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At least 289 records · Page 16

Froggatt-Nielsen meets the SMEFT

We study the matching of Froggatt-Nielsen theories of flavour onto the Standard Model Effective Field Theory (SMEFT), upon integrating out a heavy Beyond-the-Standard-Model (BSM) scalar ‘flavon’ whose vacuum expectation value breaks an Abelian flavour symmetry at energies Λ FN well above the electroweak scale, Λ FN > Λ SM . We include matching contributions to the infrared d SM = 6 (Warsaw basis) SMEFT sourced from ultraviolet contact terms suppressed up to order 1/${\Lambda}_{\textrm{UV}}^2$ in the Froggatt-Nielsen Lagrangian, where Λ UV > Λ FN is an arbitrary ultraviolet scale where further unspecified BSM particles are dynamical. This includes tree-level (one-loop) ultraviolet diagrams with d FN = 6 (5) effective vertices. We first do so with a toy model, but then generalize our findings to arbitrary Frogatt-Nielsen charges. Our results indicate a rich and non-trivial signature of Froggatt-Nielsen theories on the (otherwise) model-independent operators of the SMEFT, and we briefly speculate on extending our analysis to broader classes of BSM flavour models, e.g. non-Abelian and/or gauged theories. We thus take an important step towards determining how to use rapidly developing theoretical and experimental SMEFT technologies to gain unambiguous insight into the SM’s longstanding fermion flavour puzzle.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Discrete Superconvergence Analysis for Quantum Magnus Algorithms of Unbounded Hamiltonian Simulation

Motivated by various applications, unbounded Hamiltonian simulation has recently garnered great attention. Quantum Magnus algorithms, designed to achieve commutator scaling for time-dependent Hamiltonian simulation, have been found to be particularly efficient for such applications. When applied to unbounded Hamiltonian simulation in the interaction picture, they exhibit an unexpected superconvergence phenomenon. However, existing proofs are limited to the spatially continuous setting and do not extend to discrete spatial discretizations. Here, in this work, we provide the first superconvergence estimate in the fully discrete setting with a finite number of spatial discretization points N, and show that it holds with an error constant uniform in N. The proof is based on the two-parameter symbol class, which, to our knowledge, is applied for the first time in algorithm analysis. The key idea is to establish a semiclassical framework by identifying two parameters through the discretization number and the time step size rescaled by the operator norm, such that the semiclassical uniformity guarantees the uniformity of both. This approach may have broader applications in numerical analysis beyond the specific context of this work.

Borns-Weil, Yonah [University of California, Berke↗

Amino mapping: possibility to visualize amino-N compounds in the rhizosphere of Zea Mays L.

Abstract Understanding N uptake by plants, the N cycle, and their relationship to soil heterogeneity has generated a great deal of interest in the distribution of amino-N compounds in soil. Visualization of the spatial distribution of amino-N in soil can provide insights into the role of labile N in plant-microbial mechanisms of N acquisition and plant N uptake, but until now, it has remained technically challenging. Here, we describe a novel technique to visualize the amino-N distribution at the root-soil interface. The technique is based on time-lapse amino mapping (TLAM) using membranes saturated with the fluorogenic OPAME reagent (O-phthalaldehyde and β-mercaptoethanol). OPAME in the membrane reacts with organic compounds containing a NH 2 functional group at the membrane-soil interface, generating a fluorescent product visible under UV light and detectable by a digital camera. The TLAM amino-mapping technique was applied to visualize and quantify the concentration of amino-N compounds in the rhizosphere of maize (Zea MaysL.). A ten times greater amino-N concentration was detected in the rhizosphere compared to non-rhizosphere soil. The high content of amino-N was mainly associated with the root tips and was 3 times larger than the average amino-N content at seminal roots. The amino-N rhizosphere was 2 times broader around the root tips than around other parts of the roots. We concluded that TLAM is a promising approach for monitoring the fate of labile N in soils. However, the technique needs to be standardized for different soil types, plant species, and climate conditions to allow wider application.

