Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “function mapping”

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 829 records · Page 46
All sourcesNASA NTRSDOE OSTI
DOE OSTI2011

Exact solution of D{sub N}-type quantum Calogero model through a mapping to free harmonic oscillators

We solve the eigenvalue problem of the D{sub N}-type of Calogero model by mapping it to a set of decoupled quantum harmonic oscillators through a similarity transformation. In particular, we construct the eigenfunctions of this Calogero model from those of bosonic harmonic oscillators having either all even parity or all odd parity. It turns out that the eigenfunctions of this model are orthogonal with respect to a nontrivial inner product, which can be derived from the quasi-Hermiticity property of the corresponding conserved quantities.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1994

Correlated noise in the COBE DMR sky maps

The Cosmic Background Explorer Satellite Differential Radiometer (COBE DMR) sky maps contain low-level correlated noise. We obtain estimates of the amplitude and pattern of the correlated noise from three techniques: angular averages of the covariance matrix, Monte Carlo simulations of two-point correlation functions and direct analysis of the DMR maps. The results from the three methods are mutually consistent. The noise covariance matrix of a DMR sky maps is diagonal to an accuracy of better than 1%. For a given sky pixel, the dominant noise covariance occure with the ring of pixels at an angular separation of 60 deg due to the 60 deg separation of the DMR horns. The mean covariance at 60 deg is 0.45%((sup +0.18)(sub -0.14)) of the mean variance. Additionally, the variance in a given pixel is 0.7% greater than would be expected from a single beam experiment with the same noise properties. Autocorrelation functions suffer from a approximately 1.5 sigma positive bias at 60 deg while cross-correlations have no bias. Published COBE DMR results are not significantly affected by correlated noise.

Lineweaver, C. H.↗
DOE OSTI2011

DISK AND ENVELOPE STRUCTURE IN CLASS 0 PROTOSTARS. II. HIGH-RESOLUTION MILLIMETER MAPPING OF THE SERPENS SAMPLE

We present high-resolution CARMA 230 GHz continuum imaging of nine deeply embedded protostars in the Serpens Molecular Cloud, including six of the nine known Class 0 protostars in Serpens. This work is part of a program to characterize disk and envelope properties for a complete sample of Class 0 protostars in nearby low-mass star-forming regions. Here, we present CARMA maps and visibility amplitudes as a function of uv-distance for the Serpens sample. Observations are made in the B, C, D, and E antenna configurations, with B configuration observations utilizing the CARMA Paired Antenna Calibration System. Combining data from multiple configurations provides excellent uv-coverage (4-500 k{lambda}), allowing us to trace spatial scales from 10{sup 2} to 10{sup 4} AU. We find evidence for compact disk components in all of the observed Class 0 protostars, suggesting that disks form at very early times (t < 0.2 Myr) in Serpens. We make a first estimate of disk masses using the flux at 50 k{lambda}, where the contribution from the envelope should be negligible, assuming an unresolved disk. The resulting disk masses range from 0.04 M{sub sun} to 1.7 M{sub sun}, with a mean of approximately 0.2 M{sub sun}. Our high-resolution maps are also sensitive to binary or multiple sources with separations {approx}> 250 AU, but significant evidence of multiplicity on scales <2000 AU is seen in only one source.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2013

Extremely correlated Fermi liquids in the limit of infinite dimensions

We study the infinite spatial dimensionality limit (d→∞) of the recently developed Extremely Correlated Fermi Liquid (ECFL) theory (Shastry 2011, 2013) [17,18] for the t–J model at J=0. We directly analyze the Schwinger equations of motion for the Gutzwiller projected (i.e. U=∞) electron Green’s function G. From simplifications arising in this limit d→∞, we are able to make several exact statements about the theory. The ECFL Green’s function is shown to have a momentum independent Dyson (Mori) self energy. For practical calculations we introduce a partial projection parameter λ, and obtain the complete set of ECFL integral equations to O(λ{sup 2}). In a related publication (Zitko et al. 2013) [23], these equations are compared in detail with the dynamical mean field theory for the large U Hubbard model. Paralleling the well known mapping for the Hubbard model, we find that the infinite dimensional t–J model (with J=0) can be mapped to the infinite-U Anderson impurity model with a self-consistently determined set of parameters. This mapping extends individually to the auxiliary Green’s function g and the caparison factor μ. Additionally, the optical conductivity is shown to be obtainable from G with negligibly small vertex corrections. These results are shown to hold to each order in λ. -- Highlights: •Infinite-dimensional t–J model (J=0) studied within new ECFL theory. •Mapping to the infinite U Anderson model with self consistent hybridization. •Single particle Green’s function determined by two local self energies. •Partial projection through control variable λ. •Expansion carried out to O(λ{sup 2}) explicitly.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1984

