Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “anomalous events”

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 415 records · Page 23
All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

Semi-volatiles at Mercury: Sodium (Na) and potassium (K)

Several lines of evidence now suggest that Mercury is a planet rich in moderately-volatile elements such as Na and K. Recent mid-infrared spectral observations of Mercury's equatorial and mid-latitude region near 120 degrees mercurian longitude indicate the presence of plagioclase feldspar. Spectra of Mercury's surface exhibit spectral activity similar to labradorite (plagioclase feldspar with NaAlSi3O8: 30-50 percent) and bytownite (NaAlSi3O8: 10-30 percent). These surface studies were stimulated by the relatively large abundance of Na and K observed in Mercury's atmosphere. An enhanced column of K is observed at the longitudes of Caloris Basin and of the antipodal terrain. Extreme heating at these 'hot' longitudes and severe fracturing suffered from the large impact event could lead to enhanced outgassing from surface or subsurface materials. Alternatively, sputtering from a surface enriched in K could be the source of the observed enhancement. Recent microwave measurements of Mercury also give indirect evidence of a mercurian regolith less FeO-rich than the Moon. An anomalously high index of refraction derived from the whole-disk integrated phase curve of Danjon may also be indicative of surface sulfides contributing to a regolith that is moderately volatile-rich. The recent exciting observations of radar-bright spots at high latitudes also indicate that a substance of high volume scattering, like ice, is present in shadowed regions. Other radar-bright spots have been seen at locations of Na enhancements on the atmosphere. All combined, these pieces of evidence point to a planet that is not severely depleted in volatiles or semi-volatiles.

Sprague, A.↗
DOE OSTI2025

Regime Characterization of Offshore Wind Resource Using Unsupervised Learning

Predictability of wind resource conditions is critical for offshore wind design and operations. While many studies of extreme wind conditions focus on specific events such as low-level jets or ramps, these rely on threshold definitions that limit generality. Here we present a data-driven framework that combines principal component analysis (PCA), self-organizing maps (SOM), and k-means clustering to classify wind resource conditions as typical and anomalous from climatological data. Anomalies are defined not by fixed thresholds but by flagging samples located far from SOM node centers inside the baseline SOM structure. This reframes extremes as rare ebents and hence, likely difficult to anticipate by numerical weather prediction models. We applied this approach to 23 years (2000–2022) of hourly profiles from the NOW-23 hindcast model at the Humboldt Wind Energy Area. Classification is conducted on a feature space consisting of 10 m wind speed and direction, bulk shear and veer across 30–270 m, and a low-level jet index. Dimensionality reduction is achieved through PC. A 2 × 3 OM lattice trained on the PCA vectors identified six baseline regimes spanning weak to strong flow states. High quantization-error profiles are identified and re-clustered into four anomalous regimes. The baseline regimes exhibited clear seasonal and diurnal cycles. Meanwhile, the anomalous regimes represented <10 % of all hours but showed distinct combinations of speed, shear, and veer, when compared to the baseline regimes. Anomalous regimes are typically short-lived (~few hours), yet their transitions can lead to hub-height wind changes of −18 to +9 m s -1 . For a representative 15 MW turbine, these shifts imply rapid swings in capacity factor from near-full output to negligible generation. Validation with lidar buoy data showed 51% agreement in SOM labels across ~6,000 overlapping hours, with most mismatches confined to adjacent speed classes. HRRR comparisons further revealed that anomalous regimes were disproportionately associated with forecast biases exceeding 5 m s -1 . Together, these results reframe extremes in offshore wind from absolute maxima or minima to weather states that are difficult to anticipate from models.

17 WIND ENERGY↗
NASA NTRS1986

The role of energetic O(+) precipitation in a mid-latitude aurora

It is shown that fluxes of precipitating energetic O(+) that have been observed by satellites in the topside ionosphere can explain the magnitude of the N2+(1 N) (first negative) 3914-angstroms and N2(2 P) (second positive) 3371-angstroms emission rate observed during a mid-latitude aurora over Logan, Utah (41 degrees N, 111 degrees W), on 21-22 September 1982. Heavy particle precipitation has previously been invoked to explain the anomalously high populations in the upper vibrational levels of the N2+(1 N) system that are evident in the observed emissions. An improved model is used to investigate the impact of precipitating heavy ions on the atmosphere. The nocturnal thermospheric heating rate and ionization rate during one of these events can be equivalent to the daytime EUV heating and ionization rates. The observed spectrum can be explained by energetic O(+) precipitation to within the uncertainties of the inputs to the model.

