Flux Units Research Articles

Non-invertible symmetries in SN orbifold CFTs and holography

We study non-invertible defects in two-dimensional SN orbifold CFTs. We construct universal defects which do not depend on the details of the seed CFT and hence exist in any orbifold CFT. Additionally, we investigate non-universal defects arising from the topological defects of the seed CFT. We argue that there exist universal defects that are non-trivial in the large-N limit, making them relevant for the AdS3/CFT2 correspondence. We then focus on AdS3×S3 × M4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathcal{M}}_4 $$\\end{document} with one unit of NS-NS flux and propose an explicit realization of these defects on the worldsheet.

Equivalence of magnetic flux and energy

Magnetic flux and energy equivalence is the principle that everything that has magnetic flux has an equivalent amount of energy, and vice versa. The main methods used: transformation of natural units, algebra, analogy. The equivalence of magnetic flux and energy, despite its widespread use in describing the principles of physics, has not yet been formulated. This paper presents the formula for this equivalence. This is done based on known measurement systems, parameters and principles of physics. Five examples (Stoney units, Planck units, standard gravitational parameter, Lorentz force, and Ampere force) of the algebraic representation of this principle show its universality. Five examples should justify the universality of the new principle and its use in physics and astrophysics. Using the equivalence of magnetic flux and energy, new physical units of mass and magnetic flux are proposed, each of which is suitable for measuring both mass and magnetic flux. Natural values of electric current and voltage, linear density of electric capacitance and inductance, linear density of magnetic flux, linear density of electric charge, as well as natural units of electric voltage and current, electrical resistance, magnetic flux, electrical capacitance and inductance are also described. The article presents the Einstein field equation (additional magnetic stress–energy–momentum tensor) and a standard astrophysical parameter for refining the orbits of celestial bodies.

Engineering perturbative string duals for symmetric product orbifold CFTs

Constructing a holographic string theory dual for a CFT in the perturbative, weakly coupled regime is a holy grail for gauge/string dualities that would not only open the door for proofs of the AdS/CFT correspondence but could also provide novel examples of string duals with and without supersymmetry. In this work we consider some marginal perturbation of a family of symmetric product orbifolds in two dimensions. From their correlation functions we engineer a bosonic string theory whose amplitudes are shown to reproduce the CFT correlation function order-by-order both in the coupling and in 1/N. Our derivation does not require to compute and compare correlation functions explicitly but rather relies on a sequence of identities that can be derived using path integral methods. The bosonic string theory we engineer is based on the field content of the Kac-Wakimoto representation of strings in AdS3 with k units of pure NSNS flux, but the interaction terms we obtain are different. They include current algebra preserving interaction terms with one unit of spectral flow.

Telomeres and the Rate of Living: Linking Biological Clocks of Senescence.

AbstractTwo prominent theories of aging, one based on telomere dynamics and the other on mass-specific energy flux, propose biological time clocks of senescence. The relationship between these two theories, and the biological clocks proposed by each, remains unclear. Here, we examine the relationships between telomere shortening rate, mass-specific metabolic rate, and lifespan among vertebrates (mammals, birds, fishes). Results show that telomere shortening rate increases linearly with mass-specific metabolic rate and decreases nonlinearly with increasing body mass in the same way as mass-specific metabolic rate. Results also show that both telomere shortening rate and mass-specific metabolic rate are similarly related to lifespan and that both strongly predict differences in lifespan, although the slopes of the relationships are less than linear. On average, then, telomeres shorten a fixed amount per unit of mass-specific energy flux. So the mitotic clock of telomere shortening and the energetics-based clock described by metabolic rate can be viewed as alternative measures of the same biological clock. These two processes may be linked, we speculate, through the process of cell division.

Spectral flow and localisation in AdS3 string theory

We study string theory in three-dimensional Anti-de Sitter spacetime in the path integral formalism. We derive expressions for generic spectrally-flowed near-boundary vertex operators in the Wakimoto representation, and relate their correlation functions to covering maps from the worldsheet to the target space boundary. We show that the path integral structurally reproduces correlation functions of the dual symmetric orbifold theory. By rephrasing spectral flow as the introduction of a background gauge field, we provide a path integral derivation of the localisation property of the near boundary theory. We then focus on the case of IIB string theory on AdS3 × S3 × \U0001d54b4 with k = 1 units of NS-NS flux, where the relationship between correlation functions and covering maps can be made sharp. We also comment on the relation of the k = 1 theory and twistor theory.

