Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 4 of 4
Full-Text Articles in Physics
Quantifying Complex Systems Via Computational Fly Swarms, Troy Taylor
Quantifying Complex Systems Via Computational Fly Swarms, Troy Taylor
Senior Theses
Complexity is prevalent both in natural and in human-made systems, yet is not well understood quantitatively. Qualitatively, complexity describes a phenomena in which a system composed of individual pieces, each having simple interactions with one another, results in interesting bulk properties that would otherwise not exist. One example of a complex biological system is the bird flock, in particular, a starling murmuration. Starlings are known to move in the direction of their neighbors and avoid collisions with fellow starlings, but as a result of these simple movement choices, the flock as a whole tends to exhibit fluid-like movements and form …
The Computational Study Of Fly Swarms & Complexity, Austin Bebee
The Computational Study Of Fly Swarms & Complexity, Austin Bebee
Senior Theses
A system is considered complex if it is composed of individual parts that abide by their own set of rules, while the system, as a whole, will produce non-deterministic properties. This prevents the behavior of such systems from being accurately predicted. The motivation for studying complexity spurs from the fact that it is a fundamental aspect of innumerable systems. Among complex systems, fly swarms are relatively simple, but even so they are still not well understood. In this research, several computational models were developed to assist with the understanding of fly swarms. These models were primarily analyzed by using the …
The Advection-Diffusion Equation And The Enhanced Dissipation Effect For Flows Generated By Hamiltonians, Michael Kumaresan
The Advection-Diffusion Equation And The Enhanced Dissipation Effect For Flows Generated By Hamiltonians, Michael Kumaresan
Dissertations, Theses, and Capstone Projects
We study the Cauchy problem for the advection-diffusion equation when the diffusive parameter is vanishingly small. We consider two cases - when the underlying flow is a shear flow, and when the underlying flow is generated by a Hamiltonian. For the former, we examine the problem on a bounded domain in two spatial variables with Dirichlet boundary conditions. After quantizing the system via the Fourier transform in the first spatial variable, we establish the enhanced-dissipation effect for each mode. For the latter, we allow for non-degenerate critical points and represent the orbits by points on a Reeb graph, with vertices …
Hydrodynamic Analogues Of Hamiltonian Systems, Francisco J. Jauffred
Hydrodynamic Analogues Of Hamiltonian Systems, Francisco J. Jauffred
Graduate Masters Theses
A one-dimensional Hamiltonian system can be modeled and understood as a two-dimensional incompressible fluid in phase space. In this sense, the chaotic behavior of one-dimensional time dependent Hamiltonians corresponds to the mixing of two-dimensional fluids. Amey (2012) studied the characteristic values of one such system and found a scaling law governing them. We explain this scaling law as a diffusion process occurring in an elliptical region with very low eccentricity. We prove that for such a scaling law to occur, it is necessary for a vorticity field to be present. Furthermore, we show that a conformal mapping of an incompressible …