Chip level modeling of LSI devices

The advent of Very Large Scale Integration (VLSI) technology has rendered the gate level model impractical for many simulation activities critical to the design automation process. As an alternative, an approach to the modeling of VLSI devices at the chip level is described, including the specification of modeling language constructs important to the modeling process. A model structure is presented in which models of the LSI devices are constructed as single entities. The modeling structure is two layered. The functional layer in this structure is used to model the input/output response of the LSI chip. A second layer, the fault mapping layer, is added, if fault simulations are required, in order to map the effects of hardware faults onto the functional layer. Modeling examples for each layer are presented. Fault modeling at the chip level is described. Approaches to realistic functional fault selection and defining fault coverage for functional faults are given. Application of the modeling techniques to single chip and bit slice microprocessors is discussed.

Armstrong, J. R.↗
DOE OSTI2024

A Principled Framework to Assess the Information-Theoretic Fitness of Brain Functional Sub-Circuits

In systems and network neuroscience, many common practices in brain connectomic analysis are often not properly scrutinized. One such practice is mapping a predetermined set of sub-circuits, like functional networks (FNs), onto subjects’ functional connectomes (FCs) without adequately assessing the information-theoretic appropriateness of the partition. Another practice that goes unchallenged is thresholding weighted FCs to remove spurious connections without justifying the chosen threshold. This paper leverages recent theoretical advances in Stochastic Block Models (SBMs) to formally define and quantify the information-theoretic fitness (e.g., prominence) of a predetermined set of FNs when mapped to individual FCs under different fMRI task conditions. Our framework allows for evaluating any combination of FC granularity, FN partition, and thresholding strategy, thereby optimizing these choices to preserve the important topological features of the human brain connectomes. By applying to the Human Connectome Project with Schaefer parcellations at multiple levels of granularity, the framework showed that the common thresholding value of 0.25 was indeed information-theoretically valid for group-average FCs, despite its previous lack of justification. Our results pave the way for the proper use of FNs and thresholding methods, and provide insights for future research in individualized parcellations.

Duong-Tran, Duy (ORCID:0009000944967575)↗
DOE OSTI2022

Presentation of gas-phase-reactant-accessible single-rhodium-atom catalysts for CO oxidation, via MOF confinement of an Anderson polyoxometalate

Geometric or electronic confinement of guests within nanoporous hosts holds promise for imparting catalytic functionality, including single-metal-atom catalytic functionality, to existing materials. When the nanoporous host is a metal–organic framework (MOF), single-metal-ion catalysts have typically been installed by grafting to an open site on an inorganic node, with the node effectively becoming the support for the catalyst. This approach, however, imposes compositional constraints, as the node not only needs to be receptive to grafting, but also must be capable of stabilizing the framework against solvent evacuation, chemical exposure, and heating. Here, we show that disk-like, Anderson polyoxometalate clusters (RhMo 6 O 24 n- and Mo 7 O 24 m- ; POMs) can be confined in pore-specific and orientation-specific fashion within the hierarchically porous, Zr(IV)-based MOF, NU1K. Self-limiting loading of one cluster per pore, and associated nano-confinement, serve to isolate each POM and prevent consolidation caused by sintering. Additionally, the oriented confinement serves to expose individual rhodium atoms to candidate gas-phase reactants, while enabling the rhodium atom to employ a well-defined oxy-molybdenum cluster, rather than a MOF node, as a support. Synchrotron-based difference-electron-density maps and differential pair-distribution-function analyses of scattered X-rays establish cluster siting and orientation and confirm isolation. Nanoconfined (i.e., MOF- and POM-confined) single-rhodium(III)-atoms are catalytically competent for an illustrative gas-phase reaction, CO oxidation by O 2 , with the MOF-isolated POM enormously outperforming nonporous, MOF-free, solid (NH 4 ) 3 [H 6 RhMo 6 O 24 ]·6H 2 O. This paper highlights the value of MOF-based nano-confinement and oriented isolation of planar POMs as a means of uniformly presenting and stabilizing potent single-metal-atom catalysts, in reactant-accessible form, on well-defined supports.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Nanoscale Phase Identification Using Two-Dimensional Pair Correlation Functions: A Case Study on Hafnium Oxide

