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At least 559 records · Page 31

A reference-area-free strain mapping method using precession electron diffraction data

Here, in this work, we developed a method using precession electron diffraction data to map the residual elastic strain at the nano-scale. The diffraction pattern of each pixel was first collected and denoised. Template matching was then applied using the center spot as the mask to identify the positions of the diffraction disks. Statistics of distances between the selected diffracted disks enable the user to make an informed decision on the reference and to generate strain maps. Strain mapping on an unstrained single crystal sapphire shows the standard deviation of strain measurement is 0.5%. With this method, we were able to successfully measure and map the residual elastic strain in VO 2 on sapphire and martensite in a Ni 50.3 Ti 29.7 Hf 20 shape memory alloy. This approach does not require the user to select a “strain-free area” as a reference and can work on datasets even with the crystals oriented away from zone axes. This method is expected to provide a robust and more accessible alternative means of studying the residual strain of various material systems that complements the existing algorithms for strain mapping.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Landslide hazard mapping with selected dominant factors: A study case of Penang Island, Malaysia

Landslide is one of the destructive natural geohazards in Malaysia. In addition to rainfall as triggering factos for landslide in Malaysia, topographical and geological factors play important role in the landslide susceptibility analysis. Conventional topographic factors such as elevation, slope angle, slope aspect, plan curvature and profile curvature have been considered as landslide causative factors in many research works. However, other topographic factors such as diagonal length, surface area, surface roughness and rugosity have not been considered, especially for the research work in landslide hazard analysis in Malaysia. This paper presents landslide hazard mapping using Frequency Ratio (FR) and the study area is Penang Island of Malaysia. Frequency ratio approach is a variant of probabilistic method that is based on the observed relationships between the distribution of landslides and each landslide-causative factor. Landslide hazard map of Penang Island is produced by considering twenty-two (22) landslide causative factors. Among these twenty-two (22) factors, fourteen (14) factors are topographic factors. They are elevation, slope gradient, slope aspect, plan curvature, profile curvature, general curvature, tangential curvature, longitudinal curvature, cross section curvature, total curvature, diagonal length, surface area, surface roughness and rugosity. These topographic factors are extracted from the digital elevation model of Penang Island. The other eight (8) non-topographic factors considered are land cover, vegetation cover, distance from road, distance from stream, distance from fault line, geology, soil texture and rainfall precipitation. After considering all twenty-two factors for landslide hazard mapping, the analysis is repeated with fourteen dominant factors which are selected from the twenty-two factors. Landslide hazard map was segregated into four categories of risks, i.e. Highly hazardous area, Hazardous area, Moderately hazardous area and Not hazardous area. The maps was assessed using ROC (Rate of Curve) based on the area under the curve method (AUC). The result indicates an increase of accuracy from 77.76% (with all 22 factors) to 79.00% (with 14 dominant factors) in the prediction of landslide occurrence.

58 GEOSCIENCES↗

Synchronized states and multistability in a random network of coupled discontinuous maps

The synchronization behavior of coupled chaotic discontinuous maps over a ring network with dynamic random connections is reported in this paper. It is observed that random rewiring stabilizes one of the two strongly unstable fixed points of the local map. Depending on initial conditions, the network synchronizes to different unstable fixed points, which signifies the existence of synchronized multistability in the complex network. Moreover, the length of discontinuity of the local map has an important role in generating windows of different synchronized fixed points. Synchronized fixed point and synchronized periodic orbits are found in the network depending on coupling strength and different parameter values of the local map. We have identified the existence of period subtracting bifurcation with respect to coupling strength in the network. The range of coupling strength for the occurrence of synchronized multistable spatiotemporal fixed points is determined. This range strongly depends upon the dynamic rewiring probability and also on the local map.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Evolution families of conformal mappings with fixed points and the Löwner-Kufarev equation

The paper is concerned with evolution families of conformal mappings of the unit disc to itself that fix an interior point and a boundary point. Conditions are obtained for the evolution families to be differentiable, and an existence and uniqueness theorem for an evolution equation is proved. A convergence theorem is established which describes the topology of locally uniform convergence of evolution families in terms of infinitesimal generating functions. The main result in this paper is the embedding theorem which shows that any conformal mapping of the unit disc to itself with two fixed points can be embedded into a differentiable evolution family of such mappings. This result extends the range of the parametric method in the theory of univalent functions. In this way the problem of the mutual change of the derivative at an interior point and the angular derivative at a fixed point on the boundary is solved for a class of mappings of the unit disc to itself. In particular, the rotation theorem is established for this class of mappings. Bibliography: 27 titles.

