub
Undergraduate Student Research Internships Conference
Why do we care about eigenvalues and eigenvectors? What's the big deal? For many people enrolled in entry level linear algebra courses, these concepts seem like far fetched abstractions that become pointless exercises in computation. But in reality, these fundamental ideas are vital to how we live our lives every single day. But how?
Modeling Weather Vulnerability Dynamically: Applications Of Multiple Linear Regression To Weather Index Microinsurance, Sophie Wu
Undergraduate Student Research Internships Conference
This paper offers a broad overview of the philanthropic goals of microinsurance — namely, to provide vulnerable populations with more self-sufficient and sustainable methods of coping with risk — and through this lens, analyses the applications of multiple linear regression in developing dynamic models for microinsurance. We explain the foundations of MLR (multiple linear regression), and then give two examples for how a simple multiple linear regression model can be adapted with a novel outcome variable (famine) and dependent variables (climate change related costs). Overall, a better understanding of MLR can lend to a better understanding of how microinsurance can …