Accurate identification of local phases in nanocrystalline materials is essential for understanding their functional properties, but it remains a significant challenge for polymorphic materials to locally differentiate them at nanoscale. This challenge is further compounded in polycrystalline materials with randomly oriented grains and the coexistence of multiple phases. In this report, we present a methodology for phase and orientation identification at the nanoscale by leveraging vector pair correlation functions extracted from atomically resolved scanning transmission electron microscopy (STEM) images. We demonstrate the accuracy of the methodology on both simulated and experimental data from HfO 2 -based films, a material that exhibits multiple coexisting phases in films with thicknesses ranging from 5 to 20 nm. While demonstrated on HfO 2 films, the methodology can be extended to other polymorphic nanocrystalline systems with complex phase coexistence.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Structural Similarities and Differences between Two Functionally Distinct SecA Proteins, Mycobacterium tuberculosis SecA1 and SecA2

While SecA is the ATPase component of the major bacterial secretory (Sec) system, mycobacteria and some Gram-positive pathogens have a second paralog, SecA2. In bacteria with two SecA paralogs, each SecA is functionally distinct, and they cannot compensate for one another. Compared to SecA1, SecA2 exports a distinct and smaller set of substrates, some of which have roles in virulence. In the mycobacterial system, some SecA2-dependent substrates lack a signal peptide, while others contain a signal peptide but possess features in the mature protein that necessitate a role for SecA2 in their export. It is unclear how SecA2 functions in protein export, and one open question is whether SecA2 works with the canonical SecYEG channel to export proteins. In this study, we report the structure of Mycobacterium tuberculosis SecA2 (MtbSecA2), which is the first structure of any SecA2 protein. A high level of structural similarity is observed between SecA2 and SecA1. The major structural difference is the absence of the helical wing domain, which is likely to play a role in how MtbSecA2 recognizes its unique substrates. Importantly, structural features critical to the interaction between SecA1 and SecYEG are preserved in SecA2. Furthermore, suppressor mutations of a dominant-negative secA2 mutant map to the surface of SecA2 and help identify functional regions of SecA2 that may promote interactions with SecYEG or the translocating polypeptide substrate. Here, these results support a model in which the mycobacterial SecA2 works with SecYEG. SecA2 is a paralog of SecA1, which is the ATPase of the canonical bacterial Sec secretion system. SecA2 has a nonredundant function with SecA1, and SecA2 exports a distinct and smaller set of substrates than SecA1. This work reports the crystal structure of SecA2 of Mycobacterium tuberculosis (the first SecA2 structure reported for any organism). Many of the structural features of SecA1 are conserved in the SecA2 structure, including putative contacts with the SecYEG channel. Several structural differences are also identified that could relate to the unique function and selectivity of SecA2. Suppressor mutations of a secA2 mutant map to the surface of SecA2 and help identify functional regions of SecA2 that may promote interactions with SecYEG.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Evolution of magnetic field induced ordering in the layered quantum Heisenberg triangular-lattice antiferromagnet Ba 3 CoSb 2 O 9

