Computer program for calculating flow parameters and power requirements for cryogenic wind tunnels

A computer program has been written that performs the flow parameter calculations for cryogenic wind tunnels which use nitrogen as a test gas. The flow parameters calculated include static pressure, static temperature, compressibility factor, ratio of specific heats, dynamic viscosity, total and static density, velocity, dynamic pressure, mass-flow rate, and Reynolds number. Simplifying assumptions have been made so that the calculations of Reynolds number, as well as the other flow parameters can be made on relatively small desktop digital computers. The program, which also includes various power calculations, has been developed to the point where it has become a very useful tool for the users and possible future designers of fan-driven continuous-flow cryogenic wind tunnels

Operating envelope charts for the Langley 0.3-meter transonic cryogenic wind tunnel

To take full advantage of the unique Reynolds number capabilities of the 0.3-meter Transonic Cryogenic Tunnel (0.3-m TCT) at the NASA Langley Research Center, it was designed to accommodate test sections other than the original, octagonal, three-dimensional test section. A 20- by 60-cm two-dimensional test section was installed in 1976 and was extensively used, primarily for airfoil testing, through the fall of 1984. The tunnel was inactive during 1985 so that a new test section and improved high speed diffuser could be installed in the tunnel circuit. The new test section has solid adaptive top and bottom walls to reduce or eliminate wall interference for two-dimensional testing. The test section is 33- by 33-cm in cross section at the entrance and is 142 cm long. In the planning and running of past airfoil tests in the 0.3-m TCT, the use of operating envelope charts have proven very useful. These charts give the variation of total temperature and pressure with Mach number and Reynolds number. The operating total temperature range of the 0.3-m TCT is from about 78 K to 327 K with total pressures ranging from about 17.5 psia to 88 psia. This report presents the operating envelope charts for the 0.3-m TCT with the adaptive wall tes t section installed. They were all generated based on a 1-foot chord model. The Mach numbers vary from 0.1 to 0.95

High Reynolds number tests of the CAST 10-2/DOA 2 airfoil in the Langley 0.3-meter transonic cryogenic tunnel, phase 1

A wind tunnel investigation of an advanced technology airfoil, the CAST 10-2/DOA 2, was conducted in the Langley 0.3 meter Transonic Cryogenic Tunnel (0.3 m TCT). This was the first of a series of tests conducted in a cooperative National Aeronautics and Space Administration (NASA) and the Deutsche Forschungs- und Versuchsanstalt fur Luft- und Raumfahrt e. V. (DFVLR) airfoil research program. Test temperature was varied from 280 K to 100 K to pressures from slightly above 1 to 5.8 atmospheres. Mach number was varied from 0.60 to 0.80, and the Reynolds number (based on airfoil chord) was varied from 4 x 10 to the 8th power to 45 x 10 to the 6th power. This report presents the experimental aerodynamic data obtained for the airfoil and includes descriptions of the airfoil model, the 0.3 m TCT, the test instrumentation, and the testing procedures

Dynamic Stability Instrumentation System (DSIS). Volume 1: Hardware description

This paper is a hardware description manual for the Dynamic Stability Instrumentation System that is used in specific NASA Langley wind tunnels. The instrumentation system performs either a synchronous demodulation or a fast Fourier transform on dynamic balance strain gage signals, and ultimately computes aerodynamic coefficients. The DSIS consists of a double rack of instruments, a remote motor-generator set, two special stings each with motor driven shafts, and specially designed balances. The major components in the instrumentation rack include a personal computer, digital signal processor microcomputers, computer-controlled signal conditioners, function generator, digital multimeter, and an optional fast Fourier transform analyzer

Error-correcting code on a cactus: a solvable model

An exact solution to a family of parity check error-correcting codes is provided by mapping the problem onto a Husimi cactus. The solution obtained in the thermodynamic limit recovers the replica symmetric theory results and provides a very good approximation to finite systems of moderate size. The probability propagation decoding algorithm emerges naturally from the analysis. A phase transition between decoding success and failure phases is found to coincide with an information-theoretic upper bound. The method is employed to compare Gallager and MN codes.Comment: 7 pages, 3 figures, with minor correction

