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DOE OSTI2021

Non-local corrections to the typical medium theory of Anderson localization

We use the recently developed finite cluster typical medium approach to study the Anderson localization transition in three dimensions. Applying our method to the box and binary alloy disorder distributions, we find a fast convergence with the cluster size. We demonstrate the importance of the typical medium environment and the non-local spatial correlations for the proper characterization of the localization transition. As the cluster size increases, our typical medium cluster method recovers the correct critical disorder strength for the transition. Our findings highlight the importance of the non-local cluster corrections for capturing the localization behavior of the mobility edge trajectories. Our results demonstrate that the typical medium cluster approach developed here provides a consistent and systematic description of the Anderson localization transition in the framework of the effective medium embedding schemes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Application of the locally self-consistent embedding approach to the Anderson model with non-uniform random distributions

Highlights: • Typical Medium Theory (TMT) for the Anderson Localization. • Locally Self-Consistent Multiple Scattering Method (LSMS) for Random Disordered Systems. • Linear Scaling Computational Method for Random Disordered Systems. We apply the recently developed embedding scheme for the locally self-consistent method to random disorder electrons systems. The method is based on the locally self-consistent multiple scattering theory and the typical medium theory. The locally self-consistent multiple scattering theory divides a system into many small designated local interaction zones. The subsystem within each local interaction zone is embedded in a self-consistent field from the typical medium theory. This approximation allows the study of random systems with large numbers of sites. We present results for the three dimensional Anderson model with different random disorder potential distributions. Using the typical density of states as an indicator of Anderson localization, we find that the method can capture the localization for commonly studied disorder potentials. These include the uniform distribution, the Gaussian distribution, and even the unbounded Cauchy distribution.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Neural Network Solver for Small Quantum Clusters

Machine learning approaches have recently been applied to the study of various problems in physics. Most of these studies are focused on interpreting the data generated by conventional numerical methods or the data on an existing experimental database. An interesting question is whether it is possible to use a machine learning approach, in particular a neural network, for solving the many-body problem. In this paper, we present a neural network solver for the single impurity Anderson model, the paradigm of an interacting quantum problem in small clusters. We demonstrate that the neural-network-based solver provides quantitative accurate results for the spectral function as compared to the exact diagonalization method. This opens the possibility of utilizing the neural network approach as an impurity solver for other many-body numerical approaches, such as the dynamical mean field theory.

36 MATERIALS SCIENCE↗

NASA NTRS1982

Application of strong fluctuation random medium theory to scattering of electromagnetic waves from a half-space of dielectric mixture

The strong fluctuation random medium theory is applied to calculate scattering from a half-space of dielectric mixture. The first and second moments of the fields are calculated, respectively, by using the bilocal and the distorted Born approximations, and the low frequency limit is taken. The singularity of the dyadic Green's function is taken into account. Expressions for the effective permittivity for the full space case are derived. It is shown that the derived result of the effect permittivity is identical to that of the Polder and van Santern mixing formula. The correlation function of the random medium is obtained by using simple physical arguments and is expressed in terms of the fractional volumes and particle sizes of the constituents of the mixture. Backscattering coefficients of a half-space dielectric mixture are also calculated. Numerical results of the effective permittivity and backscattering coefficients are illustrated using typical parameters encountered in microwave remote sensing of dry and wet snow. It is also shown that experimental data can be matched with the theory by using physical parameters of the medium as obtained from ground truth measurements.

Tsang, L.↗

DOE OSTI2026

In-Band Scattering and Absorption of Infrared Blocking Foam Filters for Millimeter-wave Cameras

Expanded closed-cell polymer foams are widely used as thermal infrared (IR) blocking filters in millimeter-wave cameras, particularly for Cosmic Microwave Background observations. Precise knowledge of their millimeter-wave properties is essential for optimizing sensitivity. We present broadband (150 GHz - 2 THz) transmittance spectroscopy of Styroace-II and several Zotefoam filters, fitting their spectra with a radiative transfer model incorporating dielectric absorption and Rayleigh, Mie, and higher-order scattering. For a typical 5~cm thick filter stack at 280~GHz, Styroace-II exhibits ${\sim}10\%$ scattering with absorption estimated as ${\lesssim}5\%$ by effective-medium theory, while Zotefoam HD30 offers superior performance at ${\sim}3\%$ scattering and absorption likewise bounded to ${{\lesssim}0.3\%}$. Each model component is constrained at the ${\sim}0.1\%$ transmittance level for millimeter wavelengths. We observe batch-to-batch scattering variability of up to 2 percentage points in foams with multiple tested batches. Less commonly used Zotefoam formulations (LD15 and LD24) can further reduce in-band scattering to ${<}1\%$ while maintaining negligible in-band absorption and likely comparable IR blocking due to shared polyethylene absorption features and similar cell sizes. Based on this work, a filter constructed from the best measured LD24 batch has replaced the Styroace-II filter in a Simons Observatory 220/280 GHz Small Aperture Telescope.

