Graduate Thesis Or Dissertation
 

Classical chaotic scatting from symmetric four hill potentials

Public Deposited

Downloadable Content

Download PDF
https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/0g354j395

Descriptions

Attribute NameValues
Creator
Abstract
  • Classical chaotic scattering experiments were performed on ten different four hill potentials, unique under x-axis reflection, given by: V(x,y) = x²y²e⁻⁽ˣ² ⁺ ʸ²⁾ σᵢ where σᵢ was ±1 depending upon quadrant. Our work was based on a paper (9) that only studied the case where σᵢ =1 in all quadrants. The system used was a time independent Hamiltonian with energy conservation. Chaos manifested itself in our experiment in two ways. First, below some critical energy, particles would become almost trapped by the system. Second, above the critical energy, the particles directly strike the saddle point. Trajectories were integrated using a standard 4ᵗʰ order Runge-Kutta ODE solver. Scattering angle and time delay were measured as a function of the impact parameter. Chaos was seen in these scattering functions as discontinuities. The Lyapunov exponent was measured for a number of energies using a brute force method (separation of nearby trajectories). The capacity dimension was measured using the uncertainty exponent method (13). The critical energy was measured using both capacity dimension and Lyapunov exponent data. Five of the potentials had a critical energy within error bounds of E0.039: V₂c, V₃, V₄ₐ, V₄b, V₆. Three were with error bounds of Ec=0.135: V₁, V₂ₐ, V₅b. Potential V₂b had a value of 0.071 and V₅ₐ had 0.092. All bifurcations in this system were abrupt. Three of the potentials were generic abrupt: V₁, V₂ₐ, V₅b. Six of the potentials had abrupt crisis bifurcations: V₂b, V₂, V₃, V₄ₐ, V₄b, V₆. Potential V5A had abrupt nonhyperbolic bifurcations. The Lyapunov exponent for all ten potentials had a linear high energy behavior that had not been seen before. The systems showed chaos and the largest Lyapunov exponents for them were measured (below the critical energy) to be: V₁=0.446 + 0.013, V₂ₐ=0.472 ± 0.007, V₂b=0.663 ± 0.007, V₂c=0.683 + 0.010, V₃=0.655 ± 0.011, V₄ₐ=0.7l4 + 0.010, V₄b=0.743 + 0.003, V₅ₐ=0.74l ± 0.009, V₅b=0.46l ± 0.006, V₆=0.697 ± 0.008. We then concluded that systems that contained attractors were more chaotic than the one that did not. In addition, we saw that the sign of the hills on the left side of the system governed the shape of the scattering functions but not all of the chaotic characteristics.
License
Resource Type
Date Available
Date Issued
Degree Level
Degree Name
Degree Field
Degree Grantor
Commencement Year
Advisor
Academic Affiliation
Non-Academic Affiliation
Subject
Rights Statement
Publisher
Peer Reviewed
Language
Digitization Specifications
  • File scanned at 300 ppi (Monochrome, 256 Grayscale) using Capture Perfect 3.0.82 on a Canon DR-9080C in PDF format. CVista PdfCompressor 4.0 was used for pdf compression and textual OCR.
Replaces

Relationships

Parents:

This work has no parents.

In Collection:

Items

Thumbnail Title Date Uploaded Visibility Actions
file details BaumanJordanM2003.pdf 2017-08-15 Public Download