97 MATHEMATICS AND COMPUTING↗

Modeling adsorption properties of structurally deformed metal–organic frameworks using structure–property map

Structural deformation and collapse in metal-organic frameworks (MOFs) can lead to loss of long-range order, making it a challenge to model these amorphous materials using conventional computational methods. In this work, we show that a structure–property map consisting of simulated data for crystalline MOFs can be used to indirectly obtain adsorption properties of structurally deformed MOFs. The structure–property map (with dimensions such as Henry coefficient, heat of adsorption, and pore volume) was constructed using a large data set of over 12000 crystalline MOFs from molecular simulations. By mapping the experimental data points of deformed SNU-200, MOF-5, and Ni-MOF-74 onto this structure–property map, we show that the experimentally deformed MOFs share similar adsorption properties with their nearest neighbor crystalline structures. Furthermore, once the nearest neighbor crystalline MOFs for a deformed MOF are selected from a structure–property map at a specific condition, then the adsorption properties of these MOFs can be successfully transformed onto the degraded MOFs, leading to a new way to obtain properties of materials whose structural information is lost.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

MAPPING THE GALAXY COLOR–REDSHIFT RELATION: OPTIMAL PHOTOMETRIC REDSHIFT CALIBRATION STRATEGIES FOR COSMOLOGY SURVEYS

Calibrating the photometric redshifts of ≳10{sup 9} galaxies for upcoming weak lensing cosmology experiments is a major challenge for the astrophysics community. The path to obtaining the required spectroscopic redshifts for training and calibration is daunting, given the anticipated depths of the surveys and the difficulty in obtaining secure redshifts for some faint galaxy populations. Here we present an analysis of the problem based on the self-organizing map, a method of mapping the distribution of data in a high-dimensional space and projecting it onto a lower-dimensional representation. We apply this method to existing photometric data from the COSMOS survey selected to approximate the anticipated Euclid weak lensing sample, enabling us to robustly map the empirical distribution of galaxies in the multidimensional color space defined by the expected Euclid filters. Mapping this multicolor distribution lets us determine where—in galaxy color space—redshifts from current spectroscopic surveys exist and where they are systematically missing. Crucially, the method lets us determine whether a spectroscopic training sample is representative of the full photometric space occupied by the galaxies in a survey. We explore optimal sampling techniques and estimate the additional spectroscopy needed to map out the color–redshift relation, finding that sampling the galaxy distribution in color space in a systematic way can efficiently meet the calibration requirements. While the analysis presented here focuses on the Euclid survey, similar analysis can be applied to other surveys facing the same calibration challenge, such as DES, LSST, and WFIRST.

79 ASTRONOMY AND ASTROPHYSICS↗

Measuring the thermal Sunyaev-Zel'dovich effect through the cross correlation of Planck and WMAP maps with ROSAT galaxy cluster catalogs

We measure a significant correlation between the thermal Sunyaev-Zel'dovich effect in the Planck and WMAP maps and an X-ray cluster map based on ROSAT. We use the 100, 143 and 343 GHz Planck maps and the WMAP 94 GHz map to obtain this cluster cross spectrum. We check our measurements for contamination from dusty galaxies using the cross correlations with the 217, 545 and 857 GHz maps from Planck. Our measurement yields a direct characterization of the cluster power spectrum over a wide range of angular scales that is consistent with large cosmological simulations. The amplitude of this signal depends on cosmological parameters that determine the growth of structure (σ{sub 8} and Ω M) and scales as σ{sub 8}{sup 7.4} and Ω M{sup 1.9} around the multipole (ℓ) ∼ 1000. We constrain σ{sub 8} and Ω M from the cross-power spectrum to be σ{sub 8}(Ω M/0.30){sup 0.26} = 0.8±0.02. Since this cross spectrum produces a tight constraint in the σ{sub 8} and Ω M plane the errors on a σ{sub 8} constraint will be mostly limited by the uncertainties from external constraints. Future cluster catalogs, like those from eRosita and LSST, and pointed multi-wavelength observations of clusters will improve the constraining power of this cross spectrum measurement. In principle this analysis can be extended beyond σ{sub 8} and Ω M to constrain dark energy or the sum of the neutrino masses.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

