Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “power distribution lines”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 721 records · Page 40

Demonstrations that the Solar Wind is Not Accelerated by Waves or Turbulence

The present work uses observations and theoretical considerations to provide both qualitative and quantitative arguments that hydromagnetic waves, whether turbulent or not, cannot produce the acceleration of the fast solar wind and the related heating of the open solar corona. Waves do exist, and can play a role in the differential heating and acceleration of minor ions, but their amplitudes are not sufficient to power the wind, as demonstrated by extrapolation of magnetic spectra from Helios and Ulysses observations. Dissipation mechanisms invoked to circumvent this conclusion cannot be effective for a variety of reasons. In particular, turbulence does not play a strong role in the corona as shown both by observations of coronal striations and other features, and by theoretical considerations of line-tying to a nonturbulent photosphere, nonlocality of interactions, and the nature of the kinetic dissipation. We consider possible "ways out" of the arguments presented, and suggest that in the absence of wave or turbulent heating and acceleration, the chromosphere and transition region become the natural source, if yet unproven, of open coronal energization through the production of nonthermal particle distributions.

Roberts, D. Aaron↗

Studying the Impact of Momentary Cessation of IBRs Compliant With IEEE Std. 2800-2022 on Transmission Line Protection Elements

This paper examines the impact of inverter-based resource (IBR) momentary cessation timing on transmission system protection relays. IEEE Std. 2800 mandates voltage ride-through, requiring IBRs to remain online during voltage disturbances. However, for severe voltage dips (|V| = 0.1 p.u.), the standard permits current blocking. In practice, vendors implement momentary cessation with varying delays, potentially affecting relay operation if IBRs cease too early. This article studies the impact of the time IBRs enter momentary cessation on transmission line protective relays. Using an electromagnetic transient (EMT) simulation, this study models IBR momentary cessation with tunable delays in a realistic transmission network. COMTRADE files generated from EMT simulations are analyzed in MATLAB using detailed protective relay models. Results indicate that IBRs must sustain operation for at least one cycle to ensure proper relay response; otherwise, relays may fail to oper- ate. These findings guide IBR vendors in optimizing momentary cessation settings to enhance transmission line protection.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Supernova 1972 e in NGC 5253

New absolute energy distributions of the Type 1 supernova 1972e in NGC 5253 extending to about 700 days after maximum light were obtained. A physical model of the expanding envelope, based on the identification of the feature at 6550 A with H-alpha, is proposed. It is described as a differentially expanding atmosphere, with electron density ranging from 10 to the 10th power near maximum light to about 10 to the 7th power, 340 days later, illuminated by a photosphere with temperature in the range 10,000 K to 7,000 K. More than 200 days after maximum, the spectrum was dominated by four features between 4200 A and 5500 A. Three of these four features matched the blended emissions from over 100 lines of Fe II. Possible identifications of the fourth feature with Mg I lambda 4571 or permitted lines of Fe II are also discussed.

Kirshner, R. P.↗

Additional Results on the Radiating Properties of Ltsas and Cwsas

Results are presented on the theoretical experimental investigations of the radiating properties of Linearly Tapered Slot Antennas (LTSAs) and Constant Width Slot Antennas (CWSAs). The antenna is treated as a flared slot radiating in the presence of a conducting half plane. The aperture distribution in the flared slot is determined by approximating the tapered structure as a series of short sections of parallel slots. The slot field of a uniform slotline is determined by employing the spectral Galerkin's technique and a power conservation criterion is employed to match the fields at the step junction between two successive sections. Comparison is made between theory and experiment for several LTSAs and CWSAs etched on epsilon sub r = 2.22 and 2.55 substrates, and or flare angles 4 deg or = gamma or = 10 deg. It is shown that the theory adequately models the physics of the problem when the lateral dimension D of the antenna is large and when the propagation constant of a parallel slot line can be estimated very accurately. Newly observed effects of the lateral truncation on the radiation pattern of the antenna are discussed.

