Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “flux optimization”

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 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Optimization methods, flux conserving methods for steady state Navier-Stokes equation

Navier-Stokes equation as discretized by new flux conserving method proposed by Chang and Scott results in the system: vector F(vector x) = 0, where F is a vector valued function. The Optimization method we use is based on Quasi-Newton methods: given a nonlinear function vector F(vector x) = 0, we solve, Delta(vector x) = -BF(vector x), where Delta(vector x) is the correction term and B is the inverse Jacobian of F(x). Then, iteratively, vector(x(sub (i+1))) = vector(x (sub i)) + alpha.Delta(vector x(sub i)), where alpha is a line search correction term determined by a line search routine. We use the BFCG's update the Jacobian matrix B(sub k) at each iteration. It is well known that B(sub k) approaches B(*) at the solution X(*). This algorithm has several advantages over the Newton-Raphson method. For example, we do not need to calculate the Jacobian matrix at each iteration which is computationally very expensive.

Adeyeye, John↗
NASA NTRS2012

The NEWS Water Cycle Climatology

NASA's Energy and Water Cycle Study (NEWS) program fosters collaborative research towards improved quantification and prediction of water and energy cycle consequences of climate change. In order to measure change, it is first necessary to describe current conditions. The goal of the first phase of the NEWS Water and Energy Cycle Climatology project was to develop "state of the global water cycle" and "state of the global energy cycle" assessments based on data from modern ground and space based observing systems and data integrating models. The project was a multi-institutional collaboration with more than 20 active contributors. This presentation will describe the results of the water cycle component of the first phase of the project, which include seasonal (monthly) climatologies of water fluxes over land, ocean, and atmosphere at continental and ocean basin scales. The requirement of closure of the water budget (i.e., mass conservation) at various scales was exploited to constrain the flux estimates via an optimization approach that will also be described. Further, error assessments were included with the input datasets, and we examine these in relation to inferred uncertainty in the optimized flux estimates in order to gauge our current ability to close the water budget within an expected uncertainty range.

Rodell, Matthew↗
NASA NTRS2015

An Inversion Analysis of Recent Variability in Natural CO2 Fluxes Using GOSAT and In Situ Observations

About one-half of the global CO2 emissions from fossil fuel combustion and deforestation accumulates in the atmosphere, where it contributes to global warming. The rest is taken up by vegetation and the ocean. The precise contribution of the two sinks, and their location and year-to-year variability are, however, not well understood. We use two different approaches, batch Bayesian synthesis inversion and variational data assimilation, to deduce the global spatiotemporal distributions of CO2 fluxes during 2009-2010. One of our objectives is to assess different sources of uncertainties in inferred fluxes, including uncertainties in prior flux estimates and observations, and differences in inversion techniques. For prior constraints, we utilize fluxes and uncertainties from the CASA-GFED model of the terrestrial biosphere and biomass burning driven by satellite observations and interannually varying meteorology. We also use measurement-based ocean flux estimates and two sets of fixed fossil CO2 emissions. Here, our inversions incorporate column CO2 measurements from the GOSAT satellite (ACOS retrieval, filtered and bias-corrected) and in situ observations (individual flask and afternoon-average continuous observations) to estimate fluxes in 108 regions over 8-day intervals for the batch inversion and at 3 x 3.75 weekly for the variational system. Relationships between fluxes and atmospheric concentrations are derived consistently for the two inversion systems using the PCTM atmospheric transport model driven by meteorology from the MERRA reanalysis. We compare the posterior fluxes and uncertainties derived using different data sets and the two inversion approaches, and evaluate the posterior atmospheric concentrations against independent data including aircraft measurements. The optimized fluxes generally resemble those from other studies. For example, the results indicate that the terrestrial biosphere is a net CO2 sink, and a GOSAT-only inversion suggests a shift in the global sink from the tropics south to the north relative to the prior and to an in-situ-only inversion. We also find a smaller terrestrial sink in higher-latitude northern regions in boreal summer of 2010 relative to 2009.