THE DARKEST SHADOWS: DEEP MID-INFRARED EXTINCTION MAPPING OF A MASSIVE PROTOCLUSTER

We use deep 8 μm Spitzer-IRAC imaging of massive Infrared Dark Cloud (IRDC) G028.37+00.07 to construct a mid-infrared (MIR) extinction map that probes mass surface densities up to Σ ∼ 1 g cm{sup –2} (A{sub V} ∼ 200 mag), amongst the highest values yet probed by extinction mapping. Merging with an NIR extinction map of the region creates a high dynamic range map that reveals structures down to A{sub V} ∼ 1 mag. We utilize the map to: (1) measure a cloud mass ∼7 × 10{sup 4} M {sub ☉} within a radius of ∼8 pc. {sup 13}CO kinematics indicate that the cloud is gravitationally bound. It thus has the potential to form one of the most massive young star clusters known in the Galaxy. (2) Characterize the structures of 16 massive cores within the IRDC, finding they can be fit by singular polytropic spheres with ρ∝r{sup −k{sub ρ}} and k {sub ρ} = 1.3 ± 0.3. They have Σ-bar ≃0.1--0.4 g cm{sup −2}—relatively low values that, along with their measured cold temperatures, suggest that magnetic fields, rather than accretion-powered radiative heating, are important for controlling fragmentation of these cores. (3) Determine the Σ (equivalently column density or A{sub V} ) probability distribution function (PDF) for a region that is nearly complete for A{sub V} > 3 mag. The PDF is well fit by a single log-normal with mean A-bar {sub V}≃9 mag, high compared to other known clouds. It does not exhibit a separate high-end power law tail, which has been claimed to indicate the importance of self-gravity. However, we suggest that the PDF does result from a self-similar, self-gravitating hierarchy of structures present over a wide range of scales in the cloud.

79 ASTRONOMY AND ASTROPHYSICS↗

Chemical state mapping of simulant Chernobyl lava-like fuel containing material using micro-focused synchrotron X-ray spectroscopy

Uranium speciation and redox behaviour is of critical importance in the nuclear fuel cycle. X-ray absorption near-edge spectroscopy (XANES) is commonly used to probe the oxidation state and speciation of uranium, and other elements, at the macroscopic and microscopic scale, within nuclear materials. Two-dimensional (2D) speciation maps, derived from microfocus X-ray fluorescence and XANES data, provide essential information on the spatial variation and gradients of the oxidation state of redox active elements such as uranium. In the present work, we elaborate and evaluate approaches to the construction of 2D speciation maps, in an effort to maximize sensitivity to the U oxidation state at the U L 3 -edge, applied to a suite of synthetic Chernobyl lava specimens. Our analysis shows that calibration of speciation maps can be improved by determination of the normalized X-ray absorption at excitation energies selected to maximize oxidation state contrast. The maps are calibrated to the normalized absorption of U L 3 XANES spectra of relevant reference compounds, modelled using a combination of arctangent and pseudo-Voigt functions (to represent the photoelectric absorption and multiple-scattering contributions). We validate this approach by microfocus X-ray diffraction and XANES analysis of points of interest, which afford average U oxidation states in excellent agreement with those estimated from the chemical state maps. This simple and easy-to-implement approach is general and transferrable, and will assist in the future analysis of real lava-like fuel-containing materials to understand their environmental degradation, which is a source of radioactive dust production within the Chernobyl shelter.

36 MATERIALS SCIENCE↗

Simulated Feasibility of 3-D Lightning Mapping From Space

In addition to the awe it inspires, lightning can illuminate the microphysical processes hidden away within deep convection. The current generation of space-based lightning mapping uses mostly 2-D optical imaging to connect overall flash characteristics to their parent storm dynamics, but are missing a dimension’s worth of information. With lightning now classified as an essential climate variable, future spaceborne mappers will need improved capabilities to take advantage of the 3-D structure of lightning flashes to support meteorological and climate modeling. We report here on a study of the feasibility of high-resolution 3-D lightning mapping using a radio frequency (RF)-based network of satellites from low-Earth orbit (LEO). Lightning sources are simulated using existing lightning mapping array (LMA) tools, modified for orbital detection, and spatially reconstructed using a Levenberg–Marquardt geolocation algorithm to assess sources of uncertainty in these solutions. We analyze the benefits and limitations of this approach compared to existing orbital and ground-based methods. Results of this study show that lightning can be mapped in 3-D with a vertical location accuracy better than 2 km using as few as five satellites in LEO capable of measuring the time-of-arrival of impulsive RF signals in the very high-frequency (VHF) band. The consequence of this study is that high-resolution, spaceborne 3-D mapping of lightning is achievable across most of the globe, having crucial implications for our understanding of not only lightning, but also severe weather development, climate science, and more.