Source record↗

Gravitational microlensing - Powerful combination of ray-shooting and parametric representation of caustics

We present a combination of two very different methods for numerically calculating the effects of gravitational microlensing: the backward-ray-tracing that results in two-dimensional magnification patterns, and the parametric representation of caustic lines; they are in a way complementary to each other. The combination of these methods is much more powerful than the sum of its parts. It allows to determine the total magnification and the number of microimages as a function of source position. The mean number of microimages is calculated analytically and compared to the numerical results. The peaks in the lightcurves, as obtained from one-dimensional tracks through the magnification pattern, can now be divided into two groups: those which correspond to a source crossing a caustic, and those which are due to sources passing outside cusps. We determine the frequencies of those two types of events as a function of the surface mass density, and the probability distributions of their magnitudes. We find that for low surface mass density as many as 40 percent of all events in a lightcurve are not due to caustic crossings, but rather due to passings outside cusps.

Wambsganss, J.↗

Remotely powered line monitor

Improved devices, apparatuses, systems, and methods involving the use of field probes with voltage-controlled variable impedance elements and surface-launched acoustic wave devices, including surface acoustic wave (SAW) devices and SAW sensor-tag wireless interface devices to measure voltage and current in current carrying conductors (CCCs) via measurement of the electric fields and magnetic fields around said CCCs are disclosed. The devices, apparatuses, systems, and methods taught in the present invention include a remotely powered line-mounted measurement unit that requires no connection to electrical ground for operation, and that has no internal energy source, no energy harvesting or power conditioning circuitry, no discrete energy storage components, and no radio. The devices, apparatuses, systems, and methods taught in the present invention also provide for determining the phase (leading or lagging) of the current relative to the voltage in AC power systems, and also provide for measurement of temperature of the conductor.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Efficient and Robust Data Collection Using Compact Micro Hardware, Distributed Bus Architectures and Optimizing Software

Future In-Space propulsion systems for exploration programs will invariably require data collection from a large number of sensors. Consider the sensors needed for monitoring several vehicle systems states of health, including the collection of structural health data, over a large area. This would include the fuel tanks, habitat structure, and science containment of systems required for Lunar, Mars, or deep space exploration. Such a system would consist of several hundred or even thousands of sensors. Conventional avionics system design will require these sensors to be connected to a few Remote Health Units (RHU), which are connected to robust, micro flight computers through a serial bus. This results in a large mass of cabling and unacceptable weight. This paper first gives a survey of several techniques that may reduce the cabling mass for sensors. These techniques can be categorized into four classes: power line communication, serial sensor buses, compound serial buses, and wireless network. The power line communication approach uses the power line to carry both power and data, so that the conventional data lines can be eliminated. The serial sensor bus approach reduces most of the cabling by connecting all the sensors with a single (or redundant) serial bus. Many standard buses for industrial control and sensor buses can support several hundreds of nodes, however, have not been space qualified. Conventional avionics serial buses such as the Mil-Std-1553B bus and IEEE 1394a are space qualified but can support only a limited number of nodes. The third approach is to combine avionics buses to increase their addressability. The reliability, EMI/EMC, and flight qualification issues of wireless networks have to be addressed. Several wireless networks such as the IEEE 802.11 and Ultra Wide Band are surveyed in this paper. The placement of sensors can also affect cable mass. Excessive sensors increase the number of cables unnecessarily. Insufficient number of sensors may not provide adequate coverage of the system. This paper also discusses an optimal technique to place and validate sensors.

micro hardware↗

FiberFlex: Real-time FPGA-based Intelligent and Distributed Fiber Sensor System for Pedestrian Recognition

