Letter: Bounds on the Deficit Solid Angle Parameter from Solar System Tests

We analyze the Mercury perihelion precession, the bending of starlight, and the radar echo delay in the Schwarzschild field modified by the presence of a solid angle deficit. By using the experimental data we obtain that the parameter characterizing the solid angle deficit is less than 10^–9, 10^–8 and 10^–9, respectively, on the length scales associated with such phenomena. In particular, if the solid angle deficit is generated by a global monopole, it is shown that within the length scales associated with such phenomena, the observational data available constrain the monopole energy scale to lower bounds which are in considerable agreement with the limits derived from grand unified theory and cosmology.     

Test-based thermal explosion model for HMX

We present a thermal explosion (cookoff) model for an HMX-based plastic bonded explosive (LX-10). The thermal–chemical–mechanical response of LX-10 is modeled based on the measurements from the scaled thermal explosion experiment (STEX) at the Lawrence Livermore National Laboratory. Confined LX-10 is heated at a rate of 1 °C/h until an explosion is observed. The modeled cookoff problem is simulated by the Arbitrarily Lagrangian–Eulerian hydrocode (ALE3D) that can handle a wide spectrum of time scales that vary from a structural to a high speed shock physics time scale. In addition to a comprehensive model for energetic material, the confinement material namely an AerMet 100 steel is modeled as a Steinberg–Guinan material with a Johnson–Cook failure model with a statistical failure distribution. By using the size distribution data from the fragmentation experiment, the metal fracture and fragmentation due to an explosion are modeled. The explosion temperature is predicted to within 1°. Calculated wall strain provides violence associated with the thermal explosion process and agrees favorably with the measured STEX data.     

LETTER: Cosmological Constant, Conical Defect and Classical Tests of General Relativity

We investigate the perihelion shift of the planetary motion and the bending of starlight in the Schwarzschild field modified by the presence of a -term plus a conical defect. This analysis generalizes an earlier result obtained by Islam (Phys. Lett. A 97, 239, 1983) to the case of a pure cosmological constant. By using the experimental data we obtain that the parameter characterizing the conical defect is less than 10^–9 and 10^–7, respectively, on the length scales associated with such phenomena. In particular, if the defect is generated by a cosmic string, these values correspond to limits on the linear mass densities of 10¹⁹ g/cm and 10²¹ g/cm, respectively.     

Determination of Traces of Toxic Elements in Dimethylaminoborane upon Their Concentration for Atomic Emission Analysis

A technique of atomic emission determination of traces of toxic elements in dimethylaminoborane with detection limits of n·10^–5–10^–8 wt. % has been developed. To reduce the detection limits, a technique of separation of the basic component in the form of boron fluoride, with concentration of microimpurities on a graphite collector, was used.     

Open and traction boundary conditions for the incompressible Navier–Stokes equations

We present numerical schemes for the incompressible Navier–Stokes equations (NSE) with open and traction boundary conditions. We use pressure Poisson equation (PPE) formulation and propose new boundary conditions for the pressure on the open or traction boundaries. After replacing the divergence free constraint by this pressure Poisson equation, we obtain an unconstrained NSE. For Stokes equation with open boundary condition on a simple domain, we prove unconditional stability of a first order semi-implicit scheme where the pressure is treated explicitly and hence is decoupled from the computation of velocity. Using either boundary condition, the schemes for the full NSE that treat both convection and pressure terms explicitly work well with various spatial discretizations including spectral collocation and C⁰ finite elements. Moreover, when Reynolds number is of O(1) and when the first order semi-implicit time stepping is used, time step size of O(1) is allowed in benchmark computations for the full NSE. Besides standard stability and accuracy check, various numerical results including flow over a backward facing step, flow past a cylinder and flow in a bifurcated tube are reported. Numerically we have observed that using PPE formulation enables us to use the velocity/pressure pairs that do not satisfy the standard inf–sup compatibility condition. Our results extend that of Johnston and Liu [H. Johnston, J.-G. Liu, Accurate, stable and efficient Navier–Stokes solvers based on explicit treatment of the pressure term. J. Comp. Phys. 199 (1) (2004) 221–259] which deals with no-slip boundary conditions only.     

