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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 775 records · Page 43
All sourcesNASA NTRSDOE OSTI
NASA NTRS2014

Flight Tests of a Supersonic Natural Laminar Flow Airfoil

IR thermography was used to characterize the transition front on a S-NLF test article at chord Reynolds numbers in excess of 30 million Changes in transition due to Mach number, Reynolds number, and surface roughness were investigated - Regions of laminar flow in excess of 80% chord at chord Reynolds numbers greater than 14 million IR thermography clearly showed the transition front and other flow features such as shock waves impinging upon the surface A series of parallel oblique shocks, of yet unknown origin, were found to cause premature transition at higher Reynolds numbers. NASA has a current goal to eliminate barriers to the development of practical supersonic transport aircraft Drag reduction through the use of supersonic natural laminar flow (S-NLF) is currently being explored as a means of increasing aerodynamic efficiency - Tradeoffs work best for business jet class at M<2 Conventional high-speed designs minimize inviscid drag at the expense of viscous drag - Existence of strong spanwise pressure gradient leads to crossflow (CF) while adverse chordwise pressure gradients amplifies and Tollmien-Schlichting (TS) instabilities Aerion Corporation has patented a S-NLF wing design (US Patent No. 5322242) - Low sweep to control CF - dp/dx < 0 on both wing surfaces to stabilize TS - Thin wing with sharp leading edge to minimize wave drag increase due to reduction in sweep NASA and Aerion have partnered to study S-NLF since 1999 Series of S-NLF experiments flown on the NASA F-15B research test bed airplane Infrared (IR) thermography used to characterize transition - Non-intrusive, global, good spatial resolution - Captures significant flow features well

laminar flow↗
DOE OSTI2022

Effect of laser preheat in magnetized liner inertial fusion at OMEGA

Integrated magnetized liner inertial fusion (MagLIF) experiments on the OMEGA laser system are modeled to investigate the effects of laser preheat on implosion performance. In both simulations and experiments, preheating the fuel with a laser enhances the neutron yield, with the maximum yield occurring at an optimal preheat laser energy. Increasing the preheat energy past the optimal value reduces the neutron yield. In simulations, the rate of the drop in neutron yield depends on the inclusion of the Nernst effect. The Nernst effect advects the magnetic field away from the center of the fuel region during the preheat stage of MagLIF on OMEGA and weakens magnetic-flux compression. If the Nernst effect is not included, the simulated drop in yield past the optimal preheat laser energy is more gradual as opposed to the sharper drop seen in experiments. Simulations are able to model trend in measured ion temperatures seen in experiments. Here, a mix model is used to show that including mix from the wall in the simulated fuel region further degrades the yield and lowers the optimal preheat laser energy. Simulations with mix predict that increasing the initial axial magnetic field may still enhance yield performance in integrated implosions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1995

Some Numerical Experiments on Detonation Wave Propagation

In this paper we present the results of a series of numerical experiments done on the propagation and initiation of a detonation wave. The calculations are performed in one-dimension, with considerable grid resolution. Of particular interest are the following questions: (1) the nature of periodic and chaotic instabilities generated by the wave; (2) the influence of the grid resolution on these instabilities; (3) the influence of the 'quality' of the numerical scheme; and (4) the influence of 'noise'. In the calculations, we use a second-order Total Variation Diminishing (TVD) scheme as the basic numerical method, with grid spacings as low as a fraction of a micron. Detonations waves are generated at the closed end of a tube, and allowed to propagate for approximately 20 cm. The required energy for successful initiation of the detonation will be measured for different cases of grid resolution and numerical schemes. A modified version of the TVD scheme has also been devised, which allows for much lower numerical diffusion of the radical species in the exponentially growing region behind the shock. The effect of this modification will be demonstrated. Oscillations in peak pressure and induction length are seen to develop in some cases: the oscillations can go through a sequence of modes, from a regular, high frequency mode to a low frequency mode with period doubling. A chaotic regime can also be obtained. General conclusions on the quality of algorithms will be presented. We will also discuss the performance of a version of the code developed on the IBM SP2 parallel computer.