Agriculture↗

High-pressure crystal structure and equation of state of ferromagnesian jeffbenite: implications for stability in the transition zone and uppermost lower mantle

Jeffbenite, ideally Mg 3 Al 2 Si 3 O 12 , has been identified as inclusions in super-deep diamonds originating from depths that exceed 300 km. Although Mg-end member jeffbenite has limited stability at upper-mantle conditions, iron-bearing jeffbenite may have broader P–T stability that extends to the transition zone or uppermost lower mantle, incorporating significant amounts of ferric iron. Using synchrotron-based, single-crystal X-ray diffraction (XRD) and synchrotron Mössbauer spectroscopy (SMS) at pressures up to 29 GPa, we report the crystal structure, compressibility, and likely spin transition of iron in ferromagnesian jeffbenite (Mg 2.32 Al 0.03 Fe 2+ 1.28 Fe 3+ 1.77 Si 2.85 O 12 ). High-pressure structure refinements reveal that Fe 3+ substitution for Si in the T2 site, which shares edges with the M2 octahedron, likely stabilizes jeffbenite at high pressure, because it increases the cation-to-cation distance between these sites. Although ferromagnesian jeffbenite does not undergo a structural phase transition below 30 GPa, SMS hyperfine parameters suggest the onset of an electronic spin transition of iron from high-spin (HS) to low-spin (LS) at around 22 GPa, which may increase its stability at high pressures. Pressure–volume data were fit to a third order Birch–Murnaghan equation of state, resulting in V o = 816.54(9), K To = 181.54(1.39), and K' T0 = 2.76(14). These equation of state parameters are applicable to evaluating the encapsulation pressures of super-deep diamonds. The density and bulk modulus of ferromagnesian jeffbenite are similar to or higher than pyrope–almandine, pyrope–majorite, and skiagite–majorite solid solution garnets, further suggesting that jeffbenite may be an important ferric–iron silicate in the deeper parts of the mantle transition zone and uppermost lower mantle. Furthermore, future studies on the influence of temperature and oxidation state on the stability and equations of state of iron-bearing jeffbennite are still needed to determine what role, if any, jeffbenite plays in transition-zone mineralogy.

58 GEOSCIENCES↗

Proximal Galerkin: A Structure-Preserving Finite Element Method for Pointwise Bound Constraints

The proximal Galerkin finite element method is a high-order, low iteration complexity, nonlinear numerical method that preserves the geometric and algebraic structure of pointwise bound constraints in infinite-dimensional function spaces. This paper introduces the proximal Galerkin method and applies it to solve free boundary problems, enforce discrete maximum principles, and develop a scalable, mesh-independent algorithm for optimal design with pointwise bound constraints. This paper also introduces the latent variable proximal point (LVPP) algorithm, from which the proximal Galerkin method derives. When analyzing the classical obstacle problem, we discover that the underlying variational inequality can be replaced by a sequence of second-order partial differential equations (PDEs) that are readily discretized and solved with, e.g., the proximal Galerkin method. Throughout this work, we arrive at several contributions that may be of independent interest. These include (1) a semilinear PDE we refer to as the entropic Poisson equation; (2) an algebraic/geometric connection between high-order positivity-preserving discretizations and certain infinite-dimensional Lie groups; and (3) a gradient-based, bound-preserving algorithm for two-field, density-based topology optimization. The complete proximal Galerkin methodology combines ideas from nonlinear programming, functional analysis, tropical algebra, and differential geometry and can potentially lead to new synergies among these areas as well as within variational and numerical analysis. Open-source implementations of our methods accompany this work to facilitate reproduction and broader adoption.

97 MATHEMATICS AND COMPUTING↗

Effects of Turbulence and Temperature Fluctuations on Knock Development in an Ethanol/Air Mixture