47 OTHER INSTRUMENTATION↗

An automated workflow that generates atom mappings for large‐scale metabolic models and its application to Arabidopsis thaliana

SUMMARY Quantification of reaction fluxes of metabolic networks can help us understand how the integration of different metabolic pathways determines cellular functions. Yet, intracellular fluxes cannot be measured directly but are estimated with metabolic flux analysis (MFA), which relies on the patterns of isotope labeling of metabolites in the network. The application of MFA also requires a stoichiometric model with atom mappings that are currently not available for the majority of large‐scale metabolic network models, particularly of plants. While automated approaches such as the Reaction Decoder Toolkit (RDT) can produce atom mappings for individual reactions, tracing the flow of individual atoms of the entire reactions across a metabolic model remains challenging. Here we establish an automated workflow to obtain reliable atom mappings for large‐scale metabolic models by refining the outcome of RDT, and apply the workflow to metabolic models of Arabidopsis thaliana . We demonstrate the accuracy of RDT through a comparative analysis with atom mappings from a large database of biochemical reactions, MetaCyc. We further show the utility of our automated workflow by simulating 15 N isotope enrichment and identifying nitrogen (N)‐containing metabolites which show enrichment patterns that are informative for flux estimation in future 15 N‐MFA studies of A. thaliana . The automated workflow established in this study can be readily expanded to other species for which metabolic models have been established and the resulting atom mappings will facilitate MFA and graph‐theoretic structural analyses with large‐scale metabolic networks.

59 BASIC BIOLOGICAL SCIENCES↗

TU-A-19A-01: Image Registration I: Deformable Image Registration, Contour Propagation and Dose Mapping: 101 and 201

Deformable image registration, contour propagation and dose mapping have become common, possibly essential tools for modern image-guided radiation therapy. Historically, these tools have been largely developed at academic medical centers and used in a rather limited and well controlled fashion. Today these tools are now available to the radiotherapy community at large, both as stand-alone applications and as integrated components of both treatment planning and treatment delivery systems. Unfortunately, the details of how these tools work and their limitations are not generally documented or described by the vendors that provide them. Although “it looks right”, determining that unphysical deformations may have occurred is crucial. Because of this, understanding how and when to use, and not use these tools to support everyday clinical decisions is far from straight forward. The goal of this session will be to present both the theory (basic and advanced) and practical clinical use of deformable image registration, contour propagation and dose mapping. To the extent possible, the “secret sauce” that different vendor use to produce reasonable/acceptable results will be described. A detailed explanation of the possible sources of errors and actual examples of these will be presented. Knowing the underlying principles of the process and understanding the confounding factors will help the practicing medical physicist be better able to make decisions (about making decisions) using these tools available. Learning Objectives: Understand the basic (101) and advanced (201) principles of deformable image registration, contour propagation and dose mapping data mapping. Understand the sources and impact of errors in registration and data mapping and the methods for evaluating the performance of these tools. Understand the clinical use and value of these tools, especially when used as a “black box”.

60 APPLIED LIFE SCIENCES↗

Interindividual registration and dose mapping for voxelwise population analysis of rectal toxicity in prostate cancer radiotherapy

Purpose: Recent studies revealed a trend toward voxelwise population analysis in order to understand the local dose/toxicity relationships in prostate cancer radiotherapy. Such approaches require, however, an accurate interindividual mapping of the anatomies and 3D dose distributions toward a common coordinate system. This step is challenging due to the high interindividual variability. In this paper, the authors propose a method designed for interindividual nonrigid registration of the rectum and dose mapping for population analysis. Methods: The method is based on the computation of a normalized structural description of the rectum using a Laplacian-based model. This description takes advantage of the tubular structure of the rectum and its centerline to be embedded in a nonrigid registration-based scheme. The performances of the method were evaluated on 30 individuals treated for prostate cancer in a leave-one-out cross validation. Results: Performance was measured using classical metrics (Dice score and Hausdorff distance), along with new metrics devised to better assess dose mapping in relation with structural deformation (dose-organ overlap). Considering these scores, the proposed method outperforms intensity-based and distance maps-based registration methods. Conclusions: The proposed method allows for accurately mapping interindividual 3D dose distributions toward a single anatomical template, opening the way for further voxelwise statistical analysis.

