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NASA NTRS1988

Bidirectional reflectance properties of iron-nickel meteorites

The effects of viewing geometry and small-scale (less than 1 mm) surface roughness on the bidirectional reflectance of iron-nickel meteorites were investigated by measuring the reflectance properties of Gibeon and Canyon Diablo iron-nickel meteorites. Several cut surfaces of each of these meteorites were polished with abrasive grits to controlled surface roughness, and a series of bidirectional reflectance spectra were taken at a variety of viewing geometries using NASA's RELAB facility. The measurements show that, for optically smooth surfaces, only the specular component of reflectance exhibited red-sloped continuum characteristic of iron. Spectra of surfaces that were much rougher than the wavelength of incident light exhibited iron's characteristic red sloped continuum and could be modeled by linear combinations of facets that are oriented in specular and nonspecular geometries with respect to the observer. Spectra of this latter type exhibit good agreement with the published spectra of M-type asteroids.

Britt, D. T.↗

DOE OSTI2023

Prediction of dislocation - grain boundary interactions in FCC aluminum bicrystals using a modified continuum criterion and machine learning methods

Mechanical properties of metals such as strength and toughness are strongly correlated to complex interactions between various defects in the crystalline structure. While elementary interactions between these defects have been investigated using recent micro- and nano-characterization techniques, understanding of the detailed interaction mechanisms has hardly been obtained. To understand defect-driven plasticity at various time and length scales, it is necessary to formulate a general guideline to predict both the interaction type (transmission or reflection) and the dislocation's subsequent slip system after the interaction. Many criteria based on the geometric alignment of the defects have been developed to predict this phenomenon, but these have yet to be found to be accurate when applied to general data sets of grain boundaries (GBs). With this motivation, we conduct a systematic study using molecular dynamics (MD) models of bicrystals to analyze defect interaction process between a prismatic dislocation loop and eleven different grain boundaries of the following character: three tilt, three twist, and five mixed. Based on the MD observations, two new prediction methods are developed: the first is a new data-driven parametric score function based on the classical geometric criteria, and the second is by applying Gaussian process machine learning methods to find the probability distribution of a hidden function. In conclusion, the proposed data-driven prediction methods could pave a new way to predict the unit interaction of dislocations with various GBs, which could show much higher accuracy compared to pre-existing geometric criteria.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Advancing river corridor science beyond disciplinary boundaries with an inductive approach to catalyse hypothesis generation

Abstract A unified conceptual framework for river corridors requires synthesis of diverse site‐, method‐ and discipline‐specific findings. The river research community has developed a substantial body of observations and process‐specific interpretations, but we are still lacking a comprehensive model to distill this knowledge into fundamental transferable concepts. We confront the challenge of how a discipline classically organized around the deductive model of systematically collecting of site‐, scale‐, and mechanism‐specific observations begins the process of synthesis. Machine learning is particularly well‐suited to inductive generation of hypotheses. In this study, we prototype an inductive approach to holistic synthesis of river corridor observations, using support vector machine regression to identify potential couplings or feedbacks that would not necessarily arise from classical approaches. This approach generated 672 relationships linking a suite of 157 variables each measured at 62 locations in a fifth order river network. Eighty four percent of these relationships have not been previously investigated, and representing potential (hypothetical) process connections. We document relationships consistent with current understanding including hydrologic exchange processes, microbial ecology, and the River Continuum Concept, supporting that the approach can identify meaningful relationships in the data. Moreover, we highlight examples of two novel research questions that stem from interpretation of inductively‐generated relationships. This study demonstrates the implementation of machine learning to sieve complex data sets and identify a small set of candidate relationships that warrant further study, including data types not commonly measured together. This structured approach complements traditional modes of inquiry, which are often limited by disciplinary perspectives and favour the careful pursuit of parsimony. Finally, we emphasize that this approach should be viewed as a complement to, rather than in place of, more traditional, deductive approaches to scientific discovery.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Continuum shock mixture models for Ni+Al multilayers: Inert mesoscale simulations

