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DOE OSTI2017

The asymptotic behaviour of the scattering matrix in a neighbourhood of the endpoints of a spectral gap

The behaviour of the scattering matrix is investigated as the spectral parameter approaches an endpoint of a spectral gap of a quantum waveguide from the inside or the outside. The waveguide has two sleeves, one is cylindrical and the other periodic. When the spectral parameter traverses the spectral gap, the scattering matrix is reshaped because the number of waves inside and outside the gap is different. Notwithstanding, the smaller scattering matrix (in size) is transformed continuously into an identical block in the bigger scattering matrix and, in addition, the latter takes block diagonal form in the limit at the endpoint of the gap, that is, at the spectral threshold. The unexpected phenomena are related to the other block. It is shown that in the limit this block can only take certain values at the threshold, and taking one or other of these values depends on the structure of the continuous spectrum and also on the structure of the subspace of 'almost standing' waves at the threshold, which are solutions of the homogeneous problem that transfer no energy to infinity. A criterion for the existence of such solutions links the dimension of this subspace to the multiplicity of the eigenvalue −1 of the threshold scattering matrix. Asymptotic formulae are obtained, which show, in particular, that the phenomenon of anomalous scattering of high-amplitude waves at near-threshold frequencies, discovered by Weinstein in a special acoustic problem, also occurs in periodic waveguides. Bibliography: 38 titles. (paper)

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

A scalable transformer model for real-time decision making in neutron scattering experiments

The U.S. Department of Energy's (DOE's) neutron research facilities at Oak Ridge National Laboratory (ORNL), including the High Flux Isotope Reactor (HFIR) and the Spallation Neutron Source (SNS), are a state-of-the-art neutron scattering facility that allows researchers to study the structure and dynamics of materials at the atomic scale. At the SNS, neutrons are measured using the time-of-flight (TOF) technique as they move through a neutron beamline to interact with a sample. Large volumes of neutron scattering data are collected and recorded in neutron event mode. Optimal productivity of the TOF instrument is limited due to the lack of real-time data analysis tools. The large amount of data generated by the experiments can be challenging to process and analyze in real time, particularly for experiments that require rapid feedback and adjustment of experimental parameters. The regular computer/workstation cannot keep up with the experiment speed to provide real-time feedback to adjust experimental parameters, so connecting the supercomputers available to the neutron facility is necessary to achieve real-time data analysis and experiment steering. To address this challenge, we exploit the Frontier supercomputer at Oak Ridge Leadership Computing Facility (OLCF) to train a scalable temporal fusion transformer model for real-time decision making of TOF neutron scattering experimentation. Here, in this paper, we present the results using Frontier to provide the processing power needed to rapidly process and analyze large volumes of single-crystal diffraction data collected at TOPAZ, a neutron time-of-flight Laue single-crystal diffractometer at the SNS.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

Electronically Nonadiabatic Structural Transformations Promoted by Electron Beams

The use of scanning transmission electron microscopes to manipulate substitutional defects in graphene has recently been demonstrated and modeled using ground state molecular dynamics, but the role of electronic excitations induced through inelastic electron scattering in promoting these transformations has so-far remained unexplored. In this work, probed are the effects of electronic excitation on the structural dynamics of graphene quantum dots of differing edge morphologies that are substitutionally doped with silicon or phosphorous. The ground and excited state potential energy barriers for pyramidal inversion of these nonplanar doped species are evaluated using time-dependent density functional theory. Optically bright excited states in which the barrier is decreased are identified in the low energy region of the electronic spectrum, suggesting that photoexcitation can modulate the reactivity of defects in graphene under electron beam irradiation. Coupling matrix elements between these inversion-favoring excited states and the ground state and time-domain simulations of the material's response to a point charge impulse indicate that focusing an electron beam near the defect can also lead to population of these states, implying that beam electrons incident on a defect can both excite the material to an inversion-favoring state and transfer momentum to the defect to initiate the inversion.

