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NASA NTRS2011

TPSAS-NF1676L-13037-DND

Mineral dust has a significant and uncertain role in the direct aerosol radiative forcing of climate. Spaceborne lidars such as CALIOP help reduce these uncertainties through vertical profile measurements of aerosol optical properties. One current limitation to the accurate retrieval of aerosol extinction and optical depth from CALIOP is the assumed relationship between the aerosol extinction to aerosol backscatter (i.e. the extinction-to-backscatter ratio, also referred to here as the lidar ratio or Sa). This problem is especially acute at 1064 nm, where few estimates of the lidar ratio exist. This study uses a dataset of eight underflights of CALIOP during August 2010 by the NASA Langley Research Center airborne High Spectral Resolution Lidar (HSRL) to study Saharan dust transported across the Atlantic Ocean. The standard HSRL profile products include aerosol backscatter coefficients and depolarization ratios at both 532 nm and 1064 nm, and aerosol extinction coefficients (and therefore also lidar ratios) at 532 nm only. In this work, we further derive estimates of aerosol lidar ratios and extinction coefficients at 1064 nm via application of a two-wavelength technique that uses the 532 nm aerosol backscatter coefficients and the 1064 nm attenuated total backscatter profile. Summary statistics of the dust lidar ratio and depolarization at 532 nm and 1064 nm from these eight flights are presented. Implications for the CALIOP dust and polluted dust aerosol types and lidar ratio selection are discussed. In addition to the two-wavelength retrievals of lidar ratio at 1064 nm, a demonstration case of a 1064 nm lidar ratio retrieval over the ocean from CALIOP using the CloudSat measurement of surface scattering cross section as a constraint is presented (Josset et al, 2010).

Raymond R Rogers↗

DOE OSTI2017

Transition from nonsequential to sequential double ionization in many-electron systems

Understanding strong-field double ionization of many-electron systems is an important fundamental problem with potential implications for molecular imaging within this regime. Using mid-IR radiation, we unambiguously identify the transition from nonsequential (e, 2e) to sequential double ionization in Xe at an intensity below 10 14 W/cm 2 . Ionization from excited orbitals is found to be decisive at low intensities, but we demonstrate that such mechanisms are unimportant in the sequential regime. We utilize these facts to successfully image a molecular dication using laser-induced electron diffraction. This methodology can be used to study molecular dynamics on unprecedented few-femtosecond time scales.

74 ATOMIC AND MOLECULAR PHYSICS↗

NASA NTRS1994

Measurements of striae in CR+ doped YAG laser crystals

Striations in Czochralski (CZ) grown crystals have been observed in materials such as GaAs, silicon, photorefractive crystals used for data storage, potassium titanyl phosphate crystals and LiNbO3. Several techniques have been used for investigating these defects including electron microscopy, laser scanning tomography, selective photoetching, X-ray diffuse scattering, interference orthoscopy, laser interferometry and micro-Fourier transform infrared spectroscopy mapping. A 2mm thick sample of the material to be investigated is illuminated with light that is absorbed and non-absorbed by the ion concentration to be observed. The back surface of the sample is focused onto a solid-state image detector and images of the input beam and absorbed (and diffracted) beams are captured at two wavelengths. The variation of the coefficient of absorption asa function of distance on the sample can be derived from these measurements. A Big Sky Software Beamcode system is used to capture and display images. Software has been written to convert the Beamcode data files to a format that can be imported into a spreadsheet program such as Quatro Pro. The spreadsheet is then used to manipulate and display data. A model of the intensity map of the striae collected by the imaging system has been proposed and a data analysis procedure derived. From this, the variability of the attenuation coefficient alpha can be generated. Preliminary results show that alpha may vary by a factor of four or five over distances of 100 mu m. Potential errors and problems have been discovered and additional experiments and improvements to the experimental setup are in progress and we must now show that the measurement techniques and data analysis procedures provide 'real' information. Striae are clearly visible at all wavelengths including white light. Their basic spatial frequency does not change radically, at least when changing from blue to green to white light. Further experimental and theoretical work can be done to improve the data collection techniques and to verify the data analysis procedures.

