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At least 379 records · Page 21

Space Technology 5 Multipoint Observations of Temporal and Spatial Variability of Field-Aligned Currents

Space Technology 5 (ST5) is a constellation mission consisting of three microsatellites. It provides the first multipoint magnetic field measurements in low Earth orbit, which enables us to separate spatial and temporal variations. In this paper, we present a study of the temporal variability of field-aligned currents using the ST5 data. We examine the field-aligned current observations during and after a geomagnetic storm and compare the magnetic field profiles at the three spacecraft. The multipoint data demonstrate that mesoscale current structures, commonly embedded within large-scale current sheets, are very dynamic with highly variable current density and/or polarity in approx.10 min time scales. On the other hand, the data also show that the time scales for the currents to be relatively stable are approx.1 min for mesoscale currents and approx.10 min for large-scale currents. These temporal features are very likely associated with dynamic variations of their charge carriers (mainly electrons) as they respond to the variations of the parallel electric field in auroral acceleration region. The characteristic time scales for the temporal variability of mesoscale field-aligned currents are found to be consistent with those of auroral parallel electric field.

Le, G.↗

On interstellar accretion and the rejuvenation of white dwarfs

The paper investigates physical conditions which can give rise to thermonuclear runaways in the hydrogen envelopes of low-luminosity white dwarfs. Specifically, calculations are performed for white dwarfs of 0.5, 0.75, 1, and 1.25 solar masses with envelope masses in the range from 0.00001 to 0.001 solar mass and initial luminosities of 0.00001 to 0.01 times the solar value. It is found that envelope masses as low as 0.0001 solar mass are sufficient to initiate thermonuclear runaways on more massive white dwarfs with luminosities as low as about 0.001 the solar value. The runaway time scales under these conditions, typically of the order of a billion years, are comparable to the time scales for cooling of white dwarfs to these low luminosities. Since time-averaged accretion rates as low as a few times 10 to the -14th power solar mass per year are sufficient to reconstitute such envelopes, also on a time scale of several billion years, it is suggested that the association of novalike events with binary systems may not be unique. Accretion of interstellar matter onto isolated white dwarfs may, under some circumstances, be sufficient to rekindle and perhaps rejuvenate the dwarf. Such evolutionary behavior might define a new and distinct class of objects.

Truran, J. W.↗

A collision operator for describing dissipation in noncanonical phase space

The phase space of a noncanonical Hamiltonian system is partially inaccessible due to dynamical constraints (Casimir invariants) arising from the kernel of the Poisson tensor. When an ensemble of noncanonical Hamiltonian systems is allowed to interact, dissipative processes eventually break the phase space constraints, resulting in a thermodynamic equilibrium described by a Maxwell–Boltzmann distribution. However, the time scale required to reach Maxwell–Boltzmann statistics is often much longer than the time scale over which a given system achieves a state of thermal equilibrium. Examples include diffusion in rigid mechanical systems, as well as collisionless relaxation in magnetized plasmas and stellar systems, where the interval between binary Coulomb or gravitational collisions can be longer than the time scale over which stable structures are self-organized. Here, we focus on self-organizing phenomena over spacetime scales such that particle interactions respect the noncanonical Hamiltonian structure, but yet act to create a state of thermodynamic equilibrium. We derive a collision operator for general noncanonical Hamiltonian systems, applicable to fast, localized interactions. This collision operator depends on the interaction exchanged by colliding particles and on the Poisson tensor encoding the noncanonical phase space structure, is consistent with entropy growth and conservation of particle number and energy, preserves the interior Casimir invariants, reduces to the Landau collision operator in the limit of grazing binary Coulomb collisions in canonical phase space, and exhibits a metriplectic structure. We further show how thermodynamic equilibria depart from Maxwell–Boltzmann statistics due to the noncanonical phase space structure, and how self-organization and collisionless relaxation in magnetized plasmas and stellar systems can be described through the derived collision operator.