60 APPLIED LIFE SCIENCES↗

Development of in-use engine speed/torque heat maps across multiple heavy-duty commercial vehicle vocations

The U.S. Department of Energy (DOE) established the SuperTruck program with the goal of achieving brake thermal efficiency (BTE) greater than or equal to 55% as demonstrated in an operational heavy-duty (HD) diesel engine at a 65-miles-per-hour (mph) cruise point. Beyond the line-haul application, HD engines operate in a wide range of speed and torque conditions that are unlikely to yield the same efficiency under real-world operation. Thereby, the in-use engine heat maps described in this paper are a valuable tool to illustrate whether the engine-efficiency “sweet spot” matches the most frequent operating conditions. In this study, NREL developed engine heat maps to quantify the important operating points for various vocations using our Fleet DNA database of commercial fleet vehicle operations data. These heat maps clearly show that high-frequency operating points vary significantly according to vehicle vocation, while only a few of them match the sweet spot. Beyond the illustration, engine in-use heat maps can also be leveraged to build up reduced-order engine-efficiency models, needed by many rapid powertrain simulations. As case studies, nine reduced-order models – including line-haul truck, transfer truck, transit bus, transit bus with compressed natural gas (CNG) engine, drayage, refuse pickup, local delivery, utility truck, and school bus with CNG engine – using a trust-region reflective algorithm to fit the on-road data extracted based on the engine in-use heat maps.

33 ADVANCED PROPULSION SYSTEMS↗

Preliminary Geologic Map of the Tuscarora Geothermal Area, Elko County, Nevada

Preliminary geologic map, unit descriptions, and cross-sections of the Tuscarora geothermal area. The files within the zip are all in pdf format. The the two maps include rock and mineral deposits from different geologic time scales. Units, legend, and scales can be found on each map, and a description of the maps can be found in the "Preliminary Geologic Map of the Tuscarora Geothermal Area, Elko County, Nevada" document.

15 GEOTHERMAL ENERGY↗

Location Identifiers, Metadata, and Map for Field Measurements at the East-Taylor Watershed Community Observatory, Colorado, USA (Version 3.3)

This dataset contains identifiers, metadata, and a map of the locations where field measurements have been conducted at the East-Taylor Watershed Community Observatory located in the Upper Colorado River Basin, United States. This is version 3.3 of the dataset and replaces the prior version 3.2 (see below for details on changes between the versions). Dataset description: The East River-Taylor Watershed is the primary field site of the Watershed Function Scientific Focus Area (WFSFA) and the Rocky Mountain Biological Laboratory. Researchers from several institutions generate highly diverse hydrological, biogeochemical, climate, vegetation, geological, remote sensing, and model data at the East-Taylor Watershed in collaboration with the WFSFA. Thus, the purpose of this dataset is to maintain an inventory of the field locations and instrumentation to provide information on the field activities in the East-Taylor Watershed and coordinate data collected across different locations, researchers, and institutions. The dataset contains (1) a README file with information on the various files, (2) three csv files describing the metadata collected for each surface point location, plot and region registered with the WFSFA, (3) csv files with metadata and contact information for each surface point location registered with the WFSFA, (4) a csv file with with metadata and contact information for plots, (5) a csv file with metadata for geographic regions and sub-regions within the watershed, (6) a compiled xlsx file with all the data and metadata which can be opened in Microsoft Excel, (7) a kml map of the locations plotted in the watershed which can be opened in Google Earth, (8) a jpg image of the kml map which can be viewed in any photo viewer, and (9) a zipped file with the registration templates used by the SFA team to collect location metadata. The zipped template file contains two csv files with the blank templates (point and plot), two csv files with instructions for filling out the location templates, and one compiled xlsx file with the instructions and blank templates together. Additionally, the templates in the xlsx include drop down validation for any controlled metadata fields. Persistent location identifiers (Location_ID) are determined by the WFSFA data management team and are used to track data and samples across locations. Dataset uses: This location metadata is used to update the Watershed SFA’s publicly accessible Field Information Portal (an interactive field sampling metadata exploration tool; https://wfsfa-data.lbl.gov/watershed/), the kml map file included in this dataset, and other data management tools internal to the Watershed SFA team. Version Information: The latest version of this dataset publication is version 3.3. This version contains 167 new point locations, 1 new plot, and 2 new geographic regions. Overall, there are a total of 1439 point locations, 75 plots, and 54 geographic regions. Additionally, the kml map of locations and image now includes two boundaries (Upper Ohio Creek (UO) and Carbon Creek (CA)) outside of the East River watershed (USGS HUC-10) and accompanying stream network that represents areas of focus. Refer to methods for further details on the version history. This dataset will be updated on a periodic basis with new measurement location information. Researchers interested in having their East-Taylor Watershed measurement locations added to this list should reach out to the WFSFA data management team at wfsfa-data@googlegroups.com. Acknowledgments: Please cite this dataset if using any of the location metadata in other publications or derived products. If using the location metadata for the 2018 NEON hyperspectral campaign, additionally cite Chadwick et al. (2020). doi:10.15485/1618130. This work was supported by the Watershed Function Science Focus Area at Lawrence Berkeley National Laboratory funded by the US Department of Energy, Office of Science, Biological and Environmental Research under Contract No. DE-AC02-05CH11231. Part of this work was performed at SLAC Accelerator Laboratory funded by the US Department of Energy, Office of Science, Biological and Environmental Research under Contract No. DE-AC02-76SF00515.