Quantum fluctuations in the effective spin-12 layered triangular-lattice quantum Heisenberg antiferromagnet Ba 3 CoSb 2 O 9 lift the classical degeneracy of the antiferromagnetic ground state in magnetic field, producing a series of novel spin structures for magnetic fields applied within the crystallographic ab plane, including a celebrated collinear “up-up-down” spin ordering with magnetization equal to 1/3 of the saturation magnetization over an extended field range. Theoretically unresolved, however, are the effects of interlayer antiferromagnetic coupling and transverse magnetic fields on the ground states of this system. Additional magnetic field induced phase transitions are theoretically expected and in some cases have been experimentally observed, but details regarding their number, location, and physical character appear inconsistent with the predictions of existing models. Conversely, an absence of experimental measurements as a function of magnetic-field orientation has left other key predictions of these models untested. To address these issues, in this study we have used specific heat, neutron diffraction, thermal conductivity, and magnetic torque measurements to map out the phase diagram as a function of magnetic field intensity and orientation relative to the crystallographic ab plane. For H||ab, we have discovered an additional magnetic field induced phase transition at low temperature and an unexpected tetracritical point in the high-field phase diagram, which coupled with the apparent second-order nature of the phase transitions eliminates several theoretically proposed spin structures for the high-field phases. Our calorimetric measurements as a function of magnetic field orientation are in general agreement with theory for field-orientation angles close to plane parallel (H||a) but diverge at angles near plane perpendicular; a predicted convergence of two phase boundaries at finite angle and a corresponding change in the order of the field induced phase transition are not observed experimentally. Our results emphasize the role of interlayer coupling in selecting and stabilizing field induced phases, provide guidance on the nature of the magnetic order in each phase, and reveal the need for new physics to account for the nature of magnetic ordering in this archetypal two-dimensional spin-12 triangular-lattice quantum Heisenberg antiferromagnet.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1993

Geometrical approach to neural net control of movements and posture

In one approach to modeling brain function, sensorimotor integration is described as geometrical mapping among coordinates of non-orthogonal frames that are intrinsic to the system; in such a case sensors represent (covariant) afferents and motor effectors represent (contravariant) motor efferents. The neuronal networks that perform such a function are viewed as general tensor transformations among different expressions and metric tensors determining the geometry of neural functional spaces. Although the non-orthogonality of a coordinate system does not impose a specific geometry on the space, this "Tensor Network Theory of brain function" allows for the possibility that the geometry is non-Euclidean. It is suggested that investigation of the non-Euclidean nature of the geometry is the key to understanding brain function and to interpreting neuronal network function. This paper outlines three contemporary applications of such a theoretical modeling approach. The first is the analysis and interpretation of multi-electrode recordings. The internal geometries of neural networks controlling external behavior of the skeletomuscle system is experimentally determinable using such multi-unit recordings. The second application of this geometrical approach to brain theory is modeling the control of posture and movement. A preliminary simulation study has been conducted with the aim of understanding the control of balance in a standing human. The model appears to unify postural control strategies that have previously been considered to be independent of each other. Third, this paper emphasizes the importance of the geometrical approach for the design and fabrication of neurocomputers that could be used in functional neuromuscular stimulation (FNS) for replacing lost motor control.

Review↗
DOE OSTI2021

A VR-based volumetric medical image segmentation and visualization system with natural human interaction

Volume rendering produces informative two-dimensional (2D) images from a 3-dimensional (3D) volume. It highlights the region of interest and facilitates a good comprehension of the entire data set. However, volume rendering faces a few challenges. First, a high-dimensional transfer function is usually required to differentiate the target from its neighboring objects with subtle variance. Unfortunately, designing such a transfer function is a strenuously trial-and-error process. Second, manipulating/visualizing a 3D volume with a traditional 2D input/output device suffers dimensional limitations. To address all the challenges, we design NUI-VR 2 , a natural user interface-enabled volume rendering system in the virtual reality space. NUI-VR 2 marries volume rendering and interactive image segmentation. It transforms the original volume into a probability map with image segmentation. A simple linear transfer function will highlight the target well in the probability map. More importantly, we set the entire image segmentation and volume rendering pipeline in an immersive virtual reality environment with a natural user interface. NUI-VR 2 eliminates the dimensional limitations in manipulating and perceiving 3D volumes and dramatically improves the user experience.