Cady, Fredrick M.↗

NASA NTRS2012

Hemispherical Field-of-View Above-Water Surface Imager for Submarines

A document discusses solutions to the problem of submarines having to rise above water to detect airplanes in the general vicinity. Two solutions are provided, in which a sensor is located just under the water surface, and at a few to tens of meter depth under the water surface. The first option is a Fish Eye Lens (FEL) digital-camera combination, situated just under the water surface that will have near-full- hemisphere (360 azimuth and 90 elevation) field of view for detecting objects on the water surface. This sensor can provide a three-dimensional picture of the airspace both in the marine and in the land environment. The FEL is coupled to a camera and can continuously look at the entire sky above it. The camera can have an Active Pixel Sensor (APS) focal plane array that allows logic circuitry to be built directly in the sensor. The logic circuitry allows data processing to occur on the sensor head without the need for any other external electronics. In the second option, a single-photon sensitive (photon counting) detector-array is used at depth, without the need for any optics in front of it, since at this location, optical signals are scattered and arrive at a wide (tens of degrees) range of angles. Beam scattering through clouds and seawater effectively negates optical imaging at depths below a few meters under cloudy or turbulent conditions. Under those conditions, maximum collection efficiency can be achieved by using a non-imaging photon-counting detector behind narrowband filters. In either case, signals from these sensors may be fused and correlated or decorrelated with other sensor data to get an accurate picture of the object(s) above the submarine. These devices can complement traditional submarine periscopes that have a limited field of view in the elevation direction. Also, these techniques circumvent the need for exposing the entire submarine or its periscopes to the outside environment.

Hemmati, Hamid↗

DOE OSTI2021

SANS quantification of bound water in water-soluble polymers across multiple concentration regimes

Contrast-variation small-angle neutron scattering (CV-SANS) is a widely used technique for quantifying hydration water in soft matter systems, but it is predominantly applied in the dilute regime or for systems with a well-defined structure factor. Here, CV-SANS was used to quantify the number of hydration water molecules associating with three water-soluble polymers with different critical solution temperatures and types of water–solute interactions in dilute, semidilute, and concentrated solution through the exploration of novel methods of data fitting and analysis. Multiple SANS fitting workflows with varying levels of model assumptions were evaluated and compared to give insight into SANS model selection. These fitting pathways ranged from general, model-free algorithms to more standard form and structure factor fitting. In addition, Monte Carlo bootstrapping was evaluated as a method to estimate parameter uncertainty through simulation of technical replicates. The most robust fitting workflow for dilute solutions was found to be form factor fitting without CV-SANS ( i.e. polymer in 100% D 2 O). For semidilute and concentrated solutions, while the model-free approach can be mathematically defined for CV-SANS data, the addition of a structure factor imposes physical constraints on the optimization problem, suggesting that the optimal fitting pathway should include appropriate form and structure factor models. The measured hydration numbers were consistent with the number of tightly bound water molecules associated with each monomer unit, and the concentration dependence of the hydration number was largely governed by the chemistry-specific interactions between water and polymer. Polymers with weaker water–polymer interactions ( i.e. those with fewer hydration water molecules) were found to have more bound water at higher concentrations than those with stronger water–polymer interactions due to the increase in the number of forced water–polymer contacts in the concentrated system. This SANS-based method to count hydration water molecules can be applied to polymers in any concentration regime, which will lead to improved understanding of water–polymer interactions and their impact on materials design.

36 MATERIALS SCIENCE↗

NASA NTRS2002

Effect of Crystal Orientation on Fatigue Failure of Single Crystal Nickel Base Turbine Blade Superalloys