Cambier, Jean-Luc↗
DOE OSTI2021

Impact of Numerical Hydrodynamics in Turbulent Mixing Transition Simulations

Underresolved simulations are unavoidable in high Reynolds (Re) and Mach (Ma) number turbulent flow applications at scale. Implicit large-Eddy simulation (ILES) often becomes the effective strategy to capture the dominating effects of convectively driven flow instabilities. We evaluate the impact of three distinct numerical strategies in simulations of transition and turbulence decay with ILES: the Harten–Lax–van Leer (HLL) Riemann solver applying Strang splitting and a Lagrange-plus-Remap formalism to solve the directional sweep—denoted split; the Harten–Lax–Van Leer-Contact (HLLC) Riemann solver using a directionally unsplit strategy and parabolic reconstruction—denoted unsplit; and the HLLC Riemann solver using unsplit and a low-Ma correction (LMC)—denoted unsplit*. Three case studies are considered: (1) a shock tube problem prototyping shock-driven turbulent mixing, (2) the Taylor–Green Vortex (TGV) prototyping transition to turbulence, and, (3) an homogeneous isotropic turbulence (HIT) case, focusing on the impact of discretization on transition and decay from fixed well-characterized initial conditions. Significantly more accurate predictions are provided by the unsplit schemes, in particular, when augmented with the LMC. For given resolution, only the unsplit schemes predict the turbulent mixing transition after reshock observed in the shock tube experiments. Relevant comparisons of ILES based on Euler and Navier–Stokes equations addressing potential occurrence of low-Re regimes in the applications are presented. Unsplit schemes are instrumental in allowing to capture the spatial development of the TGV flow and its validation at prescribed Re with significantly less resolution. HIT analysis confirms higher simulated turbulence Re and increased small-scale content associated with the unsplit discretizations.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Diffuse scattering from dynamically compressed single-crystal zirconium following the pressure-induced α → ω phase transition

The prototypical α → ω phase transition in zirconium is an ideal test bed for our understanding of polymorphism under extreme loading conditions. After half a century of study, a consensus had emerged that the transition is realized via one of two distinct displacive mechanisms, depending on the nature of the compression path. However, recent dynamic-compression experiments equipped with diffraction diagnostics performed in the past few years have revealed new transition mechanisms, demonstrating that our understanding of the underlying atomistic dynamics and transition kinetics is in fact far from complete. We present classical molecular dynamics simulations of the α → ω phase transition in single-crystal zirconium shock compressed along the [0001] axis using a machine-learning-class potential. The transition is predicted to proceed primarily via a modified version of the two-stage Usikov-Zilberstein mechanism, whereby the high-pressure ω phase heterogeneously nucleates at boundaries between grains of an intermediate β phase. We further observe the fomentation of atomistic disorder at the junctions between β grains, leading to the formation of highly defective interstitial material between the ω grains. We directly compare synthetic x-ray diffraction patterns generated from our simulations with those obtained using femtosecond diffraction in recent dynamic-compression experiments, and show that the simulations produce the same unique, anisotropic diffuse scattering signal unlike any previously seen from an elemental metal. Our simulations suggest that the diffuse signal arises from a combination of thermal diffuse scattering, nanoparticlelike scattering from residual kinetically stabilized α and β grains, and scattering from interstitial defective structures. Published by the American Physical Society 2024