42 ENGINEERING↗
DOE OSTI2015

In-operando synchronous time-multiplexed O K-edge x-ray absorption spectromicroscopy of functioning tantalum oxide memristors

Memristors are receiving keen interest because of their potential varied applications and promising large-scale information storage capabilities. Tantalum oxide is a memristive material that has shown promise for high-performance nonvolatile computer memory. The microphysics has been elusive because of the small scale and subtle physical changes that accompany conductance switching. In this study, we probed the atomic composition, local chemistry, and electronic structure of functioning tantalum oxide memristors through spatially mapped O K-edge x-ray absorption. We developed a time-multiplexed spectromicroscopy technique to enhance the weak and possibly localized oxide modifications with spatial and spectral resolutions of <30 nm and 70 meV, respectively. During the initial stages of conductance switching of a micrometer sized crosspoint device, the spectral changes were uniform within the spatial resolution of our technique. When the device was further driven with millions of high voltage-pulse cycles, we observed lateral motion and separation of ∼100 nm-scale agglomerates of both oxygen interstitials and vacancies. We also demonstrate a unique capability of this technique by identifying the relaxation behavior in the material during electrical stimuli by identifying electric field driven changes with varying pulse widths. In addition, we show that changes to the material can be localized to a spatial region by modifying its topography or uniformity, as against spatially uniform changes observed here during memristive switching. The goal of this report is to introduce the capability of time-multiplexed x-ray spectromicroscopy in studying weak-signal transitions in inhomogeneous media through the example of the operation and temporal evolution of a memristor.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2010

THE STRUCTURE AND KINEMATICS OF THE CIRCUMGALACTIC MEDIUM FROM FAR-ULTRAVIOLET SPECTRA OF z {approx_equal} 2-3 GALAXIES

We present new results on the kinematics and spatial distribution of metal-enriched gas within {approx}125 kpc of star-forming ('Lyman break') galaxies at redshifts 2 {approx_lt} z {approx_lt} 3. In particular, we focus on constraints provided by the rest-frame far-ultraviolet (far-UV) spectra of faint galaxies, and demonstrate how galaxy spectra can be used to obtain key spatial and spectral information more efficiently than possible with QSO sightlines. Using a sample of 89 galaxies with (z) = 2.3 {+-} 0.3 and with both rest-frame far-UV and H{alpha} spectra, we re-calibrate the measurement of accurate galaxy systemic redshifts using only survey-quality rest-UV spectra. We use the velocity-calibrated sample to investigate the kinematics of the galaxy-scale outflows via the strong interstellar (IS) absorption lines and Ly{alpha} emission (when present), as well as their dependence on other physical properties of the galaxies. We construct a sample of 512 close (1''-15'') angular pairs of z {approx} 2-3 galaxies with redshift differences indicating a lack of physical association. Sightlines to the background galaxies provide new information on the spatial distribution of circumgalactic gas surrounding the foreground galaxies. The close pairs sample galactocentric impact parameters 3-125 kpc (physical) at (z) = 2.2, providing for the first time a robust map of cool gas as a function of galactocentric distance for a well-characterized population of galaxies. We propose a simple model of circumgalactic gas that simultaneously matches the kinematics, depth, and profile shape of IS absorption and Ly{alpha} emission lines, as well as the observed variation of absorption line strength (H I and several metallic species) versus galactocentric impact parameter. Within the model, cool gas is distributed symmetrically around every galaxy, accelerating radially outward with v{sub out}(r) increasing with r (i.e., the highest velocities are located at the largest galactocentric distances r). The inferred radial dependence of the covering fraction of cool gas (which modulates the absorption line strength) is f{sub c} (r) {proportional_to} r {sup -{gamma}} with 0.2 {approx_lt} {gamma} {approx_lt} 0.6 depending on transition. We discuss the results of the observations in the context of 'cold accretion', in which cool gas is accreting via filamentary streams directly onto the central regions of galaxies. At present, we find little observational evidence for cool infalling material, while evidence supporting the large-scale effects of superwind outflows is strong. This 'pilot' study using faint galaxy spectra demonstrates the potential of using galaxies to trace baryons within galaxies, in the circumgalactic medium, and ultimately throughout the intergalactic medium.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