Hyporheic Reaction Potential: A Framework for Predicting Reach Scale Solute Fate and Transport.

We develop a new framework, hyporheic reaction potential (HRP), to predict the influence of oxidation-reduction reactions on metal fate and transport in streams using data from tracer studies and geochemical sampling. HRP, with energy flux units [KJ m-2 s-1], is a metric calculated from both the physical and chemical properties of the hyporheic zone. We apply the HRP framework for iron reactions, using existing geochemical and geophysical data from two metal-impacted alpine streams at high and low flow. In these two systems, HRP delineates contrasting controls on iron fate and transport with biogeochemical controls in Mineral Creek and physical controls in Cement Creek. In both systems, HRP scales with discharge and hyporheic-zone extent as flows change seasonally, which demonstrates the ability of HRP to capture physical aspects of chemical reactions in the hyporheic zone. This paper provides a foundation on which HRP can be expanded to other solutes where chemical gradients in the hyporheic zone control reaction networks, making it broadly applicable to redox cycling in stream systems. This framework is useful in quantifying the role of the hyporheic zone in sourcing and storing metal(loid)s under varying hydrologic conditions with implications for water quality, mine remediation, and regional watershed management.

Tensionless strings on AdS3 orbifolds

The bound state of one NS5 brane (wrapped on a \U0001d54b4) and N NS1-branes has two dual descriptions: its low-energy dynamics is described by the symmetric orbifold of \U0001d54b4, while the near horizon geometry is captured by string theory on AdS3 × S3 × \U0001d54b4 with one unit of NS flux. The latter theory is exactly solvable in the hybrid formalism, and this allows one to prove the equivalence of the two descriptions. In this paper we extend this duality to ℤk orbifolds of this AdS3 × S3 background. In particular, we show that the corresponding worldsheet spectrum reproduces exactly the perturbative excitations on top of a certain non-perturbative state in the dual symmetric orbifold theory. Since the AdS/CFT duality map is exact for these models, we obtain an interesting picture of how the duality relates boundary and bulk descriptions.

Symmetries and covering maps for the minimal tension string on AdS3× S3× T4

This paper considers a recently-proposed string theory on AdS3 × S3 × T4 with one unit of NS-NS flux (k = 1). We discuss interpretations of the target space, including connections to twistor geometry and a more conventional spacetime interpretation via the Wakimoto representation. We propose an alternative perspective on the role of the Wakimoto formalism in the k = 1 string, for which no large radius limit is required by the inclusion of extra operator insertions in the path integral. This provides an exact Wakimoto description of the worldsheet CFT. We also discuss an additional local worldsheet symmetry, Q(z), that emerges when k = 1 and show that this symmetry plays an important role in the localisation of the path integral to a sum over covering maps. We demonstrate the emergence of a rigid worldsheet translation symmetry in the radial direction of the AdS3, for which again the presence of Q(z) is crucial. We conjecture that this radial symmetry plays a key role in understanding, in the case of the k = 1 string, the encoding of the bulk physics on the two-dimensional boundary.

A Compact THz Photometer for Solar Flare Burst Studies from Space

Recent solar flare observations reveal the presence of THz components having a few orders of magnitude higher amplitude than the Radio Frequency (RF) and microwave radiations in the solar flare spectrum. This feature makes it remarkably beneficial for the detection of solar flares of low magnitudes such as Geostationary Operational Environmental Satellite (GOES) Class C, and M flares. Hence, space agencies including National Aeronautics and Space Administration (NASA) and European Space Agency (ESA) are gearing up with THz instruments for solar flare observations. In line with this, Laboratory for Electro-Optics Systems (LEOS) has completed the development of a photometer that operates in continuum THz band, from 1.5 to 15 THz. The entire electro-opto-mechanical design was carried out to realize a compact, light-weight and power-efficient photometer to meet the size, mass and power constraints posed by inherent resource limitations of experimental satellite platforms such as Nanosatellite, Microsatellite and Polar Satellite Launch Vehicle’s 4th Stage Orbital Platform (PS4-OP). A Cassegrain optical configuration was designed to collect the sun radiation with an aperture effective area of 0.0027 m2 with ceramic low pass filters and resonant mesh filter for selective perception of THz radiation, rejecting the huge background of visible and Near Infrared (NIR) with a spectral selectivity of 107:1. Sensitivity of the Photometer was estimated to be 41.5 K/mV in 1.5 to 15 THz band by calibration using a blackbody radiation source. The radiometric resolution of the payload is 125 Solar Flux Unit (SFU) (1 SFU=1×10-22 Wm-2Hz-1). The payload was successfully developed and space-qualified for its deployment in Nanosatellite or PS4-OP platform.