Mesoscale modeling of shock waves in Ni+Al multilayers poses significant challenges that are due, in part, to shock-induced chemical reactions. Current modeling approaches utilize reactive molecular dynamics (MD), but they are limited to resolving domains of only a few hundred nanometers. In contrast, actual multilayer superlattices can be tens of micrometers thick, and they exhibit non-ideal (i.e., wavy) interfaces. The second part of our research builds upon previous work developing physically based, thermodynamically complete equations of state for various Ni and Al intermetallic compositions. Here, we introduce a novel workflow for high-fidelity mesoscale simulations of Ni+Al multilayers using a continuum hydrocode. By increasing the simulation domain size beyond MD limitations (e.g., 2 × 6 μm 2 ) and incorporating explicit interfacial roughness, we investigate the shock response of Ni+Al multilayers at previously unexplored scales. Our experimental design encompasses nine multilayer geometries with varying roughness amplitudes and tilt angles (θ = 15°, 30°, and 45°), alongside 19 flyer impact velocities ranging from 0.3 to 3.0 km/s, resulting in a total of 171 high-fidelity simulations. The bulk shock state from inert 2D mesoscale simulations aligns with the law of mixtures, while temperature and pressure fluctuations strongly correlate with multilayer geometry types. A new metric dubbed the “hot spot probability integral” shows a greater dependence on a tilt angle than interfacial roughness.

Kittell, David E. [Sandia National Laboratories (S↗

NASA NTRS2000

Cloudy 94 and Applications to Quasar Emission Line Regions

This review discusses the most recent developments of the plasma simulation code Cloudy and its application to the, emission-line regions of quasars. The longterm goal is to develop the tools needed to determine the chemical composition of the emitting gas and the luminosity of the central engine for any emission line source. Emission lines and the underlying thermal continuum are formed in plasmas that are far from thermodynamic equilibrium. Their thermal and ionization states are the result of a balance of a vast set of microphysical processes. Once produced, radiation must, propagate out of the (usually) optically thick source. No analytic solutions are possible, and recourse to numerical simulations is necessary. I am developing the large-scale plasma simulation code Cloudy as an investigative tool for this work, much as an observer might build a spectrometer. This review describes the current version of Cloudy, version 94. It describes improvements made since the, release of the previous version, C90. The major recent, application has been the development of the "Locally Optimally-Emitting Cloud" (LOC) model of AGN emission line regions. Powerful selection effects, introduced by the atomic physics and line formation process, permit individual lines to form most efficiently only near certain selected parameters. These selection effects, together with the presence of gas with a wide range of conditions, are enough to reproduce the spectrum of a typical quasar with little dependence on details. The spectrum actually carries little information to the identity of the emitters. I view this as a major step forward since it provides a method to handle accidental details at the source, so that we can concentrate on essential information such as the luminosity or chemical composition of the quasar.

Ferland, Gary J.↗

DOE OSTI2021

Appearance versus disappearance of broad absorption line troughs in quasars

ABSTRACT We present a new set of 84 broad absorption line (BAL) quasars (1.7 < zem < 4.4) exhibiting an appearance of C iv BAL troughs over 0.3–4.8 rest-frame years by comparing the Sloan Digital Sky Survey Data Release (SDSSDR)-7, SDSSDR-12, and SDSSDR-14 quasar catalogues. We contrast the nature of BAL variability in this appearing BAL quasar sample with a disappearing BAL quasar sample studied in the literature by comparing the quasar’s intrinsic, BAL trough, and continuum parameters between the two samples. We find that appearing BAL quasars have relatively higher redshift and smaller probed time-scales as compared to the disappearing BAL quasars. To mitigate the effect of any redshift bias, we created control samples of appearing and disappearing BAL quasars that have similar redshift distribution. We find that the appearing BAL quasars are relatively brighter and have shallower and wider BAL troughs compared to the disappearing BAL sample. The distribution of quasar continuum variability parameters between the two samples is clearly separated, with the appearance of the BAL troughs being accompanied by the dimming of the continuum and vice versa. Spectral index variations in the two samples also point to the anticorrelation between the BAL trough and continuum variations consistent with the ‘bluer when brighter’ trend in quasars. We show that the intrinsic dust model is less likely to be a favourable scenario in explaining BAL appearance/disappearance. Our analysis suggests that the extreme variations of BAL troughs like BAL appearance/disappearance are mainly driven by changes in the ionization conditions of the absorbing gas.

