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At least 289 records · Page 16

Investigating the broadening phenomenon in two-particle correlations induced by gluon saturation

It has been found that the gluon density inside the proton grows rapidly at small momentum fractions. Quantum chromodynamics (QCD) predicts that this growth can be regulated by nonlinear effects, ultimately leading to gluon saturation. Within the color glass condensate framework, nonlinear QCD effects are predicted to suppress and broaden back-to-back angular correlations in collisions involving heavy nuclei. While suppression has been observed in various experiments in 𝑑/𝑝 + A collisions compared to 𝑝 + 𝑝 collisions, the predicted broadening remains unobserved. This study investigates the contributions of intrinsic transverse momentum (𝑘 𝑇 ), which is associated with saturation physics, as well as parton showers and transverse motion from fragmentation (𝑝$^{frag}_{𝑇}$), which are not saturation dependent, to the width of the correlation function. Our findings show that the non-saturation dependent effects, especially the initial-state parton shower and 𝑝$^{frag}_{𝑇}$, which occur independently of the collision system, smear the back-to-back correlation more than gluon saturation does, making the broadening phenomenon difficult to observe.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Higher-order nonequilibrium term: Effective power density quantifying evolution towards or away from local thermodynamic equilibrium

A common approach to assess the nature of energy conversion in a classical fluid or plasma is to compare power densities of the various possible energy conversion mechanisms. A leading research area is quantifying energy conversion for systems that are not in local thermodynamic equilibrium (LTE), as is common in a number of fluid and plasma systems. Here we introduce the “higher-order nonequilibrium term” (HORNET) effective power density, which quantifies the rate of change of departure of a phase space density from LTE. It has dimensions of power density, which allows for quantitative comparisons with standard power densities. We employ particle-in-cell simulations to calculate HORNET during two processes, magnetic reconnection and decaying kinetic turbulence in collisionless magnetized plasmas, that inherently produce non-LTE effects. We investigate the spatial variation of HORNET and the time evolution of its spatial average. By comparing HORNET with power densities describing changes to the internal energy (pressure dilatation, Pi − D , and divergence of the vector heat flux density), we find that HORNET can be a significant fraction of these other measures (8% and 35% for electrons and ions, respectively, for reconnection; up to 67% for both electrons and ions for turbulence), meaning evolution of the system towards or away from LTE can be dynamically important. Applications to numerous plasma phenomena are discussed. Published by the American Physical Society 2024

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Opportunities and Challenges for Hydrotreating of Catalytic Fast Pyrolysis Oil to Fuels

Catalytic fast pyrolysis (CFP) provides a versatile platform for producing fuels to combat climate change and meet decarbonizing targets. In this contribution, we will discuss the hydroprocessing of CFP oils to a variety of fuels, including sustainable aviation fuel (SAF), diesel, and marine fuel. Both standalone and co-hydroprocessing with petroleum streams will be covered. Hydrotreating CFP oil at temperatures around 400 Degrees Celsius can produce a highly deoxygenated product with oxygen contents below the detection limit. However, the quality of fuel fractions produced has been a problem, manifesting as low octane numbers for the gasoline-range fraction and low cetane numbers for the diesel-range fraction. Incorporating an initial transition zone for hydrogenation during hydrotreating was shown to dramatically increase the diesel fraction cetane number from 24 to 45. A similar approach enabled the production of a cycloalkane-rich SAF fraction meeting key ASTM 4054 guidelines with respect to density, viscosity, heating value, volatility, freeze and flash point. Over 400 hours of hydrotreating for SAF was demonstrated with no signs of catalyst bed fouling, measured by pressure drop over the catalyst bed. Compared to other fuels, marine fuel is unique in that it does not require complete deoxygenation. We investigated the minimum hydrotreating requirements to produce fuel compatible with very low sulfur fuel oil, and the results suggested 30% reduction in hydrotreating costs for this approach. Co-hydroprocessing offers an opportunity to take advantage of refinery infrastructure and economies of scale although the operation is less flexible with respect to operating conditions. Co-hydroprocessing CFP oil with petroleum streams gave efficient deoxygenation at milder conditions (e.g. at temperatures of 320 Degrees Celsius) than required for standalone hydrotreating. Over 90% incorporation of biogenic carbon in the CFP oil was confirmed by carbon-14 analysis. Hydrotreating of CFP oil, whether by standalone or co-processing, can produce a variety of fuel cuts, whose quality can be tailored by changing process conditions. Challenges remain, including long-term catalyst performance and determining CFP oil quality requirements.