36 MATERIALS SCIENCE↗
DOE OSTI2020

Benchmarking boron carbide equation of state using computation and experiment

Boron carbide ( B 4 C ) is of both fundamental scientific and practical interest due to its structural complexity and how it changes upon compression, as well as its many industrial uses and potential for use in inertial confinement fusion (ICF) and high-energy density physics experiments. Here, we report the results of a comprehensive computational study of the equation of state (EOS) of B 4 C in the liquid, warm dense matter, and plasma phases. Our calculations are cross-validated by comparisons with Hugoniot measurements up to 61 megabar from planar shock experiments performed at the National Ignition Facility (NIF). Our computational methods include path integral Monte Carlo, activity expansion, as well as all-electron Green's function Korringa-Kohn-Rostoker and molecular dynamics that are both based on density functional theory. We calculate the pressure-internal energy EOS of B 4 C over a broad range of temperatures ( ~ 6 × 10 3 – 5 × 10 8 K) and densities (0.025–50 g / cm 3 ). We assess that the largest discrepancies between theoretical predictions are ≲ 5 % near the compression maximum at 1– 2 × 10 6 K. This is the warm-dense state in which the K shell significantly ionizes and has posed grand challenges to theory and experiment. By comparing with different EOS models, we find a Purgatorio model (LEOS 2122) that agrees with our calculations. The maximum discrepancies in pressure between our first-principles predictions and LEOS 2122 are ~ 18 % and occur at temperatures between 6 × 10 3 – 2 × 10 5 K, which we believe originate from differences in the ion thermal term and the cold curve that are modeled in LEOS 2122 in comparison with our first-principles calculations. To account for potential differences in the ion thermal term, we have developed three new equation-of-state models that are consistent with theoretical calculations and experiment. We apply these new models to 1D hydrodynamic simulations of a polar direct-drive NIF implosion, demonstrating that these new models are now available for future ICF design studies.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS2019

Full Facility Shock Frame Simulations of the Electric Arc Shock Tube

Radiative heating computations are performed for high speed lunar return experiments conducted in the Electric Arc Shock Tube (EAST) facility at NASA Ames Research Center. The nonequilibrium radiative transport equations are solved via NASA's in-house radiation code NEQAIR using flow field input from US3D flow solver. The post-shock flow properties for the 10 km/s Earth entry conditions are computed using the stagnation line of a blunt-body and a full facility CFD (Computational Fluid Dynamics) simulation of the EAST shock tube. The shocked gas in the blunt-body flow achieves a thermochemical equilibrium away from the shock front whereas EAST flow exhibits a nonequilibrium behavior due to strong viscous dissipation of the shock by boundary layer. The full-tube flow calculations capture the influence of the boundary layer on the shocked gas state and provide a realistic fluid dynamic input for the radiative predictions. The integrated radiance behind the shock is calculated in NEQAIR for wavelength regimes from Vacuum-UltraViolet (VUV) to InfraRed (IR), which are pertinent to the emission characteristics of high enthalpy shock waves in air. These radiance profiles are validated against corresponding EAST shots. The full-tube simulations successfully predict a sharp radiance peak at the shock front which gets smeared in the test data due to the spatial resolution in the measurements. The full facility based radiance behind the shock shows a slightly better match with the test data in the VUV and Red spectral regions, as compared to that from a blunt-body based predictions. The UV radiance is very similar for both geometries and under-predicts the test behavior. The IR test data matches better with the blunt-body based predictions where the full-tube simulations show a significant over-prediction.

Radiation↗
DOE OSTI2025

Calibration and characterization of the line-VISAR diagnostic at the HED-HIBEF instrument at the European XFEL

In dynamic-compression experiments, the line-imaging Velocity Interferometer System for Any Reflector (VISAR) is a well-established diagnostic used to probe the velocity history, including wave profiles derived from dynamically compressed interfaces and wavefronts, depending on material optical properties. Knowledge of the velocity history allows for the determination of the pressure achieved during compression. Such a VISAR analysis is often based on Fourier transform techniques and assumes that the recorded interferograms are free from image distortions. In this paper, we describe the VISAR diagnostic installed at the HED-HIBEF instrument located at the European XFEL along with its calibration and characterization. It comprises a two-color (532, 1064 nm), three-arm (with three velocity sensitivities) line imaging system. We provide a procedure to correct VISAR images for geometric distortions and evaluate the performance of the system using Fourier analysis. We finally discuss the spatial and temporal calibrations of the diagnostic. As an example, we compare the pressure extracted from the VISAR analysis of shock-compressed polyimide and silicon.

