Search NASA⌕ Search

SEARCH · Search NASA

Results for “spatial variations”

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 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Description of the Three-Dimensional Large-Scale Forcing Data from the 3D Constrained Variational Analysis (VARANAL3D)

This technical report introduces a Three-Dimensional Constrained Variational Analysis (3DCVA) (Tang and Zhang 2015) and its product of three-dimensional large-scale forcing data to drive single-column models (SCM), cloud-resolving models (CRM), and large-eddy simulation (LES) models, and to evaluate model results. The 3DCVA algorithm is an extension of the original 1D constrained variational analysis (1DCVA) (Zhang and Lin 1997, Zhang et al. 2001). The three-dimensional structure of the forcing data allows studies of spatial variation of the large-scale forcing fields and tests of physical parameterizations across scales. In the U.S. Department of Energy Atmospheric Radiation Measurement (ARM) user facility, the 3D forcing data are assigned the datastream name varanal3d. In this technical report, 3DCVA will be used to refer to the algorithm, while VARANAL3D will be used to refer to the data product.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1975

Application of spatial features to satellite land-use analysis

A Level I land-use analysis of selected training areas of the Colorado Front Range was carried out using digital ERTS-A satellite imagery. Level I land-use categories included urban, agriculture (irrigated and dryland farming), rangeland, and forests. The spatial variations in spectral response for these land-use classes were analyzed using discrete two-dimensional Fourier transforms to isolate and extract spatial features. Analysis was performed on ERTS frame 1352-17134 (July 10, 1973) and frame number 1388-17131 (August 15, 1973). On training sets, spatial features yielded 80 to 100 percent classification accuracies with commission errors ranging from 0 to 20 percent.

Smith, J.↗
NASA NTRS1994

Radio occultation studies of the Venus atmosphere with the Magellan spacecraft. 2: Results from the October 1991 experiments

On October 5 and 6, 1991, three dual-frequency ingress radio occultation experiments were conducted at Venus during consecutive orbits of the Magellan spacecraft. The radio signals probed a region of the atmosphere near 65 deg N, with a solar zenith angle of 108 deg, reaching below 35 km at 3.6 cm, and below 34 km at 13 cm (above a mean radius of 6052 km). The high effective isotropic radiated power (EIRP) of the Magellan spacecraft and highly successful attitude maneuvers allowed these signals to probe deeper than any previous radio occultation experiment and also resulted in the most accurate thermal and sulfuric acid vapor abundance profiles ever obtained at Venus through radio occultation techniques. The performance of the spacecraft and the experiment design are discussed in an accompanying paper. Average electron density profiles retrieved from the data possess peaks between 2600 and 6000/cu cm, well below typical values of 10,000/cu cm retrieved in 1979 by Pioneer Venus at similar solar zenith angles. Other basic results include vertical profiles of temperature, pressure, and density in the neutral atmosphere, 13- and 3.6-cm absorpttivity, and H2SO4 (g) abundance below the main cloud layer. H2SO4 (g) becomes significant below 50 km, reaching peaks between 18 and 24 ppm near 39 km before dropping precipitously below 38 km. These sharp decreases confirm the thermal decomposition of sulfuric acid vapor below 39 km. Since the Venus atmosphere rotated approximately 10 deg between experiments, the data contain information about the horizontal variability of the atmosphere. All derived profiles exhibit significant variations from orbit to orbit, indicating the presence of dynamical processes between 33 and 200 km. In particular, the orbit-to-orbit variations in temperature and in H2SO4 (g) abundance appear to be correlated, suggesting that a common mechanism may be responsible for the observed spatial variations.

