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DOE OSTI2020

De Sitter diagrammar and the resummation of time

Light scalars in inflationary spacetimes suffer from logarithmic infrared divergences at every order in perturbation theory. This corresponds to the scalar field values in different Hubble patches undergoing a random walk of quantum fluctuations, leading to a simple toy “landscape” on superhorizon scales, in which we can explore questions relevant to eternal inflation. However, for a sufficiently long period of inflation, the infrared divergences appear to spoil computability. Some form of renormalization group approach is thus motivated to resum the log divergences of conformal time. Such a resummation may provide insight into De Sitter holography. We present here a novel diagrammatic analysis of these infrared divergences and their resummation. Basic graph theory observations and momen- tum power counting for the in-in propagators allow a simple and insightful determination of the leading-log contributions. One thus sees diagrammatically how the superhorizon sector consists of a semiclassical theory with quantum noise evolved by a first-order, interacting classical equation of motion. This rigorously leads to the “Stochastic Inflation” ansatz developed by Starobinsky to cure the scalar infrared pathology nonperturbatively. Our approach is a controlled approximation of the underlying quantum field theory and is systematically improvable.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2001

Gravitational Core-Mantle Coupling and the Acceleration of the Earth

Gravitational core-mantle coupling may be the cause of the observed variable acceleration of the Earth's rotation on the 1000 year timescale. The idea is that density inhomogeneities which randomly come and go in the liquid outer core gravitationally attract density inhomogeneities in the mantle and crust, torquing the mantle and changing its rotation state. The corresponding torque by the mantle on the core may also explain the westward drift of the magnetic field of 0.2 deg per year. Gravitational core-mantle coupling would stochastically affect the rate of change of the Earth's obliquity by just a few per cent. Its contribution to polar wander would only be about 0.5% the presently observed rate. Tidal friction is slowing down the rotation of the Earth, overwhelming a smaller positive acceleration from postglacial rebound. Coupling between the liquid outer core of the Earth and the mantle has long been a suspected reason for changes in the length-of-day. The present investigation focuses on the gravitational coupling between the density anomalies in the convecting liquid outer core and those in the mantle and crust as a possible cause for the observed nonsecular acceleration on the millenial timescale. The basic idea is as follows. There are density inhomogeneities caused by blobs circulating in the outer core like the blobs in a lava lamp; thus the outer core's gravitational field is not featureless. Moreover, these blobs will form and dissipate somewhat randomly. Thus there will be a time variability to the fields. These density inhomogeneities will gravitationally attract the density anomalies in the mantle.

Rubincam, David Parry↗

NASA NTRS2010

A Model for Backscattering from Quasi Periodic Corn Canopies at L-Band

In this study, a model for backscattering at L-band from a corn canopy is proposed. The canopy consists of a quasi-periodic distribution of stalks and a random distribution of leaves. The Distorted Born Approximation (DBA) is employed to calculate the single scattered return from the corn field. The new feature of the method is that the coherence of the stalks in the row direction is incorporated in the model in a systematic fashion. Since the wavelength is on the order of the distance between corn stalks in a row, grating lobe behavior is observed at certain azimuth angles of incidence. The results are compared with experimental values measured in Huntsville, Alabama in 1998. The mean field and the effective dielectric constant of the canopy are obtained by using the Foldy approximation. The stalks are placed in the effective medium in a two dimensional lattice to simulate the row structure of a corn field. In order to mimic a real corn field, a quasi-periodic stalk distribution is assumed where the stalks are given small random perturbations about their lattice locations. Corn leaves are also embedded in the effective medium and the backscattered field from the stalks and the leaves is computed. The backscattering coefficient is calculated and averaged over successive stalk position perturbations. It is assumed that soil erosion has smoothed the soil sufficiently so that it can be assumed flat. Corn field backscatter data was collected from cornfields during the Huntsville 98 experimental campaign held at Alabama A&M University Research Station, Huntsville, Alabama in 1998 using the NASA/GW truck mounted radar. Extensive ground truth data was collected. This included soil moisture measurements and corn plant architectural data to be used in the model. In particular, the distances between the stalks in a single row have been measured. The L-band radar backscatter data was collected for both H and V polarizations and for look angles of 15o and 45o over a two week period under varying soil moisture conditions. These measured backscattering values will be compared with the model backscattering values and a discussion of the results will be presented.