Ishimoto, M.↗
NASA NTRS2003

Perspectives on Forced Predictability

This talk addresses the relationships between weather and El Nino/Southern Oscillation (ENSO) and various other low frequency atmospheric variations such as the Pacific/North American pattern. We focus, in particular, on the predictability of extreme wintertime precipitation events over the continental United States. We first examine fifty years of daily precipitation observations and quantify the leading patterns of winter weather variability. These weather systems, familiar to operational weather forecasters, account for many of the major flooding events on the west coast as well as the major winter snowstorms along the east coast. We next examine the statistics of these storm systems with a particular focus on the occurrence of extreme events. The leading weather systems show varying degrees of linkages to low frequency atmospheric variability. We show, for example, that on seasonal time scales the probability of occurrence of certain types of west coast storms is strongly enhanced by El Nino, while it is reduced during winters with an anomalous trough to the west of the dateline. ENSO also has a strong impact on storms that develop over the Gulf of Mexico and affect much of the eastern United States, with enhanced storminess during El Nino, and reduced storminess during La Nina conditions. We conclude with an example of how well current climate models are able to reproduce the basic linkages between weather and low frequency variability.

Schubert, S.↗
DOE OSTI2020

A Search for Neutron-Antineutron Oscillation in the NOvA Experiment

This dissertation presents the search for neutron-antineutron oscillation using the data collected in the Far Detector of the NOvA experiment. Searching for neutron anti-neutron oscillation is becoming an active research direction that promises immense values for the field of particle physics and cosmology. Experimental observation of the phenomenon would offer the possibility of new physics associated with anomalous $B$ and $B-L$ violating processes. This work is opening with a general introduction of the neutron-antineutron oscillation, its theoretical motivations, and recent empirical results related to the topic. The data-driven trigger that allows the NOvA experiment to collect the signal-like events constitutes a significant work of this study and will be described in detail. Following the discussion of the trigger, the thesis focuses on the development of a selection method to further classify collected events into the signal candidates and the background. This search chooses an analysis approach in which the real data is partially unblinded to assist the development and evaluation of the event selection. Because this is an ongoing work and essential aspects of the analysis have not been all finalized, this thesis closes out with a sensitivity study. By analyzing the data from 4 months of Far Detector exposure, a 90\% C.L. sensitivity limit of $4\times10^{30}$\,years is placed on the oscillation lifetime of bound neutrons inside the $^{12}$C targets. This limit is equivalent to a sensitivity of $0.57\times10^{8}$\,s placed on the oscillation lifetime of free neutrons. The NOvA's sensitivity is a factor of 5 below the most stringent limit of $2.7\times10^8$\,s set by the Super-Kamiokande experiment.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS2023

Changing Characteristics of Tropical Extreme Precipitation-Cloud Regimes in Warmer Climates

In this paper, we have investigated the changing characteristics of climatic scale (monthly) tropical extreme precipitation in warming climates using the Energy Exascale Earth System Model (E3SM). Results are from Atmospheric Model Intercomparison Project (AMIP)-type simulations driven by a) control experiment with present-day sea surface temperature (SST) and CO 2 concentration, b) P4K, same as in a) but with uniform increase by 4K in SST globally, and c) same as in a), but with imposed SST and CO 2 concentration from outputs of coupled E3SM forced by 4xCO 2 concentration. We find that as the surface warms under P4K and 4xCO 2 , both convective and stratiform rain increase. Importantly, there is increasing fractional contribution of stratiform rain as a function of precipitation intensity, with the most extreme but rare events occurring preferentially over land more than ocean, more so under 4xCO 2 than P4K. Extreme precipitation is facilitated by increased precipitation efficiency, reflecting accelerated rates of recycling of precipitation-cloud water (both liquid and ice phases) in regions with colder anvil cloud tops. Changes in vertical profiles of clouds, condensation heating and vertical motions indicate increasing precipitation-cloud-circulation organization from control, P4K to 4xCO 2 . Results suggest that large-scale ocean warming, i.e., P4K, is the primary cause contributing to organization structure resembling the well-known Mesoscale Convective System (MCS) for increased extreme precipitation on shorter (hourly to daily) time scales. Additional 4xCO 2 atmospheric radiative heating, and dynamically consistent anomalous SST further amplifies the MCS organization under P4K. Analyses of the surface moist static energy distribution show that increase in surface moisture (temperature) under P4K and 4xCO 2 is the key driver leading to enhanced convective instability over tropical ocean (land). However, the fast and large increase in land surface temperature and lack of available local moisture result in strong reduction in land surface relative humidity, reflecting severe drying and enhanced convective inhibition (CIN). It is argued that very extreme and rare “record-breaking” precipitation events found over land under P4K, more so under 4xCO 2 , are likely due to the delayed onset of deep convection, i.e., the longer the suppression of deep convection by CIN, the more severe the extreme precipitation when eventually occur, due to the release of large amount of stored surplus convective available potential energy in the lower troposphere during prolonged CIN.