The effects of turbulence on knock development and intensity for a thermally inhomogeneous stoichiometric ethanol/air mixture at a representative end-gas autoignition condition in internal combustion engines are investigated using direct numerical simulations with a skeletal reaction mechanism. Two- and three-dimensional simulations are performed by varying the most energetic length scale of temperature, \(l_T\) , and its relative ratio with the most energetic length scale of turbulence, \(l_T/l_e\) , together with two different levels of the turbulent velocity fluctuation, \(u'\) . It is found that \(l_T\) / \(l_e\) and the ratio of ignition delay time to eddy-turnover time, \(\tau _{ig}/\tau _t\) , are the key parameters that control the detonation development. An increase in either \(l_T\) or \(l_e\) enhances the detonation propensity by allowing a longer run-up distance for the detonation development. The characteristic length scale of the temperature field, \(l_T\) , is significantly modified by high turbulence intensity achieved by a large \(l_e\) and \(u'\) . The intense turbulence mixing effectively distributes the initial temperature field to broader scales to support the developing detonation waves, thereby increasing the likelihood of the detonation formation. On the contrary, high turbulence intensity with a short mixing time scale, achieved by a small \(l_e\) and a large \(u'\) , reduces the super-knock intensity attributed to the finer broken-up structures of detonation waves. Either \(\tau _{ig}/\tau _t\) less than unity or \(l_e = l_T\) even with a large \(u'\) is found to have no significant effect on super-knock mitigation. Finally, high turbulent intensity may induce high-pressure spikes comparable to the von Neumann spike. Overall, increased temperature and pressure by combustion heating, noticeably after the peak of heat release rate, significantly enhance the collision and interaction of multiple emerging autoignition fronts near the ending combustion process, resulting in localized high-pressure spikes.

42 ENGINEERING↗

Microbial abundances and carbon use under ambient temperature or experimental warming in a southern boreal peatland

Abstract Organic peat soils occupy relatively little of the global land surface area but store vast amounts of soil carbon in northern latitudes where climate is warming at a rapid pace. Warming may result in strong positive feedbacks of carbon loss and global climate change driven by microbial processes if warming alters the balance between primary productivity and decomposition. To elucidate effects of warming on the microbial communities mediating peat carbon dynamics, we explored the abundance of broad microbial groups and their source of carbon (i.e. old carbon versus more recently fixed photosynthate) using microbial lipid analysis (δ 13 C PLFA) of peat samples under ambient temperatures and before/after initiation of experimental peat warming (+ 2.25, + 4.5, + 6.75, and + 9 °C). This analysis occurred over a profile to 2 m depth in an undrained, ombrotrophic peat bog in northern Minnesota. We found that the total microbial biomass and individual indicator lipid abundances were stratified by depth and strongly correlated to temperature under ambient conditions. However, under experimental warming, statistically significant effects of temperature on the microbial community were sporadic and inconsistent. For example, 3 months after experimental warming the relative abundance of Gram-negative bacterial indicators across depth combined and > 50 cm depth and Gram-positive bacterial indicators at 20–50 cm depth showed significant positive relationships to temperature. At that same timepoint, however, the relative abundance of Actinobacterial indicators across depth showed a significant negative relationship to temperature. After 10 months of experimental warming, the relative abundance of fungal biomarkers was positively related to temperature in all depths combined, and the absolute abundance of anaerobic bacteria declined with increasing temperature in the 20–50 cm depth interval. The lack of observed response in the broader microbial community may suggest that at least initially, microbial community structure with peat depth in these peatlands is driven more by bulk density and soil water content than temperature. Alternatively, the lack of broad microbial community response may simply represent a lag period, with more change to come in the future. The long-term trajectory of microbial response to warming in this ecosystem then could either be direct, after this initial lag time, or indirect through other physical or biogeochemical changes in the peat profile. These initial results provide an important baseline against which to measure long-term microbial community and carbon-cycling responses to warming and elevated CO 2 .

Felice, Mark↗

The Energy Modeling Forum (EMF)-30 Study on Short-Lived Climate Forcers: Introduction and Overview

The Energy Modeling Forum (EMF)-30 inter-comparison study on short-lived climate forcers (SLCFs) focuses on black carbon (BC) and methane, two of the most important warming SLCFs. The potential impact on climate change of methane and BC-focused emission reductions in the transport and residential sectors were quantified using nine integrated assessment models and a simple climate model. These SLCF reductions reduced global temperatures by 0.18–0.26 °C in 2050 across the models for central climate parameters, with methane being the dominant contributor. The incremental impact of SLCF-focused reductions is much smaller when combined with a broader climate policy. Individual modeling groups examined the health benefits of air pollutant reductions, climate policy co-benefits, and quantified market impacts from air pollutant damages. Model structure and set-up impact on results are discussed along with areas for future work.