Lang, R.↗

DOE OSTI2021

Dynamics of a single polyampholyte chain

Polymers that feature both positive and negative charges along chains, known as polyampholytes, represent a class of materials that hold promise for a new generation of energy storage devices, the design of which will require knowledge of the underlying structure and dynamics. Here, we develop a theory based on the Rouse model for the dynamic structure factor of a single polyampholyte chain in the weak coupling regime (negligible intramolecular electrostatics) or subjected to weak external electric fields (governed by linear response). Neglecting effects of small ions, we find deviations in scaling from the classic Rouse theory and make predictions for scattering experiments performed on polyampholytes. We find that, under weak coupling with arbitrarily strong fields, the dynamics are highly dependent on the charge distribution and consequently look at two representative examples—random charge densities and periodic charge densities—with different scaling properties. Additionally, under weak fields, the dynamics are largely independent of charge distribution. Finally, we investigate the influence of hydrodynamic effects and the implications of including inertial effects in the model.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS2018

Intercomparison of Field Methods for Acquiring Ground Reflectance at Railroad Valley Playa for Spectral Calibration of Satellite Data

Ground reflectance was acquired at the Railroad Valley Playa calibration site in Nevada USA using different methods of collection. The data was collected near the time and date of Landsat 8 OLI and Sentinel-2 satellite overpasses so an inter-comparison could be made with the reflectance products to determine which method was more suitable for vicarious calibration. The field spectrometers and reference panels were characterized before the field campaign. A continuous acquisition method was compared to stop and measure collections. Both acquisition methods were collected along an 80 m east-west transect as well as for a series of north-south transects over an 80 x 320 m area, with the stop and measure method being performed at random sampling locations. The measurements were performed using two field spectrometers by three teams of two people to compare the repeatability. The aim of the field campaign was to determine the variability due to the operator and the method of collection.

Lau, Ian C.↗

NASA NTRS2018

Intercomparison of Field Methods for Acquiring Ground Reflectance at Railroad Valley Playa for Spectral Calibration of Satellite Data

Lau, Ian C.↗

NASA NTRS1992

Random-anisotropy Blume-Emery-Griffiths model

The results are described of studies of a random-anisotropy Blume-Emery-Griffiths spin-1 Ising model using mean-field theory, transfer-matrix calculations, and position-space renormalization-group calculations. The interplay between the quenched randomness of the anisotropy and the annealed disorder introduced by the spin-1 model leads to a rich phase diagram with a variety of phase transitions and reentrant behavior. The results may be relevant to the study of the phase separation of He-3 - He-4 mixtures in porous media in the vicinity of the superfluid transition.

Maritan, Amos↗

DOE OSTI2025

Stochastic Waveform Estimation at the Fundamental Quantum Limit

Although measuring the deterministic waveform of a weak classical force is a well-studied problem, estimating a random waveform, such as the spectral density of a stochastic signal field, is much less well understood despite it being a widespread task at the frontier of experimental physics. State-of-the-art precision sensors of random forces must account for the underlying quantum nature of the measurement but the optimal quantum protocol for interrogating such linear sensors is not known. We derive the fundamental precision limit: the extended-channel quantum Cramér-Rao bound. In the experimentally relevant regime in which losses dominate, we prove that non-Gaussian-state preparation and measurement are required to achieve this fundamental limit and we determine numerically the optimal non-Gaussian protocol. We discuss how this scheme could accelerate searches for signatures of quantum gravity, stochastic gravitational waves, and axionic dark matter.

Axions↗

DOE OSTI2024

Identifying Topological Defects in Lamellar Phases through Contour Analysis of Complex Wave Fields

Lamellar phases frequently contain structural imperfections that significantly affect their behaviors and properties. Our previous research successfully reconstructed real-space configurations of defective lamellar phases from diffuse scattering patterns, indicating the presence of phase vortices as a potential method for identifying topological defects disrupting the smectic ordering. Here, this report presents a mathematical framework using regularized wave fields to represent defective lamellar structures in real space. Phase singularities, resulting from the interference of random waves and indicating lamellar order disruption, are identified through a contour integral. These wave fields, derived from coherent scattering in reciprocal space, were validated via computational benchmarks analyzing small-angle neutron scattering data from AOT surfactant solutions, facilitating further statistical analysis of the defects. Our study highlights the potential to extract meaningful information about topological defects in lyotropic phases by inversely analyzing experimentally measured two-point static correlations. Our method allows for detailed structural analysis of various lyotropic phases, both particulate and nonparticulate, in their quiescent states and facilitates quantitative investigation of defects’ role in phase transitions. By integrating small-angle scattering, deep learning, and vortex tangle analysis, our comprehensive approach shows promise in addressing complex challenges in the structural analysis of soft matter systems.

