Energy Buildup Research Articles

Electrical energy and overpressure characterization of aeronautical fasteners submitted to a lightning current waveform

Understanding and controlling sparking in fasteners and jointed structures is crucial for flight safety, particularly in fuel tanks. This study investigates the relationship between dissipated electrical energy and pressure buildup within fastener cavities during lightning strikes. Experiments were performed on fasteners installed in aluminum and Carbon Fiber Reinforced Polymer (CFRP) samples, with lightning current waveforms ranging from 1 kA to 10 kA. A sensitivity analysis evaluated the influence of key parameters, such as current peak, clearance fit, sample material, polarity, and fastener coating on pressure rise and energy dissipation. Electrical energy up to 80 J and pressure levels reaching 600 bar– unprecedented compared to prior studies– were observed. The pressure-energy relationship showed an approximately linear trend, while pressure exhibited a non-linear dependence on clearance fit. Fastener coating and sample material were found to significantly influence the results, with pressure variations reaching up to a factor of 10 in some cases

Mass Inflation without Cauchy Horizons.

Mass inflation is a well established instability, conventionally associated to Cauchy horizons (which are also inner trapping horizons) of stationary geometries, leading to a divergent exponential buildup of energy. We show here that finite (but often large) exponential buildups of energy are present for dynamical geometries describing accreting black holes with slowly evolving inner trapping horizons, even in the absence of Cauchy horizons. The explicit evaluation of the adiabatic conditions behind these exponential buildups shows that this phenomenon is universally present for physically reasonable accreting conditions. This noneternal mass inflation does not require the introduction of global spacetime concepts. We also show that various known results in the literature are recovered in the limit in which the inner trapping horizon asymptotically approaches a Cauchy horizon. Our results imply that black hole geometries with nonextremal inner horizons, including the Kerr geometry in general relativity, and nonextremal regular black holes in theories beyond general relativity, can describe dynamical transients but not the long-lived end point of gravitational collapse.

Excess Energy Released Due To Proton-Proton Collisions in Condensed Matter Could Be Due To Laboratory-Made Micro Black Holes

While sodium metal dissolution in concentrated (2M) Epsom solution is very peaceful under stirring conditions in about 5 to 10s, its dissolution in a dilute (0.85) Epsom solution has turned very violent. Nearly 30s after the addition of Na, the solution exploded accompanied by the vaporization of the glass beaker. Only sodium aerosol and tiny molten needles of glass were seen around indicating a very high temperature (>1000 0C) has indeed been reached. The timing of the explosion has indicated that hydrogen released during sodium dissolution has got trapped in the salt solution and subsequent energy build-up has caused the excess energy release. A viable trapping mechanism involving the exchange of 2 hydrogen ions (H22+) with an Mg2+ ion in cavitation-induced nanocrystals of Epsom has been proposed in this regard. The two hydrogen ions are stabilized at the cation vacancy (cavity) by dative bonds with the two hydrogen ions in the water molecule trapped at a neighboring sulphate vacancy. Spring-like action between the two protons trapped at the cation vacancy due to oscillations caused by two opposing forces – one by cavitation and the other by coulombic repulsion eventually appear to have led to the collision of hydrogen ions at relativistic speeds in condensed matter. To start with, the two protons in the H22+ species are confined in a small space (72 pm cavity) at a single crystal cation lattice site in Na2SO4 nanocrystal which increases their head-on collision probability at high energies. There is no upper limit to the energies achieved through p-p collisions in this species as the Cavitation-Coulombic Repulsion Oscillations (CCRO) can continue until the endpoint is reached. Regeneration of a nanocrystal over a sufficiently small time scale and regeneration effect prior to cavitation collapse are all important so laws of thermodynamics are not violated. Extra dimensions of gravity at short distances, if present, could also assist in the high energies required for the production of mini black holes in condensed matter. Such black holes lose mass very quickly through the emission of Hawking radiation observed in the form of explosion with mass-energy equivalence of E = mc2. The possibility of tapping such explosive energy for peaceful purposes is discussed. As such it constitutes the third kind of atomic energy humans have entertained, the first two being fission and fusion.

