An analysis code for the Rapid Engineering Estimation of Momentum and Energy Losses (REMEL)

Nonideal behavior has traditionally been modeled by defining efficiency (a comparison between actual and isentropic processes), and subsequent specification by empirical or heuristic methods. With the increasing complexity of aeropropulsion system designs, the reliability of these more traditional methods is uncertain. Computational fluid dynamics (CFD) and experimental methods can provide this information but are expensive in terms of human resources, cost, and time. This report discusses an alternative to empirical and CFD methods by applying classical analytical techniques and a simplified flow model to provide rapid engineering estimates of these losses based on steady, quasi-one-dimensional governing equations including viscous and heat transfer terms (estimated by Reynold's analogy). A preliminary verification of REMEL has been compared with full Navier-Stokes (FNS) and CFD boundary layer computations for several high-speed inlet and forebody designs. Current methods compare quite well with more complex method results and solutions compare very well with simple degenerate and asymptotic results such as Fanno flow, isentropic variable area flow, and a newly developed, combined variable area duct with friction flow solution. These solution comparisons may offer an alternative to transitional and CFD-intense methods for the rapid estimation of viscous and heat transfer losses in aeropropulsion systems

Simplified, inverse, ejector design tool

A simple lumped parameter based inverse design tool has been developed which provides flow path geometry and entrainment estimates subject to operational, acoustic, and design constraints. These constraints are manifested through specification of primary mass flow rate or ejector thrust, fully-mixed exit velocity, and static pressure matching. Fundamentally, integral forms of the conservation equations coupled with the specified design constraints are combined to yield an easily invertible linear system in terms of the flow path cross-sectional areas. Entrainment is computed by back substitution. Initial comparison with experimental and analogous one-dimensional methods show good agreement. Thus, this simple inverse design code provides an analytically based, preliminary design tool with direct application to High Speed Civil Transport (HSCT) design studies

Mandelbrot's 1/f fractional renewal models of 1963-67: The non-ergodic missing link between change points and long range dependence

The problem of 1/f noise has been with us for about a century. Because it is so often framed in Fourier spectral language, the most famous solutions have tended to be the stationary long range dependent (LRD) models such as Mandelbrot's fractional Gaussian noise. In view of the increasing importance to physics of non-ergodic fractional renewal models, I present preliminary results of my research into the history of Mandelbrot's very little known work in that area from 1963-67. I speculate about how the lack of awareness of this work in the physics and statistics communities may have affected the development of complexity science, and I discuss the differences between the Hurst effect, 1/f noise and LRD, concepts which are often treated as equivalent.Comment: 11 pages. Corrected and improved version of a manuscript submitted to ITISE 2016 meeting in Granada, Spai

Anomalous spatial diffusion and multifractality in optical lattices

Transport of cold atoms in shallow optical lattices is characterized by slow, nonstationary momentum relaxation. We here develop a projector operator method able to derive in this case a generalized Smoluchowski equation for the position variable. We show that this explicitly non-Markovian equation can be written as a systematic expansion involving higher-order derivatives. We use the latter to compute arbitrary moments of the spatial distribution and analyze their multifractal properties.Comment: 5 pages, 3 figure

Playing with Prejudice: Do Colour Scheme and Hypersexualization of Women In Games Influence Player Decisions, Perceptions, and Avatar Appeal?

Hypersexualization of women video game characters through unrealistic body proportions and revealing clothes is common. Previous work suggested that overexposure to sexualized women characters can harm players, through increased self-objectification and higher rape myth acceptance; however, there have been inconsistencies across studies that we suggest may stem from variations in the study design and other visual characteristics of the characters, such as relying heavily on stereotypes reinforced by colour schemes (e.g., blonde princess). To address this, we designed a text-based game prototype and four identical women characters who varied only in their colour scheme (gold/red or purple/black) and amount of sexualization (through bikini armour and exaggerating body proportions). We measure attributes assigned to the avatar, avatar appeal, rape myth acceptance and self-objectification. 82 participants participated in our online-study in 2021. Most participants found the non-sexualized character versions more appealing than the sexualized characters and were more likely to assign ‘manipulativeness’ to the sexualized character. When presented with the sexualized characters, participants demonstrated higher rape myth acceptance, and more self-objectification

Experimental Impacts into Strength-Layered Targets: Crater Morphology and Morphometry

