Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “extreme value”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Optimized Machine Learning Model for Predicting Groundwater Contamination

The use of physical models to predict groundwater contaminant movement remains technically challenging due to the complexity of the phenomena, the heterogeneity of key parameters in nature, and the presence of poorly defined interactive and feedback processes. New approaches to address these challenges are needed. In this study, we evaluate various Artificial Intelligence (AI)-based approaches to understand a hexavalent chromium (Cr(VI)) plumes located on the U.S. Department of Energy’s (DOE) Hanford Site in Richland, WA. The groundwater monitoring dataset used in this study included data from the 100 Area along the Columbia River and included data collected between 2010 to 2019. This study investigates the most prominent contaminant, Cr(VI), with the Extreme Gradient Boosting (XGBoost) machine learning model. The XGBoost models were compared with optimized versions using an Empirical Bayes Search Cross-Validation technique for better prediction. The optimized XGBoost model yielded an R^2 value of 0.99 on the training set and 0.85 on the testing set, whereas XGBoost without optimization yielded a value of 0.83 on the training set and 0.85 on the testing set. This paper provides an overview of a computational method for groundwater contamination modeling that shows promise for improving current remediation efforts.

Mazumdar, Hirak↗
DOE OSTI2021

On the Radiation Effects of Strontium Ions on Satellite Solar Cells in Low Earth Orbits

This study focuses on the radiation effects 19 of Sr + ions—generated from high-altitude nuclear explosions (HANE)—on satellite solar cells in low-Earth orbits (LEO). Along four selected satellite orbits, ion fluences are sampled inside the evolving Sr + distributions for days, determined from our newly developed HANE environment model. These fluences, along with the help of radiation transport codes including the MULASSIS and SRIM models, enable us to quantify the radiation damages by determining the values of total ionizing doses and the equivalent 1 MeV electron fluences for displacement damages. Comparing the dose values to existing experimental data, we conclude that HANE-generated Sr + ions have limited darkening effects to quartz solar cell coverglasses in LEO with apogees of 100s to 1000 km. In addition, with the extremely high equivalent fluences, we also conclude that these Sr+ ions may cause severe or even fatal displacement damage to exposed solar photovoltaic (PV) cells on satellites in LEO. The radiation effects of Sr + ions are much less significant for the orbits with high apogees beyond ten thousand km. We also conducted model parameter sensitivity studies on the charge exchange cross-sections, neutral atmosphere density profiles and explosion local time positions, and the above conclusions stay unchanged. The methodology developed in this study can be extended to other HANE-generated heavy ion species in the future.

14 SOLAR ENERGY↗
DOE OSTI2026

Heat metrics and thresholds reshape population exposure and inequality signals

Extreme heat is intensifying worldwide, yet estimates of heat hazard and exposure inequality depend on both the heat metric and how extreme days are defined. Using summer 2022 across the Mediterranean, we quantify population heat exposure with four metrics—land surface temperature (LST), air temperature (Ta), heat index (HI), and wet-bulb globe temperature (WBGT)—under absolute (fixed-value) and relative (anomaly-based) thresholds. Under absolute thresholds, total heat exposure differs by more than two orders of magnitude across metrics (31.3 billion person-days for Ta vs 0.3 billion for HI). Geographic hotspots also diverge: WBGT concentrates in humid coastal North Africa (e.g. the Nile Delta), whereas Ta and LST are more widespread. Under relative thresholds, exposure totals converge and cross-metric hotspot agreement increases (e.g. Ta–WBGT top-tercile overlap increases from 10.7% to 29.0%), shifting hotspots toward densely populated southern Europe. Crucially, the exposure–deprivation relationship also reverses across threshold frameworks: absolute thresholds concentrate exposure in more deprived North Africa and the Middle East, whereas relative thresholds shift the burden toward less-deprived European cities. This sensitivity is decision-relevant: city rankings based on WBGT exposure duration are almost completely reordered when switching threshold frameworks. Threshold choice therefore systematically reshapes hotspot patterns and inequality signals. Reporting both absolute and relative exposures can reveal hidden hotspots and support more targeted heat-risk monitoring and intervention planning.