Mishra, Sapna↗

NASA NTRS1981

Multi-ring basin formation - Possible clues from impact cratering calculations

Finite difference continuum mechanics code calculations make it possible to vary the controlling variables in an impact event and to determine basic trends at scales unavailable to experimental analysis. Orphal et al. (1980) have summarized the results of a pair of such calculations for identical projectile/target characteristics but different impact velocities. One calculation considered a relatively low velocity iron impactor (5 km/s); the other, a high velocity iron impactor (15.8 km/s). The primary purpose was to investigate the generation and transport of impact melt for the two impact energies. Attention is given to crater growth, crater ejecta, and possible implications for basin-size events. Based on extrapolations, a new scenario is proposed. The scenario incorporates elements of several existing basin models.

Schultz, P. H.↗

DOE OSTI2023

Coarse-grained explicit-solvent molecular dynamics simulations of semidilute unentangled polyelectrolyte solutions

In this study, we present results from explicit-solvent coarse-grained molecular dynamics (MD) simulations of fully charged, salt-free, and unentangled polyelectrolytes in semidilute solutions. The inclusion of a polar solvent in the model allows for a more physical representation of these solutions at concentrations, where the assumptions of a continuum dielectric medium and screened hydrodynamics break down. The collective dynamic structure factor of polyelectrolytes, S(q, t), showed that at q > q*, where q* = 2π/ξ is the polyelectrolyte peak in the structure factor S(q) and ξ is the correlation length, the relaxation time obtained from fits to stretched exponential was $\tau$ KWW ~ q -3 , which describes unscreened Zimm-like dynamics. This is in contrast to implicit-solvent simulations using a Langevin thermostat where $\tau$ KWW ~ q -2 . At q < q*, a crossover region was observed that eventually transitions to another inflection point $\tau$ KWW ~ q -2 at length scales larger than ξ for both implicit- and explicit-solvent simulations. The simulation results were also compared to scaling predictions for correlation length, ξ ~ c$-½\atop{p}$, specific viscosity, η sp ~ c$½\atop{p}$, and diffusion coefficient, D ~ c$0\atop{p}$, where c p is the polyelectrolyte concentration. The scaling prediction for ξ holds; however, deviations from the predictions for η sp and D were observed for systems at higher c p , which are in qualitative agreements with recent experimental results. This study highlights the importance of explicit-solvent effects in molecular dynamics simulations, particularly in semidilute solutions, for a better understanding of polyelectrolyte solution behavior.

36 MATERIALS SCIENCE↗

NASA NTRS1998

A Multi-Scale Sampling Strategy for Detecting Physiologically Significant Signals in AVIRIS Imagery