36 MATERIALS SCIENCE↗

NASA NTRS1985

A multiple scattering theory for EM wave propagation in a dense random medium

For a dense medium of randomly distributed scatterers an integral formulation for the total coherent field has been developed. This formulation accounts for the multiple scattering of electromagnetic waves including both the twoand three-particle terms. It is shown that under the Markovian assumption the total coherent field and the effective field have the same effective wave number. As an illustration of this theory, the effective wave number and the extinction coefficient are derived in terms of the polarizability tensor and the pair distribution function for randomly distributed small spherical scatterers. It is found that the contribution of the three-particle term increases with the particle size, the volume fraction, the frequency and the permittivity of the particle. This increase is more significant with frequency and particle size than with other parameters.

Karam, M. A.↗

DOE OSTI2025

Geometric Delocalization in Two Dimensions

We demonstrate the existence of transient two-dimensional surfaces where a random-walking particle escapes to infinity in contrast to localization in standard flat two-dimensional space. We first prove that any rotationally symmetric two-dimensional membrane embedded in flat three-dimensional space cannot be transient. Then we formulate a criterion for the transience of a general asymmetric two-dimensional membrane. We use it to explicitly construct a class of transient two-dimensional manifolds with a nontrivial metric and height function but “zero average curvature,” which we dub “tablecloth manifolds.” The absence of the logarithmic infrared divergence of the Laplace-Beltrami operator in turn implies the absence of weak localization, nonexistence of bound states in shallow potentials, and breakdown of the Mermin-Wagner theorem and Kosterlitz-Thouless transition on the tablecloth manifolds, which may be realizable in both quantum simulators and corrugated two-dimensional materials.

Anderson localization↗

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↗

NASA NTRS1994

Interaction of the sonic boom with atmospheric turbulence

Theoretical research was carried out to study the effect of free-stream turbulence on sonic boom pressure fields. A new transonic small-disturbance model to analyze the interactions of random disturbances with a weak shock was developed. The model equation has an extended form of the classic small-disturbance equation for unsteady transonic aerodynamics. An alternative approach shows that the pressure field may be described by an equation that has an extended form of the classic nonlinear acoustics equation that describes the propagation of sound beams with narrow angular spectrum. The model shows that diffraction effects, nonlinear steepening effects, focusing and caustic effects and random induced vorticity fluctuations interact simultaneously to determine the development of the shock wave in space and time and the pressure field behind it. A finite-difference algorithm to solve the mixed type elliptic-hyperbolic flows around the shock wave was also developed. Numerical calculations of shock wave interactions with various deterministic and random fluctuations will be presented in a future report.

Rusak, Zvi↗

NASA NTRS1997

The Influence of Correlated Crustal Signals in Modelling the Main Geomagnetic Field

Algorithms used in geomagnetic main-field modelling have for the most part treated the noise in the field measurements as if it were white. A major component of the noise consists of the field due to magnetization in the crust and it has been realized for some time that such signals are highly correlated at satellite altitude. Hence approximation by white noise, while of undoubted utility, is of unknown validity. In this paper we study two plausible statistical models for the crustal magnetization, in which the magnetization is a realization of a stationary, isotropic, random process. At a typical satellite altitude the associated fields exhibit significant correlation over ranges as great as 15 deg. or more, which introduces off-diagonal elements into the covariance matrix, elements that have usually been neglected in modelling procedures. Dealing with a full covariance matrix for a large data set would present a formidable computational challenge, but fortunately most of the entries in the covariance matrix are so small that they can be replaced by zeros. The resultant matrix comprises only about 3 per cent non-zero entries and thus we can take advantage of efficient sparse matrix techniques to solve the numerical system. We construct several main-field models based on vertical-component data from a selected 5 deg. by 5 deg. data set derived from the Magsat mission. Models with and without off-diagonal terms are compared.