Mediterranean↗
DOE OSTI2025

Large Hyperfine Coupling Arising from Pseudo- 2 S Ground States in a Series of Lutetium(II) Metallocene Complexes

The synthesis of molecules with strong coupling between electronic and nuclear spins represents an important challenge in molecular quantum information science. Here, we report the synthesis and characterization of the divalent lutetium metallocene complexes Lu(Cp Me 5 )(Cp iPr 5 ) (Cp Me 5 = pentamethylcyclopentadienyl; Cp iPr 5 = pentaisopropylcyclopentadienyl), Lu(Cp iPr 4 Et ) 2 (Cp iPr 4 Et = ethyltetraisopropylcyclopentadienyl), and Lu(Cp iPr 4 ) 2 (Cp iPr 4 = tetraisopropylcyclopentadienyl). The molecular structures of these complexes, as determined through singlecrystal X-ray diffraction, feature a common bent sandwich geometry, with average Cp–Lu–Cp angles ranging from 159.9° to 152.6°. Analysis of continuous-wave electron paramagnetic resonance (EPR) spectra for the complexes reveals nearly isotropic g tensors with only a slight deviation from that of a free electron. Moreover, an extremely large splitting of the eight-line spectra indicates the presence of strong hyperfine coupling, and simulations provide isotropic hyperfine coupling constants of A iso = 4.38, 4.30, and 4.17 GHz across the series, where the value of A iso is found to decrease as the Cp–Lu–Cp angle becomes more acute. Notably, these values are the largest yet observed for any lanthanide complex. Moreover, EPR and computational analysis show that the large values of A iso stem from large s-orbital character up to 41.2% in the corresponding singly occupied molecular orbitals. To our knowledge, this degree of s-character in a molecular orbital is the largest yet reported for an open-shell isolable complex. These results outline a general strategy toward the isolation of paramagnetic molecules with strong hyperfine coupling and highly isotropic doublet electronic ground states.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Historical Power Outages of the United States and the Social Vulnerability Index

Several works have been documented in the literature to study the societal effect of power outages and to analyze their correlation with the Social Vulnerability Index (SVI). Because the SVI is calculated based on the summed rank of multiple vulnerability factors for environmental hazards, it can include factors irrelevant to power outages caused by extreme events. This work performs a detailed correlation analysis for social vulnerability and power outages by considering different SVI themes (e.g., socioeconomic status, household composition, racial and ethnic minority status, and housing and transportation) and power outages with and without a threshold for extreme weather events. Although there is some relation between specific themes and aspects of power outages and the SVI in the results, there is no strong distinction between power outage durations and low vs. high SVI values. These results point to the need for further research that grounds the specific factors and methods used to develop SVI and related indices to energy services and power systems disruptions.

Bhusal, Narayan↗
DOE OSTI2021

An Extreme-Preserving Long-Term Gridded Daily Precipitation Data Set for the Conterminous United States

Extreme daily precipitation contributes to flooding that can cause significant economic damages, and so is important to properly capture in gridded meteorological data sets. This work examines precipitation extremes, the mean precipitation on wet days, and fraction of wet days in two widely used gridded data sets over the conterminous U.S. (CONUS). When compared to the underlying station observations, the gridded data show a 27% reduction in annual 1-day maximum precipitation, 25% increase in wet day fraction, 1.5 to 2.5 day increase in mean wet spell length, 30% low bias in 20-year return values of daily precipitation, and 25% decrease in mean precipitation on wet days. It is shown these changes arise primarily from the time-adjustment applied to put the precipitation gauge observations into a uniform time frame, with the gridding process playing a lesser role. A new daily precipitation data set is developed that omits the time-adjustment (as well as extending the gridded data by 7 years) and is shown to perform significantly better in reproducing extreme precipitation metrics. When the new data set is used to force a land surface model, annually averaged 1-day maximum runoff increases 38% compared to the original data, annual mean runoff increases 17%, evapotranspiration drops 2.3%, and fewer wet days leads to a 3.3% increase in estimated solar insolation. Consequently, these changes are large enough to affect portrayals of flood risk and water balance components important for ecological and climate-change applications across the CONUS.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Molecular transport enhancement in pure metallic carbon nanotube porins