Jenkins, Jon M.↗
DOE OSTI2024

Environmental drivers of increased ecosystem respiration in a warming tundra

Abstract Arctic and alpine tundra ecosystems are large reservoirs of organic carbon 1,2 . Climate warming may stimulate ecosystem respiration and release carbon into the atmosphere 3,4 . The magnitude and persistency of this stimulation and the environmental mechanisms that drive its variation remain uncertain 5–7 . This hampers the accuracy of global land carbon–climate feedback projections 7,8 . Here we synthesize 136 datasets from 56 open-top chamber in situ warming experiments located at 28 arctic and alpine tundra sites which have been running for less than 1 year up to 25 years. We show that a mean rise of 1.4 °C [confidence interval (CI) 0.9–2.0 °C] in air and 0.4 °C [CI 0.2–0.7 °C] in soil temperature results in an increase in growing season ecosystem respiration by 30% [CI 22–38%] (n = 136). Our findings indicate that the stimulation of ecosystem respiration was due to increases in both plant-related and microbial respiration (n = 9) and continued for at least 25 years (n = 136). The magnitude of the warming effects on respiration was driven by variation in warming-induced changes in local soil conditions, that is, changes in total nitrogen concentration and pH and by context-dependent spatial variation in these conditions, in particular total nitrogen concentration and the carbon:nitrogen ratio. Tundra sites with stronger nitrogen limitations and sites in which warming had stimulated plant and microbial nutrient turnover seemed particularly sensitive in their respiration response to warming. The results highlight the importance of local soil conditions and warming-induced changes therein for future climatic impacts on respiration.

Science & Technology - Other Topics↗
NASA NTRS2011

Numerical Prediction of Radiation Measurements Taken in the X2 Facility for Mars and Titan Gas Mixtures

Thermochemical relaxation behind a normal shock in Mars and Titan gas mixtures is simulated using a CFD solver, DPLR, for a hemisphere of 1 m radius; the thermochemical relaxation along the stagnation streamline is considered equivalent to the flow behind a normal shock. Flow simulations are performed for a Titan gas mixture (98% N2, 2% CH4 by volume) for shock speeds of 5.7 and 7.6 km/s and pressures ranging from 20 to 1000 Pa, and a Mars gas mixture (96% CO2, and 4% N2 by volume) for a shock speed of 8.6 km/s and freestream pressure of 13 Pa. For each case, the temperatures and number densities of chemical species obtained from the CFD flow predictions are used as an input to a line-by-line radiation code, NEQAIR. The NEQAIR code is then used to compute the spatial distribution of volumetric radiance starting from the shock front to the point where thermochemical equilibrium is nominally established. Computations of volumetric spectral radiance assume Boltzmann distributions over radiatively linked electronic states of atoms and molecules. The results of these simulations are compared against experimental data acquired in the X2 facility at the University of Queensland, Australia. The experimental measurements were taken over a spectral range of 310-450 nm where the dominant contributor to radiation is the CN violet band system. In almost all cases, the present approach of computing the spatial variation of post-shock volumetric radiance by applying NEQAIR along a stagnation line computed using a high-fidelity flow solver with good spatial resolution of the relaxation zone is shown to replicate trends in measured relaxation of radiance for both Mars and Titan gas mixtures.

Palmer, Grant↗
NASA NTRS1990

Temporal variation of heat and moisture flux divergence in the FIFE atmospheric boundary layer during spring

A one-day investigation of the atmospheric boundary layer (ABL) is reported in which an aircraft monitors the temporal and spatial variations of heat and moisture turbulent-flux divergences. Incoming solar radiation is similar over natural prairie land and agriculturally developed land although the heat and moisture values show significant differences over the surfaces. Other temporal variations are noted which demonstrate that ABL transport of sensible and latent heat is affected by complex variables even under simple synoptic conditions.

Grossman, Robert L.↗
DOE OSTI2022

Radio-Frequency Rapid Thermal Processing Enabling Spatial Phase Transformation and Nanocrystallization of Soft Magnetic Amorphous Alloys

Thermal processing of soft magnetic amorphous and nanocrystalline alloys is explored under the influence of radio-frequency induction-heating techniques. Direct induction-heating concepts based on longitudinal and transverse flux heating are examined and the details of electromagnetic fields interaction with metallic strips are discussed by analytical calculations as well as finite element analysis. Initial experimental results confirming spatial control of phase transformations and nanocrystallization within a single strip of Finemet Fe-based amorphous ribbons are reported. Here, the degree to which primary and secondary crystallization temperature are achieved depends on the spacing between the ribbon relative to the induction coil as well as the coil design and configuration. For transverse coil configurations, the local temperature and therefore microstructural evolution is different across the lateral dimension of processed ribbons, with reduced gap sizes producing enhanced peak temperatures and larger temperature distributions with greater spatial variation in microstructure. In addition, indirect susceptor-based induction heating under tension is performed and the impact of microstructure is demonstrated. Herein, potential for exploiting spatially optimized phase transformations is illustrated through electromagnetic field–assisted processing in a scalable manufacturing process with amorphous and nanocrystalline soft magnetic alloys.