09 BIOMASS FUELS↗

Search for brown dwarfs in IC 1396 with Subaru HSC: interpreting the impact of environmental factors on substellar population

ABSTRACT Young stellar clusters are predominantly the hub of star formation and hence, ideal to perform comprehensive studies over the least explored substellar regime. Various unanswered questions like the mass distribution in brown dwarf regime and the effect of diverse cluster environment on brown dwarf formation efficiency still plague the scientific community. The nearby young cluster, IC 1396 with its feedback-driven environment, is ideal to conduct such study. In this paper, we adopt a multiwavelength approach, using deep Subaru HSC along with other data sets and machine learning techniques to identify the cluster members complete down to ∼ 0.03 M⊙ in the central 22 arcmin area of IC 1396. We identify 458 cluster members including 62 brown dwarfs which are used to determine mass distribution in the region. We obtain a star-to-brown dwarf ratio of ∼ 6 for a stellar mass range 0.03–1 M⊙ in the studied cluster. The brown dwarf fraction is observed to increase across the cluster as radial distance from the central OB-stars increases. This study also compiles 15 young stellar clusters to check the variation of star-to-brown dwarf ratio relative to stellar density and ultraviolet (UV) flux ranging within 4–2500 stars pc−2 and 0.7–7.3 G0, respectively. The brown dwarf fraction is observed to increase with stellar density but the results about the influence of incident UV flux are inconclusive within this range. This is the deepest study of IC 1396 as of yet and it will pave the way to understand various aspects of brown dwarfs using spectroscopic observations in future.

Gupta, Saumya (ORCID:0000000161843958)↗

Compressive Response and Energy Absorption of Additively Manufactured Elastomers with Varied Simple Cubic Architectures

Additive manufacturing, and particularly the vat photopolymerization process, enables the fabrication of complex geometries at high resolution and small length scales, making it well-suited for fabricating cellular structures (e.g., foams and lattices). Among these, elastomeric cellular structures are of growing interest due to their tunable compliance and energy dissipation. However, comprehensive data on the compressive behavior of these structures remains limited, especially for investigating the structure-property effects from changing the density and distribution of material within the cellular structure. This study explores how the mechanical response of polyurethane-based simple cubic structures changes when varying volume fraction, unit cell length, and unit cell patterning, which have not been systematically investigated previously in additively manufactured elastomers. Increasing volume fraction from 10% to 50% yielded significant changes in compressive stress–strain performance (decreasing strain at 0.5 MPa by 41.6% and increasing energy absorption density by 3962.5%). Although changing the unit cell length between 2.5 and 7 mm in ~30 mm parts did not result in statistically different stress–strain responses, modifying the configuration of struts of different thicknesses across designs with 30% volume fraction altered the stress–strain behavior (differences of 12.5% in strain at 0.5 MPa and 109.4% for energy absorption density). Power law relationships were developed to understand the interactions between volume fraction, unit cell length, and elastic modulus, and experimental data showed strong fits (R 2 > 0.91). These findings enhance the understanding of how multiple structural design aspects influence the performance of elastomeric cellular materials, providing a foundation for informing strategic design of tailorable materials for diverse mechanical applications.

36 MATERIALS SCIENCE↗

Comparative Life Cycle Assessment of Injection Molded and Big Area Additive Manufactured NdFeB Bonded Permanent Magnets