Models of photosynthetic production at ecosystem and global scales require multiple input parameters specifying physical and physiological surface features. While certain physical parameters (e.g., absorbed photosynthetically active radiation) can be derived from current satellite sensors, other physiologically relevant measures (e.g., vegetation type, water status, carboxylation capacity, or photosynthetic light-use efficiency), are not generally directly available from current satellite sensors at the appropriate geographic scale. Consequently, many model parameters must be assumed or derived from independent sources, often at an inappropriate scale. An abundance of ecophysiological studies at the leaf and canopy scales suggests strong physiological control of vegetation-atmosphere CO2 and water vapor fluxes, particularly in evergreen vegetation subjected to diurnal or seasonal stresses. For example hot, dry conditions can lead to stomatal closure, and associated "downregulation" of photosynthetic biochemical processes, a phenomenon often manifested as a "midday photosynthetic depression". A recent study with the revised simple biosphere (SiB2) model demonstrated that photosynthetic downregulation can significantly impact global climate. However, at the global scale, the exact significance of downregulation remains unclear, largely because appropriate physiological measures are generally unavailable at this scale. Clearly, there is a need to develop reliable ways of extracting physiologically relevant information from remote sensing. Narrow-band spectrometers offer many opportunities for deriving physiological parameters needed for ecosystem and global scale photosynthetic models. Experimental studies on the ground at the leaf- to stand-scale have indicated that several narrow-band features can be used to detect plant physiological status. One physiological signal is caused by xanthophyll cycle pigment activity, and is often expressed as the Photochemical Reflectance Index (PRI). Because the xanthophyll cycle pigments are photoregulatory pigments closely linked to photosynthetic function, this index can be used to derive relative photosynthetic rates. An additional signal with physiological significance is the 970 nm water absorption band, which provides a measure of liquid water content. This feature has been quantified both using a simple 2-band ratio (900/970 nm, here referred to as the "Water Band Index" or WBI;), and using the "continuum removal" method. Current atmospheric correction methods for AVIRIS imagery also obtain quantitative expressions of surface liquid water absorption based on the 970 nm water band and may be comparable to ground-based estimates of water content using this feature. However, physiological interpretations of both the PRI and the WBI are best understood at the leaf and canopy scales, where complications of atmospheric interference and complex stand and landscape features can be minimized, and where experimental manipulations can be readily applied. Currently it is not known whether these physiological indices can be used to derive meaningful physiological information from AVIRIS imagery. In addition to the problem of atmospheric interference, another challenge is that any simple physiological index can be confounded by multiple factors unrelated to physiology, and this problem can become more severe at progressively larger spatial scales. For example, previous work has suggested that both the PRI and the WBI, are strongly correlated with other optical measures of canopy structure (e.g., the Normalized Difference Vegetation Index or green vegetation fraction), indicating a confounding effect of structure on physiological signals at the larger, landscape scale. Furthermore, the normal operating mode of most imaging spectrometers does not allow simultaneous, ground truthing at a level of detail needed for physiological sampling. Additionally, manipulative experiments of physiology are difficult to apply at a geographic scale suitable for comparison with remote imagery, which often works at spatial scales that are several orders of magnitude larger than those typically used for physiological studies. These limitations require the consideration of alternative approaches to validating physiological information derived from AVIRIS data. In this report, we present a multi-scale sampling approach to detecting physiologically significant signals in narrow-band spectra. This approach explores the multi-dimensional data space provided by narrow-band spectrometry, and combines AVIRIS imagery at a large scale, with ground spectral sampling at an intermediate scale, and detailed ecophysiological measurements at a fine scale, to examine seasonally and spatially changing relationships between multiple structural and physiological variables. Examples of this approach are provided by simultaneous sampling of the Normalized Difference Vegetation Index (NDVI), an index of fractional PAR interception and green vegetation cover, the Water Band Index (WBI, an index of liquid water absorption, and the Photochemical Reflectance Index (PRI, an index of xanthophyll cycle pigment activity and photosynthetic light-use efficiency. By directly linking changing optical properties sampled on the ground with measurable physiological states, we hope to develop a basis for interpreting similar signals in AVIRIS imagery.

Gamon, John A.↗

DOE OSTI2021

Microscopic and Macroscopic Characterization of Grain Boundary Energy and Strength in Silicon Carbide via Machine-Learning Techniques

Predicting the properties of grain boundaries poses a challenge because of the complex relationships between structural and chemical attributes both at the atomic and continuum scales. Grain boundary systems are typically characterized by parameters used to classify local atomic arrangements in order to extract features such as grain boundary energy or grain boundary strength. The present work utilizes a combination of high-throughput atomistic simulations, macroscopic and microscopic descriptors, and machine-learning techniques to characterize the energy and strength of silicon carbide grain boundaries. Additionally, a diverse data set of symmetric tilt and twist grain boundaries are described using macroscopic metrics such as misorientation, the alignment of critical low-index planes, and the Schmid factor, but also in terms of microscopic metrics, by quantifying the local atomic structure and chemistry at the interface. These descriptors are used to create random-forest regression models, allowing for their relative importance to the grain boundary energy and decohesion stress to be better understood. Results show that while the energetics of the grain boundary were best described using the microscopic descriptors, the ability of the macroscopic descriptors to reasonably predict grain boundaries with low energy suggests a link between the crystallographic orientation and the resultant atomic structure that forms at the grain boundary within this regime. For grain boundary strength, neither microscopic nor macroscopic descriptors were able to fully capture the response individually. However, when both descriptor sets were utilized, the decohesion stress of the grain boundary could be accurately predicted. These results highlight the importance of considering both macroscopic and microscopic factors when constructing constitutive models for grain boundary systems, which has significant implications for both understanding the fundamental mechanisms at work and the ability to bridge length scales.