climate-scale extreme tropical precipitation↗
NASA NTRS1985

A search for mini-clusters in Japan-USSR Joint Experiment at Pamir

A search for mini-clusters, very collimated shower clusters of hadrons and electromagnetic particles, is made for the hadron and gamma families observed by Japan-USSR joint carbon chamber at Pamir. The existence of anomalous correlation between hadrons and electromagnetic particles is found. The decascading method is applied to the families and it is found that 11 clusters which include hadrons as members have smaller spread, Er 3.5 GeV.m and larger lateral spread, E'R' 100 GeV.m, from the family center. In the simulated events, such clusters were found to be very rare.

Source record↗
NASA NTRS1985

The Southern Hemisphere circulation during the FGGE and its representativeness

An analysis of the global redistribution of mass during the FGGE year indicates that the global circulation was highly anomalous in several respects, especially from April to July 1979. For the 56 to year period 1924-1980, sea-level pressures over the northern hemisphere during the FGGE year were second highest in spring and highest in summer. In April and June, the anomalies were 1-in-100-year events. At the same time, sea-level pressure deficits and an exceptionally deep circumpolar trough were recorded over the Southern Hemisphere. Such compensation between the hemispheres, through the constraint of conservation of mass, provides support for the highly typical nature of the circulation analyzed to exist over the Southern Hemisphere throughout the FGGE year. The Southern Hemisphere circulation was characterized by an exceptionally deep circumpolar trough, an increase in westerlies from 40 deg to 70 deg S, and a decrease in westerlies to the north. In winter, the subtropical jet was weaker and the polar jet stronger than normal, so that a pronounced double jet structure prevailed. In summer, the jet was shifted south by 3 deg latitude. A southward shift in storm tracks accompanied these changes year round in a manner consistent with theory.

Trenberth, K. E.↗
NASA NTRS1991

Preliminary results from the heavy ions in space experiment

The Heavy Ions In Space (HIIS) experiment is intended to provide a deep survey of intensely ionizing particles in low earth orbit. Intensely ionizing particles produce single event effects in microelectronic components and are now recognized as the principal cause of spacecraft anomalies. These particles also make an important contribution to radiation doses. Besides the practical applications, HIIS data will be used to study several important scientific questions. By measuring heavy ions that stop in HIIS, the anomalous component of cosmic rays can be studied, evidence can be searched for of heavy ions trapped in the earth's magnetic field and by comparing HISS data with observations from outside the magnetosphere, the mean ionic charge state can be determined of solar energetic particles. HIIS will also record relativistic ultraheavy galactic cosmic rays. Their elemental composition will be measured from tin to uranium. Results are presented on the elemental resolution for stopping heavy ions and relativistic heavy ions.