Rygaard-Hjalsted, C.↗

NASA NTRS1993

Interaction of the sonic boom with atmospheric turbulence

Theoretical research has been carried out to study the effect of free-stream turbulence on sonic boom pressure fields. A new transonic small-disturbance model to analyze the interactions of random disturbances with a weak shock has been developed. The model equation has an extended form of the classic small-disturbance equation for unsteady transonic aerodynamics. An alternative approach shows that the pressure field may be described by an equation that has an extended form of the classic nonlinear acoustics equation that describes the propagation of sound beams with narrow angular spectrum. The model shows that diffraction effects, nonlinear steepening effects, focusing and caustic effects and random induced vorticity fluctuations interact simultaneously to determine the development of the shock wave in space and time and the pressure field behind it. A finite-difference algorithm to solve the mixed-type elliptic-hyperbolic flows around the shock wave has also been developed. Numerical calculations of shock wave interactions with various deterministic and random fluctuations will be presented in a future report.

Rusak, Z.↗

NASA NTRS1974

Theoretical and observational analysis of spacecraft fields

In order to investigate the dipolar and nondipolar contributions of spacecraft magnetic fields, a simple magnetic field model is proposed. This model consists of a number N of randomly oriented dipoles of strength M sub k in a given volume. Two sets of formulas are presented that give the rms multipole field components, first, for isotropic orientations of the dipoles at given positions and second, for isotropic orientations of the dipoles distributed uniformly throughout a cube or sphere. The statistical results for a cube (8 cu m in size) together with individual examples computed numerically show the following features. Beyond about 2- to 3-m distance from the center of the cube the field is dominated by an equivalent dipole. The magnitude of the magnetic moment of the dipolar part is approximated by N to the 1/2 power times M for equal magnetic moments or generally by the Pythagorean sum of the dipole moments. The radial component tend to be greater than either of the transverse components for the dipole portion as well as for the nondipolar field contributions.

Neubauer, F. M.↗

NASA NTRS1984

Tortuosity of lightning return stroke channels

Data obtained from photographs of lightning are presented on the tortuosity of return stroke channels. The data were obtained by making piecewise linear fits to the channels, and recording the cartesian coordinates of the ends of each linear segment. The mean change between ends of the segments was nearly zero in the horizontal direction and was about eight meters in the vertical direction. Histograms of these changes are presented. These data were used to create model lightning channels and to predict the electric fields radiated during return strokes. This was done using a computer generated random walk in which linear segments were placed end-to-end to form a piecewise linear representation of the channel. The computer selected random numbers for the ends of the segments assuming a normal distribution with the measured statistics. Once the channels were simulated, the electric fields radiated during a return stroke were predicted using a transmission line model on each segment. It was found that realistic channels are obtained with this procedure, but only if the model includes two scales of tortuosity: fine scale irregularities corresponding to the local channel tortuosity which are superimposed on large scale horizontal drifts. The two scales of tortuosity are also necessary to obtain agreement between the electric fields computed mathematically from the simulated channels and the electric fields radiated from real return strokes. Without large scale drifts, the computed electric fields do not have the undulations characteristics of the data.

Levine, D. M.↗

DOE OSTI2020

Spin susceptibility, upper critical field, and disorder effect in $j = \frac{3}{2}$ superconductors with singlet–quintet mixing

Recently, a new pairing state with the mixing between the s-wave singlet channel and the isotropic d-wave quintet channel induced by centrosymmetric spin–orbit coupling has been theoretically proposed in the superconducting materials with $j = \frac{3}{2}$ electrons [J. Yu and C.-X. Liu, Phys. Rev. B 98, 104514 (2018)]. In this article, we derive the expressions of the zero-temperature spin susceptibility, the upper critical field close to the zero-field critical temperature T c , and the critical temperature with weak random non-magnetic disorders for the singlet–quintet mixed state based on the Luttinger model. Our study reveals the following features of the singlet–quintet mixing. (1) The zero-temperature spin susceptibility remains zero for the singlet–quintet mixed state if only the centrosymmetric spin–orbit coupling is taken into account and deviates from zero when the non-centrosymmetric spin–orbit coupling is introduced. (2) The singlet–quintet mixing can help enhance the upper critical field roughly because it can increase T c . (3) Although the quintet channel is generally suppressed by the non-magnetic disorder scattering, we find the strong mixing between singlet and quintet channels can help to stabilize the quintet channel. As a result, we still find a sizable quintet component mixed into the singlet channel in the presence of weak random non-magnetic disorders. Our work provides the guidance for future experiments on spin susceptibility and upper critical field of the singlet–quintet mixed superconducting states and illustrates the stability of the singlet–quintet mixing against the weak random non-magnetic disorder.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