36 MATERIALS SCIENCE↗

DOE OSTI2019

Director and Spontaneous Polarization Fluctuations in Ferroelectric Smectic-C* Cells

The correlation function of the director fluctuations in a plane-parallel smectic-C* cell with a bookshelf structure is calculated far from phase transition points. The free energy takes into account the anisotropy of the Coulomb interaction of the bound charges induced by spontaneous polarization fluctuations. This correlation function of the director fluctuations is used to calculate the scattered light intensity. Taking into account the anisotropy of the permittivity in the Coulomb interaction of bound charges is shown to change a scattering indicatrix substantially.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2014

SU-E-I-07: An Improved Technique for Scatter Correction in PET

Purpose: In positron emission tomography (PET), the single scatter simulation (SSS) algorithm is widely used for scatter estimation in clinical scans. However, bias usually occurs at the essential steps of scaling the computed SSS distribution to real scatter amounts by employing the scatter-only projection tail. The bias can be amplified when the scatter-only projection tail is too small, resulting in incorrect scatter correction. To this end, we propose a novel scatter calibration technique to accurately estimate the amount of scatter using pre-determined scatter fraction (SF) function instead of the employment of scatter-only tail information. Methods: As the SF depends on the radioactivity distribution and the attenuating material of the patient, an accurate theoretical relation cannot be devised. Instead, we constructed an empirical transformation function between SFs and average attenuation coefficients based on a serious of phantom studies with different sizes and materials. From the average attenuation coefficient, the predicted SFs were calculated using empirical transformation function. Hence, real scatter amount can be obtained by scaling the SSS distribution with the predicted SFs. The simulation was conducted using the SimSET. The Siemens Biograph™ 6 PET scanner was modeled in this study. The Software for Tomographic Image Reconstruction (STIR) was employed to estimate the scatter and reconstruct images. The EEC phantom was adopted to evaluate the performance of our proposed technique. Results: The scatter-corrected image of our method demonstrated improved image contrast over that of SSS. For our technique and SSS of the reconstructed images, the normalized standard deviation were 0.053 and 0.182, respectively; the root mean squared errors were 11.852 and 13.767, respectively. Conclusion: We have proposed an alternative method to calibrate SSS (C-SSS) to the absolute scatter amounts using SF. This method can avoid the bias caused by the insufficient tail information and therefore improve the accuracy of scatter estimation.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2016

Fourier-transform-based model for carrier transport in semiconductor heterostructures: Longitudinal optical phonon scattering

We present scattering rates for electrons at longitudinal optical phonons within a model completely formulated in the Fourier domain. The total intersubband scattering rates are obtained by averaging over the intrasubband electron distributions. The rates consist of the Fourier components of the electron wave functions and a contribution depending only on the intersubband energies and the intrasubband carrier distributions. The energy-dependent part can be reproduced by a rational function, which allows for the separation of the scattering rates into a dipole-like contribution, an overlap-like contribution, and a contribution which can be neglected for low and intermediate carrier densities of the initial subband. For a balance between accuracy and computation time, the number of Fourier components can be adjusted. This approach facilitates an efficient design of complex heterostructures with realistic, temperature- and carrier density-dependent rates.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1986

Random scattering approach to gravitational microlensing

Small random deflections of a narrow beam of radiation due to gravitational scattering by stars randomly distributed within the deflector plane are considered. Using a Fouriere transform method, the probability of scattering is obtained as a function of scattering angle for an arbitrary number of stars with an arbitrary distribution of masses. The probability density, expressed in proper units, depends on one parameter only: the effective number of stars. At small scattering angles the density is a Gaussian, and at large angles it falls off as the scattering angle to the minus fourth power. The probability distribution for scatterings is simply related to the angular distribution of the surface brightness of a macroimage, averaged over many microimages. The isophotes are ellipses, with the ratio of the major axis to the minor axis, determined by the dimensionless surface mass density and the shear of the lensing system. The number of stars that has to be included in the modeling of microlensing is proportional to the amplification due to the macrolens, and to the square of the dimensionless surface mass density.

Katz, N.↗

DOE OSTI2018

Cascade Transformer Based on the Volume Coil for Power Transmission under High Voltage

The use of an electronic cooling system at the High Intensity heavy ion Accelerator Facility (HIAF) accelerator complex, which is being developed at the Institute of Modern Physics (China), to improve the efficiency of ion injection into the accelerator and reduce the spread of ion pulses in the beam has been proposed. Electron cooling of the ion beam was carried out due to the interaction of ions with a continuous electron beam with a current of up to 3 A, energy of up to 450 keV, and energy stability at the level of 10{sup –4} or better. The electron beam energy recuperation was carried out at the expense of a power source with a power of 5–15 kW, which was located at the top of a high-voltage column—a high-voltage terminal. The operation of a prototype of power transmission system, which was based on a cascade transformer with a volumetric coil, has been considered. Such a transformer has a relatively low scattering inductance, which can significantly reduce the number of capacitors to compensate for it. It has been shown that this design made it possible to transfer power of up to 40 kW at small dimensions of the transformer and heat dissipation in it was not more than 10 kW.

