Physical Sciences and Mathematics Commons^™

Mathematical Modeling Of A Variable Mass Rocket’S Dynamics Using The Differential Transform Method, Ashwyn Sam

Honors Theses

In this paper, the mathematical modelling of a rocket with varying mass is investigated to construct a function that can describe the velocity and position of the rocket as a function of time. This research is geared more towards small scale rockets where the nonlinear drag term is of great interest to the underlying dynamics of the rocket. A simple force balance on the rocket using Newton’s second law of motion yields a Riccati differential equation for which the solution yields the velocity of the rocket at any given time. This solution can then be integrated with respect to time …

Automatic Numerical Methods For Enhancement Of Blurred Text-Images Via Optimization And Nonlinear Diffusion, Aaditya Kharel

Honors Theses

In this paper, we propose an automatic numerical method for solving a nonlinear partialdifferential- equation (PDE) based image-processing model. The Perona-Malik diffusion equation (PME) accounts for both forward and backward diffusion regimes so as to perform simultaneous denoising and deblurring depending on the value of the gradient. One of the limitations of this equation is that a large value of the gradient for backward diffusion can lead to singularity formation or staircasing. Guidotti-Kim-Lambers (GKL) came up with a bound for backward diffusion to prevent staircasing, where the backward diffusion is only limited to a specific range beyond which backward diffusion …

The Long Time Behavior Of The Predator-Prey Model With Holling Type Iii, Regen S. Mcgee

Honors Theses

In this paper, the classical Lotka-Volterra model is expanded based on functional response of Holling type III to analyze a dynamical predator-prey relationship with hunting cooperation (a) and the Allee effect among predators. The stability of equilibrium solutions was first analyzed by deriving a Jacobian matrix from partial derivatives of our model. Newly derived eigenvalues are then used to determine the stability. The viability of the model is then demonstrated by using MATLAB. The numerical results show a clear Allee effect and a variety of possible phenomena related to stability when carrying capacity (k) is varied. Two different types of …

Probabilistic Analysis Of Revenues In Online Games, Nishchal Sapkota

Honors Theses

Online games are captivating and engage users across the world. Some game formats maintain a pseudo-currency to give incentive to the players to play the game in search of rewards as set by the game provider. We model a multi-stage online game and predict how much revenue game providers obtain per game. We compare the revenues generated from different tournament formats to find the one with the maximum per-game revenue for the provider. We have also found the limiting value of the revenue as the game provider increases the number of stages.

Our methods are based on concepts of the …

Twisted Central Configurations Of The Eight-Body Problem, Gokul Bhusal

Honors Theses

The N-body problem qualifies as the problem of the twenty-first century because of its fundamental importance and difficulty to solve [1]. A number of great mathematicians and physicists have tried but failed to come up with the general solution of the problem. Due to the complexity of the problem, even a partial result will help us in the understanding of the N-body problem. Central configurations play a ‘central’ role in the understanding of the N-body problem. The well known Euler and Lagrangian solutions are both generated from three-body central configurations. The existence and classifications of central configurations have attracted number …