Adams, J. H., Jr.↗
NASA NTRS2000

Intrinsic Coupled Ocean-Atmosphere Modes of the Asian Summer Monsoon: A Re-assessment of Monsoon-ENSO Relationships

Using global rainfall and sea surface temperature (SST) data for the past two decades (1979-1998), we have investigated the intrinsic modes of Asian summer monsoon (ASM) and ENSO co-variability. Three recurring ASM rainfall-SST coupled modes were identified. The first is a basin scale mode that features SST and rainfall variability over the entire tropics (including the ASM region), identifiable with those occurring during El Nino or La Nina. This mode is further characterized by a pronounced biennial variation in ASM rainfall and SST associated with fluctuations of the anomalous Walker circulation that occur during El Nino/La Nina transitions. The second mode comprises mixed regional and basin-scale rainfall and SST signals, with pronounced intraseasonal and interannual variabilities. This mode features a SST pattern associated with a developing La Nina, with a pronounced low level anticyclone in the subtropics of the western Pacific off the coast of East Asia. The third mode depicts an east-west rainfall and SST dipole across the southern equatorial Indian Ocean, most likely stemming from coupled ocean-atmosphere processes within the ASM region. This mode also possesses a decadal time scale and a linear trend, which are not associated with El Nino/La Nina variability. Possible causes of year-to-year rainfall variability over the ASM and sub-regions have been evaluated from a reconstruction of the observed rainfall from singular eigenvectors of the coupled modes. It is found that while basin-scale SST can account for portions of ASM rainfall variability during ENSO events (up to 60% in 1998), regional processes can accounts up to 20-25% of the rainfall variability in typical non-ENSO years. Stronger monsoon-ENSO relationship tends to occur in the boreal summer immediately preceding a pronounced La Nina, i.e., 1998, 1988 and 1983. Based on these results, we discuss the possible impacts of the ASM on ENSO variability via the west Pacific anticyclone and articulate a hypothesis that anomalous wind forcings derived from the anticyclone may be instrumental in inducing a strong biennial modulation to natural ENSO cycles.

Lau, K.-M.↗
NASA NTRS2007

System for Secure Integration of Aviation Data

The Aviation Data Integration System (ADIS) of Ames Research Center has been established to promote analysis of aviation data by airlines and other interested users for purposes of enhancing the quality (especially safety) of flight operations. The ADIS is a system of computer hardware and software for collecting, integrating, and disseminating aviation data pertaining to flights and specified flight events that involve one or more airline(s). The ADIS is secure in the sense that care is taken to ensure the integrity of sources of collected data and to verify the authorizations of requesters to receive data. Most importantly, the ADIS removes a disincentive to collection and exchange of useful data by providing for automatic removal of information that could be used to identify specific flights and crewmembers. Such information, denoted sensitive information, includes flight data (here signifying data collected by sensors aboard an aircraft during flight), weather data for a specified route on a specified date, date and time, and any other information traceable to a specific flight. The removal of information that could be used to perform such tracing is called "deidentification." Airlines are often reluctant to keep flight data in identifiable form because of concerns about loss of anonymity. Hence, one of the things needed to promote retention and analysis of aviation data is an automated means of de-identification of archived flight data to enable integration of flight data with non-flight aviation data while preserving anonymity. Preferably, such an automated means would enable end users of the data to continue to use pre-existing data-analysis software to identify anomalies in flight data without identifying a specific anomalous flight. It would then also be possible to perform statistical analyses of integrated data. These needs are satisfied by the ADIS, which enables an end user to request aviation data associated with de-identified flight data. The ADIS includes client software integrated with other software running on flight-operations quality-assurance (FOQA) computers for purposes of analyzing data to study specified types of events or exceedences (departures of flight parameters from normal ranges). In addition to ADIS client software, ADIS includes server hardware and software that provide services to the ADIS clients via the Internet (see figure). The ADIS server receives and integrates flight and non-flight data pertaining to flights from multiple sources. The server accepts data updates from authorized sources only and responds to requests from authorized users only. In order to satisfy security requirements established by the airlines, (1) an ADIS client must not be accessible from the Internet by an unauthorized user and (2) non-flight data as airport terminal information system (ATIS) and weather data must be displayed without any identifying flight information. ADIS hardware and software architecture as well as encryption and data display scheme are designed to meet these requirements. When a user requests one or more selected aviation data characteristics associated with an event (e.g., a collision, near miss, equipment malfunction, or exceedence), the ADIS client augments the request with date and time information from encrypted files and submits the augmented request to the server. Once the user s authorization has been verified, the server returns the requested information in de-identified form.

