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NASA NTRS2011

Binary-Signal Recovery

Binary communication through long cables, opto-isolators, isolating transformers, or repeaters can become distorted in characteristic ways. The usual solution is to slow the communication rate, change to a different method, or improve the communication media. It would help if the characteristic distortions could be accommodated at the receiving end to ease the communication problem. The distortions come from loss of the high-frequency content, which adds slopes to the transitions from ones to zeroes and zeroes to ones. This weakens the definition of the ones and zeroes in the time domain. The other major distortion is the reduction of low frequency, which causes the voltage that defines the ones or zeroes to drift out of recognizable range. This development describes a method for recovering a binary data stream from a signal that has been subjected to a loss of both higher-frequency content and low-frequency content that is essential to define the difference between ones and zeroes. The method makes use of the frequency structure of the waveform created by the data stream, and then enhances the characteristics related to the data to reconstruct the binary switching pattern. A major issue is simplicity. The approach taken here is to take the first derivative of the signal and then feed it to a hysteresis switch. This is equivalent in practice to using a non-resonant band pass filter feeding a Schmitt trigger. Obviously, the derivative signal needs to be offset to halfway between the thresholds of the hysteresis switch, and amplified so that the derivatives reliably exceed the thresholds. A transition from a zero to a one is the most substantial, fastest plus movement of voltage, and therefore will create the largest plus first derivative pulse. Since the quiet state of the derivative is sitting between the hysteresis thresholds, the plus pulse exceeds the plus threshold, switching the hysteresis switch plus, which re-establishes the data zero to one transition, except now at the logic levels of the receiving circuit. Similarly, a transition from a one to a zero will be the most substantial and fastest minus movement of voltage and therefore will create the largest minus first derivative pulse. The minus pulse exceeds the minus threshold, switching the hysteresis switch minus, which re-establishes the data one to zero transition. This innovation has a large increase in tolerance for the degradation of the binary pattern of ones and zeroes, and can reject the introduction of noise in the form of low frequencies that can cause the voltage pattern to drift up or down, and also higher frequencies that are beyond the recognizable content in the binary transitions.

Griebeler, Elmer L.↗

NASA NTRS2006

Noise Source for Calibrating a Microwave Polarimeter

A correlated-noise source has been developed for use in calibrating an airborne or spaceborne Earth-observing correlation microwave polarimeter that operates in a in a pass band that includes a nominal frequency of 10.7 GHz. Deviations from ideal behavior of the hardware of correlation polarimeters are such as to decorrelate the signals measured by such an instrument. A correlated-noise source provides known input signals, measurements of which can be processed to estimate and correct for the decorrelation effect.

Piepmeier, Jeffrey R.↗

NASA NTRS2004

NASA Tech Briefs, April 2004

Topics covered include: Analysis of SSEM Sensor Data Using BEAM; Hairlike Percutaneous Photochemical Sensors; Video Guidance Sensors Using Remotely Activated Targets; Simulating Remote Sensing Systems; EHW Approach to Temperature Compensation of Electronics; Polymorphic Electronic Circuits; Micro-Tubular Fuel Cells; Whispering-Gallery-Mode Tunable Narrow-Band-Pass Filter; PVM Wrapper; Simulation of Hyperspectral Images; Algorithm for Controlling a Centrifugal Compressor; Hybrid Inflatable Pressure Vessel; Double-Acting, Locking Carabiners; Position Sensor Integral with a Linear Actuator; Improved Electromagnetic Brake; Flow Straightener for a Rotating-Drum Liquid Separator; Sensory-Feedback Exoskeletal Arm Controller; Active Suppression of Instabilities in Engine Combustors; Fabrication of Robust, Flat, Thinned, UV-Imaging CCDs; Chemical Thinning Process for Fabricating UV-Imaging CCDs; Pseudoslit Spectrometer; Waste-Heat-Driven Cooling Using Complex Compound Sorbents; Improved Refractometer for Measuring Temperatures of Drops; Semiconductor Lasers Containing Quantum Wells in Junctions; Phytoplankton-Fluorescence-Lifetime Vertical Profiler; Hexagonal Pixels and Indexing Scheme for Binary Images; Finding Minimum-Power Broadcast Trees for Wireless Networks; and Automation of Design Engineering Processes.