Boltzmann equation↗

The correlated X-ray and optical time variability of TT Arietis

The results of Einstein X-ray observation and simultaneous optical observations of the cataclysmic variable TT Arietis extending over several binary orbits are reported. Evidence is found for correlations between the X-ray and optical variability of TT Ari on three distinct time scales: the 3.3 hour variability that has been associated with the orbital period of the star, the about 1000 s time scale of the irregular flickering activity, and the time scale of quasi-coherent oscillations which have periods of order 10 s. There is a modulation of the X-ray flux with a period consistent with the orbital period of approximately 200 minutes, but there is no apparent modulation of the X-ray spectrum. The optical flux is modulated with a similar period and may lag the X-ray modulation by about 0.1 in phase. The X-ray spectrum is well fitted by a thermal bremsstrahlung plus Gaunt factor model. The results suggest that the hard X-ray emission may be produced in a corona above and below the inner accretion disk.

Jensen, K. A.↗

Molecular Dynamics Simulation of Complex Reactivity with the Rapid Approach for Proton Transport and Other Reactions (RAPTOR) Software Package

Simulating chemically reactive phenomena such as proton transport on nanosecond to microsecond and beyond time scales is a challenging task. Ab initio methods are unable to currently access these time scales routinely, and traditional molecular dynamics methods feature fixed bonding arrangements that cannot account for changes in the system’s bonding topology. The Multiscale Reactive Molecular Dynamics (MS-RMD) method, as implemented in the Rapid Approach for Proton Transport and Other Reactions (RAPTOR) software package for the LAMMPS molecular dynamics code, offers a method to routinely sample longer time scale reactive simulation data with statistical precision. RAPTOR may also be interfaced with enhanced sampling methods to drive simulations toward the analysis of reactive rare events, and a number of collective variables (CVs) have been developed to facilitate this. Key advances to this methodology, including GPU acceleration efforts and novel CVs to model water wire formation are reviewed, along with recent applications of the method which demonstrate its versatility and robustness.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Extended inertial range phenomenology of magnetohydrodynamic turbulence

A phenomenological treatment of the inertial range of isotropic statistically steady magnetohydrodynamic turbulence is presented, extending the theory of Kraichnan (1965). The role of Alfven wave propagation is treated on equal footing with nonlinear convection, leading to a simple generalization of the relations between the times characteristic of wave propagation, convection, energy transfer, and decay of triple correlations. The theory leads to a closed-form steady inertial range spectral law that reduces to the Kraichnan and Kolmogorov laws in appropriate limits. The Kraichnan constant is found to be related in a simple way to the Kolmogorov constant; for typical values of the latter constant, the former has values in the range 1.22-1.87. Estimates of the time scale associated with spectral transfer of energy also emerge from the new approach, generalizing previously presented 'golden rules' for relating the spectral transfer time scale to the Alfven and eddy-turnover time scales.

Matthaeus, William H.↗

Revealing and Engineering Assembly Pathways of 3D DNA Origami Crystals

Recent developments in nanomaterial self-assembly demonstrate the capability to create tailored nanostructures by engineering both the binding coordination and specificity of interactions between material subunits. DNA origami frames allow for the design and fabrication of a broad variety of ordered 3D nanoscale architectures through self-assembly, facilitated by frame-to-frame bonds with designable strength and specificity. While the bond design is critical to lattice formation, the assembly process itself is often dependent on a thermal pathway. Highly ordered nanoscale frameworks, assembled from DNA frames, are predominantly crystallized through thermal annealing pathways that typically follow a “slow” cooling approach, with experiments on the time scale of days yielding DNA origami crystals in the range of 1−10 μm. This extended assembly time scale hinders the study of crystal formation pathways, necessitating a deeper understanding of factors governing successful annealing. Lack of insight into time scale also presents a practical limitation for material fabrication. Here, we investigate key factors affecting lattice assembly pathways and demonstrate that precise engineering of assembly conditions greatly reduces assembly times by up to nearly 2 orders of magnitude. We evaluate the nucleation and growth of crystals via optical and electron microscopy, and small-angle X-ray scattering techniques, mapping the time−temperature-transformation of superlattices from the melt through single-crystal optical tracking. The results show that origami frame assembly can be described by classical nucleation and growth theory, which can, in turn, be used to prescribe the growth of the crystals. Lastly, these findings are applied to demonstrate thermal pathway-dependent assembly, forming distinct assemblies based on different thermal annealing profiles.

