The choice of trial functions in the perturbation-variation method.
Nonlinear variational trial function for atomic hydrogen dynamic polarizability, discussing first order perturbed wave function and perturbation- variation method
HYDROGEN ATOM↗
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N-stream approximations to radiative transfer
Schuster's two-stream approximation (1905) is first derived from Chandrasekhar's radiative transfer equation (1950), and then extended to an arbitrary number of streams. The resulting technique for solving the transfer function similar to the discrete ordinate and spherical harmonic methods, is useful for modeling atmospheres with complicated phase functions and moderate optical depths. The resulting n coupled linear differential equations are simple and consume less computer time than other approximations, yet have the same required accuracy. The approximation is also flexible with respect to the choice of patch functions, and no approximations are made on the form of the phase function, other than its expansion into Legendre polynomials. A four-stream approximation is evaluated for a Henyey-Greenstein phase function with an asymmetry factor equal to 0.5.
Acquista, C.↗
Density Functional Theory Study on Electronic Structures and Magnetism for Nitrogen-Doped ZnS
Using the full-potential linearized augmented plane wave method, together with the generalized gradient approximation and modified Becke-Johnson as correlation potential, the electronic structures and magnetism for nitrogen-doped ZnS are investigated. Based on the generalized gradient approximation, calculations show nitrogen-substituting sulfur (N{sub S}) would induce the ZnS to be paramagnetic metal. As the band gap increasing to the experimental results (obtained by the modified Becke-Johnson potential), the N{sub S} defects would induce the ZnS to be a ferromagnetic metal. The total magnetic moment for ZnS supercell with single N{sub S} defect is 0.85 μ{sub B}. Positive chemical pair interactions imply that N{sub S} defects would form homogeneous distribution in ZnS host. Sulfur vacancies would give rise to the ZnS with N{sub S} defects system losing the magnetism. Moderate formation energy (0.71 eV) indicates ZnS with N{sub S} defects could be fabricated experimentally.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Recommended nuclear data for medical radioisotope production: diagnostic gamma emitters
An extensive series of evaluations have been performed as part of an IAEA coordinated research project to study a set of nuclear reactions that produce the diagnostic gamma-ray emitting radionuclides Cr- 51 , Tc- 99m , In- 111 , I-123 and Tl- 201 . Recommended cross-section data in the form of excitation functions have been derived, along with quantifications of their uncertainties. These evaluations compiled the compilation of all previously published values and newly measured experimental data, followed by critical assessments and selection of those experimental datasets and accompanying uncertainties judged to be fully valid and statistically consistent for model-independent least-squares fitting by means of Pade approximations. Integral yields as a function of the energy were also calculated on the basis of the recommended cross sections deduced from these various fits. All evaluated numerical conclusions and their corresponding uncertainties are available online at www-nds.iaea.org/medical/gamma_emitters.html and also on the medical portal of the International Atomic Energy Agency/Nuclear Data Section (IAEA-NDS) www-nds.iaea.org/medportal
38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
A Method of Matching of Interior and Exterior Asymptotics in Boundary-Value Problems of Mathematical Physics
We describe applications of asymptotic methods to problems of mathematical physics and mechanics, primarily, to the solution of nonlinear singularly perturbed problems in local domains. We also discuss applications of Padé approximations for transformation of asymptotic expansions to rational or quasi-fractional functions.
97 MATHEMATICS AND COMPUTING↗
Reducing measurement costs by recycling the Hessian in adaptive variational quantum algorithms
Abstract Adaptive protocols enable the construction of more efficient state preparation circuits in variational quantum algorithms (VQAs) by utilizing data obtained from the quantum processor during the execution of the algorithm. This idea originated with Adaptive Derivative-Assembled Problem-Tailored variational quantum eigensolver (ADAPT-VQE), an algorithm that iteratively grows the state preparation circuit operator by operator, with each new operator accompanied by a new variational parameter, and where all parameters acquired thus far are optimized in each iteration. In ADAPT-VQE and other adaptive VQAs that followed it, it has been shown that initializing parameters to their optimal values from the previous iteration speeds up convergence and avoids shallow local traps in the parameter landscape. However, no other data from the optimization performed at one iteration is carried over to the next. In this work, we propose an improved quasi-Newton optimization protocol specifically tailored to adaptive VQAs. The distinctive feature in our proposal is that approximate second derivatives of the cost function are recycled across iterations in addition to optimal parameter values. We implement a quasi-Newton optimizer where an approximation to the inverse Hessian matrix is continuously built and grown across the iterations of an adaptive VQA. The resulting algorithm has the flavor of a continuous optimization where the dimension of the search space is augmented when the gradient norm falls below a given threshold. We show that this inter-optimization exchange of second-order information leads the approximate Hessian in the state of the optimizer to be consistently closer to the exact Hessian. As a result, our method achieves a superlinear convergence rate even in situations where the typical implementation of a quasi-Newton optimizer converges only linearly. Our protocol decreases the measurement costs in implementing adaptive VQAs on quantum hardware as well as the runtime of their classical simulation.