A Floor in the Sun's Photospheric Magnetic Field: Implications for an Independent Small-scale Dynamo

Clette recently showed that F 10.7 systematically approaches a quiet Sun daily value of 67 solar flux units (sfu) at solar minima as the number of spotless days on the Sun increases. Previously, a floor of ∼2.8 nT had been proposed for the solar wind (SW) magnetic field strength (B). F 10.7, which closely tracks the Sun's unsigned photospheric magnetic flux, and SW B exhibit different relationships to their floors at 11 yr solar minima during the last ∼50 yr. While F 10.7 approaches 67 sfu at each minimum, the corresponding SW B is offset above ∼2.8 nT by an amount approximately proportional to the solar polar field strength—which varied by a factor of ∼2.5 during this interval. This difference is substantiated by ∼130 yr of reconstructed F 10.7 (via the range of the diurnal variation of the East-component (rY) of the geomagnetic field) and SW B (based on the interdiurnal variability geomagnetic activity index). For the last ∼60 yr, the contribution of the slow SW to SW B has exhibited a floor-like behavior at ∼2 nT, in contrast to the contributions of coronal mass ejections and high-speed streams that vary with the solar cycle. These observations, as well as recent SW studies based on Parker Solar Probe and Solar Dynamics Observatory data, suggest that (1) the Sun has a small-scale turbulent dynamo that is independent of the 11 yr sunspot cycle; and (2) the small-scale magnetic fields generated by this nonvarying turbulent dynamo maintain a constant open flux carried to the heliosphere by the Sun's floor-like slow SW.

Predicting Solar Proton Events of Solar Cycles 22–24 Using GOES Proton and Soft-X-Ray Flux Features

Solar energetic particle (SEP) events and their major subclass, solar proton events (SPEs), can have unfavorable consequences on numerous aspects of life and technology, making them one of the most harmful effects of solar activity. Garnering knowledge preceding such events by studying operational data flows is essential for their forecasting. Considering only solar cycle (SC) 24 in our previous study, we found that it may be sufficient to only utilize proton and soft X-ray (SXR) parameters for SPE forecasts. Here, we report a catalog recording ≥10 MeV ≥10 particle flux unit SPEs with their properties, spanning SCs 22–24, using NOAA’s Geostationary Operational Environmental Satellite flux data. We report an additional catalog of daily proton and SXR flux statistics for this period, employing it to test the application of machine learning (ML) on the prediction of SPEs using a support vector machine (SVM) and extreme gradient boosting (XGBoost). We explore the effects of training models with data from one and two SCs, evaluating how transferable a model might be across different time periods. XGBoost proved to be more accurate than SVMs for almost every test considered, while also outperforming operational SWPC NOAA predictions and a persistence forecast. Interestingly, training done with SC 24 produces weaker true skill statistic and Heidke skill scores2, even when paired with SC 22 or SC 23, indicating transferability issues. This work contributes toward validating forecasts using long-spanning data—an understudied area in SEP research that should be considered to verify the cross cycle robustness of ML-driven forecasts.

Retrieval of leaf-level fluorescence quantum efficiency and NPQ-related xanthophyll absorption through spectral unmixing strategies for future VIS-NIR imaging spectroscopy

