Analytical Methods and Observational Requirements for Interpretation of Asteroid Distributions

Analytical methods and observational requirements for interpretation of asteroid distribution

Spatio-temporal correlations in Wigner molecules

The dynamical response of Coulomb-interacting particles in nano-clusters are analyzed at different temperatures characterizing their solid- and liquid-like behavior. Depending on the trap-symmetry, both the spatial and temporal correlations undergo slow, stretched exponential relaxations at long times, arising from spatially correlated motion in string-like paths. Our results indicate that the distinction between the `solid' and `liquid' is soft: While particles in a `solid' flow producing dynamic heterogeneities, motion in `liquid' yields unusually long tail in the distribution of particle-displacements. A phenomenological model captures much of the subtleties of our numerical simulations.Comment: 5 pages, 4 figures, includes supplementary material

Development of a perturbation generator for vortex stability studies

Theory predicts vortex instability when subjected to certain types of disturbances. It was desired to build a device which could introduce controlled velocity perturbations into a trailing line vortex in order to study the effects on stability. A perturbation generator was designed and manufactured which can be attached to the centerbody of an airfoil type vortex generator. Details of design tests and manufacturing of the perturbation generator are presented. The device produced controlled perturbation with frequencies in excess of 250 Hz. Preliminary testing and evaluation of the perturbation generator performance was conducted in a 4 inch cylindrical pipe. Observations of vortex shedding frequencies from a centerbody were measured. Further evaluation with the perturbation generator attached to the vortex generator in a 2 x 3 foot wind tunnel were also conducted. Hot-wire anemometry was used to confirm the perturbation generator's ability to introduce controlled frequency fluctuations. Comparison of the energy levels of the disturbances in the vortex core was made between locations 42 chord lengths and 15 chord lengths downstream

Iterated harmonic numbers

The harmonic numbers are the sequence 1, 1+1/2, 1+1/2+1/3, ... Their asymptotic difference from the sequence of the natural logarithm of the positive integers is Euler's constant gamma. We define a family of natural generalizations of the harmonic numbers. The jth iterated harmonic numbers are a sequence of rational numbers that nests the previous sequences and relates in a similar way to the sequence of the jth iterate of the natural logarithm of positive integers. The analogues of several well-known properties of the harmonic numbers also hold for the iterated harmonic numbers, including a generalization of Euler's constant. We reproduce the proof that only the first harmonic number is an integer and, providing some numeric evidence for the cases j = 2 and j = 3, conjecture that the same result holds for all iterated harmonic numbers. We also review another proposed generalization of harmonic numbers.Comment: 13 pages, 2 figure

Second coefficient of viscosity in air

Acoustic attenuation measurements in air were analyzed in order to estimate the second coefficient of viscosity. Data over a temperature range of 11 C to 50 C and at relative humidities between 6 percent and 91 percent were used. This analysis showed that the second coefficient of viscosity varied between 1900 and 20,000 times larger than the dynamic or first coefficient of viscosity over the temperature and humidity range of the data. In addition, the data showed that the molecular relaxation effects, which are responsible for the magnitude of the second coefficient of viscosity, place severe limits on the use of time-independent, thermodynamic equations of state. Compressible flows containing large streamwise velocity gradients, like shock waves, which cause significant changes in particle properties to occur during time intervals shorter than hundredths of seconds, must be modeled using dynamic equations of state. The dynamic model approach is described briefly

A methodology for selective removal of orbital debris

Earth-orbiting objects, large enough to be tracked, were surveyed for possible systematic debris removal. Based upon the statistical collision studies of others, it was determined that objects in orbits approximately 1000 km above the Earth's surface are at greatest collisional risk. Russian C-1B boosters were identified as the most important target of opportunity for debris removal. Currently, more than 100 in tact boosters are orbiting the Earth with apogees between 950 km and 1050 km. Using data provided by Energia USA, specific information on the C-1B booster, in terms of rendezvous and capture strategies, was discussed

EXCESS COMMUTING AND ITS RELATION TO URBAN FORM IN ONTARIO, CANADA

The objectives of this research are to examine the relationship between urban form and excess commuting for 10 different occupation types in 12 different Census Metropolitan Areas (CMA) across Ontario, Canada and to provide insights that could help inform the planning process. The results suggest the following: 1) that two cities with the same type of urban form may not necessarily exhibit the same level of commuting efficiency; 2) the size of the CMA and the amount of spatial interaction activities are key factors with respect to commuting efficiency; 3) certain occupations were found to have higher excess commuting than the CMA-wide measure; therefore, planners could channel land use development to attract those occupational classes; 4) some patterns of urban form could benefit from a reliable transit system, in which case planners could focus on building transit systems that connect these workers to their places of work; and 5) planners could also utilize the Brotchie\u27s urban triangles to evaluate if the current urban form is associated with an efficient commuting pattern and identify what types of urban form could give rise to more commuting efficiency. Future research may expand on this thesis by comparing urban land development and commuting efficiency changes for a particular city over time. Other opportunities may include performing similar analysis with a larger sample of CMAs across Canada, or comparing the three largest CMAs in Canada (i.e. Toronto, Montreal and Vancouver). Future research may also consider allowing workers who live in the CMA to commute to jobs outside the CMA, or live outside the CMA and commute inwards