36 MATERIALS SCIENCE↗

Climate Model Evaluation using New Datasets from the Clouds and the Earth's Radiant Energy System (CERES)

There are some in the science community who believe that the response of the climate system to anthropogenic radiative forcing is unpredictable and we should therefore call off the quest . The key limitation in climate predictability is associated with cloud feedback. Narrowing the uncertainty in cloud feedback (and therefore climate sensitivity) requires optimal use of the best available observations to evaluate and improve climate model processes and constrain climate model simulations over longer time scales. The Clouds and the Earth s Radiant Energy System (CERES) is a satellite-based program that provides global cloud, aerosol and radiative flux observations for improving our understanding of cloud-aerosol-radiation feedbacks in the Earth s climate system. CERES is the successor to the Earth Radiation Budget Experiment (ERBE), which has widely been used to evaluate climate models both at short time scales (e.g., process studies) and at decadal time scales. A CERES instrument flew on the TRMM satellite and captured the dramatic 1998 El Nino, and four other CERES instruments are currently flying aboard the Terra and Aqua platforms. Plans are underway to fly the remaining copy of CERES on the upcoming NPP spacecraft (mid-2010 launch date). Every aspect of CERES represents a significant improvement over ERBE. While both CERES and ERBE measure broadband radiation, CERES calibration is a factor of 2 better than ERBE. In order to improve the characterization of clouds and aerosols within a CERES footprint, we use coincident higher-resolution imager observations (VIRS, MODIS or VIIRS) to provide a consistent cloud-aerosol-radiation dataset at climate accuracy. Improved radiative fluxes are obtained by using new CERES-derived Angular Distribution Models (ADMs) for converting measured radiances to fluxes. CERES radiative fluxes are a factor of 2 more accurate than ERBE overall, but the improvement by cloud type and at high latitudes can be as high as a factor of 5. Diurnal cycles are explicitly resolved by merging geostationary satellite observations with CERES and MODIS. Atmospheric state data are provided from a frozen version of the Global Modeling and Assimilation Office- Data Assimilation System at the NASA Goddard Space Flight Center. In addition to improving the accuracy of top-of-atmosphere (TOA) radiative fluxes, CERES also produces radiative fluxes at the surface and at several levels in the atmosphere using radiative transfer modeling, constrained at the TOA by CERES (ERBE was limited to the TOA). In all, CERES uses 11 instruments on 7 spacecraft all integrated to obtain climate accuracy in TOA to surface fluxes. This presentation will provide an overview of several new CERES datasets of interest to the climate community (including a new adjusted TOA flux dataset constrained by estimates of heat storage in the Earth system), show direct comparisons between CERES ad ERBE, and provide a detailed error analysis of CERES fluxes at various time and space scales. We discuss how observations can be used to reduce uncertainties in cloud feedback and climate sensitivity and strongly argue why we should NOT "call off the quest".

Loeb, Norman G.↗

Nucleocosmochronology

The relative abundances of radioactive nuclides can be used to determine the time scale for nucleosynthesis of those nuclides and, by extension, of many other nuclides in the solar system. Such time scales can also yield estimates for the age of the universe, and information about the time scale for protosolar collapse.

Swindle, T. D.↗

Physics of gamma-ray bursts

Attention is given to the accumulating evidence for the view that gamma-ray bursts come from strongly magnetic neutron stars, discussing the physical properties of the emission region and the radiation processes expected in strong magnetic fields, and emphasizing that the observed burst spectra require that the emission region be optically thin. This entails that the energy of the emitting plasma and/or the plasma itself be continuously replenished during a burst, and that the cooling time scale of the emitting plasma be much shorter than the observed duration of the bursts. This characteristic of the cooling time scale implies that the burst intensity and spectrum can vary on extremely short time scales, and that the burst duration must have a separate explanation. It is emphasized that synchrotron emission is favored as the gamma-ray production mechanism; it is the only mechanism capable of satisfying the optical thinness constraint while producing the observed luminosity.

Lamb, D. Q.↗

Does Aerosol Weaken or Strengthen the South Asian Monsoon?