Ramôa, Mafalda (ORCID:0000000302187801)↗
Semi-inclusive deep-inelastic scattering on a polarized spin-1 target. II. Deuteron and spectator nucleon tagging
We develop the theoretical framework for semi-inclusive deep-inelastic scattering on a polarized spin-1 target and apply it to scattering on the polarized deuteron with spectator nucleon tagging. In Part I (previous article), we present the general form of the semi-inclusive cross section and polarization observables for the spin-1 target. In Part II (this article), we consider deep-inelastic scattering on the polarized deuteron with spectator nucleon tagging as a special case of target fragmentation. Methods of light-front quantization are employed to separate nuclear and hadronic structure in the high-energy process and achieve a composite description. The light-front wave function of the polarized deuteron is obtained from a rotationally covariant three-dimensional wave function in the center-of-mass frame of the proton-neutron system. The tagged structure functions are computed in the impulse approximation. The momentum and spin distribution of the active nucleon are controlled by the deuteron polarization and the detected spectator momentum (𝐷/𝑆 wave ratio). The cross section and spin asymmetries are evaluated for general deuteron polarization (vector and tensor, longitudinal and transverse) as functions of the spectator momentum. Tensor-polarized spin asymmetries of order unity are achieved for spectator momenta of approximately 300 MeV, which select configurations with a large 𝐷 wave. Sum rules for the tagged spin structure functions are derived. The results can be used for simulations of spectator tagging in future polarized fixed-target experiments (Jefferson Lab) or at the Electron-Ion Collider.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Efficient simulations of charge density waves in the transition metal Dichalcogenide TiSe 2
Charge density waves (CDWs) in transition metal dichalcogenides are the subject of growing scientific interest due to their rich interplay with exotic phases of matter and their potential technological applications. Here, using density functional theory with advanced meta-generalized gradient approximations (meta-GGAs) and linear response time-dependent density functional theory (TDDFT) with state-of-the-art exchange-correlation kernels, we investigate the electronic, vibrational, and optical properties in 1T-TiSe 2 with and without CDW. In both bulk and monolayer TiSe 2 , the electronic bands and phonon dispersions in either normal or CDW (semiconducting) phase are described well via meta-GGAs, which separate the valence and conduction bands just as HSE06 does but with significantly more computational feasibility. The experimentally observed humps of electron energy loss spectroscopy are successfully reproduced in TDDFT. Our work opens the door to simulating these complexities in CDW compounds from first principles by revealing meta-GGAs as an accurate low-cost alternative to HSE06.
Electronic properties and materials↗
Spatial correlations of entangled polymer dynamics
The spatial correlations of entangled polymer dynamics are examined by molecular dynamics simulations and neutron spin-echo spectroscopy. Due to the soft nature of topological constraints, the initial spatial decays of intermediate scattering functions of entangled chains are, to the first approximation, surprisingly similar to those of an unentangled system in the functional forms. However, entanglements reveal themselves as a long tail in the reciprocal-space correlations, implying a weak but persistent dynamic localization in real space. Furthermore, comparison with a number of existing theoretical models of entangled polymers suggests that they cannot fully describe the spatial correlations revealed by simulations and experiments. In particular, the strict one-dimensional diffusion idea of the original tube model is shown to be flawed. The dynamic spatial correlation analysis demonstrated in this work provides a useful tool for interrogating the dynamics of entangled polymers. Lastly, the failure of the investigated models to even qualitatively predict the spatial correlations of collective single-chain density fluctuations points to a possible critical role of incompressibility in polymer melt dynamics.
74 ATOMIC AND MOLECULAR PHYSICS↗
Progressive Response Surfaces
Response surface functions are often used as simple and inexpensive replacements for computationally expensive computer models that simulate the behavior of a complex system over some parameter space. Progressive response surfaces are ones that are built up progressively as global information is added from new sample points in the parameter space. As the response surfaces are globally upgraded based on new information, heuristic indications of the convergence of the response surface approximation to the exact (fitted) function can be inferred. Sampling points can be incrementally added in a structured fashion, or in an unstructured fashion. Whatever the approach, at least in early stages of sampling it is usually desirable to sample the entire parameter space uniformly. At later stages of sampling, depending on the nature of the quantity being resolved, it may be desirable to continue sampling uniformly over the entire parameter space (Progressive response surfaces), or to switch to a focusing/economizing strategy of preferentially sampling certain regions of the parameter space based on information gained in early stages of sampling (Adaptive response surfaces). Here we consider Progressive response surfaces where a balanced indication of global response over the parameter space is desired.We use a variant of Moving Least Squares to fit and interpolate structured and unstructured point sets over the parameter space. On a 2-D test problem we compare response surface accuracy for three incremental sampling methods: Progressive Lattice Sampling; Simple-Random Monte Carlo; and Halton Quasi-Monte-Carlo sequences. We are ultimately after a system for constructing efficiently upgradable response surface approximations with reliable error estimates.