Kulkarni, Deepak↗
DOE OSTI2023

Subseasonal Clustering of Atmospheric Rivers Over the Western United States

Abstract The serial occurrence of atmospheric rivers (ARs) along the US West Coast can lead to prolonged and exacerbated hydrologic impacts, threatening flood‐control and water‐supply infrastructure due to soil saturation and diminished recovery time between storms. Here a statistical approach for quantifying subseasonal temporal clustering among extreme events is applied to a 41‐year (1979–2019) wintertime AR catalog across the western United States (US). Observed AR occurrence, compared against a randomly distributed AR timeseries with the same average event density, reveals temporal clustering at a greater‐than‐random rate across the western US with a distinct geographical pattern. Compared to the Pacific Northwest, significant AR clusters over the northern Coastal Range of California and Sierra Nevada are more frequent and occur over longer time periods. Clusters along the California Coastal Range typically persist for 2 weeks, are composed of 4–5 ARs per cluster, and account for over 85% of total AR occurrence. Across the northwest Coast‐Cascade Ranges, clusters account for ∼50% of total AR occurrence, typically last 8–10 days, and contain 3–4 individual AR events. Based on precipitation data from a high‐resolution dynamical downscaling of reanalysis, the fractions of total and extreme hourly precipitation attributable to AR clusters are largest along the northern California coast and in the Sierra Nevada. Interannual variability among clusters highlights their importance for determining whether a particular water year is anomalously wet or dry. The mechanisms behind this unusual clustering are unclear and require further research.

Meteorology & Atmospheric Sciences↗
DOE OSTI2021

Autoencoder Based Analysis of RF Parameters in the Fermilab Low Energy Linac

Machine learning (ML) has the potential for significant impact on the modeling, operation, and control of particle accelerators due to its ability to model nonlinear behavior, interpolate on complicated surfaces, and adapt to system changes over time. Anomaly detection in particular has been highlighted as an area where ML can significantly impact the operation of accelerators. These algorithms work by identifying subtle behaviors of key variables prior to negative events. Efforts to apply ML to anomaly detection have largely focused on subsystems such as RF cavities, superconducting magnets, and losses in rings. However, dedicated efforts to understand how to apply ML for anomaly detection in linear accelerators have been limited. In this paper the use of autoencoders is explored to identify anomalous behavior in measured data from the Fermilab low-energy linear accelerator.

Edelen, Jonathan P. (ORCID:0000000215180652)↗
DOE OSTI2023

Changing Characteristics of Tropical Extreme Precipitation–Cloud Regimes in Warmer Climates

In this study, we investigated the changing characteristics of climatic scale (monthly) tropical extreme precipitation in warming climates using the Energy Exascale Earth System Model (E3SM). The results are from Atmospheric Model Intercomparison Project (AMIP)-type simulations driven by (a) a control experiment with the present-day sea surface temperature (SST) and CO 2 concentration, (b) P4K, the same as in (a) but with a uniform increase of 4K in the SST globally, and (c) the same as in (a), but with an imposed SST and CO 2 concentration from the outputs of the coupled E3SM forced by a 4xCO 2 concentration. We found that as the surface warmed under P4K and 4xCO 2 , both convective and stratiform rain increased. Importantly, there was an increasing fractional contribution of stratiform rain as a function of the precipitation intensity, with the most extreme but rare events occurring preferentially over land more than the ocean, and more so under 4xCO 2 than P4K. Extreme precipitation was facilitated by increased precipitation efficiency, reflecting accelerated rates of recycling of precipitation cloud water (both liquid and ice phases) in regions with colder anvil cloud tops. Changes in the vertical profiles of clouds, condensation heating, and vertical motions indicate increasing precipitation–cloud–circulation organization from the control and P4K to 4xCO 2 . The results suggest that large-scale ocean warming, that is, P4K, was the primary cause contributing to an organization structure resembling the well-known mesoscale convective system (MCS), with increased extreme precipitation on shorter (hourly to daily) time scales. Additional 4xCO 2 atmospheric radiative heating and dynamically consistent anomalous SST further amplified the MCS organization under P4K. Analyses of the surface moist static energy distribution show that increases in the surface moisture (temperature) under P4K and 4xCO 2 was the key driver leading to enhanced convective instability over tropical ocean (land). However, a fast and large increase in the land surface temperature and lack of available local moisture resulted in a strong reduction in the land surface relative humidity, reflecting severe drying and enhanced convective inhibition (CIN). It is argued that very extreme and rare “record-breaking” precipitation events found over land under P4K, and more so under 4xCO 2 , are likely due to the delayed onset of deep convection, that is, the longer the suppression of deep convection by CIN, the more severe the extreme precipitation when it eventually occurs, due to the release of a large amount of stored surplus convective available potential energy in the lower troposphere during prolonged CIN.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRSDate not supplied