First-principles investigation on the structural, optical, and laser-induced damage characteristics of boron impurity and boron-oxygen defect cluster in potassium dihydrogen phosphate crystals

The DFT+U method combined with HSE06 hybrid functional and finite-size correction has been employed to investigate the defect formation energies, lattice modifications and optical spectra of Potassium Dihydrogen Phosphate (KDP) crystals with Boron. The B defects contain the B interstitials (Bi), the B substituted P sites (BP), and the boron-oxygen defect clusters ([BP+VO]). The results demonstrate that these B defects can trigger lattice distortions. The BP and [BP+VO] have a minor lattice change rate and greater stability, while Bi has a relatively large local distortion inducing crystal damage. We have also utilized conformational coordinate diagrams to explore the optical absorption/emission processes arising from B defects. The BP and [BP+VO] were found to generate absorption peaks at 330 nm and 255 nm, while the Bi leads to absorption peaks near the absorption edge. The absorption peaks within the near-ultraviolet range might have an energy buildup at the defects, which would decrease laser utilization and harm the crystal.

Green synthesized Cr2O3/Bi2O3 nanocomposites for gamma ray shielding

The quest for advanced materials in gamma radiation shielding has spurred the exploration of environmentally friendly, nanotechnology-based approaches. This study introduces a novel synthesis of Cr2O3/Bi2O3 nanocomposites (NCs) using the solution combustion method, with Aloe vera extract serving as a natural reducing agent. Comprehensive analytical characterization of the synthesized NCs was conducted using powder X-ray diffraction (PXRD), scanning electron microscopy (SEM), energy-dispersive X-ray spectroscopy (EDS), Fourier-transform infrared spectroscopy (FTIR), and ultraviolet–visible (UV–Vis) spectroscopy. The gamma radiation shielding properties of the Cr2O3/Bi2O3 NCs are evaluated using a NaI(Tl) detector connected to a multichannel analyzer. Key shielding parameters, including mass attenuation coefficients, mean free path, half-value layer, tenth-value layer, energy buildup factor, and radiation protection efficiency, indicate that Cr2O3/Bi2O3 NCs are highly effective in gamma radiation shielding. The results demonstrated the feasible shielding performance of these nanocomposites across various energies within error limits of 5 %. This study highlights the potential of Cr2O3/Bi2O3 NCs as a promising, sustainable alternative to conventional shielding materials, offering enhanced gamma radiation protection with reduced environmental impact.

Investigation of structural, optical characteristics of Gd3+ doped phosphate glass for radiation shielding applications

Gadolinium doped phosphate glass was created with a composition of 70 P2O5 + 5Al2O3 + 5 Ba2CO3 + 9 KF2 + 5 MnO2 + 5 SnO+1 Gd2O3 by using the melt-quenching process. The prepared glass sample’s amorphous nature was confirmed by the X-ray diffraction analysis. FT-IR examination confirms the presence of phosphate functional groups. Glass’s optical band gap was found to be 3.5 eV using Tauc’s plot method. The photoluminescence analysis indicates that the emission band at around 311 nm. The Commission International de I’Eclairage (CIE) was employed. It was identified that the computed chromaticity coordinate values (x = 0.3164 and y = 0.3371) were situated in the summer sunlight zone, close to the white light region. The attenuation capabilities of the gadolinium-doped phosphate glass sample were validated by the gamma ray shielding parameters. The mass attenuation coefficient and Mean free path of the prepared glass were fund to be 4.41 × 105 cm2/g at 0.015 MeV and 12.4 cm at 15 MeV respectively. In terms of infiltration deepness up to 40 MFP, the energy-related energy buildup factor (EBF) and energy absorption buildup factor (EABF) of glasses were calculated using the five (a, b, c, d, and Xk) parameters of the G-P fitting scheme. All of the results show that the synthetic glass can be used as shielding materials against gamma radiation.

Rapid calibration plan for NIF's Near Backscatter Imager (NBI).

A rapid calibration system is under development for the Near Backscatter Imager (NBI) in use at the National Ignition Facility (NIF). NBI is an optical diagnostic that quantifies the stimulated Brillouin and Raman backscatter produced by NIF's targets. Specifically, NBI measures the light that does not fall directly back into the laser aperture, which is measured by the Full Aperture Backscatter System (FABS). When working in tandem with FABS, NBI allows for the full characterization of backscattered light. This informs Hohlraum laser coupling, optical damage, and laser-plasma interaction models. NBI uses a large Spectralon plate covered by a protective glass layer and is mounted inside the target chamber where it is exposed to high energy backscatter, neutrons, and build-up debris left over from the exploded targets. This gradually alters the reflectivity of the plate, meaning that NBI needs to be calibrated regularly. Described here is NIF's design for a system capable of rapid in situ calibration of NBI that is to be installed in FY25.