Romero, V. J.↗
First-Principles Investigation of Magnetic Properties and Faraday Rotation of Co Doping CdTe
In this paper, we aimed to study the effect of doping of the compound CdTe with the cobalt impurity (Co), as well as the vacancy defects in Cd sites. On one hand, this leads to the investigation of the magnetic properties and the Faraday rotation effect for the studied alloy, doped with different concentrations of cobalt (0.01, 0.05, 0.1, 0.15, 0.2, 0.25). On the other hand, we have created 0.01 of vacancy defects in Cd sites. Then, we raised the vacancy defect concentration to 0.05, keeping the same concentrations of cobalt. As a result, we have investigated that there is a magnetism appearing with the cobalt doping, while the vacancy defects in Cd sites affect the stability of the magnetic states. In general, it improves the ferromagnetic state that will be well explained in the discussion. Our calculations were performed using the KKR-CPA method within the spin-polarized density functional theory (DFT) with the local density approximation (LDA). The curves of the density of states (DOS) illustrate the results of this study which has been discussed, analyzed, and explained below. In addition, the energy of each case was calculated and given in the tables below for both the DLM (half of the cobalt spins are up while the other half are down) and the ferromagnetic state in order to confirm which one of them is stable.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Ab initio theory of the equation of state for compressed rare gas crystals
Nonempirical equations of state of compressed rare gas crystals Ne, Ar, Kr, and Xe are studied on the basis of the earlier-obtained ab initio adiabatic potential. The paired and three-body short-range repulsive potentials are calculated by the Hartree–Fock method in the basis of localized functions with their exact mutual orthogonalization and do not contain experimentally determined parameters. The theory is compared with the experiment and results of calculations by other authors. Analysis of the proposed equations of state for large compressions has shown the importance of taking into account the three-body interaction and the terms of the higher order in the overlap integral in compressed neon and the sufficiency of the quadratic approximation in the orthogonalization of functions in heavy rare gas crystals.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
On Using Intensity Interferometry for Feature Identification and Imaging of Remote Objects
We derive an approximation to the intensity covariance function of two scanning pinhole detectors, facing a distant source (e.g., a star) being occluded partially by an absorptive object (e.g., a planet). We focus on using this technique to identify or image an object that is in the line-of-sight between a well-characterized source and the detectors. We derive the observed perturbation to the intensity covariance map due to the object, showing that under some reasonable approximations it is proportional to the real part of the Fourier transform of the source's photon-flux density times the Fourier transform of the object's intensity absorption. We highlight the key parameters impacting its visibility and discuss the requirements for estimating object-related parameters, e.g., its size, velocity or shape. We consider an application of this result to determining the orbit inclination of an exoplanet orbiting a distant star. Finally, motivated by the intrinsically weak nature of the signature, we study its signal-to-noise ratio and determine the impact of system parameters.
quantum optics↗
A Study of Transport in the Near-Earth Plasma Sheet During A Substorm Using Time-Dependent Large Scale Kinetics
In this study we investigate the transport of H+ ions that made up the complex ion distribution function observed by the Geotail spacecraft at 0740 UT on November 24, 1996. This ion distribution function, observed by Geotail at approximately 20 R(sub E) downtail, was used to initialize a time-dependent large-scale kinetic (LSK) calculation of the trajectories of 75,000 ions forward in time. Time-dependent magnetic and electric fields were obtained from a global magnetohydrodynamic (MHD) simulation of the magnetosphere and its interaction with the solar wind and the interplanetary magnetic field (IMF) as observed during the interval of the observation of the distribution function. Our calculations indicate that the particles observed by Geotail were scattered across the equatorial plane by the multiple interactions with the current sheet and then convected sunward. They were energized by the dawn-dusk electric field during their transport from Geotail location and ultimately were lost at the ionospheric boundary or into the magnetopause.
