Ordinary Differential Equations and Applied Dynamics Commons^™

Swarm Intelligence For Solving Some Nonlinear Differential Equations, Ahmed Elzaghal, Mohammed Mohammed Elgamal, Ahmed H. Eltanboly

Mansoura Engineering Journal

The Euler method is a well-known numerical technique employed for solving initial value problems of ordinary differential equations. The solution obtained through Euler's method is subject to significant inaccuracies, which tend to amplify with each successive iteration. The Particle Swarm Optimization (PSO) algorithm is a highly effective method for finding optimal solutions to both linear and nonlinear optimization problems. In this particular investigation, the PSO technique was utilized to solve initial value problems associated with ordinary differential equations. The Euler method, on the other hand, employs equidistant grid points to approximate solutions, which can result in significant errors and a …

Multipatch Stochastic Epidemic Model For The Dynamics Of A Tick-Borne Disease, Milliward Maliyoni, Holly D. Gaff, Keshlan S. Govinder, Faraimunashe Chirove

Biological Sciences Faculty Publications

Spatial heterogeneity and migration of hosts and ticks have an impact on the spread, extinction and persistence of tick-borne diseases. In this paper, we investigate the impact of between-patch migration of white-tailed deer and lone star ticks on the dynamics of a tick-borne disease with regard to disease extinction and persistence using a system of Itô stochastic differential equations model. It is shown that the disease-free equilibrium exists and is unique. The general formula for computing the basic reproduction number for all patches is derived. We show that for patches in isolation, the basic reproduction number is equal to the …

Innovations In Drop Shape Analysis Using Deep Learning And Solving The Young-Laplace Equation For An Axisymmetric Pendant Drop, Andres P. Hyer

Theses and Dissertations

Axisymmetric Drop Shape Analysis (ADSA) is a technique commonly used to determine surface or interfacial tension. Applications of traditional ASDA methods to process analytical technologies are limited by computational speed and image quality. Here, we address these limitations using a novel machine learning approach to analysis. With a convolutional neural network (CNN), we were able to achieve an experimental fit precision of (+/-) 0.122 mN/m in predicting the surface tension of drop images at a rate of 1.5 ms^-1 versus 7.7 s^-1, which is more than 5,000 times faster than the traditional method. The results are validated on real images …

Dynamical Aspects In (4+1)-Body Problems, Ryan Gauthier

Theses and Dissertations (Comprehensive)

The n-body problem models a system of n-point masses that attract each other via some binary interaction. The (n + 1)-body problem assumes that one of the masses is located at the origin of the coordinate system. For example, an (n+1)-body problem is an ideal model for Saturn, seen as the central mass, and one of its outer rings. A relative equilibrium (RE) is a special solution of the (n+1)-body problem where the non-central bodies rotate rigidly about the centre of mass. In rotating coordinates, these solutions become equilibria.

In this thesis we study dynamical aspects of planar (4 + …