Aerosols are known to have the ability to block off solar radiation reaching the earth surface, causing it to cool - the so-called solar dimming (SDM) effect. In the Asian monsoon region, the SDM effect by aerosol can produce differential cooling at the surface reducing the meridional thermal contrast between land and ocean, leading to a weakening of the monsoon (Ramanathan et al. 2005). On the other hand, absorbing aerosols such as black carbon and dust, when forced up against the steep slopes of the southern Tibetan Plateau can produce upper tropospheric heating, and induce convection-dynamic feedback leading to an advance of the rainy season over northern India and an enhancement of the South Asian monsoon through the "Elevated Heat Pump" (EHP) effect (Lau et al. 2006). In this paper, we present modeling results showing that in a coupled ocean-atmosphere-land system in which concentrations of greenhouse gases are kept constant, the response of the South Asian monsoon to dust and black carbon forcing is the net result of the two opposing effects of SDM and EHP. For the South Asian monsoon, if the increasing upper tropospheric thermal contrast between the Tibetan Plateau and region to the south spurred by the EHP overwhelms the reduction in surface temperature contrast due to SDM, the monsoon strengthens. Otherwise, the monsoon weakens. Preliminary observations are consistent with the above findings. We find that the two effects are strongly scale dependent. On interannual and shorter time scales, the EHP effect appears to dominate in the early summer season (May-June). On decadal or longer time scales, the SDM dominates for the mature monsoon (July-August). Better understanding the physical mechanisms underlying the SDM and the EHP effects, the local emission and transport of aerosols from surrounding deserts and arid-regions, and their interaction with monsoon water cycle dynamics are important in providing better prediction and assessment of climate change impacts on precipitation of the Asian monsoon land regions.

Lau, William K. M.↗

Does Aerosol Weaken or Strengthen the South Asian Monsoon?

Aerosols are known to have the ability to block off solar radiation reaching the earth surface, causing it to cool - the so-called solar dimming (SDM) effect. In the Asian monsoon region, the SDM effect by aerosol can produce differential cooling at the surface reducing the meridional thermal contrast between land and ocean, leading to a weakening of the monsoon. On the other hand, absorbing aerosols such as black carbon and dust, when forced up against the steep slopes of the southern Tibetan Plateau can produce upper tropospheric heating, and induce convection-dynamic feedback leading to an advance of the rainy season over northern India and an enhancement of the South Asian monsoon through the "Elevated Heat Pump" (EHP) effect. In this paper, we present modeling results showing that in a coupled ocean-atmosphere-land system in which concentrations of greenhouse gases are kept constant, the response of the South Asian monsoon to dust and black carbon forcing is the net result of the two opposing effects of SDM and EHP. For the South Asian monsoon, if the increasing upper tropospheric thermal contrast between the Tibetan Plateau and region to the south spurred by the EHP overwhelms the reduction in surface temperature contrast due to SDM, the monsoon strengthens. Otherwise, the monsoon weakens. Preliminary observations are consistent with the above findings. We find that the two effects are strongly scale dependent. On interannual and shorter time scales, the EHP effect appears to dominate in the early summer season (May-June). On decadal or longer time scales, the SDM dominates for the mature monsoon (July-August). Better understanding the physical mechanisms underlying the SDM and the EHP effects, the local emission and transport of aerosols from surrounding deserts and arid-regions, and their interaction with monsoon water cycle dynamics are important in providing better prediction and assessment of climate change impacts on precipitation of the Asian monsoon land regions.

Lau, William K.↗

Observations of rapid X-ray flaring from Cygnus X-1

SAS-3 observations of Cyg X-1 in October 1976 show the source to be in a highly active state exhibiting rapid continual flaring on time scales of 1 to 10 s. The flares exhibit temporal structure and variable spectra, but their mean spectrum is similar to that of the source as a whole. The characteristic time scales of the source are 2 to 4 times longer than those previously observed. It is suggested that this active phase of Cyg X-1 signals a modified accretion-disk structure. The flares may result from correlated bunches of the same 'shots ' which are thought to explain the rest of the short-time-scale variability of the source. While the flares superficially resemble X-ray bursts, they are distinct in several respects.