Current and future vegetation imaging spectroscopy satellites will bring a new data stream of information, of high scientific value to refine existing remote sensing products, and develop new ones. The sensors on board ESA's Fluorescence Explorer (FLEX) will cover the entire 500–780 nm range, designed to track the photosynthetic energy partitioning based on the key pigment players in the light reactions. To quantify the actual photosynthetic efficiency unambiguously, the dynamic pigment absorption behavior is crucial to complement the fluorescence information. An important role is given by the xanthophylls, regulating the non-photosynthetic quenching (NPQ) behavior which affects the 500–600 nm range. Therefore, this work focused on the development of a non-negative least squares (NNLS) spectral unmixing algorithm for reflectance (500–780 nm) retrieving the effective absorbance of individual pigments, i.e., Chlorophyll (Chl) a and b, beta-Carotene and xanthophylls. The NNLS fitting was applied to fit the total effective absorbance at leaf level, linearly composed of pigment and background absorption coefficient spectra. The model succeeded to obtain spectral fitting errors generally below 20% across the 500–780 nm range. Further, we focused on the further use of the effective absorbance by Chlorophyll a to calculate the absorbed photosynthetically active radiation or APAR Chl a. This product was combined with the total emitted fluorescence flux (670–780 nm), expressed in photon flux units, to obtain the fluorescence quantum efficiency (FQE), capturing the stress-related fluorescence quenching in the light reactions. Finally, we applied the leaf-based algorithm to foreseen FLEX image products simulated by the FLEX End-to-End Scene Generator. We were able to retrieve APAR Chl a with a RMSE of 85.5 μmol m−2 s−1 (NNLS with additional upper fitting constraints) and 158.2 μmol m−2 s−1 (regular NNLS), and FQE retrievals could be obtained with an R2 of 0.93 and 0.90, respectively. While the subtle xanthophyll absorption could be meaningfully fitted at the leaf scale, further improvements to the algorithms and an understanding of the physiological mechanisms are needed to deal with the complexity at larger scales. Given several challenges to be overcome, the proposed bottom-up strategy using specific pigment absorbance unmixing for (imaging) spectroscopy demonstrates the ongoing developments to complement the fluorescence product, with the aim to provide an unambiguous estimate on the actual carbon sequestration of vegetation.

Solar–Stellar Connection: X-Ray Flares to Energetic (E > 10 MeV) Particle Events

Energetic particle environments are an important factor for the viability of life on exoplanets surrounding flare stars. In the heliosphere, large gradual solar energetic (E > 10 MeV) particle (SEP) events are produced by shocks from fast coronal mass ejections (CMEs). Extensive observations of solar X-ray flares, CMEs, and SEP events can provide guidance for flare star models of stellar energetic particle (StEP) events, for which stellar flares, but only rarely the associated CMEs, are observed. Comparing an extensive list of peak fluxes, timescales, and peak temperatures of 585 ≥ M3.0 solar X-ray flares with the occurrence of associated SEP events of peak flux Ip > 1.4 proton flux units, enhanced with proxy decametric–hectometric type II radio bursts, we determine guidelines for StEP event outcomes, given only stellar X-ray flare inputs. Longer timescales and lower peak temperatures of X-ray flares with a given peak X-ray flux Fp are more favorable for occurrence of associated SEP/StEP events, which, however, are only a minority of all solar flare outcomes. Most solar flares do not result in SEP events, invalidating scaling laws between stellar flares, CMEs, and StEP events. We discuss recent observations and models of the flare–CME relationship and suggest that StEP intensities Ip may often be overestimated.

Statistical analysis of microflares as observed by the 4–8 GHz spectropolarimeter

Radio observations of weak events are one of the promising methods for studying energy release and non-thermal processes in the solar corona. The development of instrumental capabilities allows for radio observations of weak transient coronal events, such as quasi-stationary brightenings and weak flares of X-ray class B and below, which were previously inaccessible for analysis. We have measured the spectral parameters of microwave radiation for thirty weak solar flares with X-ray classes ranging from A to C1.5, using observations from the Badary Broadband Microwave Spectropolarimeter (BBMS). The spectra indicate that plasma heating is caused by the appearance of non-thermal electron fluxes, which can be detected by bursts of microwave radiation, predominantly with an amplitude ~5–6 solar flux units (SFU) at 4–5 GHz frequencies. One solar flux unit (SFU) of radio emission is equal to 10–22 W/(m•Hz). The range of low-frequency spectrum growth indices fα varies widely from α=0.3 to 15. The distribution of high-frequency decay indices is similar to the distributions of regular flares. One of the explanations for the appearance of large fα values is the Razin effect, which can influence the shape of the gyrosynchrotron spectrum during the generation of bursts in dense plasma under relatively weak magnetic fields. We have detected two events in which the appearance of non-thermal electrons led to the generation of narrowband bursts at frequencies near the double plasma frequency. SRH test trials have shown the potential for measuring the structure of flare sources with fluxes of the order of 1 SFU, indicating the high diagnostic potential of the radioheliograph for detecting acceleration processes in weak flare events and their localization in active regions.

