Anomalous Velocity Distributions in Active Brownian Suspensions

Large-scale simulations and analytical theory have been combined to obtain the nonequilibrium velocity distribution, f(v), of randomly accelerated particles in suspension. The simulations are based on an event-driven algorithm, generalized to include friction. They reveal strongly anomalous but largely universal distributions, which are independent of volume fraction and collision processes, which suggests a one-particle model should capture all the essential features. We have formulated this one-particle model and solved it analytically in the limit of strong damping, where we find that f (v) decays as 1/v for multiple decades, eventually crossing over to a Gaussian decay for the largest velocities. Many particle simulations and numerical solution of the one-particle model agree for all values of the damping.

New Results Concerning Probability Distributions with Increasing Generalized Failure Rates

The generalized failure rate of a continuous random variable has demonstrable importance in operations management. If the valuation distribution of a product has an increasing generalized failure rate (that is, the distribution is IGFR), then the associated revenue function is unimodal, and when the generalized failure rate is strictly increasing, the global maximum is uniquely specified. The assumption that the distribution is IGFR is thus useful and frequently held in recent pricing, revenue, and supply chain management literature. This note contributes to the IGFR literature in several ways. First, it investigates the prevalence of the IGFR property for the left and right truncations of valuation distributions. Second, we extend the IGFR notion to discrete distributions and contrast it with the continuous distribution case. The note also addresses two errors in the previous IGFR literature. Finally, for future reference, we analyze all common (continuous and discrete) distributions for the prevalence of the IGFR property, and derive and tabulate their generalized failure rates.

Product Distributions Following Hyperthermal Collisions Between C2H4 And O(3P)

Transient Diode Laser Absorption Spectroscopy (TDLAS) was used to perform vibrational state population studies of the CO2 product from the hyperthermal reaction between C2H4 and O(3P) at room temperature using O3 as the O-atom precursor. Photodissociation of O3 using a frequency quadrupled Q-switch Nd:YAG laser pulse at 266 nm produced O(3P) atoms at high velocities which subsequently reacted with C2H4, producing several primary and secondary products including CO2. The CO2 product was detected using high-resolution TDLAS under five unique sets of reaction conditions. The vibrational distribution of the CO2 product did not follow a Boltzmann distribution at all five sets of conditions. The experiments showed a distribution in which there was a surprisingly high population in the (1000) (symmetric stretching) state compared with the other states probed, all of which contained bend excitation. In general, the CO2 population in the (1000) state was about 15-20% more populated than the Boltzmann distribution predicts. A possible explanation for this result may lie in the mechanism of CO2 evolution from the C2H4 + O(3P) reaction.

Design Simulation for Solar Energy Research and Education

Solar research is primarily conducted in regions with consistent sunlight, severely limiting research opportunities in many areas. Unfortunately, the unreliable weather in Lewisburg, PA, can prove difficult for such testing to be conducted. As such, a solar simulator was developed for educational purposes for the Mechanical Engineering department at Bucknell University. The objective of this work was to first develop a geometric model to evaluate a one sun solar simulator. This was intended to provide a simplified model that could be used without the necessity of expensive software. This model was originally intended to be validated experimentally, but instead was done using a proven ray tracing program, TracePro. Analyses with the geometrical model and TracePro demonstrated the influence the geometrical properties had results, specifically the reflector (aperture) diameter and the rim angle. Subsequently, the two were approaches were consistent with one another for aperture diameters 0.5 m and larger, and for rim angles larger than 45°. The constructed prototype, that is currently untested, was designed from information provided by the geometric model, includes a metal halide lamp with a 9.5 mm arc diameter and parabolic reflector with an aperture diameter of 0.631 meters. The maximum angular divergence from the geometrical model was predicted to be 30 mRadians. The average angular divergence in TraceProof the system was 19.5 mRadians, compared to the sun’s divergence of 9.2 mRadians. Flux mapping in TracePro showed an intensity of 1000 W/m2 over the target plane located 40 meters from the lamp. The error between spectrum of the metal halide lamp and the solar spectrum was 10.9%, which was found by comparing their respective Plank radiation distributions. The project did not satisfy the original goal of matching the angular divergence of sunlight, although the system could still to be used for optical testing. The geometric model indicated performance in this area could be improved by increasing the diameter of the reflector, as well as decreasing the source diameter. Although ray tracing software provides more information to analyze the simulator system, the geometrical model is adequate to provide enough information to design a system.