WHAT DETERMINES THE DENSITY STRUCTURE OF MOLECULAR CLOUDS? A CASE STUDY OF ORION B WITH HERSCHEL

A key parameter to the description of all star formation processes is the density structure of the gas. In this Letter, we make use of probability distribution functions (PDFs) of Herschel column density maps of Orion B, Aquila, and Polaris, obtained with the Herschel Gould Belt survey (HGBS). We aim to understand which physical processes influence the PDF shape, and with which signatures. The PDFs of Orion B (Aquila) show a lognormal distribution for low column densities until A{sub V} {approx} 3 (6), and a power-law tail for high column densities, consistent with a {rho}{proportional_to}r {sup -2} profile for the equivalent spherical density distribution. The PDF of Orion B is broadened by external compression due to the nearby OB stellar aggregates. The PDF of a quiescent subregion of the non-star-forming Polaris cloud is nearly lognormal, indicating that supersonic turbulence governs the density distribution. But we also observe a deviation from the lognormal shape at A{sub V} > 1 for a subregion in Polaris that includes a prominent filament. We conclude that (1) the point where the PDF deviates from the lognormal form does not trace a universal A{sub V} -threshold for star formation, (2) statistical density fluctuations, intermittency, and magnetic fields can cause excess from the lognormal PDF at an early cloud formation stage, (3) core formation and/or global collapse of filaments and a non-isothermal gas distribution lead to a power-law tail, and (4) external compression broadens the column density PDF, consistent with numerical simulations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

RAD51C-XRCC3 structure and cancer patient mutations define DNA replication roles

$RAD51C$ is an enigmatic predisposition gene for breast, ovarian, and prostate cancer. Currently, missing structural and related functional understanding limits patient mutation interpretation to homology-directed repair (HDR) function analysis. Here we report the RAD51C-XRCC3 (CX3) X-ray co-crystal structure with bound ATP analog and define separable RAD51C replication stability roles informed by its three-dimensional structure, assembly, and unappreciated polymerization motif. Mapping of cancer patient mutations as a functional guide confirms ATP-binding matching RAD51 recombinase yet highlights distinct CX3 interfaces. Analyses of CRISPR/Cas9-edited human cells with $RAD51C$ mutations combined with single-molecule, single-cell and biophysics measurements uncover discrete CX3 regions for DNA replication fork protection, restart and reversal, accomplished by separable functions in DNA binding and implied 5’ RAD51 filament capping. Collective findings establish CX3 as a cancer-relevant replication stress response complex, show how HDR-proficient variants could contribute to tumor development, and identify regions to aid functional testing and classification of cancer mutations.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

A method for convex black-box integer global optimization

Here we study the problem of minimizing a convex function on a nonempty, finite subset of the integer lattice when the function cannot be evaluated at noninteger points. We propose a new underestimator that does not require access to (sub)gradients of the objective; such information is unavailable when the objective is a blackbox function. Rather, our underestimator uses secant linear functions that interpolate the objective function at previously evaluated points. These linear mappings are shown to underestimate the objective in disconnected portions of the domain. Therefore, the union of these conditional cuts provides a nonconvex underestimator of the objective. We propose an algorithm that alternates between updating the underestimator and evaluating the objective function. We prove that the algorithm converges to a global minimum of the objective function on the feasible set. We present two approaches for representing the underestimator and compare their computational effectiveness. We also compare implementations of our algorithm with existing methods for minimizing functions on a subset of the integer lattice. We discuss the difficulty of this problem class and provide insights into why a computational proof of optimality is challenging even for moderate problem sizes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2011

Narrow-beam x-ray tests of CCD edge response.

The physical boundaries of a fully-depleted charged-coupled device (CCD) can lead to distorted field lines and non-uniform response. We study this response with a beam of X-rays constrained to a width of less than one pixel, and a system to map the CCD response as a function of transverse position.

79 ASTRONOMY AND ASTROPHYSICS↗