Carbon dioxide↗
NASA NTRS2015

The Observed State of the Water Cycle in the Early Twenty-First Century

This study quantifies mean annual and monthly fluxes of Earth's water cycle over continents and ocean basins during the first decade of the millennium. To the extent possible, the flux estimates are based on satellite measurements first and data-integrating models second. A careful accounting of uncertainty in the estimates is included. It is applied within a routine that enforces multiple water and energy budget constraints simultaneously in a variational framework in order to produce objectively determined optimized flux estimates. In the majority of cases, the observed annual surface and atmospheric water budgets over the continents and oceans close with much less than 10% residual. Observed residuals and optimized uncertainty estimates are considerably larger for monthly surface and atmospheric water budget closure, often nearing or exceeding 20% in North America, Eurasia, Australia and neighboring islands, and the Arctic and South Atlantic Oceans. The residuals in South America and Africa tend to be smaller, possibly because cold land processes are negligible. Fluxes were poorly observed over the Arctic Ocean, certain seas, Antarctica, and the Australasian and Indonesian islands, leading to reliance on atmospheric analysis estimates. Many of the satellite systems that contributed data have been or will soon be lost or replaced. Models that integrate ground-based and remote observations will be critical for ameliorating gaps and discontinuities in the data records caused by these transitions. Continued development of such models is essential for maximizing the value of the observations. Next-generation observing systems are the best hope for significantly improving global water budget accounting.

Numerical analysis/modeling↗
NASA NTRS1993

Solar flux forecasting using mutual information with an optimal delay

Solar flux F(sub 10.7) directly affects the atmospheric density, thereby changing the lifetime and prediction of satellite orbits. For this reason, accurate forecasting of F(sub 10.7) is crucial for orbit determination of spacecraft. Our attempts to model and forecast F(sub 10.7) uncovered highly entangled dynamics. We concluded that the general lack of predictability in solar activity arises from its nonlinear nature. Nonlinear dynamics allow us to predict F(sub 10.7) more accurately than is possible using stochastic methods for time scales shorter than a characteristic horizon, and with about the same accuracy as using stochastic techniques when the forecasted data exceed this horizon. The forecast horizon is a function of two dynamical invariants: the attractor dimension and the Lyapunov exponent. In recent years, estimation of the attractor dimension reconstructed from a time series has become an important tool in data analysis. In calculating the invariants of the system, the first necessary step is the reconstruction of the attractor for the system from the time-delayed values of the time series. The choice of the time delay is critical for this reconstruction. For an infinite amount of noise-free data, the time delay can, in principle, be chosen almost arbitrarily. However, the quality of the phase portraits produced using the time-delay technique is determined by the value chosen for the delay time. Fraser and Swinney have shown that a good choice for this time delay is the one suggested by Shaw, which uses the first local minimum of the mutual information rather than the autocorrelation function to determine the time delay. This paper presents a refinement of this criterion and applies the refined technique to solar flux data to produce a forecast of the solar activity.

Ashrafi, S.↗
NASA NTRS2019

Is There an Optimal CO2 Partial Column for Flux Inversions?

The fidelity of flux estimates from an atmospheric inversion depends on the ability of atmospheric transport models to simulate the measured quantity. For species such as CO2, with surface fluxes and a large network of surface measurements, this means correctly simulating the dynamics of the planetary boundary layer (PBL), which is one of the most uncertain aspects of atmospheric transport modeling. In contrast, the simulated total column average mole fraction of CO2 (XCO2) is largely insensitive to simulated PBL dynamics. Therefore, measurements of XCO2 provided by current and future short wave infrared (SWIR) greenhouse gas (GHG) satellites such as GOSAT and the OCO family would seem to be more appropriate to flux inversions, as far as minimizing transport model errors (the "noise") is concerned. Unfortunately, the flux-induced variation of CO2 (the "signal") is the largest within the PBL and smallest in XCO2. Therefore, assimilating XCO2 as opposed to PBL CO2 need not give us the strongest "signal to noise" in flux inversions. Recent work on GOSAT and OCO2 retrievals suggest that SWIR satellite spectra may be used to estimate a lower partial column CO2, which could be assimilated in a flux inversion, instead of XCO2.Here we report on a study to assess whether there is an optimal partial column average CO2, intermediate between PBL CO2 and XCO2, whose assimilation might yield the best signal to noise in flux inversions, where (as before) "signal" is the flux-induced variation and "noise" is the error in transport modeling. We simulate atmospheric CO2 with five different global transport models and a common surface CO2 flux over ten years. We consider the spread across the five models to be a proxy for transport model error (the "noise"), and the common variation of CO2 in all five models to be a proxy for the "signal". We compare these signals and noises at different spatiotemporal scales for different partial column specifications to investigate whether there exists an optimal partial column that has large surface flux-driven variations and yet is relatively insensitive to errors in transport models. Finally, we comment on the feasibility of estimating such a partial column from current and future SWIR GHG satellites in the light of recent work on vertically resolved CO2 from current SWIR GHG satellites.