Emergence of hyperons in failed supernovae: trigger of the black hole formation

We investigate the emergence of strange baryons in the dynamical collapse of a non-rotating massive star to a black hole by the neutrino-radiation hydrodynamical simulations in general relativity. By following the dynamical formation and collapse of nascent proto-neutron star from the gravitational collapse of a 40Msun star adopting a new hyperonic EOS table, we show that the hyperons do not appear at the core bounce but populate quickly at ~0.5-0.7 s after the bounce to trigger the re-collapse to a black hole. They start to show up off center owing to high temperatures and later prevail at center when the central density becomes high enough. The neutrino emission from the accreting proto-neutron star with the hyperonic EOS stops much earlier than the corresponding case with a nucleonic EOS while the average energies and luminosities are quite similar between them. These features of neutrino signal are a potential probe of the emergence of new degrees of freedom inside the black hole forming collapse.Comment: 11 pages, 3 figures, accepted for publication in ApJ

A Grassmann algebra for matroids

We introduce an idempotent analogue of the exterior algebra for which the theory of tropical linear spaces (and valuated matroids) can be seen in close analogy with the classical Grassmann algebra formalism for linear spaces. The top wedge power of a tropical linear space is its Plucker vector, which we view as a tensor, and a tropical linear space is recovered from its Plucker vector as the kernel of the corresponding wedge multiplication map. We prove that an arbitrary d-tensor satisfies the tropical Plucker relations (valuated exchange axiom) if and only if the d-th wedge power of the kernel of wedge-multiplication is free of rank one. This provides a new cryptomorphism for valuated matroids, including ordinary matroids as a special case

Masses of Fermions in Supersymmetric Models

We consider the mass generation for the usual quarks and leptons in some supersymmetric models. The masses of the top, the bottom, the charm, the tau and the muon are given at the tree level. All the other quarks and the electron get their masses at the one loop level in the Minimal Supersymmetric Standard Model (MSSM) and in two Supersymmetric Left-Right Models, one model uses triplets (SUSYLRT) to break $SU(2)_{R}$-symmetry and the other use doublets(SUSYLRD).Comment: 24 pages, 2 figures and 3 table

Recognizing Treelike k-Dissimilarities

A k-dissimilarity D on a finite set X, |X| >= k, is a map from the set of size k subsets of X to the real numbers. Such maps naturally arise from edge-weighted trees T with leaf-set X: Given a subset Y of X of size k, D(Y) is defined to be the total length of the smallest subtree of T with leaf-set Y . In case k = 2, it is well-known that 2-dissimilarities arising in this way can be characterized by the so-called "4-point condition". However, in case k > 2 Pachter and Speyer recently posed the following question: Given an arbitrary k-dissimilarity, how do we test whether this map comes from a tree? In this paper, we provide an answer to this question, showing that for k >= 3 a k-dissimilarity on a set X arises from a tree if and only if its restriction to every 2k-element subset of X arises from some tree, and that 2k is the least possible subset size to ensure that this is the case. As a corollary, we show that there exists a polynomial-time algorithm to determine when a k-dissimilarity arises from a tree. We also give a 6-point condition for determining when a 3-dissimilarity arises from a tree, that is similar to the aforementioned 4-point condition.Comment: 18 pages, 4 figure

Nucleotide Frequencies in Human Genome and Fibonacci Numbers

This work presents a mathematical model that establishes an interesting connection between nucleotide frequencies in human single-stranded DNA and the famous Fibonacci's numbers. The model relies on two assumptions. First, Chargaff's second parity rule should be valid, and, second, the nucleotide frequencies should approach limit values when the number of bases is sufficiently large. Under these two hypotheses, it is possible to predict the human nucleotide frequencies with accuracy. It is noteworthy, that the predicted values are solutions of an optimization problem, which is commonplace in many nature's phenomena.Comment: 12 pages, 2 figure