Thomas, Alex [Chicago U., Astron. Astrophys. Ctr.;↗

NASA NTRS1991

Photon interaction cross sections for aggregations of finite-dimensional leaves

The Ross (1981) plate turbid-medium theory, which abstracts the leaf canopy as a gaseous mixture of oriented planar nondimensional plates that are randomly distributed in the configuration space, does not account for the 'hot spot' effect typical of all layered media with finite-dimensional scattering centers. The concept of 'particle distribution functions' is presently used to derive the interaction cross sections. This formalism is statistical-mechanical in nature, since the radiative transfer equation is essentially a linearized form of the Boltzmann equation for N-body systems.

Myneni, Ranga B.↗

NASA NTRS1977

Seismic energy transmission in an intensively scattering environment

In order to account for some special features of lunar seismograms, namely, the gradual build-up of the signal, the extremely prolonged tail, and the lack of apparent coherence among three orthogonal components of ground motion, a statistical approach is proposed for describing transmission of seismic energy through a medium in which strong scattering takes place. A seismic diffusion theory is presented for a medium with randomly distributed scatterers of a given size distribution. A solution of the resulting diffusion equation for an impulsive energy source gives a curve which fairly closely reproduces the envelope of typical lunar impact seismograms. Since the model is based on constant diffusivity, long-range transmission will require a combination of diffusion and wave propagation treatments for accurate description.

Nakamura, Y.↗

DOE OSTI2022

Medium controlled aggregative growth as a key step in mesoporous silica nanoparticle formation

Near monodisperse mesoporous silica nanoparticles (MSN) represent a promising and rapidly developing type of mesoporous silica materials; however, the vast data on their synthesis remains unorganized and ill-understood. We systematically studied the formation of MSN under basic and neutral conditions using various temperatures, CTAB concentrations, hydrolyzing agents (triethanolamine, ammonia, phosphate buffers), and media with different colloidal stabilization properties (with ethanol as a cosolvent and monovalent salts). In the typical conditions for the preparation of stable MSN colloids, the particle size was controlled by colloidal stabilization by the medium (solvent type, ionic strength, and surfactant concentration) in agreement with the “aggregative growth” mechanism, rather than by solely the hydrolysis and condensation rates conventionally used for data interpretation in the classical nucleation theory. Medium properties (pH, ion types and concentration, polarity) also defined the efficiency of silica-surfactant cooperative self-assembly, which directly affected the porosity, mesopore size and pore wall thickness. Interestingly, this traditional silica-surfactant route showed a limited effect on the particle size, emphasizing the dominating role of colloidal stabilization in the studied reaction conditions. In situ pH measurements showed that every reaction medium has unique pH evolution profiles depending on the buffer capacity, hydrolysis and condensation rates. Reaction systems that fail to maintain the working pH can lead to non-porous products or undesired particle morphology and size distribution. The established particle formation mechanism allowed us to formulate comprehensive guidelines for preparing relatively concentrated colloids of near monodisperse (PDI 5–15%) mesoporous 30–700 nm silica spheres with variable porosity and mesopore size. Here, these findings will be particularly useful in designing new mesoporous silica-containing materials for biomedical applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS2017

Modeling of Electromagnetic Scattering by Discrete and Discretely Heterogeneous Random Media by Using Numerically Exact Solutions of the Maxwell Equations

In this paper, we discuss some aspects of numerical modeling of electromagnetic scattering by discrete random medium by using numerically exact solutions of the macroscopic Maxwell equations. Typical examples of such media are clouds of interstellar dust, clouds of interplanetary dust in the Solar system, dusty atmospheres of comets, particulate planetary rings, clouds in planetary atmospheres, aerosol particles with numerous inclusions and so on. Our study is based on the results of extensive computations of different characteristics of electromagnetic scattering obtained by using the superposition T-matrix method which represents a direct computer solver of the macroscopic Maxwell equations for an arbitrary multisphere configuration. As a result, in particular, we clarify the range of applicability of the low-density theories of radiative transfer and coherent backscattering as well as of widely used effective-medium approximations.