47 OTHER INSTRUMENTATION↗
NASA NTRS1994

Head-on parallel blade-vortex interaction

An experimental and computational study was carried out to investigate the parallel head-on blade-vortex interaction (BVI) and its noise generation mechanism. A shock tube, with an enlarged test section, was used to generate a compressible starting vortex which interacted with a target airfoil. The dual-pulsed holographic interferometry (DPHI) technique and airfoil surface pressure measurements were employed to obtain quantitative flow data during the BVI. A thin-layer Navier-Stokes code (BV12D), with a high-order upwind-biased scheme and a multizonal grid, was also used to simulate numerically the phenomena occurring in the head-on BVI. The detailed structure of a convecting vortex was studied through independent measurements of density and pressure distributions across the vortex center. Results indicate that, in a strong head-on BVI, the opposite pressure peaks are generated on both sides of the leading edge as the vortex approaches. Then, as soon as the vortex passes by the leading edge, the high-pressure peak suddenly moves toward the low-peak-reducing in magnitude as it moves--simultaneously giving rise to the initial sound wave. In both experiment and computation, it is shown that the viscous effect plays a significant role in head-on BVIs.

Lee, Soogab↗
DOE OSTI2021

Experimental characterization of hot-electron emission and shock dynamics in the context of the shock ignition approach to inertial confinement fusion

We report on planar target experiments conducted on the OMEGA-EP laser facility performed in the context of the shock ignition (SI) approach to inertial confinement fusion. The experiment aimed at characterizing the propagation of strong shock in matter and the generation of hot electrons (HEs), with laser parameters relevant to SI (1-ns UV laser beams with I ~10 16 W/cm 2 ). Time-resolved radiographs of the propagating shock front were performed in order to study the hydrodynamic evolution. The hot-electron source was characterized in terms of Maxwellian temperature, T h , and laser to hot-electron energy conversion efficiency η using data from different x-ray spectrometers. The post-processing of these data gives a range of the possible values for T h and η [i.e., T h [keV] ϵ (20, 50) and η ϵ (2%, 13%)]. These values are used as input in hydrodynamic simulations to reproduce the results obtained in radiographs, thus constraining the range for the HE measurements. According to this procedure, we found that the laser converts ~10% ± 4% of energy into hot electrons with T h = 27 ± 8 keV. The paper shows how the coupling of different diagnostics and numerical tools is required to sufficiently constrain the problem, solving the large ambiguity coming from the post-processing of spectrometers data. The effect of the hot electrons on the shock dynamics is then discussed, showing an increase in the pressure around the shock front. Furthermore, the low temperature found in this experiment without pre-compression laser pulses could be advantageous for the SI scheme, but the high conversion efficiency may lead to an increase in the shell adiabat, with detrimental effects on the implosion.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Argon equation of state data to 1 TPa: Shock compression experiments and simulations

Argon is the most abundant noble gas on Earth and its noble, atomic fluid nature makes it an excellent candidate for comparison of experiment and theory at extreme conditions. For this study, we performed a combined computational and experimental study on shock compressed cryogenic liquid argon. Using Sandia's Z machine, we shock compressed liquid argon to 600 GPa and reshock states up to 950 GPa. Laser shock experiments at the Omega Laser facility extend the principal Hugoniot to 1000 GPa and provided temperature data along the principal Hugoniot. The plate impact experiments and laser shock experiments used well-characterized impedance matching standards and demonstrate consistent results between the two platforms over a common range. Density functional theory based molecular dynamics simulations provided additional data on the Hugoniot to 600 GPa. The combined experimental data and simulation results provide constraints on the development of new equation of state models at extreme conditions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1985

Plasma waves associated with the AMPTE artificial comet

Numerous plasma wave effects were detected by the AMPTE/IRM spacecraft during the artificial comet experiment on December 27, 1984. As the barium ion cloud produced by the explosion expanded over the spacecraft, emissions at the electron plasma frequency and ion plasma frequency provided a determination of the local electron density. The electron density in the diamagnetic cavity produced by the ion cloud reached a peak of more than 5 x 10 to the 5th per cu cm, then decayed smoothly as the cloud expanded, varying approximately as t exp-2. As the cloud began to move due to interactions with the solar wind, a region of compressed plasma was encountered on the upstream side of the diamagnetic cavity. The peak electron density in the compression region was about 1.5 x 10 to the 4th per cu cm. Later, a very intense (140 mVolt/m) broadband burst of electrostatic noise was encountered on the sunward side of the compression region. This noise has characteristics very similar to noise observed in the earth's bow shock, and is believed to be a shocklike interaction produced by an ion beam-plasma instability between the nearly stationary barium ions and the streaming solar wind protons.