2018 NEON and 2025 CHESS Campaigns↗

Flood Susceptibility Mapping Using Machine Learning and Geospatial-Sentinel-1 SAR Integration for Enhanced Early Warning Systems

This study presents a comprehensive framework for flood susceptibility mapping by integrating geospatial factors with both statistical and machine learning models. Thirteen Flood-related factors, including DEM, slope, TWI, NDVI, etc., are extracted as features of models, and historical flood data derived from Sentinel-1 SAR from 2018 to 2023 are used as the target variables of the models. These datasets are analyzed using a frequency-based statistical model and three machine learning models, including Random Forest, XGBoost, and CNN, to generate flood susceptibility maps. The performance of each model is evaluated through AUC; and SHAP scores are separately generated for Machine learning (ML) models to explain each feature contribution in the ML model. The generated susceptibility maps are validated by high-flood-risk locations monitored by flood sensors, BLE inundation models, and flood-prone areas suggested by the Local Community Task Force. The results indicate that the XGBoost model outperforms all other models, with an AUC of 0.92 and demonstrates the highest alignment with recommended high-flood-risk locations, while the frequency-based statistical model showed the weakest performance with an AUC of 0.65. SHAP value graphs highlight the elevation, slope, and TWI as the most influential features across all models. The susceptibility maps generated by the machine learning model show strong agreement with the BLE map and high-flood-risk areas identified by the local Community Task Force.

Google Engine↗

ZEEMAN DOPPLER MAPS: ALWAYS UNIQUE, NEVER SPURIOUS?

Numerical models of atomic diffusion in magnetic atmospheres of ApBp stars predict abundance structures that differ from the empirical maps derived with (Zeeman) Doppler mapping (ZDM). An in-depth analysis of this apparent disagreement investigates the detectability by means of ZDM of a variety of abundance structures, including (warped) rings predicted by theory, but also complex spot-like structures. Even when spectra of high signal-to-noise ratio are available, it can prove difficult or altogether impossible to correctly recover shapes, positions, and abundances of a mere handful of spots, notwithstanding the use of all four Stokes parameters and an exactly known field geometry; the recovery of (warped) rings can be equally challenging. Inversions of complex abundance maps that are based on just one or two spectral lines usually permit multiple solutions. It turns out that it can by no means be guaranteed that any of the regularization functions in general use for ZDM (maximum entropy or Tikhonov) will lead to a true abundance map instead of some spurious one. Attention is drawn to the need for a study that would elucidate the relation between the stratified, field-dependent abundance structures predicted by diffusion theory on the one hand, and empirical maps obtained by means of “canonical” ZDM, i.e., with mean atmospheres and unstratified abundances, on the other hand. Finally, we point out difficulties arising from the three-dimensional nature of the atomic diffusion process in magnetic ApBp star atmospheres.

79 ASTRONOMY AND ASTROPHYSICS↗