Dlugach, Janna M.↗

DOE OSTI2024

Go with the Radflow: Thermal radiation experiments in the high energy-density regime [Slides]

Los Alamos National Laboratory is a nuclear weapons laboratory supporting our nation's defense. In support of the mission is a high energy-density physics program in which we design and execute experiments to study radiation-hydrodynamics phenomena and improve the predictive capability of our large-scale multi-physics software codes on our supercomputers. The Radflow Project is maturing a unique spectroscopic measurement that yields a spatially dependent supersonic radiation wavefront profile. The spectroscopic measurement is much more constraining than the typically used radiography, which measures the density changes due to the shock as the radiation wave goes subsonic. Recently, the spectroscopic measurement has been applied to advanced targets with a detailed heterogeneity representing a single realization of a stochastic medium. The Radflow Project also conducts opacity experiments to explain the current conundrum of the experimental iron opacity differing from theory, which is important in modeling the sun. More than that, though, we need to be able to answer these science questions and be able to validate our theory and codes.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Effect of causality constraints on Bayesian analyses of heavy-ion collisions

There have long been questions about the limits to the validity of relativistic fluid dynamics and whether it is being used outside its regime of validity in modern simulations of relativistic heavy-ion collisions. An important new tool for answering this question is a causality analysis in the nonlinear regime—if the solutions of the evolution equations do not respect relativistic causality, then they are not a faithful representation of the underlying relativistic theory (in this case, quantum chromodynamics). Using this nonlinear criterion, it has recently been shown that hydrodynamics is indeed being used outside its regime of validity in simulations, at least sometimes. Here we explore the phenomenological implications, particularly the quantitative effects of demanding limits on acausality in modern Bayesian parameter estimation. We find that, while typically only a small fraction of the system's energy is initially in an acausal regime, placing strict limits on the allowed energy fraction significantly changes the preferred properties of the initial condition, which in turn alters the extracted medium properties such as bulk viscosity, where large values are no longer favored. Furthermore, these findings highlight the importance of developing better theoretical descriptions of the early-time, out-of-equilibrium dynamics of relativistic heavy-ion collisions.

Bayesian methods↗

NASA NTRS1979

HF-induced parametric decay in presence of field-aligned irregularities

A nonlinear theory for the saturation of the HF-induced parametric decay instability is formulated in terms of the normal modes of a field-aligned plasma wave duct. Coupling coefficients between modes are derived, and a saturation spectrum is computed numerically for a typical irregularity. The computed spectrum shows that unstable waves may propagate at larger angles to the magnetic field than would be the case in a regular medium. The relevance of this work to the experiment of Muldrew and Showen (1977), concerning the height of the HF-induced plasma line at Arecibo, is discussed. A possible explanation is also found for the 'decay line' feature in comparison with the 'broad bump' in the observed backscatter spectrum.

Rypdal, K.↗

NASA NTRS1989

Analytical optical scattering in clouds

An analytical optical model for scattering of light due to lightning by clouds of different geometry is being developed. The self-consistent approach and the equivalent medium concept of Twersky was used to treat the case corresponding to outside illumination. Thus, the resulting multiple scattering problem is transformed with the knowledge of the bulk parameters, into scattering by a single obstacle in isolation. Based on the size parameter of a typical water droplet as compared to the incident wave length, the problem for the single scatterer equivalent to the distribution of cloud particles can be solved either by Mie or Rayleigh scattering theory. The super computing code of Wiscombe can be used immediately to produce results that can be compared to the Monte Carlo computer simulation for outside incidence. A fairly reasonable inverse approach using the solution of the outside illumination case was proposed to model analytically the situation for point sources located inside the thick optical cloud. Its mathematical details are still being investigated. When finished, it will provide scientists an enhanced capability to study more realistic clouds. For testing purposes, the direct approach to the inside illumination of clouds by lightning is under consideration. Presently, an analytical solution for the cubic cloud will soon be obtained. For cylindrical or spherical clouds, preliminary results are needed for scattering by bounded obstacles above or below a penetrable surface interface.

Phanord, Dieudonne D.↗

NASA NTRS1975

Strong scintillations in astrophysics. II - A theory of temporal broadening of pulses

A theory of temporal broadening of pulses propagating in a turbulent medium is developed on the basis of the Markov approximation. The theory may be applied to quite general turbulence spectra and to thin or thick turbulent regions. Since the basis of the theory is the wave equation, no reliance is placed on geometrical optics and no assumptions are made about the scattered angular spectrum. The observed smearing is found to be the combination of three effects: the dispersion effect, the pure refractive effect, and the diffraction effect. The last of these dominates for typical pulsar parameters. Pulse shapes are calculated for both Gaussian and Kolmogorov turbulence spectra and it is shown how these scale with the various turbulence parameters.