Impact cratering is a fundamental physical process that has dominated the evolution and modification of nearly every planetary surface in the Solar System. Impact craters serve as a means to probe the subsurface structure of a planetary body and provide hints about target surface properties. By examining small craters on the lunar maria and comparing these to experimental impacts in the laboratory, Oberbeck and Quaide first suggested that crater morphology can be used to estimate the thickness of a regolith layer on top of a more competent unit. Lunar craters show a morphological progression from a simple bowl shape to flat-floored and concentric craters as crater diameter increases for a given regolith thickness. This quantitative relationship is commonly used to estimate regolith thicknesses on the lunar surface and has also been explored via numerical and experimental studies. Here we report on a series of experimental impact craters formed in targets com-posed of a thin layer of loose sand on top of a stronger substrate at the Experimental Impact Laboratory at NASA Johnson Space Center

Experimental Impacts into Strength-Layered Targets: Ejecta Kinematics

AImpact cratering has dominated the evolution and modification of planetary surfaces through-out the history of the solar system. Impact craters can serve as probes to understanding the details of a planetary subsurface; for example, Oberbeck and Quaide, suggested that crater morphology can be used to estimate the thickness of a regolith layer on top of a more competent unit. Lunar craters show a morphological progression from a simple bowl shape to flat-floored and concentric craters as crater diameter in-creases for a given regolith thickness. The final shape of the impact crater is a result of the subsurface flow-field initiated as the projectile transfers its energy and momentum to the target surface at the moment of impact. Therefore, when a regolith layer is present over a stronger substrate, such as is the case on the lunar surface, the substrate modifies the flow-field and thereby the excavation flow of the crater, which is reflected in the morphology of the final crater. Here we report on a series of experimental impacts into targets composed of a thin layer of loose sand on top of a stronger substrate. We use the Ejection-Velocity Measurement System developed to examine the ejecta kinematics during the formation of these craters

The E8 geometry from a Clifford perspective

This paper considers the geometry of $E_8$ from a Clifford point of view in three complementary ways. Firstly, in earlier work, I had shown how to construct the four-dimensional exceptional root systems from the 3D root systems using Clifford techniques, by constructing them in the 4D even subalgebra of the 3D Clifford algebra; for instance the icosahedral root system $H_3$ gives rise to the largest (and therefore exceptional) non-crystallographic root system $H_4$. Arnold's trinities and the McKay correspondence then hint that there might be an indirect connection between the icosahedron and $E_8$. Secondly, in a related construction, I have now made this connection explicit for the first time: in the 8D Clifford algebra of 3D space the $120$ elements of the icosahedral group $H_3$ are doubly covered by $240$ 8-component objects, which endowed with a `reduced inner product' are exactly the $E_8$ root system. It was previously known that $E_8$ splits into $H_4$-invariant subspaces, and we discuss the folding construction relating the two pictures. This folding is a partial version of the one used for the construction of the Coxeter plane, so thirdly we discuss the geometry of the Coxeter plane in a Clifford algebra framework. We advocate the complete factorisation of the Coxeter versor in the Clifford algebra into exponentials of bivectors describing rotations in orthogonal planes with the rotation angle giving the correct exponents, which gives much more geometric insight than the usual approach of complexification and search for complex eigenvalues. In particular, we explicitly find these factorisations for the 2D, 3D and 4D root systems, $D_6$ as well as $E_8$, whose Coxeter versor factorises as $W=\exp(\frac{\pi}{30}B_C)\exp(\frac{11\pi}{30}B_2)\exp(\frac{7\pi}{30}B_3)\exp(\frac{13\pi}{30}B_4)$. This explicitly describes 30-fold rotations in 4 orthogonal planes with the correct exponents $\{1, 7, 11, 13, 17, 19, 23, 29\}$ arising completely algebraically from the factorisation

Easing into Reality: Experimental Impacts into Slopes and Layers

Impact cratering is the dominant geo-logic process affecting the surfaces of solid bodies throughout our solar system. Because large impacts are (luckily) rare on Earth, the process is studied through experiments, observations of existing structures, numerical modeling, and theory, most of which make the simplifying assumptions that the target is homogeneous, with no substantial topography. Craters do not always form on level targets com-posed of homogeneous loose material. Rather (Fig. 1), they often form on sloped surfaces and in layered tar-gets, both of which significantly influence the excavation and ejecta deposition processes. Such craters are common on the Moon and asteroids. We are investigating crater formation in two separate suites of experiments using sloped and layered targets (Fig. 2) at the Experimental Impact Laboratory at NASA Johnson Space Center. An experiment was also performed in a flat, homogenous target to serve as a reference