Basu, Sourish↗
NASA NTRS2015

Mission Adaptive UAS Platform for Earth Science Resource Assessment

NASA Ames Research Center has led a number of important Earth science remote sensing missions including several directed at the assessment of natural resources. A key asset for accessing high risk airspace has been the 180 kg class SIERRA UAS platform, providing mission durations of up to 8 hrs at altitudes up to 3 km. Recent improvements to this mission capability are embodied in the incipient SIERRA-B variant. Two resource mapping problems having unusual mission characteristics requiring a mission adaptive capability are explored here. One example involves the requirement for careful control over solar angle geometry for passive reflectance measurements. This challenges the management of resources in the coastal ocean where solar angle combines with sea state to produce surface glint that can obscure the ocean color signal. Furthermore, as for all scanning imager applications, the primary flight control priority to fly the UAS directly to the next waypoint should compromise with the requirement to minimize roll and crab effects in the imagery. A second example involves the mapping of natural resources in the Earth's crust using precision magnetometry. In this case the vehicle flight path must be oriented to optimize magnetic flux gradients over a spatial domain having continually emerging features, while optimizing the efficiency of the spatial mapping task. These requirements were highlighted in several recent Earth Science missions including the October 2013 OCEANIA mission directed at improving the capability for hyperspectral reflectance measurements in the coastal ocean, and the Surprise Valley Mission directed at mapping sub-surface mineral composition and faults, using high-sensitivity magentometry. This paper reports the development of specific aircraft control approaches to incorporate the unusual and demanding requirements to manage solar angle, aircraft attitude and flight path orientation, and efficient (directly geo-rectified) surface and sub-surface mapping, including the near-time optimization of these sometimes conflicting requirements. *

Flight Control↗
NASA NTRS2002

Defining Top-of-Atmosphere Flux Reference Level for Earth Radiation Budget Studies

To estimate the earth's radiation budget at the top of the atmosphere (TOA) from satellite-measured radiances, it is necessary to account for the finite geometry of the earth and recognize that the earth is a solid body surrounded by a translucent atmosphere of finite thickness that attenuates solar radiation differently at different heights. As a result, in order to account for all of the reflected solar and emitted thermal radiation from the planet by direct integration of satellite-measured radiances, the measurement viewing geometry must be defined at a reference level well above the earth s surface (e.g., 100 km). This ensures that all radiation contributions, including radiation escaping the planet along slant paths above the earth s tangent point, are accounted for. By using a field-of- view (FOV) reference level that is too low (such as the surface reference level), TOA fluxes for most scene types are systematically underestimated by 1-2 W/sq m. In addition, since TOA flux represents a flow of radiant energy per unit area, and varies with distance from the earth according to the inverse-square law, a reference level is also needed to define satellite-based TOA fluxes. From theoretical radiative transfer calculations using a model that accounts for spherical geometry, the optimal reference level for defining TOA fluxes in radiation budget studies for the earth is estimated to be approximately 20 km. At this reference level, there is no need to explicitly account for horizontal transmission of solar radiation through the atmosphere in the earth radiation budget calculation. In this context, therefore, the 20-km reference level corresponds to the effective radiative top of atmosphere for the planet. Although the optimal flux reference level depends slightly on scene type due to differences in effective transmission of solar radiation with cloud height, the difference in flux caused by neglecting the scene-type dependence is less than 0.1%. If an inappropriate TOA flux reference level is used to define satellite TOA fluxes, and horizontal transmission of solar radiation through the planet is not accounted for in the radiation budget equation, systematic errors in net flux of up to 8 W/sq m can result. Since climate models generally use a plane-parallel model approximation to estimate TOA fluxes and the earth radiation budget, they implicitly assume zero horizontal transmission of solar radiation in the radiation budget equation, and do not need to specify a flux reference level. By defining satellite-based TOA flux estimates at a 20-km flux reference level, comparisons with plane-parallel climate model calculations are simplified since there is no need to explicitly correct plane-parallel climate model fluxes for horizontal transmission of solar radiation through a finite earth.