Detonability limits in thin annular channels

In this paper, detonability limits in two-dimensional annular channels are investigated. Since the channel heights are small in comparison to the tube diameter, curvature effects can be neglected and the annular channels can be considered to be essentially two-dimensional. Mixtures that are highly diluted with argon are used since previous investigations seem to indicate that detonations in such mixtures are “stable” in that cellular instabilities play minor roles on the propagation of the detonation. For stable detonations where the ZND structure is valid, boundary layer effects can be modeled as a flow divergence term in the conservation of mass equation following the pioneering work of Fay [J.A. Fay, Phys. Fluids 2(3) (1959) 283–289]. Expansion due to flow divergence in the reaction zone results in a velocity deficit. There exists a maximum deficit when an eigenvalue detonation velocity can no longer be found, which can be taken as the onset of the detonability limits. Experimentally, it was found that unlike “unstable” detonations, the detonability limits for “stable” detonations are well-defined. No unstable near-limit phenomena (e.g., galloping detonations) was observed. Good agreement is found between the theoretical predictions and the experimentally obtained velocity deficits and limits in the two channel heights of 2.2 and 6.9 mm for hydrogen–oxygen and acetylene–oxygen mixtures diluted with over 50% argon. It may be concluded that at least for these special mixtures where the detonation is “stable,” the failure mechanism is due to flow divergence caused by the negative displacement thickness of the boundary layer behind the leading shock front of the detonation wave.     

Intense, broadband, pulsed I-R source at the national synchrotron light source

We describe a broadband (1 m–1 mm) synchrotron radiation infrared source, pulsed each 20–180 nseconds and delivering about 10¹⁵ photons/sec/1% bandpass into f10 optics. The source size is diffraction limited. This source is thus 100–1000 times brighter than a 2000°K black body, very stable and capable of being used for calibration.Work supported by the U.S. Department of Energy.     

Scattering of waves of the SW range in oblique propagation in the ionosphere

Conclusions In summing up the analysis carried out here, we note that for one-discontinuity paths on the order of 1000 km long at field frequencies on the order of 10 MHz the approximation of plane waves of (11) is suitable for describing scattering inhomogeneities with a total size not exceeding several kilometers. For disturbances of larger size it is necessary to allow for the finite curvature of the fronts of the emitted and secondary fields. If the characteristic scale of variation of the properties of the disturbance comprises a value on the order of 10 km or more, then Eqs. (15) and (16) of geometrical optics are applicable. For disturbances with characteristic scales lying in the range of 1–10 km one must allow for diffraction effects with the help of (14).Equations (11) and (14)–(16) can be used to analyze scattering on inhomogeneities of a statistical nature in the inhomogeneous ionosphere.Leningrad State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 23, No. 2, pp. 151–158, February, 1980.     

Experimental test of the variability ofG using Viking lander ranging data

Results are presented from the analysis of solar system astrometric data, notably the range data to the Viking landers on Mars. A least-squares fit of the parameters of the solar system model to these data limits a simple time variation in the effective Newtonian gravitational constant to (0.2 ± 0.4) × 10^–11 year^–1 and a rate of drift of atomic clocks relative to the implicit clock of relativistic dynamics to (0.1 ± 0.8) × 10^–11 year^–1. The error limits quoted are the result of uncertainties in the masses of the asteroids.This paper is reprinted with minor editorial modifications fromPhysical Review Letters,51, 1609 (1983).     

Data-Driven Model Reduction for Stochastic Burgers Equations

We present a class of efficient parametric closure models for 1D stochastic Burgers equations. Casting it as statistical learning of the flow map, we derive the parametric form by representing the unresolved high wavenumber Fourier modes as functionals of the resolved variable’s trajectory. The reduced models are nonlinear autoregression (NAR) time series models, with coefficients estimated from data by least squares. The NAR models can accurately reproduce the energy spectrum, the invariant densities, and the autocorrelations. Taking advantage of the simplicity of the NAR models, we investigate maximal space-time reduction. Reduction in space dimension is unlimited, and NAR models with two Fourier modes can perform well. The NAR model’s stability limits time reduction, with a maximal time step smaller than that of the K-mode Galerkin system. We report a potential criterion for optimal space-time reduction: the NAR models achieve minimal relative error in the energy spectrum at the time step, where the K-mode Galerkin system’s mean Courant–Friedrichs–Lewy (CFL) number agrees with that of the full model.     

