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

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

Image set for deep learning: field images of maize annotated with disease symptoms

Objectives Automated detection and quantification of plant diseases would enable more rapid gains in plant breeding and faster scouting of farmers’ fields. However, it is difficult for a simple algorithm to distinguish between the target disease and other sources of dead plant tissue in a typical field, especially given the many variations in lighting and orientation. Training a machine learning algorithm to accurately detect a given disease from images taken in the field requires a massive amount of human-generated training data. Data description This data set contains images of maize (Zea mays L.) leaves taken in three ways: by a hand-held camera, with a camera mounted on a boom, and with a camera mounted on a small unmanned aircraft system (sUAS, commonly known as a drone). Lesions of northern leaf blight (NLB), a common foliar disease of maize, were annotated in each image by one of two human experts. The three data sets together contain 18,222 images annotated with 105,705 NLB lesions, making this the largest publicly available image set annotated for a single plant disease

Elucidating glycosaminoglycan–protein–protein interactions using carbohydrate microarray and computational approaches

Glycosaminoglycan polysaccharides play critical roles in many cellular processes, ranging from viral invasion and angiogenesis to spinal cord injury. Their diverse biological activities are derived from an ability to regulate a remarkable number of proteins. However, few methods exist for the rapid identification of glycosaminoglycan–protein interactions and for studying the potential of glycosaminoglycans to assemble multimeric protein complexes. Here, we report a multidisciplinary approach that combines new carbohydrate microarray and computational modeling methodologies to elucidate glycosaminoglycan–protein interactions. The approach was validated through the study of known protein partners for heparan and chondroitin sulfate, including fibroblast growth factor 2 (FGF2) and its receptor FGFR1, the malarial protein VAR2CSA, and tumor necrosis factor-α (TNF-α). We also applied the approach to identify previously undescribed interactions between a specific sulfated epitope on chondroitin sulfate, CS-E, and the neurotrophins, a critical family of growth factors involved in the development, maintenance, and survival of the vertebrate nervous system. Our studies show for the first time that CS is capable of assembling multimeric signaling complexes and modulating neurotrophin signaling pathways. In addition, we identify a contiguous CS-E-binding site by computational modeling that suggests a potential mechanism to explain how CS may promote neurotrophin-tyrosine receptor kinase (Trk) complex formation and neurotrophin signaling. Together, our combined microarray and computational modeling methodologies provide a general, facile means to identify new glycosaminoglycan–protein–protein interactions, as well as a molecular-level understanding of those complexes