43 PARTICLE ACCELERATORS↗

NASA NTRS2011

Compact Polarimetry in a Low Frequency Spaceborne Context

Compact polarimetry has been shown to be an interesting alternative mode to full polarimetry when global coverage and revisit time are key issues. It consists on transmitting a single polarization, while receiving on two. Several critical points have been identified, one being the Faraday rotation (FR) correction and the other the calibration. When a low frequency electromagnetic wave travels through the ionosphere, it undergoes a rotation of the polarization plane about the radar line of sight for a linearly polarized wave, and a simple phase shift for a circularly polarized wave. In a low frequency radar, the only possible choice of the transmit polarization is the circular one, in order to guaranty that the scattering element on the ground is illuminated with a constant polarization independently of the ionosphere state. This will allow meaningful time series analysis, interferometry as long as the Faraday rotation effect is corrected for the return path. In full-polarimetric (FP) mode, two techniques allow to estimate the FR: Freeman method using linearly polarized data, and Bickel and Bates theory based on the transformation of the measured scattering matrix to a circular basis. In CP mode, an alternate procedure is presented which relies on the bare surface scattering properties. These bare surfaces are selected by the conformity coefficient, invariant with FR. This coefficient is compared to other published classifications to show its potential in distinguishing three different scattering types: surface, doublebounce and volume. The performances of the bare surfaces selection and FR estimation are evaluated on PALSAR and airborne data. Once the bare surfaces are selected and Faraday angle estimated over them, the correction can be applied over the whole scene. The algorithm is compared with both FP techniques. In the last part of the paper, the calibration of a CP system from the point of view of classical matrix transformation methods in polarimetry is proposed.

radar polarization diversity↗

DOE OSTI2025

Real-Space Local Dynamics in 1,2,3-Triazole Using Inelastic Neutron Scattering

Enhancing proton transport in polymer electrolytes is crucial for advancing next-generation solid-state batteries, yet our understanding of proton conductivity in nonaqueous environments remains limited due to a lack of atomic-scale insights. Here, in this study, we investigated the atomic-scale dynamics of 1,2,3-triazole, a small molecule capable of dynamic hydrogen bonding, as a model system for proton hopping in nonaqueous environments. Using the real-space correlation function determined by the double Fourier transformation of inelastic neutron scattering spectra, we identified that the self-motion of protons and intermolecular dynamics occur on comparable time scales. Furthermore, we observed that the activation energy associated with the intermolecular dynamics matches the energy barrier for molecular rotations determined through Density Functional Theory calculations. These findings underscore the importance of controlling molecular dynamics at the atomic scale to control proton transport. Additionally, we demonstrated that intermolecular dynamics in systems involving protons can be studied using inelastic neutron scattering even without deuteration, thereby providing a broader avenue for studying atomic-scale dynamics in soft matter systems.

Shinohara, Yuya [Oak Ridge National Laboratory (OR↗

NASA NTRS2016

Scattering of Gaussian Beams by Disordered Particulate Media

A frequently observed characteristic of electromagnetic scattering by a disordered particulate medium is the absence of pronounced speckles in angular patterns of the scattered light. It is known that such diffuse speckle-free scattering patterns can be caused by averaging over randomly changing particle positions and/or over a finite spectral range. To get further insight into the possible physical causes of the absence of speckles, we use the numerically exact superposition T-matrix solver of the Maxwell equations and analyze the scattering of plane-wave and Gaussian beams by representative multi-sphere groups. We show that phase and amplitude variations across an incident Gaussian beam do not serve to extinguish the pronounced speckle pattern typical of plane-wave illumination of a fixed multi-particle group. Averaging over random particle positions and/or over a finite spectral range is still required to generate the classical diffuse speckle-free regime.

radiative transfer theory↗

DOE OSTI2019

In-situ observation of an unusual phase transformation pathway with Guinier-Preston zone-like precipitates in Zr-based bulk metallic glasses