Artemis I Orion IMU Flight Performance

The Orion flight software’s parity algorithm runs onboard to verify all three OIMUs (Orion Inertial Measurement Units) are sensing relatively uniform rate and acceleration and to quickly identify any unit which is in significant disagreement with the other two units. During the Artemis-I Wet Dress Rehearsal tests and Launch Countdowns, one of the three OIMUs regularly reported an anomalous parity signature for a brief period of time during sensor warm up. This paper will review this anomalous performance on the pad and review flight data with the intent to supplement the findings of the initial root cause investigation. Outside of this start up behavior, initial investigation into Artemis I flight data did not reveal any behavior of the OIMUs outside of preflight expectations. Flight data from any significant parity events and relevant IMU calibrations will be presented. A brief discussion of impacts to future Artemis mission operations strategy will be provided.

Robert Earl↗
DOE OSTI2023

Measurement of Rayleigh Scattering in Liquid Argon at Vacuum Ultraviolet Wavelengths

Liquid argon based detectors are limited in scintillation light analysis capabilities due to inconsistent measurements of fundamental constants essential for the reconstruction of scintillation events. This experiment measures the Rayleigh scattering length of vacuum ultraviolet light propagating in liquid argon in support of liquid argon experiments. Preliminary results are presented for the Rayleigh scattering length in a range of vacuum ultraviolet wavelengths. Current data collection and analysis methods in this measurement require further advancements to understand and eliminate anomalous phenomena in the data. Future measurements in this experiment aim to precisely measure the liquid argon ultraviolet light scattering length. Results will contribute to the development of new photon system analysis methods for liquid argon experiments.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS2018

Radiation Testing Electronics with Heavy Ions-The Best Way to Hit a Target Moving Ever Exponentially Faster

In 1972, when engineers at Hughes Aircraft Corporation discovered that errors in their satellite avionics were being caused by cosmic rays (so-called single-event effects, or SEE), Moore's Law was only 7 years old. Now, more than 45 years on, the scaling that drove Moore's Law for its first 35 years has reached its limits. However, electronics technology continues to evolve exponentially and SEE remain a formidable issue for use of electronics in space. SEE occur when a single ionizing particle passes through a sensitive volume in an active semiconductor device and generates sufficient charge to cause anomalous behavior or failure in the device. Because SEE can occur at any time during the mission, the emphasis of SEE risk management methodologies is ensuring that all SEE modes in a device under test are detected by the test. Because a particle's probability of causing an SEE generally increases as the particle becomes more ionizing, heavy-ion beams have been and remain the preferred tools for elucidating SEE vulnerabilities. In this talk we briefly discuss space radiation environments and SEE mechanisms, describe SEE test methodologies and discuss current and future challenges for use of heavy-ion beams for SEE testing in an era when the continued validity of Moore's law depends on innovation rather than CMOS scaling.

space radiation environments↗
DOE OSTI2020

Imaging Polarity in Two Dimensional Materials by Breaking Friedel's Law

Friedel's law guarantees an inversion-symmetric diffraction pattern for thin, light materials where a kinematic approximation or a single-scattering model holds. Typically, breaking Friedel symmetry is ascribed to multiple scattering events within thick, non-centrosymmetric crystals. However, two-dimensional (2D) materials such as a single monolayer of MoS 2 can also violate Friedel's law, with unexpected contrast between conjugate Bragg peaks. Here, we show analytically that retaining higher order terms in the power series expansion of the scattered wavefunction can describe the anomalous contrast between hkl and $\bar{hkl}$ peaks that occurs in 2D crystals with broken in-plane inversion symmetry. These higher-order terms describe multiple scattering paths starting from the same atom in an atomically thin material. Furthermore, 2D materials containing heavy elements, such as WS 2 , always act as strong phase objects, violating Friedel's law no matter how high the energy of the incident electron beam. Experimentally, this understanding can enhance diffraction-based techniques to provide rapid imaging of polarity, twin domains, in-plane rotations, or other polar textures in 2D materials.

2D materials↗