In recent years, security monitoring of public places and critical infrastructure has heavily relied on the widespread use of cameras, raising concerns about personal privacy violations. To balance the need for effective security monitoring with the protection of personal privacy, we explore the potential of optical fiber sensors for this application. This article proposes FiberFlex, an intelligent and distributed fiber sensor system. Ultizing Field Programmable Gate Arrays (FPGA) high-level synthesis (HLS) acceleration, FiberFlex offers real-time pedestrian detection by co-designing the entire pipeline of optical signal acquisition, processing, and recognition networks based on the principles of optical fiber sensing. As a promising alternative to traditional camera-based monitoring systems, FiberFlex achieves pedestrian detection by analyzing the vibration patterns caused by pedestrian footsteps, enabling security monitoring while preserving individual privacy. FiberFlex comprises three modules: First , fiber-optic sensing system: A fiber-optic distributed acoustic sensing (DAS) system is built and used to measure the ground vibration waves generated by people walking. Second , algorithms: We first collect the training data by measuring the ground vibration waves, label the data, and use the data to train the neural network models to perform pedestrian recognition. Third , hardware accelerators: We use HLS tools to design hardware modules on FPGA for data collection and pre-processing and integrate them with the downstream neural network accelerators to perform in-line real-time pedestrian detection. The final detection results are sent back from FPGA to the host CPU. We implement our system FiberFlex with the in-house built DAS system and AMD/Xilinx Kintex7 FPGA KC705 board and verify the whole system using the real-world collected data. We conduct recognition tests on five test subjects of varying ages, heights, and weights in a fixed sensing area. Each subject experienced 20 real-time recognition tests using their daily walking habits, and the subjects were given adequate rest between tests. After 100 tests on five test subjects, the overall real-time recognition accuracy exceeded \(88.0\%\) . The whole system uses 55 W of power, 33 W in the optical DAS system and 22 W in the FPGA. Relying on its end-to-end interdisciplinary design, FiberFlex seamlessly combines fiber-optic sensors with FPGA accelerators to enable low-power real-time security monitoring without compromising privacy, making it a valuable addition to the existing security monitoring network. According to FiberFlex, more valuable research can be conducted in the future, such as fall monitoring for the elderly, migration of identification networks between different application scenarios, and improvement of anti-interference performance in more complex environments. In future perception networks, where the “eyes” are not feasible, let’s use fiber optic touch instead.

Distributed↗

Global Prompt Proton Sensor Network: Monitoring Solar Energetic Protons Based on GPS Satellite Constellation

Energetic particle instruments on board Global Positioning System (GPS) satellites form a powerful global prompt proton sensor network (GPPSn) that provides an unprecedented opportunity to monitor and characterize solar energetic protons targeting the Earth. The medium-Earth orbits of the GPS constellation have the unique advantage of allowing solar energetic protons to be simultaneously measured from multiple points in both open- and closed-field line regions. Examining two example intervals of solar proton events, we showcase in this study how GPS proton data are prepared, calibrated, and utilized to reveal important features of solar protons, including their source, acceleration/scattering by interplanetary shocks, the relative position of Earth when impinged by these shocks, the shape of solar particle fronts, the access of solar protons inside the dynamic geomagnetic field, and temporally varying proton distributions in both energy and space. By comparing to Van Allen Probes data, GPS proton observations are further demonstrated not only to be useful for qualitatively monitoring the dynamics of solar protons but also for quantitative scientific research including determining cutoff L-shells. Finally, our results establish that this GPPSn can join forces with other existing solar proton monitors and contribute to observing, warning, understanding, and ultimately forecasting the incoming solar energetic proton events.

47 OTHER INSTRUMENTATION↗

Stability analysis of Alfvén eigenmodes excited by ion cyclotron resonance heating on EAST

Alfvén wave instabilities driven by energetic particles are common in fusion devices. Understanding their behavior is essential for the good confinement of fusion plasma. For this purpose, a series of experiments are performed on EAST to investigate the excitation of toroidal Alfvén eigenmodes (TAEs). Experimentally, it was found that AEs with frequencies around 80, 134, 157 kHz are excited by ion cyclotron resonance heating (ICRH) hydrogen minority heating scenario. Moreover, the excitation of AEs is independent of the wall-coating materials, but determined with the generation and confinement of the fast ions. Statistical analysis suggests that the TAEs can only be excited when the ICRH power is larger than 2 MW and the H 98 factor is larger than 1.15. In line with the experiments, a set of simulations using TORIC, ASCOT, and NOVA-C is performed. The simulation results show that with the experimental density profile and safety factor, the measured TAE with frequency of 134 kHz is well reproduced by taking into account the plasma toroidal rotation frequency. However, the appearance of the 80 kHz mode cannot be captured in the simulations. The ICRH-generated fast hydrogen ions mainly have banana orbits and that their perpendicular velocity is much larger than that of the parallel ions. The stability analysis with NOVA-C suggests that the radial gradient of the fast H ion distribution is the only driving source of TAEs. For TAEs locate in the center of Alfvén continuum, the D ion Landau damping is the dominant damping term; For most other TAEs which have intersections with the continuum boundary, the continuum damping becomes the dominant damping mechanism.