The pathway of amorphous-to-crystalline phase transformation in Zr 52.5 Cu 17.9 Ni 14.6 Al 10 Ti 5 bulk metallic glasses was studied using a suite of in-situ techniques. Multi-scale structure evidence reveals a five-stage pathway, analogous to the non-equilibrium transformation process with Guinier-Preston zones during aging in precipitation-hardened alloys, by the following sequence upon isothermal annealing the alloy in the supercooled liquid region: polyamorphous phase transition, chemical phase separation, the formation of a poorly-ordered metastable phase, and the formation of a final crystalline product. The changeable incubation periods at different annealing temperatures, and the abrupt multi-scale structure changes, as well as a latent heat release in the calorimetric measurements, support the first-order nature of the phase transformation at early stages. The structure evolution in real-space indicates that the enhancement of cluster connectivity on the medium-range scale plays essential roles in the early stages of the phase transformation, while the interface-limited ordering dominates the later stages. The experimental results suggest the phase transformation pathway with "Guinier-Preston zone-like" precipitates accompanied by the kinematic development of core-shell structures of diffuse interfaces with order parameters gradients, enabling the step-by-step decrease of free energy of the alloy system during phase transformation, which might be a universal behavior for alloys with excellent glass-forming ability.

36 MATERIALS SCIENCE↗

DOE OSTI2015

Periodically distributed objects with quasicrystalline diffraction pattern

It is possible to construct fully periodically distributed objects with a diffraction pattern identical to the one obtained for quasicrystals. These objects are probability distributions of distances obtained in the statistical approach to aperiodic structures distributed periodically. The diffraction patterns have been derived by using a two-mode Fourier transform—a very powerful method not used in classical crystallography. It is shown that if scaling is present in the structure, this two-mode Fourier transform can be reduced to a regular Fourier transform with appropriately rescaled scattering vectors and added phases. Detailed case studies for model sets 1D Fibonacci chain and 2D Penrose tiling are discussed. Finally, it is shown that crystalline, quasicrystalline, and approximant structures can be treated in the same way.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2015

The nonsinglet structure function evolution by Laplace method

We derive a general scheme for the evolution of the nonsinglet structure function at the leadingorder (LO) and next-to-leading-order (NLO) by using the Laplace-transform technique. Results for the nonsinglet structure function are compared with MSTW2008, GRV, and CKMT parameterizations and also EMC experimental data in the LO and NLO analysis. The results are in good agreement with the experimental data and other parameterizations in the low- and large-x regions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Phenomenological R -Matrix parameterization of direct, doorway, and compound nuclear reactions [Abstract]

Although formal expressions for scattering matrix accounting for direct, doorway, and compound nuclear (CN) resonant reactions have been derived several decades ago in both the transition ( T -)matrix formalism and the reactance ( K -)matrix formalism, the absence of corresponding expressions in phenomenological R -matrix formalism has limited the application of the latter to CN resonant reactions only. We remove this limitation by parameterizing direct, doorway, and CN resonant reactions in a phenomenological R -matrix scattering matrix, and provide a parameterization for a corresponding Reich-Moore approximation of eliminated capture channels. Direct reactions induce (previously neglected) mixing among the incoming or outgoing R -matrix channel wave functions, parameterized by real and orthonormal channel-rotation matrix, M , whereby the original scattering matrix U is transformed into M T UM . Any real and orthonormal matrix, M , can be equivalently expressed as e η , where η is a real and skew-symmetric 2 rotation-generating matrix that subsequently yields a more intuitive parameterization of eliminated direct capture reactions in Reich-Moore approximation. A phenomenological R -matrix parameterization of doorway reactions is inferred by equating the expression for reactance ( K -)matrix, given in terms of Brune’s alternative R -matrix parameterization, to a corresponding expression derived using Feshbach’s projection operator formalism. Assuming that all doorway states, just like CN states, are confined within spheres defined by R -matrix channel radii, a new R -matrix-like term induced by doorway states is gleaned, wherein each doorway state is parameterized by its energy, width, and the strength of its coupling to each CN state. Since a Reich-Moore approximation for retained-channel scattering matrix ought to approximate the effect of eliminated capture channels taking place via direct, doorway, or CN reactions, each of the three kinds of reactions contributing to the capture entails a corresponding Reich-Moore parameterization in a first-order approximation: direct contribution is parameterized by introducing finite diagonal elements of a retained-channel rotation-generating matrix, doorway contribution is parameterized by doorway capture widths, while CN contribution is parameterized by conventional Reich-Moore capture widths. We will present evidence of direct and doorway reactions observed in recent measurements of resolved resonance cross sections at the Gaerttner LINAC Center at Rensselaer Polytechnic Institute, and will outline a path for implementing this new R -matrix parameterization into the SAMMY nuclear data evaluation code.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Data Reproducibility of Spin-Echo Small-Angle Neutron Scattering Instruments