Modeling of a dislocation source in the field of activated and unactivated discrete barriers

In this work, computer-modeling methods have been used to consider the formation of a dislocation loop. The barrier strengths correspond to the reacting (unactivated) and unreacting (activated) forest dislocations. It is determined that the minimum operating stress of the source coincides with the classical, critical Frank-Read stress only for a rather narrow range of length of the sources. In a majority of the cases, it is comparable to the critical stress for flow past a network of barriers. Beyond the front of the dislocations propagating from the source, dislocation loops formed by the Orowan mechanism remain, the total length of which is equal to 12–14% of the length of the loop formed.Tomsk Structural Engineering Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 20–24, October, 1992.     

New Models for the Solution of Intermediate Regimes in Transport Theory and Radiative Transfer: Existence Theory, Positivity, Asymptotic Analysis, and Approximations

In this paper we propose, derive, and establish the mathematical foundations of new models for the solution of intermediate regimes in transport theory and radiative transfer. These new models consist of coupling the transport equations with their diffusion approximations. Our mathematical theory includes the existence theory, the positivity of the solutions, and the asymptotic analysis. We also give the rate of the asymptotic decay. In order to solve the new coupled problem we propose to use the transmission time marching algorithm introduced and studied in refs. 10, 13–15. We then study the convergence of the resulting algorithm. These studies are based in an essential way on the methods we introduced in refs. 14, 15.     

Coupled Criticality Analysis of Inflation and Unemployment

In this paper, we focus on the critical periods in the economy that are characterized by unusual and large fluctuations in macroeconomic indicators, like those measuring inflation and unemployment. We analyze U.S. data for 70 years from 1948 until 2018. To capture their fluctuation essence, we concentrate on the non-Gaussianity of their distributions. We investigate how the non-Gaussianity of these variables affects the coupling structure of them. We distinguish “regular” from “rare” events, in calculating the correlation coefficient, emphasizing that both cases might lead to a different response of the economy. Through the “multifractal random wall” model, one can see that the non-Gaussianity depends on time scales. The non-Gaussianity of unemployment is noticeable only for periods shorter than one year; for longer periods, the fluctuation distribution tends to a Gaussian behavior. In contrast, the non-Gaussianities of inflation fluctuations persist for all time scales. We observe through the “bivariate multifractal random walk” that despite the inflation features, the non-Gaussianity of the coupled structure is finite for scales less than one year, drops for periods larger than one year, and becomes small for scales greater than two years. This means that the footprint of the monetary policies intentionally influencing the inflation and unemployment couple is observed only for time horizons smaller than two years. Finally, to improve some understanding of the effect of rare events, we calculate high moments of the variables’ increments for various q orders and various time scales. The results show that coupling with high moments sharply increases during crises.     

Central peak in the pseudogap of high T<Subscript> c</Subscript> superconductors

We study the effect of antiferromagnetic (AF) correlations in the three-band Emery model, with respect to the experimental situation in weakly underdoped and optimally doped BSCCO. In the vicinity of the vH singularity of the conduction band there appears a central peak in the middle of a pseudogap, which is in an antiadiabatic regime, insensitive to the time scale of the mechanism responsible for the pseudogap. We find a quantum low-temperature regime corresponding to experiment, in which the pseudogap is created by zero-point motion of the magnons, as opposed to the usual semiclassical derivation, where it is due to a divergence of the magnon occupation number. Detailed analysis of the spectral functions along the (π,0)–(π,π) line show significant agreement with experiment, both qualitative and, in the principal scales, quantitative. The observed slight approaching-then-receding of both the wide and narrow peaks with respect to the Fermi energy is also reproduced. We conclude that optimally doped BSCCO has a well-developed pseudogap of the order of 1000 K. This is only masked by the narrow antiadiabatic peak, which provides a small energy scale, unrelated to the AF scale, and primarily controlled by the position of the chemical potential.     