Design and characterization of borosilicate glass modified with TiO2 for enhanced optical and radiation shielding applications

This work investigates the potential of borosilicate glass doped with titanium dioxide (TiO2) for radiation shielding applications. The study explored the impact of varying TiO2 concentrations on the glass structure, optical properties, and radiation shielding effectiveness. X-ray diffraction (XRD) and Raman spectroscopy confirmed the amorphous nature of the glasses. The addition of TiO2 affected the glass network structure, as evidenced by changes in the Raman spectra and density measurements. UV–Vis spectroscopy revealed a red shift in the absorption edge (416–481 nm) and a decrease in the indirect optical band gap (2.91–2.70 eV) with increasing TiO2 content. The refractive index also increased from 2.54 to 3.54 with TiO2 concentration. The mass attenuation coefficient (MAC) and linear attenuation coefficient (LAC) increased significantly with TiO2 addition, indicating enhanced radiation attenuation capability. The inclusion of TiO2 reduced the half-value layer (HVL), tenth-value layer (TVL), and mean free path (MFP), while increasing the effective atomic number (Zeff). The effective electron density (Neff) and effective conductivity (Ceff) showed a slight increase with TiO2 content. Energy build-up factors (EBF and EABF) indicated a higher rate of radiation intensity increase and energy absorption within the glass due to the presence of TiO2. Finally, the incorporation of TiO2 into borosilicate glass offered a promising approach to developing improved optical and radiation shielding glasses.

No Black Holes from Light.

We show that it is not possible to concentrate enough light to precipitate the formation of an event horizon. We argue that the dissipative quantum effects coming from the self-interaction of light (such as vacuum polarization) are enough to prevent any meaningful buildup of energy that could create a black hole in any realistic scenario.

Predominance of Yb3+ and Ce3+ on the AlTaBaBO: Yb and BaTiSbBPO: Ce glasses for effective photoluminescence and radiation shielding properties towards w-LED and γ-ray shielding applications

Alumino tantalum barium borate - 65B2O3 +10Al2O3 +5SrCO3 +5BaCO3 +14Li2CO3 +4Ta2O5 +1Yb2O3 (AlTaBaBO: Yb) and barium antimony borophosphate - 35P2O5 +35B2O3 +10TiO2 +5 KF +10Li2CO3 +4SbO3 +1CeO3 (BaTiSbBPO: Ce) glasses were prepared using melt – quenching technique. The structural property of as-prepared glass materials is investigated by powder X–ray diffraction to identify the amorphous nature of the materials. FTIR and FT-Raman spectroscopic analyses examined various functional groups of glasses. The linear optical behaviours were characterized using UV–visible spectroscopy, and besides the different linear optical parameters such as refractive index and optical bandgap, optical conductivity was estimated. Excitation and emission spectra of the harvested glasses were characterized using a Photoluminescence spectrophotometer. Rare earth – R.E (Yb3+ and Ce3+) doped both glasses have greater emission efficiency due to their 2F7/2 → 2F5/2 (951 nm) and 5d1 → 2F5/2, 2F7/2 (550 and 663 nm) electronic transitions, which shows that the as-prepared glass materials have their potential applications. Colour chromaticity (CIE) diagrams of the cultivated glasses were examined with colour co – ordinations x = 0.3054, y = 0.2881 for AlTaBaBO: Yb and x = 0.3874, y = 0.3436 for BaTiSbBPO: Ce and the obtained outcomes confirmed w-LED device fabrication. Moreover, the various γ– ray shielding parameters were analyzed theoretically using Phy-X software. The five (a, b, c, d, and Xk) parameters of the Geometric Progression (G-P) fitting scheme were used to determine the energy-related energy buildup factor (EBF) as well as energy absorption buildup factor (EABF) of glasses in terms of infiltration deepness up to 40 mfp. At lower photon energy, the AlTaBaBO: Yb and BaTiSbBPO: Ce glasses have the highest μ/ρ values of 4.47 × 105 cm2/g and 3.864 × 103 cm2/g, respectively. For AlTaBaBO: Yb and BaTiSbBPO: Ce glasses, the calculated mean free path (MFP) values at 15 MeV photon energy are 0.143 cm and 12.18 cm, respectively. The result of all findings reveals that the synthesised glasses are viable materials for the futuristic utilization of w-LED and neutron radiation shielding applications.

