Advanced Supersonic Technology Study: Engine Program Summary. Supersonic Propulsion: 1971 to 1976

Sustained supersonic cruise propulsion systems for military applications are studied. The J79-5 in the Mach 2 B-58; YJ93 in the Mach 3.0 B-70 and the current F101 in the B-1, are all examples of military propulsion systems and airplanes operated at sustained supersonic cruise speeds. The Mach 2.7 B2707 transport powered by GE4 turbojet engines was the only non-military, sustained supersonic cruise vehicle intended for commercial passenger service

Design, Fabrication and Test of Composite Curved Frames for Helicopter Fuselage Structure

Aspects of curved beam effects and their importance in designing composite frame structures are discussed. The curved beam effect induces radial flange loadings which in turn causes flange curling. This curling increases the axial flange stresses and induces transverse bending. These effects are more important in composite structures due to their general inability to redistribute stresses by general yielding, such as in metal structures. A detailed finite element analysis was conducted and used in the design of composite curved frame specimens. Five specimens were statically tested and compared with predicted and test strains. The curved frame effects must be accurately accounted for to avoid premature fracture; finite element methods can accurately predict most of the stresses and no elastic relief from curved beam effects occurred in the composite frames tested. Finite element studies are presented for comparative curved beam effects on composite and metal frames

Magnetic flux pumping in 3D nonlinear magnetohydrodynamic simulations

A self-regulating magnetic flux pumping mechanism in tokamaks that maintains the core safety factor at $q\approx 1$, thus preventing sawteeth, is analyzed in nonlinear 3D magnetohydrodynamic simulations using the M3D-C$^1$ code. In these simulations, the most important mechanism responsible for the flux pumping is that a saturated $(m=1,n=1)$ quasi-interchange instability generates an effective negative loop voltage in the plasma center via a dynamo effect. It is shown that sawtoothing is prevented in the simulations if $\beta$ is sufficiently high to provide the necessary drive for the $(m=1,n=1)$ instability that generates the dynamo loop voltage. The necessary amount of dynamo loop voltage is determined by the tendency of the current density profile to centrally peak which, in our simulations, is controlled by the peakedness of the applied heat source profile.Comment: submitted to Physics of Plasmas (23 pages, 15 Figures

On the asymptotic normality of persistent Betti numbers

Persistent Betti numbers are a major tool in persistent homology, a subfield of topological data analysis. Many tools in persistent homology rely on the properties of persistent Betti numbers considered as a two-dimensional stochastic process $(r,s) \mapsto n^{-1/2} (\beta^{r,s}_q ( \mathcal{K}(n^{1/d} S_n))-\mathbb{E}[\beta^{r,s}_q ( \mathcal{K}( n^{1/d} S_n))])$. So far, pointwise limit theorems have been established in different set-ups. In particular, the pointwise asymptotic normality of (persistent) Betti numbers has been established for stationary Poisson processes and binomial processes with constant intensity function in the so-called critical (or thermodynamic) regime, see Yogeshwaran et al. [2017] and Hiraoka et al. [2018]. In this contribution, we derive a strong stabilizing property (in the spirit of Penrose and Yukich [2001] of persistent Betti numbers and generalize the existing results on the asymptotic normality to the multivariate case and to a broader class of underlying Poisson and binomial processes. Most importantly, we show that the multivariate asymptotic normality holds for all pairs $(r,s)$, $0\le r\le s<\infty$, and that it is not affected by percolation effects in the underlying random geometric graph

The autoregression bootstrap for kernel estimates of smooth nonlinear functional time series

Functional times series have become an integral part of both functional data and time series analysis. This paper deals with the functional autoregressive model of order 1 and the autoregression bootstrap for smooth functions. The regression operator is estimated in the framework developed by Ferraty and Vieu [2004] and Ferraty et al. [2007] which is here extended to the double functional case under an assumption of stationary ergodic data which dates back to Laib and Louani [2010]. The main result of this article is the characterization of the asymptotic consistency of the bootstrapped regression operator

A new explanation of the sawtooth phenomena in tokamaks

The ubiquitous sawtooth phenomena in tokamaks are so named because the central temperature rises slowly and falls rapidly, similar to the blades of a saw. First discovered in 1974, it has so far eluded a theoretical explanation that is widely accepted and consistent with experimental observations. We propose here a new theory for the sawtooth phenomena in auxiliary heated tokamaks, which is motivated by our recent understanding of "magnetic flux pumping." In this theory, the role of the (m, n) = (1, 1) mode is to generate a dynamo voltage, which keeps the central safety factor, q(0), just above 1.0 with low central magnetic shear. When central heating is present, the temperature on axis will increase until at some point, and the configuration abruptly becomes unstable to ideal MHD interchange modes with equal poloidal and toroidal mode numbers, m = n &gt; 1. It is these higher order modes and the localized magnetic stochasticity they produce that cause the sudden crash of the temperature profile, not magnetic reconnection. Long time 3D MHD simulations demonstrate these phenomena, which appear to be consistent with many experimental observations.</p