Gurnett, D. A.↗
NASA NTRS1993

Extrapolation of space weathering processes to other small solar system bodies

A diverse range of processes were invoked as the dominant factor or as important contributory factors in the modification of the optical surface and regolith of the moon. These include impact vitrification by large and small projectiles, solar wind implantation and the reduction of oxidized iron during energetic events, sputtering and crystal lattice damage by energetic cosmic rays, shock metamorphism of minerals, mixing of diverse lithologies by impacts, and contamination by external materials. These processes are also potentially important on the rocky surfaces of other small solar system bodies. For icy bodies, several additional processes are also possible, including formation of complex organic compounds from methane and ammonia-bearing ices by ultraviolet irradiation and the condensation of vapor species to form frost layers in the polar or cooler regions of objects at appropriate heliocentric distances. The lunar case, even when completely understood, will not extend in a simple linear fashion to other small rocky objects, nor will the optical surfaces of those objects all be affected to the same degree by each process. The major factors that will control the relative efficacy of a possible mechanism include the efficiency of ejecta retention and the degree to which the regolith materials experience multiple events (primarily a function of body size, escape velocity, and impactor velocities); the mean duration of typical regolith particle exposure at the optical surface and within reach of the micrometeorite, cosmic ray, solar wind, or UV fluxes (a function of the rate and scale of regolith mixing, production, and removal processes); the incident flux of solar (low energy) cosmic rays, solar wind, or UV radiation (inverse square of heliocentric distance) or of galactic (high energy) cosmic rays (slowly increasing flux with heliocentric distance); and the compositional and mineralogical nature of the surface being affected. In general, those processes that depend upon either the retention of impact ejecta or on the presence of multigenerational regoliths should be substantially less effective on smaller bodies with lower escape velocities. However, there are important exceptions to this generalization. For example, a process that involves the hypervelocity impact of small particles into a fine-grained regolith may be able to effectively retain highly shocked or melted material due to the nature of shock wave propagation in such a heterogeneous material.

Gaffey, M. J.↗
NASA NTRS2005

Local Flow Conditions for Propulsion Experiments on the NASA F-15B Propulsion Flight Test Fixture

Local flow conditions were measured underneath the National Aeronautics and Space Administration F-15B airplane to support development of future experiments on the Propulsion Flight Test Fixture (PFTF). The local Mach number and flow angles were measured using a conventional air data boom on a cone-cylinder mounted under the PFTF and compared with the airplane air data nose boom measurements. At subsonic flight speeds, the airplane and PFTF Mach numbers were approximately equal. Transonic Mach number values were up to 0.1 greater at the PFTF than the airplane, which is a counterintuitive result. The PFTF local supersonic Mach numbers were as much as 0.46 less than the airplane values. The maximum local Mach number at the PFTF was approximately 1.6 at an airplane Mach number near 2.0. The PFTF local angle of attack was negative at all Mach numbers, ranging from -3 to -8 degrees. When the airplane angle of sideslip was zero, the PFTF local value was zero between Mach 0.8 and Mach 1.1, -2 degrees between Mach 1.1 and Mach 1.5, and increased from zero to 1 degree from Mach 1.5 to Mach 2.0. Airplane inlet shock waves crossed the aerodynamic interface plane between Mach 1.85 and Mach 1.90.

Vachon, Michael J.↗
NASA NTRS1994

Partial Spreading of a Laser Beam into a Light Sheet by Shock Waves and Its Use as a Shock Detection Technique

It is observed that when a laser beam is allowed to fall on a shock surface at a grazing incidence, a small part of the beam spreads out in a thin, diverging sheet of light normal to the surface, and both upstream and downstream of the shock. The phenomenon is visualized by observing a cross section of the light sheet on a screen placed normal to the laser path after it touches a shock. The light sheet disappears when the beam is moved to any other locations where there is no shock or the beam pierces the shock surface, i.e., at a non-grazing incidence. The spread angle of the light sheet is considerably higher than the angle by which the beam may bend as it passes through the shock, which produces a small difference of refractive index. Various details indicate that the spread light is a result of diffraction of a small part of the laser beam by the shock whose thickness is nearly the same as that of the laser wavelength. Shocks formed in underexpanded free jets of fully expanded Mach numbers 1.4 to 1.8 are used for this experiment. The above optical phenomenon is used as the basis of a novel shock detection technique which depends on sensing the spread light using a photomultiplier tube (PMT). The locations of the shock surfaces in the underexpanded supersonic jet, obtained using this technique, match with those inferred from the Schlieren photographs and velocity measurements. Moreover, if the shock oscillates, a periodic PMT signal is obtained which provides information about the frequency and amplitude of shock motion.