Solar Eruptions in Nested Magnetic Flux Systems

The magnetic topology of erupting regions on the Sun is a key factor in the energy buildup and release, and the subsequent evolution of flares and coronal mass ejections (CMEs). The presence/absence of null points and separatrices dictates whether and where current sheets form and magnetic reconnection occurs. Numerical simulations show that energy buildup and release via reconnection in the simplest configuration with a null, the embedded bipole, is a universal mechanism for solar eruptions. Here we demonstrate that a magnetic topology with nested bipoles and two nulls can account for more complex dynamics, such as failed eruptions and CME–jet interactions. We investigate the stalled eruption of a nested configuration on 2013 July 13 in NOAA Active Region 11791, in which a small bipole is embedded within a large transequatorial pseudo-streamer containing a null. In the studied event, the inner active region erupted, ejecting a small flux rope behind a shock accompanied by a flare; the flux rope then reconnected with pseudo-streamer flux and, rather than escaping intact, mainly distorted the pseudo-streamer null into a current sheet. EUV and coronagraph images revealed a weak shock and a faint collimated outflow from the pseudo-streamer. We analyzed Solar Dynamics Observatory and Solar TErrestrial RElations Observatory observations and compared the inferred magnetic evolution and dynamics with three-dimensional magnetohydrodynamics simulations of a simplified representation of this nested fan-spine system. The results suggest that the difference between breakout reconnection at the inner null and at the outer null naturally accounts for the observed weak jet and stalled ejection. We discuss the general implications of our results for failed eruptions.

Reinforcement learning-based energy storage management in smart grids

This study investigates the use of reinforcement learning (RL) techniques as a dynamic control mechanism to enhance the management of energy storage in smart grid systems. The research aims to optimize the efficiency of energy storage operations by analyzing collected data from different time intervals in a simulated smart grid scenario. An evaluation of the energy storage status reveals a consistent upward trend in the quantity of stored energy, with a 30% cumulative growth across time intervals. An examination of the demand and supply of the grid indicates a persistent insufficiency of energy, with an average shortfall of 15% in meeting the requirements of the system. Through the use of reinforcement learning (RL) methodologies, the system exhibits a remarkable 450% improvement in cumulative rewards, providing substantiation of its capacity to acquire knowledge and adjust its behavior over time. The system's actions indicate a purposeful shift in strategy, with 75% of instances involving charging procedures, emphasizing a commitment to energy preservation and the buildup of stored energy. Despite a shift in approach, persistent disparities between grid demand and supply need the implementation of more accurate technologies for effective energy management. The findings highlight the effectiveness of using reinforcement learning (RL) for managing energy storage in smart grids. This approach improves energy reserves and optimizes energy storage by altering actions accordingly. These insights contribute to the advancement of adaptive energy management strategies, resulting in the development of sustainable and resilient smart grid infrastructures.

Energy build-up factors estimation for BaZr0.10Ti0.90O3, Ba0.90La0.10TiO3 and Ba0.90La0.10Zr0.10Ti0.90O3 ceramics in shielding applications

The search for materials that serve as good shields for radiation has become very important in light of the increasing exposure to ionizing radiation in various vital sectors. The aim is to search for novel materials with better radiation shielding properties that are stable, nontoxic, and abundant and environment friendly. The solid-state reaction approach has been used to synthesize a few ceramics, including BaZrXTi1-XO3, Ba1-XLaXTiO3 and Ba1-XLaXZrXTi1-XO3 (with x = 0.10) i.eBaZr0.10Ti0.90O3 (BZT), Ba0.90La0.10TiO3 (BLT), and Ba0.90La0.10Zr0.10Ti0.90O3 (BLZT). The density of the prepared samples varies from 6.3471 to 11.6003 g/cm3. The X-ray diffraction technique, shows strong peaks to confirm the crystalline structure of prepared ceramic samples. Using the G-P fitting approach, the advanced radiation shielding parameters (build-up factor) have been evaluated in the photon energy region of 1.5 keV–15 MeV. It is observed from the results that exposure buildup factor (EBF) and energy absorption buildup factor (EABF) are maximum for BLZT and has the minimum value for BZT in the entire photon energy regime. The results of this work should be useful in radiation shielding applications such as in industry, medicine, and nuclear engineering.