High cycle fatigue (HCF) induced failures in aircraft gas turbine and rocket engine turbopump blades is a pervasive problem. Single crystal nickel turbine blades are being utilized in rocket engine turbopumps and jet engines throughout industry because of their superior creep, stress rupture, melt resistance, and thermomechanical fatigue capabilities over polycrystalline alloys. Currently the most widely used single crystal turbine blade superalloys are PWA 1480/1493, PWA 1484, RENE' N-5 and CMSX-4. These alloys play an important role in commercial, military and space propulsion systems. Single crystal materials have highly orthotropic properties making the position of the crystal lattice relative to the part geometry a significant factor in the overall analysis. The failure modes of single crystal turbine blades are complicated to predict due to the material orthotropy and variations in crystal orientations. Fatigue life estimation of single crystal turbine blades represents an important aspect of durability assessment. It is therefore of practical interest to develop effective fatigue failure criteria for single crystal nickel alloys and to investigate the effects of variation of primary and secondary crystal orientation on fatigue life. A fatigue failure criterion based on the maximum shear stress amplitude /Delta(sub tau)(sub max))] on the 24 octahedral and 6 cube slip systems, is presented for single crystal nickel superalloys (FCC crystal). This criterion reduces the scatter in uniaxial LCF test data considerably for PWA 1493 at 1200 F in air. Additionally, single crystal turbine blades used in the alternate advanced high-pressure fuel turbopump (AHPFTP/AT) are modeled using a large-scale three-dimensional finite element model. This finite element model is capable of accounting for material orthotrophy and variation in primary and secondary crystal orientation. Effects of variation in crystal orientation on blade stress response are studied based on 297 finite element model runs. Fatigue lives at critical points in the blade are computed using finite element stress results and the failure criterion developed. Stress analysis results in the blade attachment region are also presented. Results presented demonstrates that control of secondary and primary crystallographic orientation has the potential to significantly increase a component S resistance to fatigue crack growth with- out adding additional weight or cost. [DOI: 10.1115/1.1413767]

Arakere, N. K.↗

DOE OSTI2021

Experimental characterization of hot-electron emission and shock dynamics in the context of the shock ignition approach to inertial confinement fusion

We report on planar target experiments conducted on the OMEGA-EP laser facility performed in the context of the shock ignition (SI) approach to inertial confinement fusion. The experiment aimed at characterizing the propagation of strong shock in matter and the generation of hot electrons (HEs), with laser parameters relevant to SI (1-ns UV laser beams with I ~10 16 W/cm 2 ). Time-resolved radiographs of the propagating shock front were performed in order to study the hydrodynamic evolution. The hot-electron source was characterized in terms of Maxwellian temperature, T h , and laser to hot-electron energy conversion efficiency η using data from different x-ray spectrometers. The post-processing of these data gives a range of the possible values for T h and η [i.e., T h [keV] ϵ (20, 50) and η ϵ (2%, 13%)]. These values are used as input in hydrodynamic simulations to reproduce the results obtained in radiographs, thus constraining the range for the HE measurements. According to this procedure, we found that the laser converts ~10% ± 4% of energy into hot electrons with T h = 27 ± 8 keV. The paper shows how the coupling of different diagnostics and numerical tools is required to sufficiently constrain the problem, solving the large ambiguity coming from the post-processing of spectrometers data. The effect of the hot electrons on the shock dynamics is then discussed, showing an increase in the pressure around the shock front. Furthermore, the low temperature found in this experiment without pre-compression laser pulses could be advantageous for the SI scheme, but the high conversion efficiency may lead to an increase in the shell adiabat, with detrimental effects on the implosion.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2016

Identifying barriers to charge-carriers in the bulk and surface regions of Cu 2 ZnSnS 4 nanocrystal films by x-ray absorption fine structures (XAFSs)

Solar cell performance is most affected by the quality of the light absorber layer. For thin-film devices, this becomes a two-fold problem of maintaining a low-cost design with well-ordered nanocrystal (NC) structure. The use of Cu 2 ZnSnS 4 (CZTS) NCs as the light absorber films forms an ideal low-cost design, but the quaternary structure makes it difficult to maintain a well-ordered layer without the use of high-temperature treatments. There is little understanding of how CZTS NC structures affect the photoconversion efficiency, the charge-carriers, and therefore the performance of the device manufactured from it. To examine these relationships, the measured photoresponse from the photo-generation of charge-carrier electron-hole pairs was compared against the crystal structure, as short-range and long-range crystal orders for the films. The photoresponse simplifies the electronic properties into three basic steps that can be associated with changes in energy levels within the band structure. These changes result in the formation of barriers to charge-carrier flow. In this work, the extent of these barriers was determined using synchrotron-based X-ray absorbance fine structure to probe the individual metal centers in the film, and comparing these to molecular simulations of the ideal extended xray absorbance fine structure scattering. This allowed for the quantification of bond lengths, and thus an interpretation of the distortions in the crystal lattice. The various characteristics of the photoresponse were then correlated to the crystallographic order and used to gain physical insight into barriers to charge-carriers in the bulk and surface regions of CZTS films.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Unitary Bethe-Salpeter Methods in Two- and Three-Body Systems