36 MATERIALS SCIENCE↗
NASA NTRS1996

The Lunar Crust: Global Structure and Signature of Major Basins

New lunar gravity and topography data from the Clementine Mission provide a global Bouguer anomaly map corrected for the gravitational attraction of mare fill in mascon basins. Most of the gravity signal remaining after corrections for the attraction of topography and mare fill can be attributed to variations in depth to the lunar Moho and therefore crustal thickness. The large range of global crustal thickness (approx. 20-120 km) is indicative of major spatial variations in melting of the lunar exterior and/or significant impact-related redistribution. The 6l-km average crustal thickness, constrained by a depth-to-Moho measured during the Apollo 12 and 14 missions, is preferentially distributed toward the farside, accounting for much of the offset in center-of-figure from the center-of-mass. While the average farside thickness is 12 km greater than the nearside, the distribution is nonuniform, with dramatic thinning beneath the farside, South Pole-Aitken basin. With the global crustal thickness map as a constraint, regional inversions of gravity and topography resolve the crustal structure of major mascon basins to half wavelengths of 150 km. In order to yield crustal thickness maps with the maximum horizontal resolution permitted by the data, the downward continuation of the Bouguer gravity is stabilized by a three- dimensional, minimum-slope and curvature algorithm. Both mare and non-mare basins are characterized by a central upwarped moho that is surrounded by rings of thickened crust lying mainly within the basin rims. The inferred relief at this density interface suggests a deep structural component to the surficial features of multiring lunar impact basins. For large (greater than 300 km diameter) basins, moho relief appears uncorrelated with diameter, but is negatively correlated with basin age. In several cases, it appears that the multiring structures were out of isostatic equilibrium prior to mare emplacement, suggesting that the lithosphere was strong enough to maintain their state of stress to the present.

Neumann, Gregory A.↗
NASA NTRS2004

Topography of the Flattest Surface on Earth: using ICESAT, GPS, and MISR to Measure Salt Surface Topography on Salar de Uyuni, Bolivia

Salt flats are aptly named: they are composed largely of salt, and are maintained as nearly equipotential surfaces via frequent flooding. The salar de Uyuni, on the Altiplano in southwestern Bolivia, is the largest salt flat on Earth, with an area of 9,800 sq km. Except for a few bedrock islands, it has less than 40 cm of relief. The upper-most salt unit averages 5 m thick and contains 50 cu km of nearly pure halite. It includes most of the salt that was in solution in paleolake Minchin, which attained a maximum area of 60,000 sq km and a maximum depth of 150 m, roughly 15 kyr ago. Despite approx. 10 m of differential isostatic rebound since deposition, the salar surface has been actively maintained as an extraordinarily flat and smooth surface by annual flooding during the rainy season. We have used the strong optical absorption properties of water in the visible band to map spatial variations in water depth during a time when the salar was flooded. As water depth increases, the initially pure white surface appears both darker and bluer. We utilized MISR images taken during the interval from April to November 2001. The red and infra-red bands (672 and 867 nm wavelength) were most useful since the water depth is small and the absorption at those wavelengths is quite strong. Nadir pointed MISR images have 275 m spatial resolution. To aid in our evaluation of water depth variations over the saiar surface, we utilized two sources of direct topographic measurements: several ICESAT altimetry tracks cross the area, and a 40x50 km GPS grid was surveyed to calibrate ICESAT. A difficulty in using these data types is that both give salt surface elevations relative to the ellipsoid, whereas the water surface will, in the absence of wind or tidal disturbances, follow an equipotential surface. Geoid height is not known to the required accuracy of a few cm in the central Andes. As a result, before comparing optical absorption from MISR to salt surface topography from GPS or ICESAT, we removed the longest wavelengths from both.