The impact of global warming on polar marine life

The global region is currently facing enormous environmental issues of global warming, which is affecting the entire Earth's ecosystem, especially the natural environment of the oceans. Global warming is a natural phenomenon caused by energy imbalances caused by the cumulative greenhouse effect absorbed and released by the terrestrial air system. The ongoing energy buildup in the terrestrial air system has led to rising temperatures and global warming. Natural disasters and biological chain fracturing are just two examples of the dangers that climate change poses to various facets of humanity. The primary cause of this phenomena is one of the key causes of global farming. In addition, it poses a major threat to the equilibrium of natural ecosystems because of the astounding amount of carbon dioxide emissions produced annually, which directly contributes to an increase in atmospheric carbon dioxide levels. Climate change on the surface of the Earth is a direct outcome of this "greenhouse effect." Environmental pollution, which is getting worse every day, has grown to be a significant global issue and is one of the main causes of global warming. Today, studies on global climate change have amply demonstrated that the Earth's surface temperature has been increasing since the end of the last century. At the same time, this phenomenon has had a significant impact and harm on human survival.

A comparative study on the oxidation behavior and failure mechanisms of conventional NiCoCrAl alloy and in-situ composite AlCoCrFeNi2.1 eutectic high-entropy alloy at 1300 °C

We present a comparative study on oxidation behavior and failure mechanisms of conventional NiCoCrAl alloys doped with Y and Hf (CNA) and in-situ composite AlCoCrFeNi2.1 eutectic high-entropy alloy doped with Y and Hf (ISC-EHEA) at 1300 °C. We demonstrate that the ISC-EHEA has much stronger resistance to surface rumpling and oxide spallation than CNA. Hybrid molecular dynamics (MD) and Monte Carlo (MC) simulations show that the diffusion coefficients of the metal elements in the Al-depletion layer of the ISC-EHEA are 50 % lower than those in the CNA. The low diffusion coefficients lead to low growth stress in the thermally grown Al2O3 scale on the ISC-EHEA and improve the creep resistance of the metal in contact with the scale, thus preventing the occurrence of rumpling. The oxidation rate constant of the ISC-EHEA is ∼32 % lower in comparison to those of the CNA, which is attributed to the coarser columnar Al2O3 grains that effectively mitigate grain boundary diffusion. The rumpling-free metal/oxide interface, the low residual stress and the low oxide growth rate for the ISC-EHEA result in strong resistance to scale spallation. Owing to the strong scale/alloy bonding at the interface and the build-up of strain energy during prolonged oxidation, damage in the Al2O3 scale on the ISC-EHEA is initiated as surface cracks rather than interface decohesion. When re-oxidized at 1300 °C, the ingress of oxygen along the surface cracks results in fast growth of new oxides at the metal/oxide interface, which causes local stress concentration, interface crack propagation and scale spallation.

The Contribution of Plasma Sheet Bubbles to Stormtime Ring Current Buildup and Evolution of Its Energy Composition

AbstractThe formation of the stormtime ring current is a result of the inward transport and energization of plasma sheet ions. Previous studies have demonstrated that a significant fraction of the total inward plasma sheet transport takes place in the form of bursty bulk flows, known theoretically as flux tube entropy‐depleted “bubbles.” However, it remains an open question to what extent bubbles contribute to the buildup of the stormtime ring current. Using the Multiscale Atmosphere Geospace Environment Model, we present a case study of the 17 March 2013 storm, including a quantitative analysis of the contribution of plasma transported by bubbles to the ring current. We show that bubbles are responsible for at least 50% of the plasma energy enhancement within 6 RE during this strong geomagnetic storm. The bubbles that penetrate within 6 RE transport energy primarily in the form of enthalpy flux, followed by Poynting flux and relatively little as bulk kinetic flux. Return flows can transport outwards a significant fraction of the plasma energy being transported by inward flows, and therefore must be considered when quantifying the net contribution of bubbles to the energy buildup. Data‐model comparison with proton intensities observed by the Van Allen Probes show that the model accurately reproduces both the bulk and spectral properties of the stormtime ring current. The evolution of the ring current energy spectra throughout the modeled storm is driven by both inward transport of an evolving plasma sheet population and by charge exchange with Earth's geocorona.