Permanent magnets are expected to play a crucial role in the realization of the clean economy. In particular, the neodymium-iron-boron (Nd2Fe14B or NdFeB) magnets, which have the highest energy density among rare earth permanent magnets, are needed for building more efficient windmill generators, electric vehicle motors, etc. Currently, near-net shape magnets can be either made through sintering and compression molding with extensive post machining or directly through injection molding. However, injection molding has a loading volume fraction limitation of 0.65 for nylon binders. A novel method of manufacturing bonded permanent magnets with loading fraction greater than 0.65 has been demonstrated using Big Area Additive Manufacturing (BAAM) printers. As energy density is directly proportional to the square of the magnet loading fraction, magnets produced using BAAM printers require less volume and magnetic material compared to that of injection molded magnets on average. A comparative LCA shows that this difference in magnetic powder consumption nearly constitutes the difference in the environmental impact categories. Even after assuming recycled magnetic input, the BAAM magnets perform better environmentally than injection molded magnets, especially in the ozone depletion category. Since BAAM printers can accommodate even higher loading fractions, at scale, BAAM printers possibly can bring about a significant decrease in rare earth mineral consumption and environmental emissions. So furthermore, single screw extrusion enables BAAM printers to have high print speeds and allow them to be economically competitive against injection molding. Therefore, BAAM printed magnets show promise in transitioning towards the clean economy.

36 MATERIALS SCIENCE↗

Smaller feature size impairs densification in digital light processing 3D printed ceramic samples

In this study, we investigate how geometric miniaturization affects the sintering densification behavior of alumina cylinders with various wall thicknesses (down to ∼500 µm in green body) fabricated via digital light processing (DLP). As the wall thickness decreased, the density of the sintered samples consistently declined. Microstructural characterization revealed the presence of a crack-rich surface skin that is ∼500 µm thick. As the wall thickness decreases, the skin's volume fraction rises, and its poor local densification increasingly dominates the part average, leading to an overall decrease in the density of the sintered samples. For the thinnest wall (500 µm) cylinder, macroscopic warping occurred during sintering. We suggest that warping further disrupts particle packing and induces through-thickness nonuniformity, further impairing densification in addition to the skin-fraction effect. These results highlight how geometric miniaturization may adversely influence the sintering behavior and final density of DLP-printed ceramics through distinct densification-limiting mechanisms.

Materials science↗

Comparative post-irradiation examination of high burnup U-19Pu-10Zr: Assessing steady-state irradiation behavior against historical and modeled fuel performance

Here, the development of next-generation sodium-cooled fast reactors necessitates comprehensive research on metallic fuels to maximize economic performance while ensuring safe operation. In this study, we investigated the steady-state irradiation behavior of two high burnup U-19Pu-10Zr fuel pins, DP-36 and DP-40, in preparation for planned safety testing. Post-irradiation examination (PIE) was performed to quantify fuel column elongation, regions of low-density at the top of the fuel column, pin deformation, fission product distribution, fractional fission gas release, microstructural evolution, and fuel constituent redistribution. Benchmarking against existing PIE data from U-19Pu-10Zr fuel pins irradiated in EBR-II revealed consistent patterns in fuel column elongation and cladding diametral strain. However, both pins exhibited longer low-density structures, and destructive examination of DP-36 revealed more complex constituent redistribution patterns compared to previously reported data for ternary fuel pins. The steady-state irradiation of both pins was also modeled using BISON. Comparisons of PIE results with modeled predictions showed overall agreement in fractional fission gas release but consistent overestimation of axial and radial swelling due to gaseous and solid swelling models. These findings underscore the critical importance of pre-test characterization on test and sibling pins to accurately capture steady-state fuel behavior ahead of transient testing, thus establishing a baseline for post-test comparison. Additionally, these analyses identified key data gaps that warrant further investigation to improve the understanding and prediction of fuel swelling, thereby enhancing the synergy between modeling and experimental efforts in supporting accident testing.

BISON↗

Emergence of the temperature–density relation in the low-density intergalactic medium

We examine the evolution of the phase diagram of the low-density intergalactic medium during the Epoch of Reionization in simulation boxes with varying reionization histories from the Cosmic Reionization on Computers project. The probability density function (PDF) of gas temperature at fixed density exhibits two clear modes: a warm and a cold temperature mode, corresponding to the gas inside and outside of ionized bubbles. We find that the transition between the two modes is ‘universal’ in the sense that its timing is accurately parametrized by the value of the volume-weighted neutral fraction for any reionization history. This ‘universality’ is more complex than just a reflection of the fact that ionized gas is warm and neutral gas is cold: it holds for the transition at a fixed value of gas density, and gas at different densities transitions from the cold to the warm mode at different values of the neutral fraction, reflecting a non-trivial relationship between the ionization history and the evolving gas density PDF. Furthermore, the ‘emergence’ of the tight temperature–density relation in the warm mode is also approximately ‘universally’ controlled by the volume-weighted neutral fraction for any reionization history. In particular, the ‘emergence’ of the temperature–density relation (as quantified by the rapid decrease in its width) occurs when the neutral fraction is 10 –4 ≲ X HI ≲ 10 –3 for any reionization history. Our results indicate that the neutral fraction is a primary quantity controlling the various properties of the temperature–density relation, regardless of reionization history.