The study of resonances, unstable particles formed in particle scattering, is motivated by the questions about the strong interaction and the composition of hadrons. In order to advance this study in the intermediate energy region, a variety of techniques are used. In this thesis, we present work done on two different analyses that use the principle of unitarity and the Bethe-Salpeter equation to study the resonances Lambda(1405), Sigma(1385), and a1(1260). Firstly, we perform a simultaneous analysis of Sand P-waves of the Strangeness = -1 two-body meson-baryon scattering amplitude using all low-energy data. For the first time, differential cross section data are included for chiral unitary coupled-channel models. From this model, S- and P-wave amplitudes are extracted and we observe both well-known I(JP)=0(1/2^-) S-wave states as well as a new I(JP)=1(1/2^+) state absent in quark models and lattice QCD results. Multiple statistical and phenomenological tests suggest that, while the data clearly require an I =1 P-wave resonance, the new state just accounts for the absence of the decuplet Sigma(1385)3/2+ in the model which is subsequently included in the parameterization. Secondly, we formulate the final state interaction of the a1(1260) resonance decay in a manifestly three-body-unitary parameterization and fit it to the a1(1260) lineshape measured by the ALEPH experiment. Dalitz plots calculated from this fit are presented. The work demonstrates the feasibility to numerically solve a previously derived amplitude and its generalization to isobars with spin and coupled channels. The model is a good test case because it can also be applied to other meson decays including exotic states and modified for the finite-volume problem as it arises in lattice QCD due to its manifest unitarity. The understanding of the resonances being analyzed in both the two-body work and the three-body work gives a better understanding of intermediate energy QCD.

Sadasivan, Daniel↗

NASA NTRS2008

The Time Series Technique for Aerosol Retrievals over Land from MODIS: Algorithm MAIAC

Atmospheric aerosols interact with sun light by scattering and absorbing radiation. By changing irradiance of the Earth surface, modifying cloud fractional cover and microphysical properties and a number of other mechanisms, they affect the energy balance, hydrological cycle, and planetary climate [IPCC, 2007]. In many world regions there is a growing impact of aerosols on air quality and human health. The Earth Observing System [NASA, 1999] initiated high quality global Earth observations and operational aerosol retrievals over land. With the wide swath (2300 km) of MODIS instrument, the MODIS Dark Target algorithm [Kaufman et al., 1997; Remer et al., 2005; Levy et al., 2007] currently complemented with the Deep Blue method [Hsu et al., 2004] provides daily global view of planetary atmospheric aerosol. The MISR algorithm [Martonchik et al., 1998; Diner et al., 2005] makes high quality aerosol retrievals in 300 km swaths covering the globe in 8 days. With MODIS aerosol program being very successful, there are still several unresolved issues in the retrieval algorithms. The current processing is pixel-based and relies on a single-orbit data. Such an approach produces a single measurement for every pixel characterized by two main unknowns, aerosol optical thickness (AOT) and surface reflectance (SR). This lack of information constitutes a fundamental problem of the remote sensing which cannot be resolved without a priori information. For example, MODIS Dark Target algorithm makes spectral assumptions about surface reflectance, whereas the Deep Blue method uses ancillary global database of surface reflectance composed from minimal monthly measurements with Rayleigh correction. Both algorithms use Lambertian surface model. The surface-related assumptions in the aerosol retrievals may affect subsequent atmospheric correction in unintended way. For example, the Dark Target algorithm uses an empirical relationship to predict SR in the Blue (B3) and Red (B1) bands from the 2.1 m channel (B7) for the purpose of aerosol retrieval. Obviously, the subsequent atmospheric correction will produce the same SR in the red and blue bands as predicted, i.e. an empirical function of 2.1. In other words, the spectral, spatial and temporal variability of surface reflectance in the Blue and Red bands appears borrowed from band B7. This may have certain implications for the vegetation and global carbon analysis because the chlorophyll-sensing bands B1, B3 are effectively substituted in terms of variability by band B7, which is sensitive to the plant liquid water. This chapter describes a new recently developed generic aerosol-surface retrieval algorithm for MODIS. The Multi-Angle Implementation of Atmospheric Correction (MAIAC) algorithm simultaneously retrieves AOT and surface bi-directional reflection factor (BRF) using the time series of MODIS measurements.