Smith, Steven J.↗

‘The Cloud is Not Not IT’: Ecological Change in Research Computing in the Cloud

Along with a number of other computing technologies, cloud computing services are increasingly being promoted as a way of enabling openness, reproducibility, and the acceleration of scientific work. While there have been a variety of studies of the cloud in terms of computing performance, there has been little empirical attention to the changes going on around cloud computing at the level of work and practice. Through a qualitative, ethnographic study, we follow a cosmology research group’s transition from a shared high performance computing cluster to a cloud computing service, and examine the cloud service as a coordinative artifact being integrated into a larger ecology of existing practices and artifacts. We find that the transition involves both change and continuity in the group’s coordinative work and maintenance work, and point out some of the effects this adoption has on the group’s larger set of practices. Finally, we discuss practical implications this has for the broader adoption of cloud computing in university-based scientific work.

97 MATHEMATICS AND COMPUTING↗

The Cauchy Problem for Boltzmann Bi-linear Systems: The Mixing of Monatomic and Polyatomic Gases

Abstract From a unified vision of vector valued solutions in weighted Banach spaces, this paper establishes the existence and uniqueness for space homogeneous Boltzmann bi-linear systems with conservative collisional forms arising in complex gas dynamical structures. This broader vision is directly applied to dilute multi-component gas mixtures composed of both monatomic and polyatomic gases. Such models can be viewed as extensions of scalar Boltzmann binary elastic flows, as much as monatomic gas mixtures with disparate masses and single polyatomic gases, providing a unified approach for vector valued solutions in weighted Banach spaces. Novel aspects of this work include developing the extension of a general ODE theory in vector valued weighted Banach spaces, precise lower bounds for the collision frequency in terms of the weighted Banach norm, energy identities, angular or compact manifold averaging lemmas which provide coerciveness resulting into global in time stability, a new combinatorics estimate for p -binomial forms producing sharper estimates for the k -moments of bi-linear collisional forms. These techniques enable the Cauchy problem improvement that resolves the model with initial data corresponding to strictly positive and bounded initial vector valued mass and total energy, in addition to only a $$2^+$$ 2 + moment determined by the hard potential rates discrepancy, a result comparable in generality to the classical Cauchy theory of the scalar homogeneous Boltzmann equation.

Physics↗

Changing the Rules of the Game: Used Fuel Studies Outside of a Remote Handling Facility

Recent advances in micro-fabrication tools like the FEI Helios NanoLab 660 dual Focused Ion Beam (FIB) and Scanning Electron Microscope (SEM) now make it possible to easily and reliably prepare micron (or smaller) specimens for analyses or further experimentation. Pacific Northwest National Laboratory (PNNL) has leveraged this capability at the Category II Nuclear Facility, the Radiochemical Processing Laboratory, to facilitate nuclear materials analysis and experimentation of used nuclear fuel. Micron-scale specimens of un-irradiated UO2 fuel pellets of various enrichments from depleted to 4.95% enriched, relative to 235U, were prepared at PNNL and shipped to the University of Missouri’s Research Reactor (MURR) for irradiation. Prior to shipping, samples were attached to commercially available Transmission Electron Microscopy half-grids via ion deposition, which were then housed in specially designed aluminum sample holders approved for use at the reactor facility. This minimized handling and preparation requirements prior to materials analysis after irradiation. Samples were irradiated to a burnup equivalent of 8 – 3,700 MWd/MTU. Additionally, by reducing the size of the specimens, and therefore their emitted radiation dose, the required cooling time after irradiation and prior to analysis was greatly diminished, and handling of these samples could proceed outside of a hot cell facility. Results from these experiments provided insight into the initial production of noble metal phase particles in used nuclear fuel at extremely low burnup levels. Some incompatibility with the container was observed at higher burnup. Micro-scale irradiation experiments were performed at roughly 1/7th of the time, effort and expense a similar bulk-scale study requiring a shielded hot cell facility would require. Conducting nuclear materials analysis at the micron-scale holds the promise of enhancing collaboration and material accessibility to the broader research community, improving accessibility to cutting edge research tools by the nuclear materials science community, lowering the risk to the scientist by reducing radiation dose and exposure, reducing facility and research costs associated with the requirement to conduct nuclear materials science within glovebox or remote handling facilities, and minimizing waste.