Source record↗

NASA NTRS2004

Active Suppression of Instabilities in Engine Combustors

A method of feedback control has been proposed as a means of suppressing thermo-acoustic instabilities in a liquid- fueled combustor of a type used in an aircraft engine. The basic principle of the method is one of (1) sensing combustor pressure oscillations associated with instabilities and (2) modulating the rate of flow of fuel to the combustor with a control phase that is chosen adaptively so that the pressure oscillations caused by the modulation oppose the sensed pressure oscillations. The need for this method arises because of the planned introduction of advanced, lean-burning aircraft gas turbine engines, which promise to operate with higher efficiencies and to emit smaller quantities of nitrogen oxides, relative to those of present aircraft engines. Unfortunately, the advanced engines are more susceptible to thermoacoustic instabilities. These instabilities are hard to control because they include large dead-time phase shifts, wide-band noise characterized by amplitudes that are large relative to those of the instabilities, exponential growth of the instabilities, random net phase walks, and amplitude fluctuations. In this method (see figure), the output of a combustion-pressure sensor would be wide-band-pass filtered and then further processed to generate a control signal that would be applied to a fast-actuation valve to modulate the flow of fuel. Initially, the controller would rapidly take large phase steps in order to home in, within a fraction of a second, to a favorable phase region within which the instability would be reduced. Then the controller would restrict itself to operate within this phase region and would further restrict itself to operate within a region of stability, as long as the power in the instability signal was decreasing. In the phase-shifting scheme of this method, the phase of the control vector would be made to continuously bounce back and forth from one boundary of an effective stability region to the other. Computationally, this scheme would be implemented by the adaptive sliding phaser averaged control (ASPAC) algorithm, which requires very little detailed knowledge of the combustor dynamics. In the ASPAC algorithm, the power of the instability signal would be calculated from the wide-bandpass- filtered combustion-pressure signal and averaged over a period of time (typically of the order of a few hundredths of a second) corresponding to the controller updating cycle [not to be confused with the controller sampling cycle, which would be much shorter (typically of the order of 10(exp -4) second)].

Kopasakis, George↗

NASA NTRS2004

Laser-Induced-Fluorescence Photogrammetry and Videogrammetry

An improved method of dot-projection photogrammetry and an extension of the method to encompass dot-projection videogrammetry overcome some deficiencies of dot-projection photogrammetry as previously practiced. The improved method makes it possible to perform dot-projection photogrammetry or videogrammetry on targets that have previously not been amenable to dot-projection photogrammetry because they do not scatter enough light. Such targets include ones that are transparent, specularly reflective, or dark. In standard dot-projection photogrammetry, multiple beams of white light are projected onto the surface of an object of interest (denoted the target) to form a known pattern of bright dots. The illuminated surface is imaged in one or more cameras oriented at a nonzero angle or angles with respect to a central axis of the illuminating beams. The locations of the dots in the image(s) contain stereoscopic information on the locations of the dots, and, hence, on the location, shape, and orientation of the illuminated surface of the target. The images are digitized and processed to extract this information. Hardware and software to implement standard dot-projection photogrammetry are commercially available. Success in dot-projection photogrammetry depends on achieving sufficient signal-to-noise ratios: that is, it depends on scattering of enough light by the target so that the dots as imaged in the camera(s) stand out clearly against the ambient-illumination component of the image of the target. In one technique used previously to increase the signal-to-noise ratio, the target is illuminated by intense, pulsed laser light and the light entering the camera(s) is band-pass filtered at the laser wavelength. Unfortunately, speckle caused by the coherence of the laser light engenders apparent movement in the projected dots, thereby giving rise to errors in the measurement of the centroids of the dots and corresponding errors in the computed shape and location of the surface of the target. The improved method is denoted laser-induced-fluorescence photogrammetry.