Lyapustin, Alexei↗

DOE OSTI2024

Explainable AI classification for parton density theory

Quantitatively connecting properties of parton distribution functions (PDFs, or parton densities) to the theoretical assumptions made within the QCD analyses which produce them has been a longstanding problem in HEP phenomenology. To confront this challenge, we introduce an ML-based explainability framework, XAI4PDF, to classify PDFs by parton flavor or underlying theoretical model using ResNet-like neural networks (NNs). By leveraging the differentiable nature of ResNet models, this approach deploys guided backpropagation to dissect relevant features of fitted PDFs, identifying x-dependent signatures of PDFs important to the ML model classifications. By applying our framework, we are able to sort PDFs according to the analysis which produced them while constructing quantitative, human-readable maps locating the x regions most affected by the internal theory assumptions going into each analysis. This technique expands the toolkit available to PDF analysis and adjacent particle phenomenology while pointing to promising generalizations.

Artificial Intelligence↗

NASA NTRS1972

Apollo 15 contamination photography

The problem of optical contamination in the form of particulates in the vicinity of a spacecraft has been a source of concern for any astronomical experiment that must be performed in sunlight. This concern prompted a photographic photometric experiment on Apollo 15 to measure the brightness of the residual contamination cloud as well as the cloud produced by dumping waste water overboard. An upper limit of 10 to the minus 12.3 power B (B designates the brightness of the solar disc) was placed on the residual cloud at a 90 deg sun angle, which is comparable to the zodiacal light. The brightness of the cloud produced by the waste dump was estimated to be 10 to the minus 9.2 power B. It was observed to decrease rapidly to 10 to the -11.6 power B in minutes, then fluctuate in brightness for at least 25 minutes as additional material left the spacecraft. The cloud was observed to consist of individually resolved particle tracks estimated to be particles ranging from millimeters to centimeters in diameter in addition to a background of unresolved particles with an average diameter of 10.5 microns. Most of the tracks proceeded in straight-line paths from the dump nozzle. Several tracks violated this direction, apparently having been scattered by collisions. A few tracks appeared to have definite curvatures, which are believed to be caused by charged particle interactions.

Naumann, R. J.↗

NASA NTRS2018

Solar Surfing: Final Report on a Phase I NASA Innovative Advanced Concepts Study

The Sun sustains life on Earth and NASA has made its study one of the four pillars of the Science Mission Directorate. A specific area of study, the coronal heating problem, has been of significant concern for nearly 80years; namely how does the 5800 K surface of the Sun heat the nearby corona to over 1,000,000 K. Differing theories have been proposed to explain this process, but verification by actual measurement would not only resolve this issue, it would provide close-up measurements of the Sun never before obtained. However, this requires the development of a solar shield that can protect a satellite located less than 10,000 km from the Sun's surface. Steps towards that capability are the goal of this NIAC project. The current state-of-the-art in solar shielding is best shown by the upcoming Parker Solar Probe Mission, so the approach taken by that satellite is discussed and used as a starting point; allowing a distance of 9.5 solar radii from the Sun's center to be reached. It is then shown that state-of-the-art solar reflectors do not improve this performance. Next, we review the use of pressed powder as a better solar reflector and show that there is some improvement, but not sufficient to reach the Sun's surface. We spend some time on this architecture because the Parker Solar Probe has a thin scattering layer on its solar shield and it is important to discuss the advantages and disadvantages of this feature.

solar surfing↗

NASA NTRS2012

Models Support Energy-Saving Microwave Technologies

During the Apollo Program, astronauts on the Moon encountered a small menace that created big problems: lunar dust. Similar to how tiny bits of Styrofoam behave on Earth adhering to anything they touch lunar dust sticks to spacesuits, spacecraft, tools, and equipment, and is extremely difficult to remove. The clingy nature of the substance is partly due to its electrostatic charge but is also due to its physical characteristics: The sharp, irregularly shaped grains have edges like burrs and feel like abrasive talcum powder to the touch. Not only a nuisance, Moon dust is also a potential health and safety risk. Because it is often laden with ultraviolet radiation and high iron content, it can be detrimental if it gets into the eyes or lungs. In fact, some of the particles are so small that the human body does not even detect them in order to expel them. On the Apollo missions, equipment covered with the dark-colored Moon dust suffered from the absorption of sunlight and tended to overheat. NASA has investigated tools and techniques to manage the sticky stuff, including magnets, vacuums, and shields. In 2009, Kennedy Space Center collaborated with a small business to investigate a method to harden the Moon's surface in a sense, to pave the surface so astronauts and robots could land, drive, and work without disrupting and scattering the material.