Comstock, Robert L.↗
DOE OSTI2020

Spatial BCS-BEC crossover in superconducting $\textit{p–n}$ junctions

Here, we present a theory of superconducting $\textit{p–n}$ junctions. To this end, we consider a two band model of doped bulk semiconductors with attractive interactions between the charge carriers and derive the superconducting order parameter, the quasiparticle density of states, and the chemical potential as a function of the semiconductor gap $Δ_0$ and the doping level ε. We verify previous results for the quantum phase diagram for a system with constant density of states in the conduction and valence band, which show BCS-superconductor to Bose-Einstein-condensation (BEC) and BEC-to-insulator transitions as a function of doping level and the size of the band gap. Then, we extend this formalism to a density of states which is more realistic for 3D systems and derive the corresponding quantum phase diagram, where we find that a BEC phase can only exist for small band gaps $Δ_0 < Δ ^{\ast}_0$. For larger band gaps, we find rather a direct transition from an insulator to a BCS phase. Next, we apply this theory to study the properties of superconducting $\textit{p–n}$ junctions. We derive the spatial variation of the superconducting order parameter along the $\textit{p–n}$ junction. As the potential difference across the junction leads to energy band bending, we find a spatial crossover between a BCS and BEC condensate, as the density of charge carriers changes across the $\textit{p–n}$ junction. For the two-dimensional system, we find two possible regimes, when the bulk is in a BCS phase, a BCS-BEC-BCS junction with a single BEC layer in the space charge region, and a BCS-BEC-I-BEC-BCS junction with two layers of BEC condensates separated by an insulating layer. In three dimensions we find that there can also be a conventional BCS-I-BCS junction for semiconductors with band gaps exceeding $Δ^{\ast}_0$. Thus, we find that there can be BEC layers in the well controlled setting of doped semiconductors, where the doping level can be varied to change and control the thickness of BEC and insulator layers, making Bose-Einstein condensates thereby possibly accessible to experimental transport and optical studies in solid-state materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

ENSO-Induced Teleconnection: Process-Oriented Diagnostics to Assess Rossby Wave Sources and Ambient Flow Properties in Climate Models

Climate model fidelity in representing ENSO-induced teleconnection is assessed with process-oriented diagnostics that examine a chain of processes, from equatorial Pacific precipitation to the midlatitude circulation pattern over the Pacific–North American regions. Such processes are rarely addressed during model development. Using an upper-tropospheric divergent level, local vorticity gradient of the ambient zonal flow (∂ 2 U¯/∂y 2 ) and a restoring force for Rossby waves (β * ) are estimated, the equivalent barotropic vorticity equation is solved, and an anomalous Rossby wave source (RWS') quantified. The analysis is applied to AMIP5 and AMIP6 simulations. For a realistic circulation response representation, the hypothesis that models accurately represent the strength and location of RWS', and spatial variations in β * is tested. Compared to AMIP5, in AMIP6 there are clear improvements in representing RWS' and β * . To validate the hypothesis, the analysis identifies two metrics: spatially coherent RWS' in the subtropical North Pacific, and longitudes of negative β * over the western-central North Pacific. By projecting these metrics in two and three-dimensional views, improvements or degradations in model versions are apparent. If a model’s fidelity in representing ∂ 2 U¯/∂y 2 and RWS' are compromised, then radiated Rossby waves are reflected more equatorward, resulting in zonally elongated circulation anomalies over the central North Pacific. Thus, during climate model development, applying this analysis frequently will keep a regular check on the fidelity of the modeled response to anomalous El Niño convection in conjunction with changing model ambient flow dependencies. As a result, this analysis is intended to form a process-oriented diagnostics package, a community contribution to the NOAA Model Diagnostics Task Force.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Improved high-resolution mapping of phase-matching conditions in second-order nonlinear crystals via imaging

Large-aperture nonlinear crystals for frequency conversion and parametric amplification exhibit spatial variations in phase-matching conditions, which affect the performance of high-power laser systems. We demonstrate significant improvements in speed and resolution to a technique that spatially maps these phase-matching conditions using imaging of the beam resulting from detuned second-harmonic generation. The phase-matching conditions at the pyramidal sector boundary of partially deuterated potassium dihydrogen phosphate (DKDP) are mapped with sub-0.1-mm resolution. We examine the effect of further increases in scan rate on the precision of the technique and demonstrate a scan rate of 0.8 cm 2 per minute at the aforementioned resolution.

Wampler, R. [Univ. of Rochester, NY (United States↗
NASA NTRS1981

The effect of minority carrier mobility variations on solar cell spectral response

Analysis of multistep diffused, high voltage 0.1 ohm-cm solar cells suggests that the increased voltage capability of these cells is correlated with localized variations in the base minority carrier mobility. An attempt to calculate the behavior of those cells revealed unexpected results. It is shown, contrary to what was expected, that spatial variations in the mobility effects severe changes in the short-circuit current and the spectral response. Variations in cell output as a result of imposing abrupt, linear, and exponential mobility variations are presented.