Danehy, Paul↗

NASA NTRS2003

Compact, Pneumatically Actuated Filter Shuttle

A compact, pneumatically actuated filter shuttle has been invented to enable alternating imaging of a wind-tunnel model in two different spectral bands characteristic of the pressure and temperature responses of a pressure and temperature-sensitive paint. This filter shuttle could also be used in other settings in which there are requirements for alternating imaging in two spectral bands. Pneumatic actuation was chosen because of a need to exert control remotely (that is, from outside the wind tunnel) and because the power leads that would be needed for electrical actuation would pose an unacceptable hazard in the wind tunnel. The entire shuttle mechanism and its housing can be built relatively inexpensively [<$500 (prices as of year 2000)] from off-the-shelf parts. The shuttle mechanism (see Figure 1) is contained in a housing that has dimensions of 4 by 6 by 2 in. (about 10 by 15 by 5 cm). Two 2-in. (=5-cm)-diameter standard scientific-grade band-pass filters are mounted on sliding panels in a dual-track frame. The mechanism is positioned and oriented so the panels slide sideways with respect to the optical axis of a charge-coupled-device camera used for viewing the wind-tunnel model. The mechanism includes a pneumatic actuator connected to a linkage. The linkage converts the actuator stroke to a scissor-like motion that places one filter in front of the camera and the other filter out of the way. Optoelectronic sensors detect tabs on the sliding panels for verification of the proper positioning of the filters.

Leighy, Bradley D.↗

NASA NTRS2011

The Role of African Easterly Wave on Dust Transport and the Interaction Between Saharan Dust Layer and Atlantic ITCZ During Boreal Summer

Saharan dust outbreaks not only transport large amount of dust to the northern Atlantic Ocean, but also alter African easterly jet and wave activities along the jet by changing north-south temperature gradient. Recent modeling and observational studies show that during periods of enhance outbreaks, rainfall on the northern part of ITCZ increases in conjunction with a northward shift of ITCZ toward the dust layer. In this paper, we study the radiative forcing of Saharan dust and its interactions with the Atlantic Inter-tropical Convergence Zone (ITCZ), through African easterly waves (AEW), African easterly jet (AEJ), using the Terra/Aqua observations as well as MERRA data. Using band pass filtered EOF analysis, we find that African easterly waves propagating westward along two principal tracks, centered at 15-25N and 5-10N respectively. The easterly waves in the northern track are slower, with propagation speed of 9 ms-1, and highly correlated with major dust outbreak over North Africa. On the other hand, easterly waves along the southern track are faster with propagating speed of 10 ms-1, and are closely tied to rainfall/cloud variations along the Atlantic ITCZ. Dust transport along the southern track leads rainfall/cloud anomalies in the same region by one or two days, suggesting the southern tracks of dust outbreak are regions of strong interaction between Saharan dust layer and Atlantic ITCZ. Possible linkage between two tracks of easterly waves, as well as the long-term change of easterly wave activities and dust outbreaks, are also discussed.

Kim, Kyu-Myong↗

NASA NTRS2012

The Role of African Easterly Wave on Dust Transport and the Interaction Between Saharan Dust Layer and Atlantic ITCZ During Boreal Summer