Source record↗

DOE OSTI2016

Optical signal quality improvement due to nonlinear interaction between spectral channels

This paper examines stimulated Brillouin scattering (SBS) suppression in multichannel DWDM systems owing to nonlinear cross interaction between the channels and its effect on optical signal quality (1/OSNR{sub R}) in a communication link. We present an experimental study of single-, three- and five-channel systems with 10 Gbit s{sup −1} NRZ channels. The optical signal quality in the three- and five-channel systems is shown to be better than that in the single-channel system. The reason for this is that cross-phase modulation broadens the spectrum of the signal and raises the SBS threshold. This in turn ensures a more pronounced optical signal quality improvement due to self-phase modulation. (paper)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Designing a Dynamic Material via Interlocking Kraft Lignin with Ultrahigh Molecular Weight Poly(ethylene oxide)

The environmental issues stemming from plastic waste and the excessive use of petroleum-based chemicals are both concerning and urgent. To effectively address this problem, we need to adopt a comprehensive approach involving developing more sustainable and renewable materials. These materials should be capable of demonstrating similar or even better performance than functional polymers synthesized from petroleum-based chemicals. Our research aims to develop more sustainable materials by leveraging the intrinsic characteristics of a natural polymer, lignin, a byproduct of the biorefinery industries. We utilized the three-dimensional branching structure of lignin as a material framework. We employed an approach to co-reactive melt processing of kraft lignin with aliphatic flexible chains of soft cross-linkers through the reaction of the cross-linker epoxy chain ends with lignin functional groups. Our study demonstrates that the interlocked structure formed from the co-blending of kraft lignin with ultrahigh molecular weight poly(ethylene oxide) and the cross-linking of lignin chains through a solvent-free process can manipulate the macromolecular interactions and relaxation. This manipulation results in materials that exhibit a wide range of thermomechanical properties and self-healing and shape memory effects, with drastically improved stiffness in a single material. We have explored the fundamental understanding of the macromolecular chain relaxation dynamics originating from the interlocking structure formation. In conclusion, this investigation utilized various techniques, including thermal, mechanical, rheology, and quasi-elastic neutron scattering.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Sharp boundaries for the swampland

We reconsider the problem of bounding higher derivative couplings in consistent weakly coupled gravitational theories, starting from general assumptions about analyticity and Regge growth of the S-matrix. Higher derivative couplings are expected to be of order one in the units of the UV cutoff. Our approach justifies this expectation and allows to prove precise bounds on the order one coefficients. Our main tool are dispersive sum rules for the S-matrix. We overcome the difficulties presented by the graviton pole by measuring couplings at small impact parameter, rather than in the forward limit. We illustrate the method in theories containing a massless scalar coupled to gravity, and in theories with maximal supersymmetry.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Enabling attractive-repulsive potentials in binary-collision-approximation monte-carlo codes for ion-surface interactions

Abstract Binary Collision Approximation (BCA) codes for ion-material interactions, such as SRIM, Tridyn, F-TRIDYN, and SDtrimSP, have historically been limited to screened Coulomb potentials even at low energies due to the difficulty in numerically solving the Distance of Closest Approach (DOCA) problem for attractive-repulsive potentials. Techniques such as direct n-body simulation or modifications to Newton’s method are either prohibitively costly or not guaranteed to work for all potentials. Advanced rootfinding techniques, such as companion matrix solvers, offer a solution. For many attractive-repulsive potentials, however, a companion matrix cannot be used directly, because there is no way to put the associated functions into a monomial basis form. A complementary technique is proxy rootfinding—by finding the best-fit polynomial approximant of a function, the zeros of the approximant can be guaranteed to be close to the zeros of the function. Using the Chebyshev basis and grid offers additional guarantees with regards to the quality of the approximation, the speed of convergence, and the avoidance of Runge’s phenomenon. By finding Chebyshev interpolants and using the Chebyshev-Frobenius companion matrix, the zeros of any real function on a bounded domain can be found. Here we show that using an Adaptive Chebyshev Proxy Rootfinder with Automatic Subdivision (ACPRAS) with appropriate scaling functions, numerical issues presented by attractive-repulsive potentials, including those of scale, can be handled. Using these techniques, we show that it is possible to include any physically reasonable interatomic potential in a BCA code, and to guarantee correctness of the resulting scattering angle calculations.

Materials Science↗

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