Статистический анализ микровспышек по данным Cпектрополяриметра 4-8 ГГц

Radio observations of weak events are one of the promising methods for studying energy release and non-thermal processes in the solar corona. The development of instrumental capabilities allows for radio observations of weak transient coronal events, such as quasi-stationary brightenings and weak flares of X-ray class B and below, which were previously inaccessible for analysis. We have measured the spectral parameters of microwave radiation for thirty weak solar flares with X-ray classes ranging from A to C1.5, using observations from the Badary Broadband Microwave Spectropolarimeter (BBMS). The spectra indicate that plasma heating is caused by the appearance of non-thermal electron fluxes, which can be detected by bursts of microwave radiation, predominantly with an amplitude ~5–6 solar flux units (SFU) at 4–5 GHz frequencies. One solar flux unit (SFU) of radio emission is equal to 10–22 W/(m•Hz). The range of low-frequency spectrum growth indices fα varies widely from α=0.3 to 15. The distribution of high-frequency decay indices is similar to the distributions of regular flares. One of the explanations for the appearance of large fα values is the Razin effect, which can influence the shape of the gyrosynchrotron spectrum during the generation of bursts in dense plasma under relatively weak magnetic fields. We have detected two events in which the appearance of non-thermal electrons led to the generation of narrowband bursts at frequencies near the double plasma frequency. SRH test trials have shown the potential for measuring the structure of flare sources with fluxes of the order of 1 SFU, indicating the high diagnostic potential of the radioheliograph for detecting acceleration processes in weak flare events and their localization in active regions.

The Calibration of the 35–40 GHz Solar Radio Spectrometer with the New Moon and a Noise Source

Calibrating solar radio flux has always been a concern in the solar community. Previously, fluxes were calibrated by matching load or the new Moon for relative calibration, and at times with the assistance of other stations’ data. Moreover, the frequency coverage seldom exceeded 26 GHz. This paper reports the upgraded and calibrated Chashan Broadband Solar millimeter spectrometer (CBS) working from 35 to 40 GHz at the Chashan Solar Observatory (CSO). Initially, the calibration of the solar radiation brightness temperature is accomplished using the new Moon as the definitive source. Subsequently, the 35–40 GHz standard flux is achieved by establishing the correlation between the solar radio flux, brightness temperature, and frequency. Finally, the calibration of the solar radio flux is implemented by utilizing a constant temperature-controlled noise source as a reference. The calibration in 2023 February and March reveals that the solar brightness temperature is 11,636 K at 37.25 GHz with a standard deviation (STD) of 652 K. The solar radio flux’s intensity is ∼3000–4000 solar flux units (SFU) in the range of 35–40 GHz with a consistency bias of ±5.3%. The system sensitivity is about ∼5–8 SFU by a rough evaluation, a noise factor of about 200 K, and the coefficient of variation of the system transmission slope of 6.5% @ 12 hr at 37.25 GHz. It is expected that the upgraded CBS will capture more activity during the upcoming solar cycle.

Estimating uncertainty in streamflow and solute fluxes at the Hubbard Brook Experimental Forest, New Hampshire, USA

AbstractStream fluxes are commonly reported without a complete accounting for uncertainty in the estimates, which makes it difficult to evaluate the significance of findings or to identify where to direct efforts to improve monitoring programs. At the Hubbard Brook Experimental Forest in the White Mountains of New Hampshire, USA, stream flow has been monitored continuously and solute concentrations have been sampled approximately weekly in small, gaged headwater streams since 1963, yet comprehensive uncertainty analyses have not been reported. We propagated uncertainty in the stage height–discharge relationship, watershed area, analytical chemistry, the concentration–discharge relationship used to interpolate solute concentrations, and the streamflow gap‐filling procedure to estimate uncertainty for both streamflow and solute fluxes for a recent 6‐year period (2013–2018) using a Monte Carlo approach. As a percentage of solute fluxes, uncertainty was highest for NH4+ (34%), total dissolved nitrogen (8.8%), NO3− (8.1%), and K+ (7.4%), and lowest for dissolved organic carbon (3.7%), SO42− (4.0%), and Mg2+ (4.4%). In units of flux, uncertainties were highest for solutes in highest concentration (Si, DOC, SO42−, and Na+) and lowest for those lowest in concentration (H+ and NH4+). Laboratory analysis of solute concentration was a greater source of uncertainty than streamflow for solute flux, with the exception of DOC. Our results suggest that uncertainty in solute fluxes could be reduced with more precise measurements of solute concentrations. Additionally, more discharge measurements during high flows are needed to better characterize the stage‐discharge relationship. Quantifying uncertainty in streamflow and element export is important because it allows for determination of significance of differences in fluxes, which can be used to assess watershed response to disturbance and environmental change.

