Chaotic enhancement of dark matter density in binary systems

We study the capture of galactic dark matter particles (DMP) in two-body and few-body systems with a symplectic map description. This approach allows modeling the scattering of $10^{16}$ DMPs after following the time evolution of the captured particle on about $10^9$ orbital periods of the binary system. We obtain the DMP density distribution inside such systems and determine the enhancement factor of their density in a center vicinity compared to its galactic value as a function of the mass ratio of the bodies and the ratio of the body velocity to the velocity of the galactic DMP wind. We find that the enhancement factor can be on the order of tens of thousands.Comment: 6 pages, 9 figure

Living tiny legally

Over the last 40 years, the average new United States house has increased in size by more than 1,000 square feet, from an average size of 1,660 square feet in 1973 (earliest year available from the Census Bureau) to 2,687 square feet last year (Perry, 2016). In that same time period, there was a 91% increase in home square footage per inhabitant and a decrease in average household size. According to the U.S. Census Bureau, the average home in the United States costs approximately $358,000 to build, an increase of roughly$200,000 since 1998. Meanwhile, the average annual income in the U.S. has remained unchanged for the last several years, at approximately $52,000 per year. As costs increased, the U.S. homeownership rate fell to its lowest point in over 50 years. Since 1965, the homeownership rate has decreased to 62.9These trends have created a dire need for affordable housing. This project addresses this problem, while proposing tiny houses as a solution, and following the triple bottom line. This is an economic model that focuses on economy, ecology, and equity as the dimensions of success. Tiny homes are sustainable as they are more energy efficient and require less materials, as well as less space. In congruence with less materials and less land required, technology such as passive solar design, high R-value insulation, or energy star appliances can drastically reduce energy costs (Morrison, 2015). Depending on the size, tiny homes use only 10$72,000, whereas the cost of new construction for a 200 square foot tiny house can be as low as $35,000. Socially the tiny house lifestyle promotes a greater sense of community, more socio-economic accessibility, and the benefits of minimalism. This project takes all of these principles and applies them to examine the feasibility of implementing tiny homes within the Harrisonburg area

Symplectic map description of Halley's comet dynamics

The main features of 1P/Halley chaotic dynamics can be described by a two dimensional symplectic map. Using Mel'nikov integral we semi-analytically determine such a map for 1P/Halley taking into account gravitational interactions from the Sun and the eight planets. We determine the Solar system kick function ie the energy transfer to 1P/Halley along one passage through the Solar system. Our procedure allows to compute for each planet its contribution to the Solar system kick function which appears to be the sum of the Keplerian potential of the planet and of a rotating circular gravitational dipole potential due to the Sun movement around Solar system barycenter. We test the robustness of the symplectic Halley map by directly integrating Newton's equations over $\sim 2.4\cdot 10^4$ yr around Y2K and by reconstructing the Solar system kick function. Our results show that the Halley map with fixed parameters gives a reliable description of comet dynamics on time scales of $10^4$ yr while on a larger scales the parameters of the map are slowly changing due to slow oscillations of orbital momentum.Comment: To be published in Physics Letter A, 8 pages, 5 figures, supplementary material at http://perso.utinam.cnrs.fr/~lages/publications/sm/sm21.htm

Cooling Characteristics of a 2-Row Radial Engine

This report presents the results of cooling tests conducted on a calibrated GR-1535 Pratt and Whitney Wasp, Jr. Engine installed in a Vought X04U-2 airplane. The tests were made in the NACA full-scale tunnel at air speeds from 70 to 120 miles per hour, at engine speeds from 1,500 to 2,600 r.p.m., and at manifold pressures from 19 to 33 inches of mercury absolute. A Smith controllable propeller was used to facilitate obtaining the different combinations of engine speed, power, and manifold pressure

Air Flow Around Finned Cylinders

Report presents the results of a study made to determine the air-flow characteristics around finned cylinders. Air-flow distribution is given for a smooth cylinder, for a finned cylinder having several fin spacings and fin widths, and for a cylinder with several types of baffle with various entrance and exit shapes. The results of these tests show: that flow characteristics around a cylinder are not so critical to changes in fin width as they are to fin spacing; that the entrance of the baffle has a marked influence on its efficiency; that properly designed baffles increase the air flow over the rear of the cylinder; and that these tests check those of heat-transfer tests in the choice of the best baffle

Pressure Drop Across Finned Cylinders Enclosed in a Jacket

The pressure drop across finned cylinders in a jacket for a range of air speeds from approximately 13 to 230 miles per hour has been investigated. Tests were made to determine the effect on the pressure drop of changes in fin space, fin width, jacket entrance and exit areas, skirt-approach radius, and the use of fillets and a separator plate at the rear of the cylinder. The pressure drop across the cylinder increased as the fin space decreased, the increase being very rapid at fin spaces smaller than approximately 0.20 inch. Fin width had little effect on the pressure drop for the range of widths tested. The pressure drop across the cylinder was nearly halved by increasing the skirt-approach radius from 3/4 inch to 1-1/4 inches, but fillets and a separator plate at the rear of the cylinder had little effect on the pressure drop. The pressure drop across a cylinder with tapered fins was greater than that for a cylinder having rectangular fins with the same effective fin spacing