Weizer, V. G.↗
NASA NTRS1981

Analytical description of charged particle transport along arbitrary guiding-field configurations

Focused particle transport is analyzed in terms of partial differential equations which are applicable to arbitrary spatial variations of the mean free path and the focusing length. A distribution function for transport is written in two forms of the Boltzmann equation and a coefficient of spatial diffusion is defined. Changes from a nearly coherent propagation of flare particles in regions of strong focusing near the sun to ordinary diffusion in the outer solar system are described as supercoherent transitions. A solution to the steady state problem is developed and results are presented for a monopolar guiding field configuration with isotropic diffusion gradually giving way to anisotropy in a region suggestive of a collimated beam of particles streaming away from its source.

Earl, J. A.↗
NASA NTRS2004

Meridional Variations of C2H2 and C2H6 in Jupiter's Atmosphere from Cassini CIRS Infrared Spectra

Hydrocarbons such as acetylene (C2H2) and ethane (C2H6) are important tracers in Jupiter's atmosphere, constraining our models of the chemical and dynamical processes. However, our knowledge of the vertical and meridional variations of their abundances has remained sparse. During the flyby of the Cassini spacecraft in December 2000, the Composite Infrared Spectrometer (CIRS) instrument was used to map the spatial variation of emissions from 10-1400 cm(sup -1) (1000-7 microns). In this paper we analyze a zonally-averaged set of CIRS spectra taken at the highest (0.5 cm(sup -1)) resolution, to infer atmospheric temperatures in the stratosphere at 0.5-20 mbar via the v4 band of CH4, and in the troposphere at 150-400 mbar, via the H2 absorption at 600-800 cm(sup -1). Simultaneously, we retrieve the abundances of C2H2 and C2H6 via the v5 and vg bands respectively. Tropospheric absorption and stratospheric emission are highly anti-correlated at the CIRS resolution, introducing a non-uniqueness into the retrievals, such that vertical gradient and column abundance cannot both be found without additional constraints. Assuming profile gradients from photochemical calculations, we show that the column abundance of C2H2 decreases sharply towards the poles by a factor approximately 4, while C2H6 is unchanged in the north and increasing in the south, by a factor approximately 1.8. An explanation for the meridional trends is proposed in terms of a combination of photochemistry and dynamics. Poleward, the decreasing UV flux is predicted to decrease the abundances of C2H2 and C2H6 by factors 2.7 and 3.5 respectively at a latitude 70 deg. However, the lifetime of C2H6 in the stratosphere (5 x 10(exp 9)) is much longer than the dynamical timescale for meridional motions inferred from SL-9 debris (5 x 10(exp 8 s)), and therefore the constant or rising abundance towards high latitudes likely indicates that meridional mixing dominates over photochemical effects. For C2H2, the opposite occurs, with the relatively short photochemical lifetime (3 x 10(exp 7 s)), compared to meridional mixing times, ensuring that the expected photochemical trends are visible.

Nixon, C. A.↗
NASA NTRS2019

Improvements in the Uncertainty Model in the Goddard Institute for Space Studies Surface Temperature (GISTEMP) Analysis

We outline a new and improved uncertainty analysis for the Goddard Institute of Space Studies (GISS) Surface Temperature product version 4 (GISTEMP v4). Historical spatial variations in surface temperature anomalies are derived from historical weather station data and ocean data from ships, buoys and other sensors. Uncertainties arise from measurement uncertainty, changes in spatial coverage of the station record, and systematic biases due to technology shifts and land cover changes. Previously published uncertainty estimates for GISTEMP included only the effect of incomplete station coverage. Here, we update this term using currently available spatial distributions of source data, state‐of‐the‐art reanalyses and incorporate independently derived estimates for ocean data processing, station homogenization and other structural biases. The resulting 95% uncertainties are near 0.05° C in the global annual mean for the last 50 years, and increase going back further in time reaching 0.15° C in 1880. In addition, we quantify the benefits and inherent uncertainty due to the GISTEMP interpolation and averaging method. We use the total uncertainties to estimate the probability for each record year in the GISTEMP to actually be the true record year (to that date), and conclude with 86% likelihood that 2016 was indeed the hottest year of the instrumental period (so far).