79 ASTRONOMY AND ASTROPHYSICS↗

In situ study of microstructure evolution and α → ω phase transition in annealed and pre-deformed Zr under hydrostatic loading

The detailed study of the effect of the initial microstructure on its evolution under hydrostatic compression before, during, and after the irreversible α → ω phase transformation and during pressure release in Zr using in situ x-ray diffraction is presented. Two samples were studied: one is plastically pre-deformed Zr with saturated hardness and the other is annealed. Phase transformation α → ω initiates at lower pressure for a pre-deformed sample but for a volume fraction of ω Zr, c > 0.7, a larger volume fraction is observed for the annealed sample. This implies that the proportionality between the athermal resistance to the transformation and the yield strength in the continuum phase transformation theory is invalid; an advanced version of the theory is outlined. Phenomenological plasticity theory under hydrostatic loading is outlined in terms of microstructural parameters, and plastic strain is estimated. During transformation, the first rule is suggested, i.e., the average domain size, microstrain, and dislocation density in ω Zr for c < 0.8 are functions of the volume fraction, c of ω Zr only, which are independent of the plastic strain tensor prior to transformation and pressure. The microstructure is not inherited during phase transformation. Surprisingly, for the annealed sample, the final dislocation density and the average microstrain after pressure release in the ω phase are larger than for the severely pre-deformed sample. The results suggest that an extended experimental basis is required for the predictive models for the combined pressure-induced phase transformations and microstructure evolutions.

36 MATERIALS SCIENCE↗

Characterizing core and edge turbulence regimes with fluctuation imaging diagnostics in Wendelstein 7-X

Two density fluctuation imaging systems, phase contrast imaging (PCI) and gas puff imaging (GPI) measure spatially resolved density fluctuations with high time resolution throughout the core plasma (PCI) and in the scrape-off layer (GPI) of the Wendelstein 7-X (W7-X) stellarator. Both systems combined give a comprehensive overview of overall fluctuation levels, spectral properties such as their distribution in frequency and wavenumber space as well as their spatial distribution. These tools are used to assess changes in density turbulence in three representative discharges that transition into stable divertor detachment by different strategies (impurity seeding, density ramping and power starvation). Several general trends are identified when the radiated power fraction is systematically increased: In the plasma edge, the line emission observed by GPI shifts radially inward with a drop in electron temperature, and normalized intensity fluctuation profiles follow this inward shift. Skewness and kurtosis of these edge fluctuations are reduced, indicating a reduction of large intermittent transport events, and poloidal phase velocities decrease in magnitude. These observations are consistent with a reduced power input into the plasma edge and a general reduction of turbulent activity. Core density fluctuation levels remain nearly constant in the impurity seeding scenario, indicating that detachment does not significantly impact turbulence there. However, a strong reduction in the dominant outboard fluctuation phase velocity is observed that deviates from the previous interpretation of neoclassical radial electric field changes, showing that the core plasma is not completely unaffected. In the density ramp and power starvation scenarios, undesirable and irregular large-scale events arise clearly in both diagnostic systems as the radiative fraction is increased. Impurity seeding therefore seems to be a promising strategy on W7-X to achieve detachment without significantly altering core turbulence, especially when targeting a specific operating point in core density and heating power.