Nanofluidic channels impose extreme confinement on water and ions, giving rise to unusual transport phenomena strongly dependent on the interactions at the channel–wall interface. Yet how the electronic properties of the nanofluidic channels influence transport efficiency remains largely unexplored. Here we measure transport through the inner pores of sub-1 nm metallic and semiconducting carbon nanotube porins. We find that water and proton transport are enhanced in metallic nanotubes over semiconducting nanotubes, whereas ion transport is largely insensitive to the nanotube bandgap value. Molecular simulations using polarizable force fields highlight the contributions of the anisotropic polarizability tensor of the carbon nanotubes to the ion–nanotube interactions and the water friction coefficient. We also describe the origin of the proton transport enhancement in metallic nanotubes using deep neural network molecular dynamics simulations. Finally, these results emphasize the complex role of the electronic properties of nanofluidic channels in modulating transport under extreme nanoscale confinement.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2024

Hydrogen-Steam Separation Using Mechanical Vapor Recompression Cycle

Solar thermochemical hydrogen and fuel production is a promising pathways for producing sustainable fuels and chemicals. One of the main challenges in the development of these systems is their low steam conversion extent, dictated by its restrictive thermodynamics requiring extremely high temperatures and low oxygen partial pressure to obtain conversions over 10 \%. While condensing the unreacted steam is technically simple, the latent heat is thus lost, which can be larger than the producd hydrogen higher heating value. We propose to use a modified mechanical vapor recompression cycle, allowing to recover the latent heat by compressing the steam-hydrogen mixture prior to the condensation process, thus creating a temperature different between the hot exhaust and cold inlet streams. We show that this method can recover over 90 % of the latent heat, thus increasing the viability of solar thermochemical hydrogen production cycles even under limited conversion conditions.

hydrogen technology↗
DOE OSTI2023

Frequency Recovery in Power Grids Using High-Performance Computing

Maintaining electric power system stability is paramount, especially in extreme contingencies involving unexpected outages of multiple generators or transmission lines that are typical during severe weather events. Such outages often lead to large supply-demand mismatches followed by subsequent system frequency deviations from their nominal value. The extent of frequency deviations is an important metric of system resilience, and its timely mitigation is a central goal of power system operation and control. This paper develops a novel nonlinear model predictive control (NMPC) method to minimize frequency deviations when the grid is affected by an unforeseen loss of multiple components. Our method is based on a novel multi-period alternating current optimal power flow (ACOPF) formulation that accurately models both nonlinear electric power flow physics and the primary and secondary frequency response of generator control mechanisms. We develop a distributed parallel Julia package for solving the large-scale nonlinear optimization problems that result from our NMPC method and thereby address realistic test instances on existing high-performance computing architectures. Our method demonstrates superior performance in terms of frequency recovery over existing industry practices, where generator levels are set based on the solution of single-period classical ACOPF models.

nonlinear model predictive control↗
DOE OSTI2024

ARPA-E Grid Optimization (GO) Competition Challenge 3

Synthetic Input Data and Team Results for the GO Competition Challenge 3 for Events 1 - 4 and the Sandbox, along with problem and format descriptions and code to validate data and solutions, are available here. Data for industry scenarios will not be made public. The Grid Optimization (GO) Competition Challenge 3 focused on the security-constrained optimal power flow (SCOPF) problem. It is part of a continuing effort begun with Challenges 1 and 2, to successfully discover, develop, and test innovative and disruptive software solutions for critical energy challenges and to overcome existing barriers. The broader goal of the of the GO Competition is to accelerate the development of transformational and disruptive methods for solving problems related to the electric power grid and to provide a transparent, fair, and comprehensive evaluation of new solution methods. Challenge 3 used multiperiod dynamic markets, including advisory models for extreme weather events, day-ahead markets, and the real-time markets with an extended look-ahead. In Event 4, whose submission window was August 31-September 4, 2023, 14 teams solved for the objective values of 669 scenarios (39 scenarios required solutions both with and without line switching being allowed). The 591 synthetic scenarios from 9 network models (3.6 GB) are available here. Ten teams were funded to participate and 7 won prizes totaling $2,400,000. The largest prize ($550,000) went to Mississippi State University. An additional $600,000 was awarded in Event 3 (6/15-16/2023). No prizes were awarded in Events 1 (1/25-27/2023) or 2 (4/13-14/2023). For more information on the competition and challenge see the "GO Competition Challenge 3 Information" resource below.