Alfvén eigenmodes↗

The Escape Velocity Profile of the Milky Way from Gaia DR3

Abstract The escape velocity profile of the Milky Way offers a crucial and independent measurement of its underlying mass distribution and dark matter (DM) properties. Using a sample of stars from the third data release of Gaia with 6D kinematics and strict quality cuts, we obtain an escape velocity profile of the Milky Way from 4 to 11 kpc in Galactocentric radius. To infer the escape velocity in radial bins, we model the tail of the stellar speed distribution with both traditional power-law models and a new functional form that we introduce. While power-law models tend to rely on extrapolation to high speeds, we find our new functional form gives the most faithful representation of the observed distribution. Using this for the escape velocity profile, we constrain the properties of the Milky Way’s DM halo modeled as a Navarro–Frenck–White profile. Combined with constraints from the circular velocity at the solar position, we obtain a concentration and mass of c 200 c DM = 13.9 − 4.3 + 6.2 and M 200 c DM = 0.55 − 0.14 + 0.15 × 10 12 M ⊙ . This corresponds to a total Milky Way mass of M 200 c = 0.64 − 0.14 + 0.15 × 10 12 M ⊙ , which is on the low end of the historic range of the galaxy’s mass, but in line with other recent estimates.

Astronomy & Astrophysics↗

Theta(1) and gamma Tauri: Understanding the coronal structure of Hyades giants. EUV spectroscopy of BY Dra systems

These programs involve: (1) analysis and interpretation of EUVE spectrometer observations of the active giant beta Cet in comparison to the Hyades giant theta(1) Tau, and (2) analysis and interpretation of EUVE spectrometer observations of the BY Dra systems FK Aqr, DH Leo, and BH Lyn. EUVE carried out observations of beta Cet, but has yet to perform an observation of theta(1) Tau. In beta Cet, a number of Fe lines from high ionization species were observed, up to Fe XXIV. The spectrum overall resembles that seen in the active binary Capella (alpha Aur). All three BY Dra systems were observed by EUVE, and show evidence of high temperature (approximately 10(exp 7) K) plasma; FK Aqr and DH Leo show significant variability in their Deep Survey lightcurves. In FK Aqr, spectral differences between its 'quiescent' and 'active' states suggest possible differences in the plasma density. In DH Leo, the Deep Survey lightcurve, taken over nearly 8 days, shows a distinct period of approximately 1.05 days, similar to the photometric period. The emission measure distributions of all three systems are rather similar in shape, and can be well-represented by a power law with slope approximately 1.5 from 6.2-7.0 in log T.

Stern, Robert A.↗

Assessment of Thin Plastic Scintillation Detectors for Beta-Particle Measurements at the Advanced Test Reactor Critical Facility

The Fission Wire Measurement System is a custom measurement system designed in the 1960s to measure the beta-particle activity of irradiated uranium-aluminum fission wires. This measurement is conducted to determine the fission rate profile of the Advanced Reactor Test Critical facility. The Advanced Test Reactor Critical facility is an open-pool, low-power test reactor used to qualify experiment configurations and verify core models prior to full-power experiment irradiations in the Advanced Test Reactor. Power distribution measurements in ATR-C use uranium-aluminum wires that are distributed throughout the core to validate simulation and modeling results. These measurements require from 340 to 1500 wires to be irradiated and measured within a 12-hour window. The system consists of 4 measurement channels and one reference channel, each with a 2-pi proportional gas flow detector and the measurement channels each have an automated sample changer. The gas flow detectors are of a custom design for this detector system that use methane gas with a large anode wire compared to modern proportional counters. These detectors, which are nearly 60 years old are irreplaceable. The measurements from these gas detectors are affected by the gas flow rate, atmospheric and line pressure, and are very sensitive to the applied high voltage. Recent improvements have been made to the control and data acquisition system, but the detectors have remained the same. The nature of the measurement of the fission product decay activity is such that the energy spectrum of the signal is changing with time. Thin, 250-um thick, plastic scintillators were commercially obtained as a potential replacement for the gas flow detectors. The original calibration of the uranium-aluminum fission wires was conducted in 1965 using a series of irradiations of gold foils and the wires in a well-characterized thermal neutron field. These measurements provided a time-dependent fission rate conversion factor from the gold foil data to calibrate the fission wires based on the response from the 2-pi proportional gas detectors. Transitioning to the new detectors requires qualification and testing. The sensitivity of the scintillators to changes in the energy spectrum of the fission wires and translation of the calibration factor have been completed. These measurements indicated that the sensitivity of the scintillators over time changes at a different rate than the sensitivity of the gas flow detectors. However, the inverse activity of measurements of both detector types is linear with time. Initial results indicate that the scintillator detectors will be a sufficient replacement for the gas detectors with minor adjustments to the fission rate conversion factor. Replacement of the detectors will improve the fission wire measurements and provide a more stable and reliable measurement system.