Schwantes, Jon M.↗

High-precision measurements of half-lives for 69 Ge, 73 Se, 83 Sr, 85 mSr, and 63 Zn radionuclides relevant to the astrophysical p-process via photoactivation at the Madison Accelerator Laboratory

The ground state half-lives of 69 Ge, 73 Se, 83 Sr, 63 Zn, and the half-life of the 1/2 - isomer in 85 Sr have been measured with high precision using the photoactivation technique at an unconventional bremsstrahlung facility that features a repurposed medical electron linear accelerator. The γ -ray activity was counted over about 6 half-lives with a high-purity germanium detector, enclosed into an ultra low-background lead shield. The measured half-lives are: T 1/2 ( 69 Ge) = 38.82 ± 0.07 (stat) ± 0.06 (sys) h; T 1/2 ( 73 Se) = 7.18 ± 0.02 (stat) ± 0.004 (sys) h; T 1/2 ( 83 Sr) = 31.87 ± 1.16 (stat) ± 0.42 (sys) h; T 1/2 ( 85m Sr) = 68.24 ± 0.84 (stat) ± 0.11 (sys) min; T 1/2 ( 63 Zn) = 38.71 ± 0.25 (stat) ± 0.10 (sys) min. These high-precision half-life measurements will contribute to a more accurate determination of corresponding ground-state photoneutron reaction rates, which are part of a broader effort of constraining statistical nuclear models needed to calculate stellar nuclear reaction rates relevant for the astrophysical p -process nucleosynthesis.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Noble gas constraints on spent fuel irradiation histories

Fission gas isotopic compositions are sensitive to a variety of reactor operating parameters that include the neutron flux, neutron fluence at different neutron energies, and operating temperature. Measurements of fission gas isotopic compositions thus have potential to constrain reactor simulations for nuclear forensics and safeguards applications. In this paper, we present Kr and Xe isotope measurements from a suite of samples obtained from locations that span the axial length a fuel pin with a well-characterized irradiation history and compare these data to spatially resolved reactor simulations. Here, we observed positive correlations between fluence sensitive isotopic ratios and burnup and between a flux sensitive ratio and power, although some discrepancies are observed between the measured data and model predictions. These differences may be due to simplifications in the model and/or inaccuracies in the cross sections. A much broader measurement to model comparison is required to better understand the discrepancies.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Sample screening of uranium ore concentrates using portable spectrophotometers: investigating the correlation between visible colors and chemical signatures

A research collaboration between the Japan Atomic Energy Agency and the Department of Energy’s National Nuclear Security Administration examined nuclear forensic signatures and analytical methods for tracing the origins of uranium ore concentrates (UOCs). Here, this study focuses on utilizing portable spectrophotometers capable of reflectance measurements in the visible light spectrum as a potential rapid screening tool for nuclear forensics analysis. Unlike laboratory-based near-infrared spectroscopy or digital image analysis, this research investigated the potential to correlate visible color measurements with key nuclear forensics signatures using seven types of UOC samples with known origins and three UOC certified reference materials. Results demonstrated that distinct color groups, quantified using CIELAB values, correlated with major uranium compounds. Furthermore, the findings indicated that trace elements can influence the UOC colors, providing additional insights into material characteristics. Although this approach requires further validation across a broader range of UOC species, this study demonstrated that simple colorimetric analysis using visible spectrophotometry, which does not require complex sample preparation or data processing, can serve as a practical and novel rapid tool for preliminary screening and attribution in nuclear forensics investigations.

and nuclear chemistry↗

Capacitated p -hub approach for park-and-ride facility location problem under nested logit demand function: polyhedral approaches

By generalizing the unconstrained p-hub approach for the park-and-ride (P&R) facility location problem under the multinomial logit demand function, the capacitated p-hub approach for the problem under the nested logit demand function captures a broader range of real-world cases. To solve this problem optimally, we introduce a mixed-integer linear program and accelerate its solution by enhancing the branch-and-cut procedure. To address the problem at a large scale, we introduce two other polyhedral approaches: variable neighborhood search (VNS) and adaptive randomized rounding (ARR). Downtown areas in Seoul have a high modal share of public transportation and congested road traffic, yet P&R has not been widely implemented. Therefore, we apply the ARR procedure to solve a real-world problem using traffic and geographic data from the Seoul metropolitan area. ARR performs better than VNS and addresses real-world cases. The solutions obtained by ARR present a phased expansion plan that encourages policymakers to start installing a small number of P&Rs immediately.