Loeb, N. G.↗
NASA NTRS1994

Optimal experimental designs for the estimation of thermal properties of composite materials

Reliable estimation of thermal properties is extremely important in the utilization of new advanced materials, such as composite materials. The accuracy of these estimates can be increased if the experiments are designed carefully. The objectives of this study are to design optimal experiments to be used in the prediction of these thermal properties and to then utilize these designs in the development of an estimation procedure to determine the effective thermal properties (thermal conductivity and volumetric heat capacity). The experiments were optimized by choosing experimental parameters that maximize the temperature derivatives with respect to all of the unknown thermal properties. This procedure has the effect of minimizing the confidence intervals of the resulting thermal property estimates. Both one-dimensional and two-dimensional experimental designs were optimized. A heat flux boundary condition is required in both analyses for the simultaneous estimation of the thermal properties. For the one-dimensional experiment, the parameters optimized were the heating time of the applied heat flux, the temperature sensor location, and the experimental time. In addition to these parameters, the optimal location of the heat flux was also determined for the two-dimensional experiments. Utilizing the optimal one-dimensional experiment, the effective thermal conductivity perpendicular to the fibers and the effective volumetric heat capacity were then estimated for an IM7-Bismaleimide composite material. The estimation procedure used is based on the minimization of a least squares function which incorporates both calculated and measured temperatures and allows for the parameters to be estimated simultaneously.

Scott, Elaine P.↗
NASA NTRS1996

Design Optimization for a Maglev System Employing Flux Eliminating Coils

Flux eliminating coils have received no little attention over the past thirty years as an alternative for realizing lift in a MAGLEV system. When the magnets on board the vehicle are displaced from the equilibrium or null flux point of these coils, they induce current in those coils which act to restore the coil to its null flux or centerline position. The question being addressed in this paper is that of how to choose the best coil for a given system. What appears at first glance to be an innocent question is in fact one that is actually quite involved, encompassing both the global economics and physics of the system. The real key in analyzing that question is to derive an optimization index or functional which represents the cost of the system subject to constraints, the primary constraint being that the vehicle lift itself at a certain threshold speed. Outlined in this paper is one scenario for realizing a total system design which uses sequential quadratic programming techniques.

Davey, Kent R.↗
NASA NTRS2017

High Count-Rate Study of Two TES X-Ray Microcalorimeters With Different Transition Temperatures

We have developed transition-edge sensor (TES) microcalorimeter arrays with high count-rate capability and high energy resolution to carry out x-ray imaging spectroscopy observations of various astronomical sources and the Sun. We have studied the dependence of the energy resolution and throughput (fraction of processed pulses) on the count rate for such microcalorimeters with two different transition temperatures T(sub c). Devices with both transition temperatures were fabricated within a single microcalorimeter array directly on top of a solid substrate where the thermal conductance of the microcalorimeter is dependent upon the thermal boundary resistance between the TES sensor and the dielectric substrate beneath. Because the thermal boundary resistance is highly temperature dependent, the two types of device with different T(sub c)(sup s) had very different thermal decay times, approximately one order of magnitude different. In our earlier report, we achieved energy resolutions of 1.6 and 2.eV at 6 keV from lower and higher T(sub c) devices, respectively, using a standard analysis method based on optimal filtering in the low flux limit. We have now measured the same devices at elevated x-ray fluxes ranging from 50 Hz to 1000 Hz per pixel. In the high flux limit, however, the standard optimal filtering scheme nearly breaks down because of x-ray pile-up. To achieve the highest possible energy resolution for a fixed throughput, we have developed an analysis scheme based on the socalled event grade method. Using the new analysis scheme, we achieved 5.0 eV FWHM with 96 Percent throughput for 6 keV x-rays of 1025 Hz per pixel with the higher T(sub c) (faster) device, and 5.8 eV FWHM with 97 Percent throughput with the lower T(sub c) (slower) device at 722 Hz.