An energetics tale of the 2022 mega-heatwave over central-eastern China

It remains a major challenge to attribute heatwave’s lifecycle characteristics quantitatively to interwoven atmospheric and surface actions. By constructing a process-resolving, energetics-based attribution framework, here we quantitatively delineate the lifecycle of the record-breaking 2022 mega-heatwave over central-eastern China from a local energetics perspective. It is found that the cloudlessness induced radiative heating and atmospheric dynamics dominate the total energy buildup during the developing stage, while the land-atmosphere coupling and atmospheric horizontal advection act most effectively to sustain and terminate the heatwave, respectively. A reduction in anthropogenic aerosols provides a persistent positive contribution during the event, suggesting that pollution mitigation measures may actually increase the amplitudes of future heatwaves. With this framework, initial efforts are made to unravel culprits in a model’s sub-seasonal prediction of this mega-heatwave, demonstrating the framework’s potential for efficiently detecting the origins of climate extremes and quantitatively assessing the impacts of mitigation policies for sustainable development.

An experimental approach to determine the gamma radiation interaction mean free path and exposure buildup factor for biomolecules

This experimental approach was designed to understand the gamma interaction parameters for the essential biomolecules, including starch soluble, cholesterol, myristic acid, glucose, oxalic acid, dextrose, salicylic acid, ethyl cellulose and sucrose. The empirical determination of gamma interaction parameters, such as interaction mean-free-path (MFP), buildup factor, and effective atomic number (Zeff) was performed by measuring mass attenuation coefficient (μ/ρ) at energies of 356 keV, 511 keV, 662 keV, 1173 keV, 1275 keV and 1332 keV. This was achieved using weak radioactive sources and a NaI(Tl) scintillation spectrometer with collimated and non-collimated transmission geometry. The experimentally determined values of gamma-ray interaction parameters were obtained non-destructively and precisely agreeing with the expected values from simulations and codes. In addition, the research findings also revealed a novel trend in gamma interaction mean free path as a function of energy and variable buildup factors for the selected biomolecules. These research findings provide valuable insight into the process of gamma radiation interaction. This approach may fulfil the increasing demand of medical, technical and academic research laboratories for a cost-effective and reliable empirical methodology to understand gamma radiation interaction with matter.

Numerical simulations of internal gravity wave resonant triads

We investigate the triadic resonance interactions using numerical simulations of freely propagating internal waves at near-inertial frequency. We force multiple combinations of normal modes at primary frequency ω0 from the left boundary of the computational domain and study the spatiotemporal evolution of the superharmonic waves. Both the resonant and off-resonant simulations show distinct peaks of energy in the higher harmonics at 2ω0,3ω0, and 4ω0 close to the forcing region. The spatial evolution of modal amplitudes shows that higher normal modes of primary wave decay faster and the higher normal modes of superharmonic waves grow faster. Away from the forcing region, these distinct peaks in the resonant simulations weaken and redistribute the energy into continuous spectra, whereas in the off-resonant simulations, these distinct peaks at superharmonic frequencies sustain throughout the domain. The off-resonant simulations also show significant energy in sub-harmonic frequencies, and we see a buildup of energy in the near-inertial frequency regime far from the forcing region. The frequency and the wavenumber spectra for resonant simulations reveal a −2 power law consistent with the Garrett–Munk spectrum (E(ω,m)∝ω−2m−2).

A Statistical Search for a Uniform Trigger Threshold in Solar Flares from Individual Active Regions

Solar flares result from the sudden release of energy deposited by subphotospheric motions into the magnetic field of the corona. The deposited energy accumulates secularly between events. One may interpret the observed event statistics as resulting from a state-dependent Poisson process in which the instantaneous flare rate is a function of the stress in the system and a flare becomes certain as the stress approaches a threshold set by the microphysics of the flare trigger. If the system is driven fast, and if the threshold is static and uniform globally, a cross-correlation is predicted between the size of a flare and the forward waiting time to the next flare. This cross-correlation is broadly absent from the Geostationary Operational Environmental Satellite (GOES) soft X-ray flare database. One also predicts higher cross-correlations in active regions where the shapes of the waiting time and size distributions match. Again, there is no evidence for such an association in the GOES data. The data imply at least one of the following: (i) the threshold at which a flare is triggered varies in time; (ii) the rate at which energy is driven into active regions varies in time; (iii) historical flare catalogs are incomplete; or (iv) the description of solar flares as resulting from a buildup and release of energy, once a threshold is reached, is incomplete.