Canizares, C. R.↗

Understanding latent timescales in neural ordinary differential equation models of advection-dominated dynamical systems

The neural ordinary differential equation (ODE) framework has shown considerable promise in recent years in developing highly accelerated surrogate models for complex physical systems characterized by partial differential equations (PDEs). For PDE-based systems, state-of-the-art neural ODE strategies leverage a two-step procedure to achieve this acceleration: a nonlinear dimensionality reduction step provided by an autoencoder, and a time integration step provided by a neural-network based model for the resultant latent space dynamics (the neural ODE). This work explores the applicability of such autoencoder-based neural ODE strategies for PDEs in which advection terms play a critical role. More specifically, alongside predictive demonstrations, physical insight into the sources of model acceleration (i.e., how the neural ODE achieves its acceleration) is the scope of the current study. Such investigations are performed by quantifying the effects of both autoencoder and neural ODE components on latent system time-scales using eigenvalue analysis of dynamical system Jacobians. To this end, the sensitivity of various critical training parameters – de-coupled versus end-to-end training, latent space dimensionality, and the role of training trajectory length, for example – to both model accuracy and the discovered latent system timescales is quantified. Furthermore, this work specifically uncovers the key role played by the training trajectory length (the number of rollout steps in the loss function during training) on the latent system timescales: larger trajectory lengths correlate with an increase in limiting neural ODE time-scales, and optimal neural ODEs are found to recover the largest time-scales of the full-order (ground-truth) system. Demonstrations are performed across fundamentally different unsteady fluid dynamics configurations influenced by advection: (1) the Kuramoto–Sivashinsky equations (2) Hydrogen-Air channel detonations (the compressible reacting Navier–Stokes equations with detailed chemistry), and (3) 2D Atmospheric flow.

Advection-dominated dynamical systems↗

Biosignatures in the Context of Low Energy Flux

Many of the features that are thought of as biosignatures - including the mediation of chemical and physical processes with speed, specificity, and selectivity - result directly or indirectly from life's unique capability to mediate and direct energy flux. As such, it is important to consider the impact that differences in energy flux may have on the quantity and quality of evidence for life. Earth differs from every other body in our solar system in the magnitude of biologically-usable energy flux into a liquid water environment. On a global basis, the capture of light energy into photosynthesis and the flux of chemical energy represented in the products of that photosynthesis (organic material + O2) are about six and four orders of magnitude larger, respectively, than the flux of energy represented in geochemical sources. Our conception of what an inhabited world "looks like" and our intuition about how to search for life are based in this high-energy context. Energy fluxes on worlds beyond Earth may be better approximated by the million-fold smaller flux provided to Earth's biosphere by geochemical sources. As a result, the nature, abundance, and quality of evidence for life that could be expected on an inhabited extraterrestrial world within our solar system may differ profoundly from that found on Earth. Understanding this potential difference in quantitative terms provides important context for the formulation of life detection strategies. The influence of energy flux on biosignatures can be evaluated through reference to the two basic purposes into which life partitions energy flux: (1) Life expends energy to sustain existing biomass in a metabolic steady state (metabolically functional but non-growing). The formal representation of this relationship in the traditional microbiology literature equates biomass directly with energy flux. The direct implication is that worlds having lower energy flux will have correspondingly lower potential to support biomass. Life detection strategies that directly target extant organisms should therefore be prepared to encounter average biomass densities that may be many orders of magnitude smaller than those found in most of Earth's surface environments (2) Life expends energy to synthesize new biomass. An end-member case in which new biomass is created at the energy-limited rate and the corresponding cells are immediately destroyed (so that the energy partitioned to cell maintenance is minimized) establishes an upper bound on the rate at which biological material can enter a bulk global pool. For a specified bulk concentration [i] of any particular biological compound, i, or for biologically produced matter overall, this synthesis rate, R (sub i), defines a characteristic time scale tau (sub i) equals [i] divided by R (sub i). tau (sub i) can be thought of as (a) the minimum time required for biosynthesis to yield a specific bulk concentration (e.g., a detection threshold) of i, and (b) the average residence time of i within a bulk pool when [i] is held in steady state through a balance between biosynthesis and attrition by physical, chemical, or biological consumption. tau (sub i) becomes an important quantity in considering the potential utility of enantiomeric excess (as a product of homochiral biosynthesis) as a biosignature. Spontaneous racemization of amino acids acts to "erase" the signature of homochiral synthesis over time scales that may range from hundreds to hundreds of thousands of years, depending on temperature. For environments in which low energy flux translates to low rates of biosynthesis, including the synthesis of homochiral amino acids, amino acid residence times in pools having detectable concentrations may compare to or significantly exceed the time scale for racemization. This and similar consequences of long residence times should be considered in the formulation of life detection strategies based on detection of biologically-produced species. Fluxes of biologically-useful energy on potentially habitable worlds within our solar system are, at present, not well constrained. Improving such constraint has the potential to inform priorities in the formulation and targeting of search-for-life strategies, based on the implications of energy flux for the abundance and quality of biosignatures overall, and in specific categories.