ACOPF↗
DOE OSTI2026

Extremized nonlinear and linearized responses in soft metamaterials enabled by gradient-based design and grayscale digital light processing

In this study, we develop a gradient-based design approach that exploits grayscale digital light processing (DLP) 3D printing for extremizing the nonlinear and linearized response of soft metamaterials — materials that harness engineered geometric instabilities to undergo large and programmable changes in configuration. Grayscale DLP approaches modulate local mechanical properties at the pixel scale by tuning the light intensity within a single grayscale image, unlocking an exceptionally large design space. To effectively navigate this space, we develop smooth mappings between local light intensity values and global quantities of interest that characterize the behavior of soft metamaterials. Enabling these smooth mappings are robust and differentiable nonlinear finite element simulations powered by a trust region solver. A PDE-constrained optimization problem is then solved to invert these mappings and produce light intensity distributions that endow the printed part with varying stiffness and flexibility in distinctive regions. It is shown that optimizing the distribution of soft and stiff phases throughout a metamaterial structure results in markedly different buckling and self-contact configurations to drive extremized nonlinear compression and linearized vibration responses. Optimized light intensity distributions are translated to grayscale images and directly used to print soft metamaterial samples, showing remarkable agreement between the buckling and self-contact response in simulated and measured deformed configurations.

Additive manufacturing↗
DOE OSTI2023

129 I, 99 Tc, And U Distribution Coefficients of Subsurface Sediments Collected from the Proposed Site of the Environmental Management Disposal Facility

Performance Assessment calculations were completed in 2020 to evaluate the Environmental Management Disposal Facility (EMDF), a proposed new low-level radioactive waste (LLW) disposal facility on the U.S. Department of Energy’s Oak Ridge Reservation (ORR). Among the large number of input parameters needed for such calculations, are distribution coefficients (K d values; radionuclide concentration solid:liquid ratio) that provide a measure of the tendency of radionuclides to bind to sediments. The objective of this study was to measure K d values of three radionuclides that may pose a disproportionately large amount of risk, U, 129 I and 99 Tc. The average I K d value for the 14 geological materials recovered from the proposed EMDF site was 37.8 mL/g and ranged from -1.8 to 140.9 mL/g. These values were consistent, but somewhat larger than previous measurements made with ORR sediments and were about an order of magnitude greater than those used in previous EMDF PA calculations. The median Tc K d value was 365.7 mL/g, much greater than previously reported using ORR geological materials. Five of the 14 tested geological materials sorbed large quantities of Tc, suggesting that the weakly sorbing Tc(VII) species had been reduced to the sparingly soluble Tc(IV) species. The five strongly sorbing sediments had apparent Tc solubility values of approximately <10 -8 mol/L. The median U K d value was 5,726 mL/g. All of the tested geological materials had large K d values, ranging from 625 to >10,208 mL/g. Among the sediment samples that exhibited strong U binding, the apparent solubility value was approximately <10 -9 mol/L. Based on sediment properties and general ORR geological considerations, it was proposed that much of the I and Tc retention could be attributed to the site materials exhibiting low pH (average pH = 4.94), low redox status, and/or the elevated levels of iron oxides, manganese oxides, and natural organic matter. Similarly, the extremely high U binding measured in these sediments may also be attributed to the low conditions of carbonates, which can complex and therefore solubilize uranyl in these tests due to the low pH, and also the relatively high concentrations of iron and organic coatings on these samples. An implication of this study is that the areas of the EMDF subsurface environment may have natural properties for attenuating I, Tc, and U movement, and potentially other radionuclides, thereby possibly reducing risk posed by burial of LLW at this site. This document is a revision of SRNL-STI-2021-00404, Revision 0 that includes new data describing U K d values and new I and Tc K d values for four Nolichucky sediments. These new results were integrated into the data presented in the original document.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2020

Uncertainty analysis of correlated parameters in automated reaction mechanism generation