Capacitated p-hub approach↗

High salt-induced PSI-supercomplex is associated with high CEF and attenuation of state transitions

Abstract While PSI-driven cyclic electron flow (CEF) and assembly of thylakoid supercomplexes have been described in model organisms like Chlamydomonas reinhardtii , open questions remain regarding their contributions to survival under long-term stress. The Antarctic halophyte, C. priscuii UWO241 (UWO241), possesses constitutive high CEF rates and a stable PSI-supercomplex as a consequence of adaptation to permanent low temperatures and high salinity. To understand whether CEF represents a broader acclimation strategy to short- and long-term stress, we compared high salt acclimation between the halotolerant UWO241, the salt-sensitive model, C. reinhardtii , and a moderately halotolerant Antarctic green alga, C. sp. ICE-MDV (ICE-MDV). CEF was activated under high salt and associated with increased non-photochemical quenching in all three Chlamydomonas species. Furthermore, high salt-acclimated cells of either strain formed a PSI-supercomplex, while state transition capacity was attenuated. How the CEF-associated PSI-supercomplex interferes with state transition response is not yet known. We present a model for interaction between PSI-supercomplex formation, state transitions, and the important role of CEF for survival during long-term exposure to high salt.

59 BASIC BIOLOGICAL SCIENCES↗

Queue wait time prediction in high performance computing (HPC) systems

High Performance Computing (HPC) systems are critical enablers for groundbreaking scientific research across various domains. Efficient resource allocation, facilitated by job scheduling, is paramount for maximizing the utilization of HPC systems. However, the variability in wait times for queued jobs poses challenges for users, necessitating accurate job wait time estimation. This paper explores the influence of job characteristics, including job size (the number of nodes requested and walltime), the queue to which the job is submitted and other resource requirements, on job wait times in leadership-class HPC systems. Focusing on the Theta Cray XC40 and Polaris machines at Argonne National Laboratory, the study evaluates the performance of different supervised learning algorithms in predicting job wait times. It also evaluates the impact of data preprocessing, including outlier detection, Principal Component Analysis (PCA), and feature selection, on the performance of wait time prediction models. The findings reveal insights into the relationship between job characteristics and wait times, offering a foundation for optimizing resource allocation and enhancing user experience. The methodologies and tools developed in this study are adaptable to other leadership-class HPC systems, providing a valuable contribution to the broader HPC community aiming to improve job scheduling efficiency and user satisfaction.

Okafor, Nwamaka↗

Trace elements and heavy metals in black vultures ( Coragyps atratus ) and turkey vultures ( Cathartes aura ) in the southeastern United States

Many vulture species worldwide are declining at alarming rates due to a variety of anthropogenic causes, including exposure to pollutants and pharmaceuticals through consumption of contaminated carrion. However, little is known about the extent to which vultures are exposed to various contaminants as well as toxicity thresholds for trace elements and heavy metals. Our objective was to quantify levels of trace elements and heavy metals within black vulture (Coragyps atratus) and turkey vulture (Cathartes aura) tissues to determine the extent to which populations in the southeastern United States are exposed to carrion that contains high levels of contaminants. We collected black vulture liver samples and examined differences in trace element and heavy metal concentrations between sexes and age classes (adult and juvenile). Further, we collected 81 blood and 42 feather samples from additional black and turkey vultures and compared differences between species and age classes. We found similar element concentrations between juvenile and adult black vultures with the exception of Cu, where levels 40 were higher in juveniles compared to adults. However, we did observe substantial differences in element concentrations between species for both blood and feather samples, with black vultures generally having higher concentrations of most elements. Our data revealed higher element levels in both species compared to toxicity thresholds found in other bird of prey species, such as blood and liver toxicity threshold suggestions for Pb poisoning in Falconiformes. Further, while average contaminant levels were generally low, extreme outliers were observed for some elements, including Pb, suggesting some individuals were exposed to high levels of potentially toxic elements. In conclusion, more research is needed to better understand contaminant exposure in black and turkey vultures across a broader geographic region, as well as elucidate toxicity thresholds and non-lethal impacts of contaminant exposure in these species.

63 RADIATION, THERMAL, AND OTHER ENVIRON. POLLUTAN↗