Lee, L. C.↗

NASA NTRS2022

The 21-cm Signal From the Cosmic Dawn: Metallicity Dependence of High Mass X-Ray Binaries

X-rays from high-mass X-ray binaries (HMXBs) are likely the main source of heating of the intergalactic medium (IGM) during Cosmic Dawn (CD), before the completion of reionization. This Epoch of Heating (EoH; z ∼10–15) should soon be detected via the redshifted 21-cm line from neutral hydrogen, allowing us to indirectly study the properties of HMXBs in the unseen, first galaxies. Low-redshift observations, as well as theoretical models, imply that the integrated X-ray luminosity to star formation rate of HMXBs (L_X/SFR) should increase in metal-poor environments, typical of early galaxies. Here, we study the impact of the metallicity (Z) dependence of L_X/SFR during the EoH. For our fiducial models, galaxies with star formation rates of order 10^(−3)–10^(−1)M_⊙ yr^(−1) and metallicities of order 10^(−3) –10^(−2) Z_⊙ are the dominant contributors to the X-ray background (XRB) during this period. Different L_X/SFR–Z relations result in factors of ∼ 3 differences in these ranges, as well as in the mean IGM temperature and the large-scale 21-cm power, at a given redshift. We compute mock 21-cm observations adopting as a baseline a 1000 h integration with the upcoming Square Kilometer Array (SKA) for two different L_X/SFR–Z relations. We perform inference on these mock observations using the common simplification of a constant L_X/SFR, finding that constant L_X/SFR models can recover the IGM evolution of the more complicated L_X/SFR–Z simulations only during the EoH. At z < 10, where the typical galaxies are more polluted, constant L_X/SFR models overpredict the XRB and its relative contribution to the early stages of the reionization.

galaxies: high-redshift↗

NASA NTRS1971

Singular perturbation methods and the warm plasma model

The application of techniques of the singular perturbation theory to the analysis of warm plasma is discussed. Typically, the cold plasma model can be applied over wide ranges of parameters and only over narrow ranges forming so-called boundary layers is the warm plasma model used. Simplified equations can be used and the solutions matched on both sides of the layer's boundary. Simple examples to illustrate the solution are presented. The analysis confirms that some results are highly sensitive to the values of: (1) wire radius or gap size for an antenna, (2) temperature of the medium, and (3) incident angle of a plane wave.

Lee, S. W.↗

NASA NTRS1986

Impulsively generated fast coronal pulsations

Rapid oscillations in the corona are discussed from a theoretical standpoint, developing some previous work on ducted, fast magnetoacoustic waves in an inhomogeneous medium. In the theory, impulsively (e.g., flare) generated mhd (magnetohydrodynamic) waves are ducted by regions of low Alfven speed (high density) such as coronal loops. Wave propagation in such ducts is strongly dispersive and closely akin to the behavior of Love waves in seismology, Pekeris waves in oceanography and guided waves in fiber optics. Such flare-generated magnetoacoustic waves possess distinctive temporal signatures consisting of periodic, quasi-periodic and decay phases. The quasi-periodic phase possesses the strongest amplitudes and the shortest time scales. Time scales are typically of the order of a second for inhomogeneities (coronal loop width) of 1000 km and Alfven speeds of 1000/kms, and pulse duration times are of tens of seconds. Quasi-periodic signatures have been observed in radio wavelengths for over a decade and more recently by SMM. It is hoped that the theoretical ideas outlined may be successfully related to these observations and thus aid the interpretation of oscillatory signatures recorded by SMM. Such signatures may also provide a diagnostic of coronal conditions. New aspects of the ducted mhd waves, for example their behavior in smoothly varying as opposed to tube-like inhomogeneities, are currently under investigation. The theory is not restricted to loops but applied equally to open field regions.

Edwin, P. M.↗

NASA NTRS2013

Coherent Backscattering and Opposition Effects Observed in Some Atmosphereless Bodies of the Solar System

The results of photometric and polarimetric observations carried out for some bright atmosphere-less bodies of the Solar system near the zero phase angle reveal the simultaneous existence of two spectacular optical phenomena, the so-called brightness and polarization opposition effects. In a number of studies, these phenomena were explained by the influence of coherent backscattering. However, in general, the interference concept of coherent backscattering can be used only in the case where the particles are in the far-field zones of each other, i.e., when the scattering medium is rather rarefied. Because of this, it is important to prove rigorously and to demonstrate that the coherent backscattering effect may also exist in densely packed scattering media like regolith surface layers of celestial bodies. From the results of the computer modeling performed with the use of numerically exact solutions of the macroscopic Maxwell equations for discrete random media with different packing densities of particles, we studied the origin and evolution of all the opposition phenomena predicted by the coherent backscattering theory for low-packing-density media. It has been shown that the predictions of this theory remain valid for rather high-packing densities of particles that are typical, in particular, of regolith surfaces of the Solar system bodies. The results allow us to conclude that both opposition effects observed simultaneously in some high-albedo atmosphereless bodies of the Solar system are caused precisely by coherent backscattering of solar light in the regolith layers composed of microscopic particles.

Regolith↗