Spin-echo small-angle neutron scattering (SESANS) is a unique method to measure structures of materials in real space with length scales from ∼ 30 μm to ∼20 µm. As shown in Figure 1, the accessible length scale of SESANS is given by its ability to encode the momentum transfer into the Larmor phase, namely Φ = $\vec{𝛿}$ ⋅ $\vec{𝑄}$, where $\vec{𝑄}$ is the momentum transfer and $\vec{𝛿}$ is the encoding vector of the setup and its projection along Q (δQ) is called spin-echo length (SEL). The spin echo length, which is synonymous with the spatial correlation distance probed, is defined as the following 𝛿𝑄 ∝ 𝜆 2 𝐵𝐿cot𝜃 where 𝜆 is neutron wavelength, B is magnetic field, L is length of the parallelogram magnetic field region, and 𝜃 is the angle between the inclined magnetic field boundary and the beam direction, as shown in Figure 1. The result of the SESANS experiment is a Hankel transformation of the SANS scattering function I(Q), which yields the correlation function of the sample in real space.

47 OTHER INSTRUMENTATION↗

DOE OSTI2016

Theory of thermal conductivity in the disordered electron liquid

We study thermal conductivity in the disordered two-dimensional electron liquid in the presence of long-range Coulomb interactions. We describe a microscopic analysis of the problem using the partition function defined on the Keldysh contour as a starting point. We extend the renormalization group (RG) analysis developed for thermal transport in the disordered Fermi liquid and include scattering processes induced by the long-range Coulomb interaction in the sub-temperature energy range. For the thermal conductivity, unlike for the electrical conductivity, these scattering processes yield a logarithmic correction that may compete with the RG corrections. The interest in this correction arises from the fact that it violates the Wiedemann–Franz law. We checked that the sub-temperature correction to the thermal conductivity is not modified either by the inclusion of Fermi liquid interaction amplitudes or as a result of the RG flow. We therefore expect that the answer obtained for this correction is final. We use the theory to describe thermal transport on the metallic side of the metal–insulator transition in Si MOSFETs.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2016

Extraction of organic compounds from representative shales and the effect on porosity

This study is an attempt to understand how native organics are distributed with respect to pore size to determine the relationship between hydrocarbon chemistry and pore structure in shales, as the location and accessibility of hydrocarbons is key to understanding and improving the extractability of hydrocarbons in hydraulic fracturing. Selected shale cores from the Eagle Ford and Marcellus formations were subjected to pyrolysis gas chromatography (GC), thermogravimetric analysis, and organic solvent extraction with the resulting effluent analyzed by GC-mass spectrometry (MS). Organics representing the oil and gas fraction (0.1 to 1 wt. %) were observed by GC-MS. For most of the samples, the amount of native organic extracted directly related to the percentage of clay in the shale. The porosity and pore size distribution (0.95 nm to 1.35 m) in the Eagle Ford and Marcellus shales was measured before and after solvent extraction using small angle neutron scattering (SANS). An unconventional method was used to quantify the background from incoherent scattering as the Porod transformation obscures the Bragg peak from the clay minerals. Furthermore, the change in porosity from SANS is indicative of the extraction or breakdown of higher molecular weight bitumen with high C/H ratios (asphaltenes and resins). This is mostly likely attributed to complete dissolution or migration of asphaltenes and resins. These longer carbon chain lengths, C30-C40, were observed by pyrolysis GC, but either were too heavy to be analyzed in the extracts by GC-MS or were not effectively leached into the organic solvents. Thus, experimental limitations meant that the amount of extractable material could not be directly correlated to the changes in porosity measured by SANS. But, the observable porosity generally increased with solvent extraction. A decrease in porosity after extraction as observed in a shale with high clay content and low maturity was attributed to swelling of pores with solvent uptake or migration of resins and asphaltenes.

04 OIL SHALES AND TAR SANDS↗