In this paper, we investigate the relationships among Saharan dust outbreak and transport, African easterly waves (AEW), African easterly jet (AEJ) and associated convective activities of Atlantic Intertropical Convergence Zone (ITCZ) using Cloudsat-Calipso, MODIS and MERRA data. We find that a major Saharan dust outbreak is associated with the formation of a westward propagating strong cyclone around 15-25N over the western part northern Saharan. The strong cyclonic flow mobilizes and lifts the dust from the desert surface to a high elevation. As the cyclone propagate westward, it transports a thick elevated dust layer between 900 -500 hPa from the African continent to the eastern Atlantic. Cloudiness is reduced within the warm, dry dusty layer, but enhanced underneath it, possibly due to the presence of a shallow inversion layer over the marine boundary layer. The dust outbreak is linked to enhanced deep convection in the northern part of Atlantic ITCZ, abutting the southern flank of the dust layer, and a strengthening of the northward flank of the AEJ. As the dust layer spreads westward, it loses elevation and becomes increasing diffused as it reaches the central and western Atlantic. Using band pass filtered EOF analysis of MERRA winds, we find that AEWs propagating westward along two principal tracks, centered at 15-25N and 5-10N respectively. The easterly waves in the northern track are highly correlated with major dust outbreak over North Africa and associated with slower moving systems, with a quasi-periodicity of 6-9 day. On the other hand, easterly waves along the southern track are faster, with quasi-periodicity of 3-5 days. These faster easterly waves are closely tied to rainfall/cloud variations along the Atlantic ITCZ. Dust transport along the southern track by the faster waves generally leads rainfall/cloud anomalies in the same region by one or two days, suggesting the southern tracks of dust outbreak are regions of strong interaction between Saharan dust layer and Atlantic ITCZ.

Lau, William K. M.↗

NASA NTRS2012

Turbulent Statistics from Time-Resolved PIV Measurements of a Jet Using Empirical Mode Decomposition

Empirical mode decomposition is an adaptive signal processing method that when applied to a broadband signal, such as that generated by turbulence, acts as a set of band-pass filters. This process was applied to data from time-resolved, particle image velocimetry measurements of subsonic jets prior to computing the second-order, two-point, space-time correlations from which turbulent phase velocities and length and time scales could be determined. The application of this method to large sets of simultaneous time histories is new. In this initial study, the results are relevant to acoustic analogy source models for jet noise prediction. The high frequency portion of the results could provide the turbulent values for subgrid scale models for noise that is missed in large-eddy simulations. The results are also used to infer that the cross-correlations between different components of the decomposed signals at two points in space, neglected in this initial study, are important.

Dahl, Milo D.↗

NASA NTRS2012

Turbulent Statistics from Time-Resolved PIV Measurements of a Jet Using Empirical Mode Decomposition

Dahl, Milo D.↗

NASA NTRS2013

Turbulent Statistics From Time-Resolved PIV Measurements of a Jet Using Empirical Mode Decomposition

Dahl, Milo D.↗

NASA NTRS2011

Observing Tsunamis in the Ionosphere Using Ground Based GPS Measurements

Ground-based Global Positioning System (GPS) measurements of ionospheric Total Electron Content (TEC) show variations consistent with atmospheric internal gravity waves caused by ocean tsunamis following recent seismic events, including the Tohoku tsunami of March 11, 2011. We observe fluctuations correlated in time, space, and wave properties with this tsunami in TEC estimates processed using JPL's Global Ionospheric Mapping Software. These TEC estimates were band-pass filtered to remove ionospheric TEC variations with periods outside the typical range of internal gravity waves caused by tsunamis. Observable variations in TEC appear correlated with the Tohoku tsunami near the epicenter, at Hawaii, and near the west coast of North America. Disturbance magnitudes are 1-10% of the background TEC value. Observations near the epicenter are compared to estimates of expected tsunami-driven TEC variations produced by Embry Riddle Aeronautical University's Spectral Full Wave Model, an atmosphere-ionosphere coupling model, and found to be in good agreement. The potential exists to apply these detection techniques to real-time GPS TEC data, providing estimates of tsunami speed and amplitude that may be useful for future early warning systems.

total electron content (TEC)↗

NASA NTRS2013

Inter-Calibration and Concatenation of Climate Quality Infrared Cloudy Radiances from Multiple Instruments