Wendelstein 7-X↗

Topological phase diagram of generalized Su-Schrieffer-Heeger models with interactions

We investigate interacting Su-Schrieffer-Heeger (SSH) chains with two- and three-site unit cells using density matrix renormalization group (DMRG) simulations. By selecting appropriate filling fractions and sweeping across interaction strength 𝐽 𝑧 and dimerization 𝛿, we map out their phase diagrams and identify transition lines via entanglement entropy and magnetization measurements. In the two-site model, we observe the emergence of an interaction-induced antiferromagnetic intermediate phase between the topologically trivial and nontrivial regimes, as well as a critical region at negative 𝐽 𝑧 with suppressed magnetization and finite-size scaling of entanglement entropy. In contrast, the three-site model lacks an intermediate phase and exhibits asymmetric edge localization and antiferromagnetic ordering in both positive and negative 𝐽 𝑧 regimes. We further examine the response of edge states to Ising perturbations. In the two-site model, zero-energy edge modes are topologically protected and remain robust up to a finite interaction strength. However, in the three-site model, where the edge states reside at finite energy, this protection breaks down. Despite this, the edge-localized nature of these states survives in the form of polarized modes whose spatial profiles reflect the noninteracting limit.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Fractionated and purified hybrid poplar lignins as a polyol replacement in rigid polyurethane/polyisocyanurate foams

This study introduces fractionated lignin as an innovative component in the formulation of rigid polyurethane/polyisocyanurate (PUR/PIR) foams. Low-density PUR/PIR rigid foams were prepared by replacing 80% of the petrochemical-based polyol with a hybrid poplar (HP) lignin, recovered via alkaline pretreatment, and also with a fraction of this lignin, isolated via the Aqueous Lignin Purification with Hot Agents (ALPHA) process. The as-recovered HP and ALPHA-fractionated HP lignins were characterized to determine hydroxyl content, molecular weight (Mw) distribution, and pH. Both lignin-based foams met minimum standard requirements in terms of closed cell content, compression strength, and thermal conductivity. Notably, the foams made with ALPHA-based lignin outperformed the as-recovered lignin-based foams in all measured foam properties. Moreover, the ALPHA-based foam had comparable performance to the control foam (without lignin) except for density and even surpassed the control foam in closed cell content and compressive strength. This investigation of the molecular properties of lignin suggests that significant reductions in lignin average molecular weight and polydispersity (PDI) can positively impact the properties of lignin-based rigid foams.

09 BIOMASS FUELS↗

Method for estimating the density of high-level nuclear waste glass

A database of over 1100 silicate glass compositions and densities was compiled and used to evaluate the efficacy of an algorithm for estimating the density of silicate glass compositions. We sought to develop a parsimonious algorithm based on the additivity of partial molar volumes of individual oxide components weighted by their mole fraction in a glass composition. Bound molar volumes were used for oxides in which the density of the oxide bound in a glass matrix was previously determined. The bound molar volumes were known for oxides covering 97.5 mole percent of the database compositional space. The measured glass densities were plotted against the estimated glass densities and a linear regression yielded an R 2 adj. = 0.95 and a slope and intercept of approximately one and zero, respectively. This regression suggests that glass densities estimated by the algorithm, within analysis uncertainty, are equal to the measured densities of the glasses. In addition to the development of the density estimation, we corroborated many of the referenced bound molar volume data used in the parameterization of the estimation algorithm via linear regression of the individual partial molar volumes versus the inverse measured densities (specific volumes) of the glasses in the database.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Triboplasma assisted chemical conversion in granular systems: a semi-analytic model

We present a semi-analytic model for a novel plasma-assisted chemical conversion pathway using triboplasmas generated in granular flows. Triboelectric charge relaxation is a well known phenomena where the potential generated from contact charging of particles exceeds the breakdown voltage of the background gas. In this work, we extend the triboelectric charge relaxation theory to include non equilibrium plasma energy and particle balance equations to predict the formation of dissociated and excited species that act as precursors to chemical conversion, for example in plasma-assisted ammonia synthesis. Our example case study with nitrogen background gas and teflon/aluminum tribomaterial system yielded high excited nitrogen species densities per collision that are comparable to current plasma-assisted conversion pathways. We also present a regime diagram for various gases where Paschen breakdown parameters are used to determine whether triboplasmas can be formed for a given effective work-function difference between two materials. Our sensitivity studies indicate particle velocity, particle radius, solids fraction and space charge effects play a critical role in overall plasma densities and excited species production.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Detection of a pair density wave state in UTe2