El-Alaoui, M.↗
On the Applicability of High-frequency Approximations to Lilley's Equation
Three forms of the high-frequency asymptotic Green's function for Lilley's equation are reviewed and compared to the exact solution over wide range of Strouhal numbers. The asymmetric approximation, which applies to sources away form the jet axis, and the quasi-symmetric approximation, which is arrived at by making a near-axis source assumption, are both obtained for parallel round jets from a formal Fourier-transform solution. The ray-theory solution, which is the only high-frequency approximation that can be applied to more general mean flows, follows from a WKB ansatz and is shown to be closely related to the asymmetric approximation. The comparisons show that the best overall prediction of the exact Green's function is given by the asymmetric approximation which remains accurate down to a Strouhal number of 1/2. The close relationship between the asymmetric and ray-theory approximations suggests that the high-frequency asymptotic Green's function for more general mean flows would be similarly successful.
Wundrow, David W.↗
HfZr_BCC_SolidSolution_128atoms_VASP6
We performed density functional theory (DFT) calculations for body-centered-cubic (BCC) structures with 128 lattices sites of solid solution binary alloys hafnium-zirconium (Hf-Zr). The electronic structures of alloys have been calculated using Vienna Ab initio Simulation Package (VASP). Within this package the DFT approach is used to reduce many-body Schrodinger equation to set of single particle Kohn-Sham (KS) equations. The generalized electronic exchange-correlation functional is described by generalized gradient approximation with the Perdew-Burke-Ernzerhof parametrization. The electron-ion interactions is described by pseudopotentials developed within the plane-wave basis projector augmented-wave (PAW) approach. These pseudopotentials are available at the VASP portal (http://cms.mpi.univie.ac.at/vasp/). Our calculations have been run with the pseudopotentials treating s and p semi-core states as valence in case for the elements Hf and Zr. The electronic densities and potentials are expanded over plane-waves with energy cutoff of 350 eV. 2x2x2 k-mesh and normal precision were used. The alloys were modeled by supercell containing 128 randomly distributed atoms. At initial step the atoms occupy perfect bcc lattice cites. This initial structure was optimized until energy changes less than 1e-6 eV, while forces acting on atoms don't exceed 1e-2 eV/angstrom. The electron-ion interaction is described by PAW pseudopotentials. The calculations have been collected by sampling chemical compositions across the entire compositional range. The chemical compositions have been sampled by progressively changing the number of atoms per constituent by 4. For each chemical composition of binaries and ternaries, the first-principle calculations have been run for 100 randomized arrangements of the constituents on the BCC lattice sites. We collected data for a total of 3,100 randomized atomic structures over 31 chemical compositions.
36 MATERIALS SCIENCE↗
Local convergence analysis of an inexact trust-region method for nonsmooth optimization
In Baraldi, we introduced an inexact trust-region algorithm for minimizing the sum of a smooth nonconvex function and a nonsmooth convex function in Hilbert space—a class of problems that is ubiquitous in data science, learning, optimal control, and inverse problems. Furthermore, this algorithm has demonstrated excellent performance and scalability with problem size. In this paper, we enrich the convergence analysis for this algorithm, proving strong convergence of the iterates with guaranteed rates. In particular, we demonstrate that the trust-region algorithm recovers superlinear, even quadratic, convergence rates when using a second-order Taylor approximation of the smooth objective function term.
97 MATHEMATICS AND COMPUTING↗
Heat Transfer Through Turbulent Friction Layers
The "general Prandtl number" Pr(exp 1) - A(sub q)/A Pr, aside from the Reynolds number determines the ratio of turbulent to molecular heat transfer, and the temperature distribution in turbulent friction layers. A(sub q) = exchange coefficient for heat; A = exchange coefficient for momentum transfer. A formula is derived from the equation defining the general Prandtl number which describes the temperature as a function of the velocity. For fully developed thermal boundary layers all questions relating to heat transfer to and from incompressible fluids can be treated in a simple manner if the ratio of the turbulent shear stress to the total stress T(sub t)/T in the layers near the wall is known, and if the A(sub q)/A can be regarded as independent of the distance from the wall. The velocity distribution across a flat smooth channel and deep into the laminar sublayer was measured for isothermal flow to establish the shear stress ratio T(sub t)/T and to extend the universal wall friction law. The values of T(sub t)/T which resulted from these measurements can be approximately represented by a linear function of the velocity in the laminar-turbulent transition zone. The effect of the temperature relationship of the material values on the flow near the wall is briefly analyzed. It was found that the velocity at the laminar boundary (in contrast to the thickness of the laminar layer) is approximately independent of the temperature distribution. The temperature gradient at the wall and the distribution of temperature and heat flow in the turbulent friction layers were calculated on the basis of the data under two equations. The derived formulas and the figures reveal the effects of the Prandtl number, the Reynolds number, the exchange quantities and the temperature relationship of the material values.
Reichardt, H.↗