A change in climate is not likely captured from any single instrument, since no single instrument can span decades of time. Therefore, to detect signals of global climate change, observations from many instruments on different platforms have to be concatenated. This requires careful and detailed consideration of instrumental differences such as footprint size, diurnal cycle of observations, and relative biases in the spectral brightness temperatures. Furthermore, a common basic assumption is that the data quality is independent of the observed scene and therefore can be determined using clear scene data. However, as will be demonstrated, this is not necessarily a valid assumption as the globe is mostly cloudy. In this study we highlight challenges in inter-calibration and concatenation of infrared radiances from multiple instruments by focusing on the analysis of deep convective or anvil clouds. TRMM/VIRS is potentially useful instrument to make correction for observational differences in the local time and foot print sizes, and thus could be applied retroactively to vintage instruments such as AIRS, IASI, IRIS, AVHRR, and HIRS. As the first step, in this study, we investigate and discuss to what extent AIRS and VIRS agree in capturing deep cloudy radiances at the same local time. The analysis also includes comparisons with one year observations from CrIS. It was found that the instruments show calibration differences of about 1K under deep cloudy scenes that can vary as a function of land type and local time of observation. The sensitivity of footprint size, view angle, and spectral band-pass differences cannot fully explain the observed differences. The observed discrepancies can be considered as a measure of the magnitude of issues which will arise in the comparison of legacy data with current data.

cloudy radiance↗

NASA NTRS2010

Observing Traveling Ionospheric Disturbances Caused by Tsunamis Using GPS TEC Measurements

Ground-based Global Positioning System (GPS) measurements of ionospheric Total Electron Content (TEC) show variations consistent with atmospheric internal gravity waves caused by ocean tsunamis following two recent seismic events: the American Samoa earthquake of September 29, 2009, and the Chile earthquake of February 27, 2010. Fluctuations in TEC correlated in time, space, and wave properties with these tsunamis were observed in TEC estimates processed using JPL's Global Ionospheric Mapping Software. These TEC estimates were band-pass filtered to remove ionospheric TEC variations with wavelengths and periods outside the typical range of internal gravity waves caused by tsunamis. Observable variations in TEC appear correlated with the tsunamis in certain locations, but not in others. Where variations are observed, the typical amplitude tends to be on the order of 1% of the background TEC value. Variations with amplitudes ~ 0.1 - 0.2 TECU are observable with periods and timing affiliated with the tsunami. These observations are compared to estimates of expected tsunami-driven TEC variations produced by Embry Riddle Aeronautical University's Spectral Full Wave Model, an atmosphere-ionosphere coupling model, and found to be in good agreement in some locations, though there are cases when the model predicts an observable tsunami-driven signature and none is observed. These TEC variations are not always seen when a tsunami is present, but in these two events the regions where a strong ocean tsunami was observed did coincide with clear TEC observations, while a lack of clear TEC observations coincided with smaller tsunami amplitudes. There exists the potential to apply these detection techniques to real-time GPS TEC data, providing estimates of tsunami speed and amplitude that may be useful for early warning systems.