Lee, Sang-Jun↗
NASA NTRS1992

Adjustment of footprint correction for airborne flux mapping over the FIFE site

A meaningful interpretation of airborne flux estimates over nonuniform terrain must consider local advection from nonhomogeneous source distributions (footprint correction). An empirical procedure for footprint correction of airborne flux data obtained in the First ISLSCP Field Experiment (FIFE) 1989 is presented, based on simple analytical solutions of the diffusion equation which have been adjusted to approximate more realistic solutions. Optimized estimates of surface flux 'maps' derived from airborne observations are then constructed for maximum correlation between flux estimates and independently observed surface characteristics. This paper also includes an analysis of resolution for the given procedure, in terms of amplitude recovery of hypothetical square-wave distributions of surface flux density, and discusses its implications for the interpretation of the optimized estimates of FIFE surface flux maps. Results show that corrected spatial sink distributions are obtained by the current empirical procedure at the cost of considerable reduction in amplitude recovery of small-scale variations in surface flux density. The high spatial correlation observed between corrected flux maps and surface characteristics such as greenness or surface temperature excess is ascribed to the approximately correct positioning of the main flux gradients across the site, which can be expected to have been reproduced with amplitude recovery equal to or greater than 60 percent.

Schuepp, P. H.↗
NASA NTRS2000

A Compact X-Ray System for Macromolecular Crystallography

We describe the design and performance of a high flux x-ray system for macromolecular crystallography that combines a microfocus x-ray generator (40 gm FWHM spot size at a power level of 46.5Watts) and a 5.5 mm focal distance polycapillary optic. The Cu K(sub alpha) X-ray flux produced by this optimized system is 7.0 times above the X-ray flux previously reported. The X-ray flux from the microfocus system is also 3.2 times higher than that produced by the rotating anode generator equipped with a long focal distance graded multilayer monochromator (Green optic; CMF24-48-Cu6) and 30% less than that produced by the rotating anode generator with the newest design of graded multilayer monochromator (Blue optic; CMF12-38-Cu6). Both rotating anode generators operate at a power level of 5000 Watts, dissipating more than 100 times the power of our microfocus x-ray system. Diffraction data collected from small test crystals are of high quality. For example, 42,540 reflections collected at ambient temperature from a lysozyme crystal yielded R(sub sym) 5.0% for the data extending to 1.7A, and 4.8% for the complete set of data to 1.85A. The amplitudes of the reflections were used to calculate difference electron density maps that revealed positions of structurally important ions and water molecules in the crystal of lysozyme using the phases calculated from the protein model.

Gubarev, Mikhail↗
NASA NTRS2016

Constraining the Sulfur Dioxide Degassing Flux from Turrialba Volcano, Costa Rica Using Unmanned Aerial System Measurements

Observed sulfur dioxide (SO2)mixing ratios onboard unmanned aerial systems (UAS) duringMarch 11-13, 2013 are used to constrain the three-day averaged SO2 degassing flux fromTurrialba volcanowithin a Bayesian inverse modeling framework. A mesoscale model coupled with Lagrangian stochastic particle backward trajectories is used to quantify the source-receptor relationships at very high spatial resolutions (i.e., b1 km). The model shows better performance in reproducing the near-surface meteorological properties and observed SO2 variations when using a first-order closure non-local planetary boundary layer (PBL) scheme. The optimized SO2 degassing fluxes vary from 0.59 +/- 0.37 to 0.83 +/- 0.33 kt d−1 depending on the PBL scheme used. These fluxes are in good agreement with ground-based gas flux measurements, and correspond to corrective scale factors of 8-12 to the posteruptive SO2 degassing rate in the AeroCom emission inventory. The maximum a posteriori solution for the SO2 flux is highly sensitive to the specification of prior and observational errors, and relatively insensitive to the SO2 loss term and temporal averaging of observations. Our results indicate relatively low degassing activity but sustained sulfur emissions from Turrialba volcano to the troposphere during March 2013. This study demonstrates the utility of low-cost small UAS platforms for volcanic gas composition and flux analysis.