46 - INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AN↗

Countercurrent distribution of biological cells

Detailed physiochemical studies of dextran/poly(ethylene glycol) (PEG) two phase systems were carried out to characterize and provide understanding of the properties of the systems which determine cell partition and the electrophoretic behavior of phase drops responsible for electric field driven phase separation. A detailed study of the electrostatic and electrokinetic potentials developed in these systems was carried out. The salt partition was examined both in phase systems and with pure polymer solutions via equilibrium dialysis and mechanism of sulfate, chloride and phosphate partition shown to be exclusion by PEG rather than binding by dextran. Salt partition was shown to have a strong effect on the polymer compositions of the phases as well, an effect which produces large changes in the interfacial tension between them. These effects were characterized and the interfacial tension shown to obey a power law with respect to its dependence on the length of the tie line describing the system composition on a phase diagram. The electrostatic potential differences measured via salt bridges were shown to obey thermodynamic predictions. The electrophoretic mobilities measured were utilized to provide a partial test of Levine's incomplete theory of phase drop electrophoresis. The data were consistent with Levine's expression over a limited range of the variables tested.

Brooks, D. E.↗

First experimental confirmation of island SOL geometry effects in a high radiation regime on W7-X

Abstract This work characterizes the detachment behavior and radiation characteristics of the low
iota configuration in the Wendelstein 7-X (W7-X) stellarator. The island scrape-off layer (SOL) of the
low iota has a poloidal mode number of 6 islands surrounding the last closed flux surface (LCFS).
The island geometry of the low iota configuration is significantly different to that of the standard
magnetic field configuration, whose detachment characteristics have already been described in previous
work[2, 3, 4]. Experimental results show that the radiation pattern in the low iota configuration
is starkly different to that of the standard magnetic field configuration, with radiation concentrated
at the island SOL O-points, rather than the X-points. Additionally, this O-point localized radiation
pattern is associated with unstable detachment, with both radiation oscillations in experiments and the
lack of a self-consistent plasma solution at high radiated power fraction in EMC3-Eirene simulations.
EMC3-Eirene simulations are used to understand the radiation distribution. It was found that the O-
point localized radiation arises first from local impurity accumulation near the parallel flow stagnation,
which is located close to the geometrical center of the island (”O-point”). The local cooling in this
region leads to plasma condensation in the islands in closest magnetic connection to the divertor target
plates. The heat source to this region of the island, which is thermally isolated from the upstream heat
source in terms of parallel transport, must arise via perpendicular heat transport. This heat source is
expected to be large for the low iota configuration due to its very small internal island field line pitch.
This work highlights the importance (complementary to previous work, e. g. [5, 6]) of the internal
island field line pitch not only on the radiation pattern, but also the detachment performance of the
island divertor.