Galvan, David A.↗

NASA NTRS2016

Ocular Vestibular Evoked Myogenic Potentials Using Head Striker Stimulation

Introduction: Over the last two decades, several studies have been published on the impact of long-duration (i.e., 22 days or longer) spaceflight on the central nervous system (CNS). In consideration of the health and performance of crewmembers in flight and post-flight, we are conducting a controlled prospective longitudinal study to investigate the effects of spaceflight on the extent, longevity and neural bases of sensorimotor, cognitive, and neural changes. Multiple studies have demonstrated the effects of spaceflight on the vestibular system. One of the supporting tests conducted in this protocol is the Vestibular Evoked Myogenic Potential (VEMP) test that provides a unilateral measure of otolith (saccule and utricle) function. A different approach was taken for ocular VEMP (oVEMP) testing using a head striker system (Wackym et al. 2012). The oVEMP is generally considered to be a measure of utricle function. The the otolithic input to the inferior oblique muscle is predominately from the utricular macula. Thus, quantitatively, oVEMP tests utricular function. Another practical extension of these relationships is that the oVEMP reflects the superior vestibular nerve function. Methods: Ground testing was administered on 16 control subjects and for 8 subjects over four repeated sessions spanning 70 days. The oVEMP was elicitied via a hand held striker by a vibrotactile pulse presented at the rate of 1 Hz for 24 seconds on the side of the head as subjects lay supine on a gurney. Subjects were directed to gaze approximately 25 degrees above straight ahead in semi-darkness. For the oVEMP electromyograms will be recorded with active bipolar electrodes (Delsys Inc., Boston, MA) on the infra-orbital ridge 1 cm below the eyelid with a reference electrode on the below the knee cap. The EMG potentials were amplified; band-pass filtered using a BagnoliTM Desktop EMG System (Delsys Inc., Boston, MA, USA). This EMG signal is sampled at 10 kHz and the data stimulus onset to 100 MS was averaged over 24 trial repetitions for the vibrotactile VEMP. The typical oVEMP EMG response is an excitatory potential with first peak occurring at 11-12 ms and second peak at 18 ms. This requires a total recording time of approximately 29 seconds per trial which includes 5 seconds of no vibrotactile stimulation at the beginning of the protocol. The primary dependent measures consist of the latency and peak-to-peak amplitude from the EMG signals, which will be normalized to EMG levels at the beginning of the protocol. Data were collected for 3 repeated trials with striker stimulation on both the left and right side of the head Results: The oVEMP p1 range was observed at 3-14 ms and n1 at 7-19 ms. The striker system provided a consistent and rapid method for oVEMP testing. Discussion: Crew testing is in progress to determine changes in results between pre and post flight.

De Dios, Y. E.↗

NASA NTRS2016

Improving Photometric Calibration of Meteor Video Camera Systems

We present the results of new calibration tests performed by the NASA Meteoroid Environment Oce (MEO) designed to help quantify and minimize systematic uncertainties in meteor photometry from video camera observations. These systematic uncertainties can be categorized by two main sources: an imperfect understanding of the linearity correction for the MEO's Watec 902H2 Ultimate video cameras and uncertainties in meteor magnitudes arising from transformations between the Watec camera's Sony EX-View HAD bandpass and the bandpasses used to determine reference star magnitudes. To address the rst point, we have measured the linearity response of the MEO's standard meteor video cameras using two independent laboratory tests on eight cameras. Our empirically determined linearity correction is critical for performing accurate photometry at low camera intensity levels. With regards to the second point, we have calculated synthetic magnitudes in the EX bandpass for reference stars. These synthetic magnitudes enable direct calculations of the meteor's photometric ux within the camera band-pass without requiring any assumptions of its spectral energy distribution. Systematic uncertainties in the synthetic magnitudes of individual reference stars are estimated at 0:20 mag, and are limited by the available spectral information in the reference catalogs. These two improvements allow for zero-points accurate to 0:05 􀀀 0:10 mag in both ltered and un ltered camera observations with no evidence for lingering systematics.

Ehlert, Steven↗

NASA NTRS2016

Design and Deployment of a Multichroic Polarimeter Array on the Atacama Cosmology Telescope

We present the design and the preliminary on-sky performance with respect to beams and pass bands of a multichroic polarimeter array covering the 90 and 146 GHz cosmic microwave background bands and its enabling broad-band optical system recently deployed on the Atacama Cosmology Telescope (ACT). The constituent pixels are feedhorn-coupled multichroic polarimeters fabricated at NIST. This array is coupled to the ACT telescope via a set of three silicon lenses incorporating novel broad-band metamaterial anti-reflection coatings. This receiver represents the first multichroic detector array deployed for a CMB experiment and paves the way for the extensive use of multichroic detectors and broad-band optical systems in the next generation of CMB experiments.

passbands↗

NASA NTRS2016

Photospheric Current Spikes and Their Possible Association with Flares - Results from an HMI Data Driven Model