Xi, Xin↗
NASA NTRS1998

Design of the Experimental Exposure Conditions to Simulate Ionizing Radiation Effects on Candidate Replacement Materials for the Hubble Space Telescope

In this effort, experimental exposure times for monoenergetic electrons and protons were determined to simulate the space radiation environment effects on Teflon components of the Hubble Space Telescope. Although the energy range of the available laboratory particle accelerators was limited, optimal exposure times for 50 keV, 220 keV, 350 keV, and 500 KeV electrons were calculated that produced a dose-versus-depth profile that approximated the full spectrum profile, and were realizable with existing equipment. For the case of proton exposure, the limited energy range of the laboratory accelerator restricted simulation of the dose to a depth of .5 mil. Also, while optimal exposure times were found for 200 keV, 500 keV and 700 keV protons that simulated the full spectrum dose-versus-depth profile to this depth, they were of such short duration that the existing laboratory could not be controlled to within the required accuracy. In addition to the obvious experimental issues, other areas exist in which the analytical work could be advanced. Improved computer codes for the dose prediction- along with improved methodology for data input and output- would accelerate and make more accurate the calculational aspects. This is particularly true in the case of proton fluxes where a paucity of available predictive software appears to exist. The dated nature of many of the existing Monte Carlo particle/radiation transport codes raises the issue as to whether existing codes are sufficient for this type of analysis. Other areas that would result in greater fidelity of laboratory exposure effects to the space environment is the use of a larger number of monoenergetic particle fluxes and improved optimization algorithms to determine the weighting values.

Smith, L. Montgomery↗
NASA NTRSDate not supplied

Mechanisms of Interfacial Mixing in the Blown Powder Deposition of Inconel 625 to Copper Alloy for Liquid Rocket Engine Applications

There is an increasing need for functional materials to support high heat flux applications and optimize weight by using bimetallic additive manufacturing (AM). While one promising fabrication technology is the use of blown powder directed energy deposition (DED) AM, challenges remain with bi-metallic combinations. Prominent among these challenges is the need to understand mixing of materials at the bimetallic interface for forming stronger, more durable and reliable joints to extend the versatility of AM into critical applications. One application is the manufacturing of combustion chambers with copper-alloy liners and Superalloy structural jackets. In this application, material combinations are selected for effective heat dissipation, using copper, and retention of strength at high temperatures using Inconel 625. Currently, the dominant problem with this configuration is the highly variable strength of the interface and its correlation with deposition parameters. In this study, samples were fabricated at several vendors with Inconel 625 deposited onto wrought C-18150 (Cu-Cr-Zr) to form a bimetallic interface. Characterization of the interfaces were achieved through optical and electron microscopy, mechanical testing of mini tensile specimens, and electron dispersion spectroscopy to understand diffusion and bulk mixing behaviors at the joint. A theoretical framework was constructed in the context of solidification and mixing mechanisms to explain the resulting differences in the interface. This qualitative approach utilized a fluid dynamics perspective to sum the order of magnitudes of the various acting forces on the weld pool during deposition to predict convection trends based off known parameters. The predicted trends for each vendor are compared to obtain a better understanding of how mixing in the molten pool varied based on deposition parameters.

Additive Manufacturing↗
NASA NTRS2000

A Compact X-Ray System for Macromolecular Crystallography

We describe the design and performance of a high flux x-ray system for a macromolecular crystallography that combines a microfocus x-ray generator (40 micrometer full width at half maximum spot size at a power level of 46.5 W) and a collimating polycapillary optic. The Cu Ka lpha x-ray flux produced by this optimized system through a 500,um diam orifice is 7.0 times greater than the x-ray flux previously reported by Gubarev et al. [M. Gubarev et al., J. Appl. Crystallogr. 33, 882 (2000)]. The x-ray flux from the microfocus system is also 2.6 times higher than that produced by a rotating anode generator equipped with a graded multilayer monochromator (green optic, Osmic Inc. CMF24-48-Cu6) and 40% less than that produced by a rotating anode generator with the newest design of graded multilayer monochromator (blue optic, Osmic, Inc. CMF12-38-Cu6). Both rotating anode generators operate at a power level of 5000 W, dissipating more than 100 times the power of our microfocus x-ray system. Diffraction data collected from small test crystals are of high quality. For example, 42 540 reflections collected at ambient temperature from a lysozyme crystal yielded R(sub sym)=5.0% for data extending to 1.70 A, and 4.8% for the complete set of data to 1.85 A. The amplitudes of the observed reflections were used to calculate difference electron density maps that revealed positions of structurally important ions and water molecules in the crystal of lysozyme using the phases calculated from the protein model.

Gubarev, Mikhail↗