Abstract Spin-triplet topological superconductors should exhibit many unprecedented electronic properties, including fractionalized electronic states relevant to quantum information processing. Although UTe 2 may embody such bulk topological superconductivity 1–11 , its superconductive order parameter Δ( k ) remains unknown 12 . Many diverse forms for Δ( k ) are physically possible 12 in such heavy fermion materials 13 . Moreover, intertwined 14,15 density waves of spin (SDW), charge (CDW) and pair (PDW) may interpose, with the latter exhibiting spatially modulating 14,15 superconductive order parameter Δ( r ), electron-pair density 16–19 and pairing energy gap 17,20–23 . Hence, the newly discovered CDW state 24 in UTe 2 motivates the prospect that a PDW state may exist in this material 24,25 . To search for it, we visualize the pairing energy gap with μeV-scale energy resolution using superconductive scanning tunnelling microscopy (STM) tips 26–31 . We detect three PDWs, each with peak-to-peak gap modulations of around 10 μeV and at incommensurate wavevectors P i =1,2,3 that are indistinguishable from the wavevectors Q i =1,2,3 of the prevenient 24 CDW. Concurrent visualization of the UTe 2 superconductive PDWs and the non-superconductive CDWs shows that every P i : Q i pair exhibits a relative spatial phase δϕ ≈ π. From these observations, and given UTe 2 as a spin-triplet superconductor 12 , this PDW state should be a spin-triplet PDW 24,25 . Although such states do exist 32 in superfluid 3 He, for superconductors, they are unprecedented.

Science & Technology - Other Topics↗

Leading jets and energy loss

The formation and evolution of leading jets can be described by jet functions which satisfy non-linear DGLAP-type evolution equations. Different than for inclusive jets, the leading jet functions constitute normalized probability densities for the leading jet to carry a longitudinal momentum fraction relative to the initial fragmenting parton. We present a parton shower algorithm which allows for the calculation of leading-jet cross sections where logarithms of the jet radius and threshold logarithms are resummed to next-to-leading logarithmic (NLL') accuracy. By calculating the mean of the leading jet distribution, we are able to quantify the average out-of-jet radiation, the so-called jet energy loss. When an additional reference scale is measured, we are able to determine the energy loss of leading jets at the cross section level which is identical to parton energy loss at leading-logarithmic accuracy. We identify several suitable cross sections for an extraction of the jet energy loss and we present numerical results for leading subjets at the LHC. In addition, we consider hemisphere and event-wide leading jets in electron-positron annihilation similar to measurements performed at LEP. Besides the average energy loss, we also consider its variance and other statistical quantities such as the KL divergence which quantifies the difference between quark and gluon jet energy loss. We expect that our results will be particularly relevant for quantifying the energy loss of quark and gluon jets that propagate through hot or cold nuclear matter.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Grey Galaxies’ as an endpoint of the Kerr-AdS superradiant instability

Kerr-AdS d+1 black holes for d ≥ 3 suffer from classical superradiant instabilities over a range of masses above extremality. We conjecture that these instabilities settle down into Grey Galaxies (GGs) — a new class of coarse-grained solutions to Einstein’s equations which we construct in d = 3. Grey Galaxies are made up of a black hole with critical angular velocity ω = 1 in the ‘centre’ of AdS, surrounded by a large flat disk of thermal bulk gas that revolves around the centre of AdS at the speed of light. The gas carries a finite fraction of the total energy, as its parametrically low energy density and large radius are inversely related. GGs exist at masses that extend all the way down to the unitarity bound. Their thermodynamics is that of a weakly interacting mix of Kerr-AdS black holes and the bulk gas. Their boundary stress tensor is the sum of a smooth ‘black hole’ contribution and a peaked gas contribution that is delta function localized around the equator of the boundary sphere in the large N limit. We also construct another class of solutions with the same charges; ‘Revolving Black Holes (RBHs)’. RBHs are macroscopically charged SO(d, 2) descendants of AdS-Kerr solutions, and consist of ω = 1 black holes revolving around the centre of AdS at a fixed radial location but in a quantum wave function in the angular directions. RBH solutions are marginally entropically subdominant to GG solutions and do not constitute the endpoint of the superradiant instability. Nonetheless, we argue that supersymmetric versions of these solutions have interesting implications for the spectrum of supersymmetric states in, e.g. N = 4 Yang-Mills theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