ENERGY FLUX↗

Low-frequency variations of circulation and high cloudiness in the northern extratropics - Spatial and temporal relationships

The spatial and temporal relationships between fluctuations in geopotential height and high-cloud fractional area in low-pass (periods greater than 10 days) and intermediate-pass (10-30 days) time scales are investigated and compared with spatial and temporal relationships in the fast-pass (2.5-6 days) time scale, using NMC 500-hPa height and Nimbus-7 THIR-TOMS high-cloud data for October-March winter months of 1979-1985. It was found that, when moving from the low-pass and intermediate-pass time scales to the fast-pass regime, the temporal variance of the height field decreases, but the temporal variance of the high cloudiness increases. The spatial phase relationships between the height and the cloud fields in the low-pass and the fast-pass regimes were found to be different.

Charlock, Thomas P.↗

2D analysis of tokamak divertor-plasma detachment-bifurcation with operational parameters and geometries

UEDGE simulations with density scans for various input power, transport coefficients and outer poloidal leg length are performed to study the conditions for the existence of a bifurcation-like drop of T e at the outer strike point, commonly referred to as a detachment cliff, when transitioning to a detached plasma from an attached plasma in the outer divertor as the upstream density increases (McLean et al., 2015). The simulation results show that a detachment cliff tends to occur with a higher power input regardless of diffusivities and leg length. Further analysis of change of plasma profiles at a cliff indicate that, in addition to the sharp reduction of the E x B drift fluxes in the outer divertor studied in Jaervinen et al., (2018), the substantial change of the Mach number in the outer divertor and the decrease of the outer mid-plane T e due to the radiation front moving across the separatrix into the confinement region above the X-point consistently occur for all UEDGE density scans that have a detachment cliff. UEDGE time-dependent simulation of the evolution of a detachment cliff shows that the rapid increase of radiation above the X-point occurs in a time scale of ~0.3–0.5, which could possibly be the trigger for the formation of a detachment cliff, quicker than the Mach number change in a time scale of ~1 ms and the drop of T e in a time scale of ~2–3 ms in the outer divertor.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Modelling the Soft X-Ray and EUV Emission in Classical Novae: EUVE and ROSAT Observations of V1974 Cygni

We have conducted an extensive analysis of the observability of Classical Novae with the EUVE Lex/B and Al/Ti/C detectors. Predicted count rates have been computed using optically thin, isothermal plasma models for solar and metal-rich compositions, and hot ONeMg white dwarf model atmospheres. We find EUVE to be quite sensitive to both the EUV and soft X-ray emission emitted by the underlying hot white dwarf during novae outbursts, except for the coolest temperatures with very high intervening hydrogen column density. These results are used to interpret the emission detected during the EUVE all-sky survey of Nova Cygni 1992 (approx. = V1974 Cyg), 279-290 days after visual maximum. We find the best fit to the observed emission from V1974 Cyg arises from a hot ONeMg white dwarf with surface temperature approx. 4 x l0(exp 5) K and a mas of approx. 1.2 solar mass, and derive an interstellar hydrogen column density of approx. 3 x 10(exp 21)/sq cm. Virtually all this emission arises from supersoft X-rays rather than the EUV. We also report the detection of V1974 Cyg with the EUVE Deep Survey detector at 549 days after visual maximum. This observation is compatible with the above properties, indicating that the mechanism responsible for the soft X-ray emission, connected with the underlying white dwarf, had not yet entirely turned off. We also present analysis of a ROSAT PSPC observation which is contemporaneous with the EUVE survey observations; this independently confirms the high column density we derived from the EUVE survey observation. Light curves for the EUVE and ROSAT observations are presented. Statistical tests for variability show that all of these observations are indeed highly variable over various time scales. The EUVE survey data shows one day variations, the EUVE DS data show approx. 30 minute fluctuations, while the ROSAT data vary rapidly on time scales of seconds. The EUVE data shows no periodic variability on any time scale. The implications of the rapid variability are briefly discussed.

Stringfellow, Guy S.↗