Nathan J L Lenssen↗
DOE OSTI2020

Environmental impacts of dam reservoir filling in the East Amazon

Mitigating the environmental impacts caused by hydroelectric dams is a worldwide challenge. The aquatic ecosystem is the most impacted during the reservoir filling phase, yet biogeochemical dynamics at this stage are not well-studied. Here we evaluate water quality and hydraulic parameters in the Araguari River (Amapá/Brazil) during the filling of the Ferreira Gomes Hydroelectric Power Plant reservoir (UHEFG). Five field campaigns were performed from July 2014 to August 2015 across nine sample sites within the reservoir (P1, P2, …P9) and only one downstream (P10). The following key variables were monitored: Trophic State Index (TSI), Total Coliforms (TC), E. coli (EC) and Chlorophyll-a (Chl-a), along with physical and chemical variables (Temperature, Suspended Solids, Total Dissolved Solids, Electrical Conductivity, Turbidity, Color, pH, DO, Al3+, NH4+, Cl-, Mg1+, Ca2+, total Phosphorous, NH3, NO3-, and SO42). Besides that, hydraulic-operational variables were also investigated: inflows (Qa), outflows (Qd), and variation in reservoir volume (Vol%). Multiple Regression Analyses showed that the key parameters were both significantly influenced by physio-chemical and hydraulic variables (0.46=R2adj=0.99, p<0.05). The DO showed significant spatial variation, being influenced by the turbulence from the Coaracy Nunes dam (UHECN) upstream and the UHEFG dam downstream. The Vol% influenced the TSI, which ranged from oligotrophic to hypertrophic and eventually stabilized at mesotrophic. The levels of TSI, TC, and Chl-a decreased and the level of E. coli increased (p<0.05) as a function of Vol%. A Cluster Analysis showed the formation of three spatial groups - two inside the reservoir and one downstream (P10). This suggests that in the rainy season or transition season, the hydraulic residence time in the reservoir is very low (16 = thr = 36 h) when hydrodynamic processes are dominant. In the dry season (thr ˜ 1 month), biogeochemical and hydrodynamic processes occur at similar time scales to the nutrient and microbial abundance. These results confirm the hypothesis that the filling phase has significant impacts on the key parameters of the water quality (p<0.05). We conclude that the filling phase of the UHEFG reservoir generated significant environmental impacts, which have repercussions even retrospectively.

Amazon, biogeochemistry, ecosystem, extreme event,↗
DOE OSTI2024

Charge Conservation beyond Uniformity: Spatially Inhomogeneous Electromagnetic Response in Periodic Solids

Nonlinear electromagnetic response functions have reemerged as a crucial tool for studying quantum materials, due to recently appreciated connections between optical response functions, quantum geometry, and band topology. Most attention has been paid to responses to spatially uniform electric fields, relevant to low-energy optical experiments in conventional solid state materials. However, magnetic and magnetoelectric phenomena are naturally connected by responses to spatially varying electric fields due to Maxwell’s equations. Furthermore, in the emerging field of moiré materials, characteristic lattice scales are much longer, allowing spatial variation of optical electric fields to potentially have a measurable effect in experiments. In order to address these issues, we develop a formalism for computing linear and nonlinear responses to spatially inhomogeneous electromagnetic fields. Starting with the continuity equation, we derive an expression for the second-quantized current operator that is manifestly conserved and model independent. Crucially, our formalism makes no assumptions on the form of the microscopic Hamiltonian and so is applicable to model Hamiltonians derived from tight-binding or calculations. We then develop a diagrammatic Kubo formalism for computing the wave vector dependence of linear and nonlinear conductivities, using Ward identities to fix the value of the diamagnetic current order by order in the vector potential. We apply our formula to compute the magnitude of the Kerr effect at oblique incidence for a model of a moiré-Chern insulator and demonstrate the experimental relevance of spatially inhomogeneous fields in these systems. We further show how our formalism allows us to compute the (orbital) magnetic multipole moments and magnetic susceptibilities in insulators. Turning to nonlinear response, we use our formalism to compute the second-order transverse response to spatially varying transverse electric fields in our moiré-Chern insulator model, with an eye toward the next generation of experiments in these systems. Published by the American Physical Society 2024

Physics↗