36 MATERIALS SCIENCE↗

NASA NTRS1999

Ultraviolet, Optical and X-Ray Imaging of Selected Cygnus Loop Fields

During the Astro-1 and Astro-2 Space Shuttle missions in 1990 and 1995, far ultraviolet (FUV) images of five 40 ft diameter fields around the rim of the Cygnus Loop Super Nova Remnants (SNR) were observed with the Ultraviolet Imaging Telescope (UIT). These fields sample a broad range of SNR conditions including both radiative and non-radiative shocks in various geometries and scales. The UIT B5 band images discussed here sample predominantly ion-C4 lambda 1550 and the 2-photon continuum. Smaller contributions are made by emission lines of ion He-2 lambda 1640 and ion 03 lambda 1666. A unique aspect of the B5 band is its ability to sample the hydrogen 2-photon continuum from regions where the gas is recombining. We present these new FUV images and compare them with optical H-alpha and [ion O13], and ROSAT HRI X-ray images. In non-radiative shocks, existing 2-photon flux measurements from spectra and the H-alpha images suggest we are seeing approximately equal contributions from 2-photon and ion C4 emission. In radiative filaments, however, shock models and our images suggest ion C4 should dominate while spectra of specific locations seem to indicate that 2-photon emission dominates. We surmise that spectral observations on specific bright filaments have decreased locally-observed levels of ion C41 emission due to resonance scattering in that line.

Danforth, C. W.↗

NASA NTRS1992

Hubble Space Telescope imaging of distant galaxies - 4C 41.17 at z = 3.8

The Hubble Space Telescope has been used to image the continuum emission from 4C 41.17 at z = 3.8, the most distant galaxy known. The galaxy was detected with good signal-to-noise ratio and was spatially resolved at the 0.1 arcsec (440 pc) HST resolution. About 35 percent of this emission is in the form of a high brightness clumpy region extending by about 0.5 arcsec (1.7 kpc), whose morphology is remarkably similar to that of the radio components. A fainter more diffuse region of optical emission extends westward from the center of the nuclear complex for about 1.2 arcsec (5.3 kpc) out along the radio axis. The clumpiness of the optical emission and its close correspondence with the radio structure on the subkiloparsec scale is discussed in the light of current models for high-redshift galaxies. Our observations imply that the material in the center of this galaxy is clumpy on the subkiloparsec scale.

Miley, G. K.↗

DOE OSTI2023

Past-completeness of inflationary spacetimes

Here, we discuss the question of whether or not inflationary spacetimes can be geodesically complete in the infinite past. Geodesic completeness is a necessary condition for averting an initial singularity during eternal inflation. It is frequently argued that cosmological models which are expanding sufficiently fast (having average Hubble expansion rate H avg > 0) must be incomplete in null and timelike past directions. This well-known conjecture relies on specific bounds on the integral of the Hubble parameter over a past- directed timelike or null geodesic. As stated, we show this claim is an open issue. We show that the calculation of H avg yields a continuum of results for a given spacetime predicated upon the underlying topological assumptions. We present an improved definition for H avg and introduce an uncountably infinite cohort of cosmological solutions which are geodesically complete despite having H avg > 0. We discuss a standardized definition for inflationary spacetimes as well as quantum (semiclassical) cosmological concerns over physically reasonable scale factors.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1998

A Radio-Jet-Galaxy Interaction in 3C441

Multi-wavelength imaging and spectroscopy of the zeta = 0.708 radio galaxy 3C441 and a red aligned optical/infrared component are used to show that the most striking aspect of the radio-optical "alignment effect" in this object is due to the interaction of the radio jet with a companion galaxy in the same group or cluster. The stellar population of the red aligned continuum component is predominately old, but with a small post-starburst population superposed, and it is surrounded by a low surface- brightness halo, possibly a face-on spiral disc. The [OIII]500.7/[OII]372.7 emission line ratio changes dramatically from one side of the component to the other, with the low-ionisation material apparently having passed through the bow shock of the radio source and been compressed. A simple model for the interaction is used to explain the velocity shifts in the emission line gas, and to predict that the ISM of the interacting galaxy is likely to escape once the radio source bow shock has passed though. We also discuss another, much fainter, aligned component, and the sub-arcsecond scale alignment of the radio source host galaxy. Finally we comment on the implications of our explanation of 3C441 for theories of the alignment effect.