Abstract Uncertainty analysis is a useful tool for inspecting and improving detailed kinetic mechanisms because it can identify the greatest sources of model output error. Owing to the very nonlinear relationship between kinetic and thermodynamic parameters and computed concentrations, model predictions can be extremely sensitive to uncertainties in some parameters while uncertainties in other parameters can be irrelevant. Error propagation becomes even more convoluted in automatically generated kinetic models, where input uncertainties are correlated through kinetic rate rules and thermodynamic group values. Local and global uncertainty analyses were implemented and used to analyze error propagation in Reaction Mechanism Generator (RMG), an open‐source software for generating kinetic models. A framework for automatically assigning parameter uncertainties to estimated thermodynamics and kinetics was created, enabling tracking of correlated uncertainties. Local first‐order uncertainty propagation was implemented using sensitivities computed natively within RMG. Global uncertainty analysis was implemented using adaptive Smolyak pseudospectral approximations as implemented in the MIT Uncertainty Quantification Library to efficiently compute and construct polynomial chaos expansions to approximate the dependence of outputs on a subset of uncertain inputs. Cantera was used as a backend for simulating the reactor system in the global analysis. Analyses were performed for a phenyldodecane pyrolysis model. Local and global methods demonstrated similar trends; however, many uncertainties were significantly overestimated by the local analysis. Both local and global analyses show that correlated uncertainties based on kinetic rate rules and thermochemical groups drastically reduce a model's degrees of freedom and have a large impact on the determination of the most influential input parameters. These results highlight the necessity of incorporating uncertainty analysis in the mechanism generation workflow.

Gao, Connie W.↗
DOE OSTI2021

Analysis of Completion Design Impact on Cluster Efficiency and Pressure-Based Well Communication in HFTS-2 Delaware Basin

The Hydraulic Fracturing Test Site 2 (HFTS-2) is a joint industry project in the Delaware basin to advance hydraulic fracturing understanding and improve productivity in shale reservoirs. The project integrates multi-disciplinary approaches to evaluate different completion designs, well spacing, inter-well communication, and stimulated rock volume, among other factors. This paper focused on two major areas related to hydraulic fracture performance. First, an analysis of different completion designs on cluster efficiency based on near well Distributed Acoustic Sensing (DAS). Second, an evaluation of well and completion designs on inter-well fracture driven interactions (FDIs) based on downhole pressure monitoring. Fluid/sand distribution and cluster efficiency analyses were based on near wellbore DAS data collected from two adjacent horizontal wells completed in two different landing zones in the Wolfcamp formation. These wells had different completion designs aiming to evaluate the effect of normal vs. extended stage lengths, perforation hole tapering and limited entry. Standard deviation from ideal fluid/sand distribution and waterfall plots were used to evaluate cluster efficiency for each design and stage. Inter-well FDIs analysis was conducted among the horizontal wells and a vertical monitor well. One horizontal well served as the monitor well while the other horizontal well was being treated. The vertical well was instrumented with downhole pressure and temperature gauges to aid monitoring fracture height growth. The pressure response during and after fracturing was characterized based on maximum pressure increase value and slope. Pressure response vs. FDIs trigger factors such distance, cluster efficiency and stage fluid volume were also analyzed. Based on the different completion and perforation designs tested, DAS analysis suggests that limited entry design worked best. Extreme limited entry showed the potential of high perforation erosion and reduced cluster efficiency. Here, the limited entry and tapered perforation design demonstrated potential to improve the cluster efficiency for extended stage lengths. Pressure monitoring across formation units proved to be critical to understand fracture interactions and fracture vertical growth. Pressure communication across different formation units during hydraulic fracturing operation indicate fractures grew upwards during Wolfcamp wells fracturing. However, this pressure communication dissipated over time. High intensity FDIs were recorded when the frac stages Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/21URTC/1-21URTC/D011S018R001/2477607/urtec-2021-5289-ms.pdf/1 by Carol Worster on 28 February 2022 URTeC 5289 were closer to the pressure gauge location in the monitor wells. Some of these stages that produced high intensity FDIs also had high fluid volume per cluster and low cluster efficiency. The multi-disciplinary and high-quality data collected from HFTS-2 helped to further understand why completion approaches such as limited entry and tapered perforation design are successful in improving cluster efficiency. The DAS data combined with downhole high-resolution pressure measurements also helped to quantify the effect of lower cluster efficiency data on the incidence and intensity of FDIs.