Winters, Victoria (ORCID:0000000181087774)↗

Temperature/pressure and water vapor sounding with microwave spectroscopy

Two intense microwave spectra lines exist in the martian atmosphere that allow unique sounding capabilities: water vapor at 183 GHz and the (2-1) rotational line of CO at 230 GHz. Microwave spectra line sounding is a well-developed technique for the Earth's atmosphere for sounding from above from spacecraft and airplanes, and from below from fixed surface sites. Two simple instruments for temperature sounding on Mars (the CO line) and water vapor measurements are described. The surface sounder proposed for the MESUR sites is designed to study the boundary layer water vapor distribution and the temperature/pressure profiles with vertical resolution of 0.25 km up to 1 km with reduced resolution above approaching a scale height. The water channel will be sensitive to a few tenths of a micrometer of water and the temperature profile will be retrieved to an accuracy between 1 and 2 K. The latter is routinely done on the Earth using oxygen lines near 60 GHz. The measurements are done with a single-channel heterodyne receiver looking into a 10-cm mirror that is canned through a range of elevation angles plus a target load. The frequency of the receiver is sweep across the water and CO lines generating the two spectra at about 1-hr intervals throughout the mission. The mass and power for the proposed instrument are 2 kg and 5-8 W continuously. The measurements are completely immune to the atmospheric dust and ice particle loads. It was felt that these measurements are the ultimate ones to properly study the martian boundary layer from the surface to a few kilometers. Sounding from above requires an orbiting spacecraft with multichannel microwave spectrometers such as the instrument proposed for MO by a subset of the authors, a putative MESUR orbiter, and a proposed Discovery mission called MOES. Such an instrument can be built with less than 10 kg and use less than 15 W. The obvious advantage of this approach is that the entire atmosphere can be sounded for temperature and water vapor in a few hours with somewhat better than a scale height resolution. If a bigger mirror is used (greater than 30 cm) limb sounding geometry can be employed and half scale height resolution achieved to altitudes up to at least 60 km. Again, the measurements are immune to dust and ice loads. Water vapor sensitivity of 0.1 micrometer can be achieved (even with a nadir instrument) and temperature profiles retrieved to an accuracy of better than 2 K from the surface to about 60 km. Winds can be measured from the doppler shifts of CO lines in the limb sounding mode.

Muhleman, D. O.↗

Demonstrations that the Solar Wind Is Not Accelerated by Waves

The present work uses both observations and theoretical considerations to show that hydromagnetic waves cannot produce the acceleration of the fast solar wind and the related heating of the open solar corona. Waves do exist, and can play a role in the differential heating and acceleration of minor ions, but their amplitudes are not sufficient to power the wind, as demonstrated by extrapolation of magnetic spectra from Helios and Ulysses observations. Dissipation mechanisms invoked to circumvent this conclusion cannot be effective for a variety of reasons. In particular, turbulence does not play a strong role in the corona as shown by both observations of coronal striations and theoretical considerations of line-tying to a nonturbulent photosphere, nonlocality of interactions, and the nature of the kinetic dissipation. In the absence of wave heating and acceleration, the chromosphere and transition region become the natural source of open coronal energization. We suggest a variant of the 'velocity filtration' approach in which the emergence and complex churning of the magnetic flux in the chromosphere and transition region continuously and ubiquitously produces the nonthermal distributions required. These particles are then released by magnetic carpet reconnection at a wide range of scales and produce the wind as described in kinetic approaches. Since the carpet reconnection is not the main source of the energization of the plasma, there is no expectation of an observable release of energy in nanoflares.

Roberts, Aaron↗

Observational and Theoretical Challenges to Wave or Turbulence Accelerations of the Fast Solar Wind

We use both observations and theoretical considerations to show that hydromagnetic waves or turbulence cannot produce the acceleration of the fast solar wind and the related heating of the open solar corona. Waves do exist as shown by Hinode and other observations, and can play a role in the differential heating and acceleration of minor ions but their amplitudes are not sufficient to power the wind, as demonstrated by extrapolation of magnetic spectra from Helios and Ulysses observations. Dissipation mechanisms invoked to circumvent this conclusion cannot be effective for a variety of reasons. In particular, turbulence does not play a strong role in the corona as shown by both eclipse observations of coronal striations and theoretical considerations of line-tying to a nonturbulent photosphere, nonlocality of interactions, and the nature of kinetic dissipation. In the absence of wave heating and acceleration, the chromosphere and transition region become the natural source of open coronal energization. We suggest a variant of the velocity filtration approach in which the emergence and complex churning of the magnetic flux in the chromosphere and transition region continuously and ubiquitously produces the nonthermal distributions required. These particles are then released by magnetic carpet reconnection at a wide range of scales and produce the wind as described in kinetic approaches. Since the carpet reconnection is not the main source of the energization of the plasma, there is no expectation of an observable release of energy in nanoflares.

Roberts, D. Aaron↗