A data driven, near photospheric magnetohydrodynamic model predicts spikes in the horizontal current density, and associated resistive heating rate per unit volume Q. The spikes appear as increases by orders of magnitude above background values in neutral line regions (NLRs) of active regions (ARs). The largest spikes typically occur a few hours to a few days prior to M or X flares. The spikes correspond to large vertical derivatives of the horizontal magnetic field. The model takes as input the photospheric magnetic field observed by the Helioseismic & Magnetic Imager (HMI) on the Solar Dynamics Observatory (SDO) satellite. This 2.5 D field is used to determine an analytic expression for a 3 D magnetic field, from which the current density, vector potential, and electric field are computed in every AR pixel for 14 ARs. The field is not assumed to be force-free. The spurious 6, 12, and 24 hour Doppler periods due to SDO orbital motion are filtered out of the time series of the HMI magnetic field for each pixel using a band pass filter. The subset of spikes analyzed at the pixel level are found to occur on HMI and granulation scales of 1 arcsec and 12 minutes. Spikes are found in ARs with and without M or X flares, and outside as well as inside NLRs, but the largest spikes are localized in the NLRs of ARs with M or X flares. The energy to drive the heating associated with the largest current spikes comes from bulk flow kinetic energy, not the electromagnetic field, and the current density is highly non-force free. The results suggest that, in combination with the model, HMI is revealing strong, convection driven, non-force free heating events on granulation scales, and that it is plausible these events are correlated with subsequent M or X flares. More and longer time series need to be analyzed to determine if such a correlation exists. Above an AR dependent threshold value of Q, the number of events N(Q) with heating rates greater than or equal to Q obeys a scale invariant power law distribution for each AR given by N(Q) varies Q(sup -s), where 0.40 less than or equal to S less than or equal to 0.53, with a mean and standard deviation across the 14 ARs of 0.47 and 0.045, showing there is little variation of S from one AR to another. These properties of N(Q) are in close agreement with those of the distribution N(E) for the total energy E of solar flares, determined from observations to be N(E) = constant x E(sup -alpha). From observations of nanoflares in the 0.7 to 4 MK range, and from observations of flares in hard X-rays, it is found that 0.51 less than or equal to alpha less than or equal to 0.57, and 0.4 less than or equal to alpha less than or equal to 0.6, respectively (Crosby et al. 1993, Sol. Phys., 143, 275; Aschwanden & Parnell 2002, ApJ, 572, 1048). Observations also show that, as is found here for the exponent S, there is little variation of alpha with AR (Wheatland 2000, ApJ, 532, 1209), indicating N(E) and N(Q) are largely independent of individual properties of ARs such as area, total magnetic flux, and distribution of current density (i.e. non-potentiality). Therefore the power law scaling of the photospheric heating rate Q computed here on granulation scales is essentially identical to that found for coronal observations of flare energies on scales 1-2 orders of magnitude larger. This suggests the physical mechanisms that cause Q and coronal flares are closely related. It seems likely that Q is the signature of a magnetic reconnection process in an energy range and volume orders of magnitude smaller than those of flares. In this context, at least the larger spikes in Q might be signatures of UV photospheric or lower chromospheric bombs in which plasma is heated to temperatures approximately 10(exp -5) K (Peter et al. 2014, Science 346, 1255726; Judge 2015, ApJ, 808, 116). In addition, lattice based avalanche simulations of flare energy release predict 0.4 less than or equal to alpha less than or equal to 0.5, while analytic, fractal-diffusive self-organized criticality models predict 0.4 less than or equal to alpha less than or equal to 0.67, in excellent agreement with observations, and the results presented here (Aschwanden & Parnell 2002, ApJ, 572, 1048; Aschwanden 2012, A&A, 539, A2; Aschwanden 2013, in "Self Organized Criticality Systems"; Aschwanden et al. 2016, SSR, 198, 47).

Goodman, Michael↗