John Dewey’s Radical Temporalism

The author presents John Dewey’s mature account of temporal continuity, showing how Dewey’s position can be identified as a form of radical temporalism. Even at the most elemental level (that of subatomic particles), natural existence is for such a temporalist an irreducibly temporal affair. While he focuses primarily on Dewey’s “Time and Individuality” (1940), the author supplements his account by drawing upon Experience and Nature (1925), “Events and the Future” (1926), and to a lesser extent, other texts. In his magnum opus, Dewey draws a crucial distinction between temporal quality and temporal seriality. In an essay published the following year, he insists, contra C. D. Broad, on qualitative heterogeneity being an intrinsic trait of even the thinnest slice of the tem-poral continuum. The most elemental units of the temporal flux are neither “eternal and immu-table”, nor qualitatively homogenous. They also exhibit a from-to-through structure, with the dimensions of time being defined by these terms (pastness as from which, futurity as toward which, and presentness as through which). By relating the distinction between temporal quality and temporal seriality as well as the central claims made in “Events and the Future” to “Time and Individuality”, the author brings into clear focus the contours of Dewey’s radical temporalism.

Free-standing nanowire printed surfaces with high variability in substrate selection for boiling heat transfer enhancement

Nanowires (NWs) constitute a promising solution to the overheating of high-heat-load surfaces in multiphase heat transfer. Typical nanostructure fabrication methods such as complex photolithography and metal-assisted chemical etching (MACE) that utilize patterned templates are limited by high manufacturing costs and type of substrate materials. These limitations significantly hinder the industrial applicability of NW structures in high heat flux units. In this study, we first examine the effect of the morphology of Zinc oxide (ZnO) NW printed substrates, fabricated via microcontact printing (µCP) and solution based growing, on the heat transfer characteristics in pool boiling. Unlike advanced photolithography, µCP offers greater variability and convenience in terms of the substrate selection and large area creation for NW fabrication. Compared with the silicon substrate, the underlying mechanisms for enhancing both the critical heat flux and heat transfer coefficient of ZnO NW substrates are explored by analyzing the surface morphology, bubble, and wicking characteristics of the test surfaces, in order to determine the applicability of boiling heat transfer using ZnO NWs in industrial fields.

High-Resolution Fluoro-Respirometry of Equine Skeletal Muscle.

Mitochondrial function-oxidative phosphorylation and the generation of reactive oxygen species-is critical in both health and disease. Thus, measuring mitochondrial function is fundamental in biomedical research. Skeletal muscle is a robust source of mitochondria, particularly in animals with a very high aerobic capacity, such as horses, making them ideal subjects for studying mitochondrial physiology. This article demonstrates the use of high-resolution respirometry with concurrent fluorometry, with freshly harvested skeletal muscle mitochondria, to quantify the capacity to oxidize substrates under different mitochondrial states and determine the relative capacities of distinct elements of mitochondrial respiration. Tetramethylrhodamine methylester is used to demonstrate the production of mitochondrial membrane potential resulting from substrate oxidation, including calculation of the relative efficiency of the mitochondria by calculating the relative membrane potential generated per unit of concurrent oxygen flux. The conversion of ADP to ATP results in a change in the concentration of magnesium in the reaction chamber, due to differing affinities of the adenylates for magnesium. Therefore, magnesium green can be used to measure the rate of ATP synthesis, allowing the further calculation of the oxidative phosphorylation efficiency (ratio of phosphorylation to oxidation [P/O]). Finally, the use of Amplex UltraRed, which produces a fluorescent product (resorufin) when combined with hydrogen peroxide, allows the quantification of reactive oxygen species production during mitochondrial respiration, as well as the relationship between ROS production and concurrent respiration. These techniques allow the robust quantification of mitochondrial physiology under a variety of different simulated conditions, thus shedding light on the contribution of this critical cellular component to both health and disease.