Panda, J.↗
DOE OSTI2021

High-pressure phase diagram of beryllium from ab initio free-energy calculations

In this report we use first-principles molecular dynamics simulations coupled with the thermodynamic integration method to study the hexagonal close-packed (hcp) to body-centered cubic (bcc) transition and melting of beryllium up to a pressure of 1600 GPa. We derive the melting line by equating solid and liquid Gibbs free energies and represent it by a Simon-Glatzel fit T m = 1564 K [1 + P/(15.6032 GPa)] 0.383 , which is in good agreement with previous two-phase simulations <6000 K. We also derive the hcp-bcc solid-solid phase boundary and show that the quasiharmonic approximation underestimates the stability of the hcp structure, predicting lower transition pressures between hcp and bcc phases. Our results are consistent with the stability regime predicted by the phonon quasiparticle method. We also predict that the hcp-bcc-liquid triple point is located at 164.7 GPa and 4314 K. In addition, we compute the shock Hugoniot curve and show that it is in good agreement with experiments, intersecting our derived melting curve at ~235 GPa and 4900 K. Finally, we make predictions for future ramp compression experiments. Starting with an isentropic compression of the liquid, we predict the path to intersect the melting line at low pressure and temperature, then to continue along the melting line over a large temperature interval of 7000 K as the sample remains in the mixed solid-liquid state before it enters the solid phase.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Direct observations of shock-induced melting in a porous solid using time-resolved x-ray diffraction

Here in this work we provide direct evidence of shock-induced melting and associated kinetics in a porous solid (aluminum powder) using time-resolved x-ray diffraction. Unambiguous evidence of melting in 50% porous aluminum (Al) powder samples, shocked to peak pressures between ~13 - 19 GPa, was provided by the broadening of the Debye-Scherrer ring corresponding to the (111) peak. Shocked Al powder did not melt completely in any of our experiments within the durations of measurement. Incomplete (partial) melting of the powder, even after several hundreds of nanoseconds of shock loading, provides insights into thermal transport with Al powder particles under high-pressure dynamic loading. Such insights are quite valuable for developing well-constrained melting models and thermodynamic equations of state for porous Al and other porous solids relevant to planetary and materials science.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Fluid dynamic mathematical aspects of supernova remnants

Supernovae—explosions of stars—are a central problem in astrophysics since they contain information on the entire process of stellar evolution and nucleosynthesis. Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) instabilities, developing during the supernova blast, lead to intense interfacial RT/RM mixing of the star's materials and couple astrophysical to atomic scales. This work analyzes some fluid dynamic mathematical aspects of the titanic task of supernova's blast. We handle mathematical challenges of RT/RM dynamics in supernova relevant conditions by directly linking the conservation laws governing RT/RM dynamics to symmetry-based momentum model, by exactly deriving the model parameters in the scale-dependent and scale-invariant regimes, and by exploring the special self-similar class for RT/RM interfacial mixing with variable accelerations. Here we reveal that RT/RM dynamics is strongly influenced by deterministic (the initial and the flow) conditions in the scale-dependent linear and nonlinear regimes and in the self-similar mixing regime. The theory outcomes are consistent with the observations of supernova remnants, explain the results of the scaled laboratory experiments in high energy density plasmas, and yield the design of future experiments for the accurate quantification of RT/RM dynamics in supernova relevant conditions. We find that from fluid dynamic mathematical perspectives, supernovae can be regarded as an astrophysical initial value problem. Along with the guidance of what explodes at microscopic scales, supernova remnants encapsulate information on the explosion hydrodynamics and the associated deterministic conditions at macroscopic scales. We urge such effects be considered in interpretations of the observational data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