Lacy, Mark↗

NASA NTRSDate not supplied

Validating Drag and Heating Coefficients for Hollow Reentry Objects in Continuum Flow Using a Mach 7 Ludwieg Tube

Drag and heating coefficient databases and models are crucial to destructive reentry simulation. The NASA Orbital Debris Program Office (ODPO) develops, maintains, and performs analysis with the Object Reentry Survival Analysis Tool (ORSAT), which comprises drag and heating models for free molecular, transitional, and continuum flow regimes. These models have, in the past, only included solid, convex, blunt shapes (such as boxes, spheres, and cylinders). Previous work led by ODPO includes the extension of these models to hollow cylinders and square boxes in free molecular and transitional flow using the Direct Simulation Monte Carlo (DSMC) method. Since 2019, the ODPO has continued its program of DSMC simulations and extended the project to include analyses with the NASA Data Parallel Line Relaxation (DPLR) program on hollow cylinders and boxes (with varying wall thickness-diameter ratio). In fall 2022, the ODPO began a collaboration with the University of Texas San Antonio (UTSA) to use the Mach 7 Ludwieg Tube facility to validate the model built using numerical simulations. This facility can replicate (at a scale of approximately 100:1) the conditions seen by reentering objects near typical demise altitudes. We present here the drag and heating coefficients derived from the continued DSMC simulations, the new DPLR simulations, and the 26-test series at UTSA.

Chris Ostrom↗

NASA NTRS2023

Validating Drag and Heating Coefficients for Hollow Reentry Objects in Continuum Flow Using a Mach 7 Ludwieg Tube

Chris Ostrom↗

DOE OSTI2021

Insights into the emergence of mass from studies of pion and kaon structure

There are two mass generating mechanisms in the standard model of particle physics (SM). One is related to the Higgs boson and fairly well understood. The other is embedded in quantum chromodynamics (QCD), the SM’s strong interaction piece; and although responsible for emergence of the roughly 1 GeV mass scale that characterises the proton and hence all observable matter, the source and impacts of this emergent hadronic mass (EHM) remain puzzling. As bound states seeded by a valence-quark and -antiquark, pseudoscalar mesons present a simpler problem in quantum field theory than that associated with the nucleon. Consequently, there is a large array of robust predictions for pion and kaon properties whose empirical validation will provide a clear window onto many effects of both mass generating mechanisms and the constructive interference between them. This has now become significant because new-era experimental facilities, in operation, construction, or planning, are capable of conducting such tests and thereby contributing greatly to resolving the puzzles of EHM. These aspects of experiment, phenomenology, and theory, along with contemporary successes and challenges, are reviewed herein. In addition to providing an overview of the experimental status, we focus on recent progress made using continuum Schwinger function methods and lattice-regularised QCD. Further, advances made using other theoretical tools are also sketched. Our primary goal is to highlight the potential gains that can accrue from a coherent effort aimed at finally reaching an understanding of the character and structure of Nature’s Nambu–Goldstone modes.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

The photon content of the proton in the CT18 global analysis

Recently, two photon PDF sets based on implementations of the LUX ansatz into the CT18 global analysis were released. In CT18lux, the photon PDF is calculated directly using the LUX master formula for all scales, \mu μ . In an alternative realization, CT18qed, the photon PDF is initialized at the starting scale, \mu_0 μ 0 , using the LUX formulation and evolved to higher scales \mu(>\mu_0) μ ( > μ 0 ) with a combined QED+QCD kernel at \mathcal{O}(\alpha),~\mathcal{O}(\alpha\alpha_s) 𝒪 ( α ) , 𝒪 ( α α s ) and \mathcal{O}(\alpha^2) 𝒪 ( α 2 ) . In the small- x x region, the photon PDF uncertainty is mainly induced by the quark and gluon PDFs, through the perturbative DIS structure functions. In comparison, the large- x x photon uncertainty comes from various low-energy, nonperturbative contributions, including variations of the inelastic structure functions in the resonance and continuum regions, higher-twist and target-mass corrections, and elastic electromagnetic form factors of the proton. We take the production of doubly-charged Higgs pairs, (H^{++}H^{--}) ( H + + H − − ) , as an example of scenarios beyond the Standard Model to illustrate the phenomenological implications of these photon PDFs at the LHC.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