Two-level discretizations of nonlinear closure models for proper orthogonal decomposition

Proper orthogonal decomposition has been successfully used in the reduced-order modeling of complex systems. Its original promise of computationally efficient, yet accurate approximation of coherent structures in high Reynolds number turbulent flows, however, still remains to be fulfilled. To balance the low computational cost required by reduced-order modeling and the complexity of the targeted flows, appropriate closure modeling strategies need to be employed. Since modern closure models for turbulent flows are generally nonlinear, their efficient numerical discretization within a proper orthogonal decomposition framework is challenging. This paper proposes a two-level method for an efficient and accurate numerical discretization of general nonlinear closure models for proper orthogonal decomposition reduced-order models. The two-level method computes the nonlinear terms of the reduced-order model on a coarse mesh. Compared with a brute force computational approach in which the nonlinear terms are evaluated on the fine mesh at each time step, the two-level method attains the same level of accuracy while dramatically reducing the computational cost. We numerically illustrate these improvements in the two-level method by using it in three settings: the one-dimensional Burgers equation with a small diffusion parameter ν = 10^?3, the two-dimensional flow past a cylinder at Reynolds number Re = 200, and the three-dimensional flow past a cylinder at Reynolds number Re = 1000.     

基于浸入式边界的流固耦合的非定常数值模拟研究

本文针对工程中关心的流固耦合以及复杂边界物体绕流问题,采用算子分裂的方法求解二维不可压N-S方程,采用完全正交的矩形网格,用浸入式边界模拟静止和运动物体的边界.使用这种方法,本文分别对低雷诺数下的光滑平板绕流,圆柱绕流,低KC数下的振荡圆柱进行了数值模拟.计算结果与以往的数值和试验结果吻合得很好,证明了浸入式边界方法和所发展的程序的可靠性.     

Frequency stabilization and measurements of 543 nm HeNe lasers

In this paper we report our investigations on the frequency stabilization and frequency measurements of 543 nm HeNe laser. It contains following four different works. (1) Using a metal laser tube we have built an iodine-stabilized 543 nm HeNe laser by the Frequency-Modulation (FM) spectroscopy. The signal-to-noise ratio of the hyperfine spectrum reached 2 × 10^–12 at 1 s sampling time. (2) We have built a compact iodine-stabilized 543 nm HeNe laser system using the third-harmonic locking technique. Stability better than 1 × 10^–12 for sampling time >1 s is obtained. We also suggest the b₁₀ line for the future recommendation. (3) We constructed the Lamb-dip stabilized He-²⁰Ne and He-²²Ne lasers and measured their frequency stability, reproducibility, and absolute frequencies. The results suggest that the Lamb-dip stabilized lasers are appropriate for secondary wavelength standards. We have also deduced the isotope shift of Ne atom at 543 nm. (4) We have developed two two-mode stabilized 543 nm HeNe lasers using the bang-bang control method. The Allan variance is 1 × 10^–11 at 1 s sampling time.     

Megawatt Gyrotrons for ECR Heating and Current-Drive Systems in Controlled-Fusion Facilities

We discuss the results and main trends in developing megawatt gyrotrons used as microwave sources for electron-cyclotron wave systems in controlled-fusion facilities. Such systems require gyrotrons with power no less than 1 MW operable during a time of about 1000 s in the frequency range 110–170 GHz. We also highlight the main design principles of such gyrotrons and the most striking aspects and prospects of their development in the last years.     

The effect of cerium oxide argon-annealed coatings on the high temperature oxidation of a FeCrAl alloy

Ceria coatings were applied in order to improve the adherence of alumina scales developed on a model Fe–20Cr–5Al alloy during oxidation at high temperature. These coatings were performed by argon annealing of a ceria sol–gel coating at temperatures ranging between 600 and 1000 °C. The influence of these coatings on the alloy oxidation behaviour was studied at 1100 °C. In situ X-ray diffraction (XRD) was performed to characterize the coating crystallographic nature after annealing and during the oxidation process. The alumina scale morphologies were studied by means of scanning electron microscopy (SEM) coupled with energy dispersive X-ray spectroscopy (EDS). The present work shows that the alumina scale morphology observed on cerium sol–gel coated alloy was very convoluted. On the cerium sol–gel coated alloy, argon annealing results in an increase of the oxidation rate in air, at 1100 °C. The 600 °C argon annealing temperature results in a good alumina scale adherence under thermal cycling conditions at 1100 °C.