58 GEOSCIENCES↗
DOE OSTI2026

Extreme Temperature Cryptography Based On Nitrogen-Incorporated Ultrananocrystalline Diamond

Physical entropy sources that remain stable under extreme temperatures are essential for cryptography in emerging technological frontiers in deep space exploration, geothermal energy harvesting, and nuclear energy. However, conventional semiconductor platforms fail to generate stable and reliable cryptographic keys above 200 degrees C due to performance degradation. Here, we report a diamond-based cryptographic primitive that exploits the defect-rich sp 2 -bonded grain boundary network in nitrogen-incorporated ultrananocrystalline diamond (n-UNCD) film as a robust entropy source to generate cryptographic keys that remain operationally stable even after enduring extreme temperatures of 700 degrees C for 54 h while also surviving thermal cycling between room temperature and 700 degrees C for 48 h. The strength of the generated keys is assessed through several cryptographic metrics such as bit uniformity, entropy, hamming distances, and correlation coefficients, all of which are found to be near their respective ideal values. Moreover, the generated keys pass the NIST SP 800 and SP 800-90B tests and are also resilient to supply bias variations and a regression-based machine learning attack model based on the Fourier series. The robustness of the keys is attributed to the better thermal stability and chemical inertness of the n-UNCD film. This is supported by high-resolution energy-dispersive X-ray spectroscopy (EDS), which shows no significant lateral diffusion of metal atoms into the n-UNCD layer, and by Raman spectroscopy, which reveals no significant changes in the bonding configuration of the n-UNCD structure. Our findings highlight the remarkable potential of n-UNCD film for extreme environment cryptography by expanding the operational limits of conventional hardware security platforms.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Continuously tunable uniaxial strain control of van der Waals heterostructure devices

Uniaxial strain has been widely used as a powerful tool for investigating and controlling the properties of quantum materials. However, existing strain techniques have so far mostly been limited to use with bulk crystals. Although recent progress has been made in extending the application of strain to two-dimensional van der Waals (vdW) heterostructures, these techniques have been limited to optical characterization and extremely simple electrical device geometries. Here, we report a piezoelectric-based in situ uniaxial strain technique enabling simultaneous electrical transport and optical spectroscopy characterization of dual-gated vdW heterostructure devices. Critically, our technique remains compatible with vdW heterostructure devices of arbitrary complexity fabricated on conventional silicon/silicon dioxide wafer substrates. We demonstrate a large and continuously tunable strain of up to –0.15% at millikelvin temperatures, with larger strain values also likely achievable. We quantify the strain transmission from the silicon wafer to the vdW heterostructure, and further demonstrate the ability of strain to modify the electronic properties of twisted bilayer graphene. Our technique provides a highly versatile new method for exploring the effect of uniaxial strain on both the electrical and optical properties of vdW heterostructures and can be easily extended to include additional characterization techniques.

Electrical properties and parameters↗
DOE OSTI2025

Multicentered black hole saddles for supersymmetric indices

The supersymmetric index in string theory can sometimes have a discontinuous integer-valued jump at co-dimension one surfaces in moduli space called walls of marginal stability. When the index counts black hole microstates, crossing such walls of marginal stability amounts to the appearance or disappearance of a large number of such states. While wall-crossing has been understood in string theory and through the disappearance of extremal Lorentzian supergravity solutions as the moduli are varied, there has been no understanding about how the discontinuous changes in the index occur at the level of the gravitational path integral. In this paper, we find the finite-temperature saddles in $4d$ flatspace supergravity in which fermionic fields are periodic when going around the thermal circle that correspond to the multi-center black hole contributions to the index. By analyzing these saddles, we can explain how wall-crossing occurs: as the scalar moduli in supergravity are varied at the asymptotic boundary, for a given split of the charges, the saddle point equations can no longer be solved and, consequently, the corresponding multi-center saddle no longer contributes to the index. While the values of the scalars and the jump in the index when a wall is crossed all agree with the prediction from previously found Lorentzian supergravity solutions, the saddles in the index exhibit a much richer moduli space, which we analyze in detail.

FOS: Physical sciences↗