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At least 235 records · Page 13

Strong Hilbert space fragmentation and fractons from subsystem and higher-form symmetries

Here, we introduce a route to Hilbert space fragmentation in high dimensions leveraging the group-word formalism. We show that taking strongly fragmented models in one dimension and “lifting” to higher dimensions using subsystem symmetries can yield strongly fragmented dynamics in higher dimensions, with subdimensional (e.g., lineonic) excitations. This provides a route to higher-dimensional strong fragmentation, and also a route to fractonic behavior. Meanwhile, lifting one-dimensional fragmented models to higher dimensions using higher-form symmetries yields models with topologically robust fragmentation. In three or more spatial dimensions, one can also “mix and match” subsystem and higher-form symmetries, leading to canonical fracton models such as X cube. We speculate that this approach could also yield a route to non-Abelian fractons. These constructions unify a number of phenomena that have been discussed in the literature, as well as furnishing models with unique properties.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Phase segregation mechanisms of small molecule-polymer blends unraveled by varying polymer chain architecture

As phase separation between the small-molecule semiconductor and the polymer binder is the key enabler of blend-based organic field-effect transistors (OFETs) fabricated by low-cost solution processing, it is crucial to understand the underlying phase separation mechanisms that determine the phase morphology, which significantly impacts device performance. Beyond the parameter space investigated in previous work, here we investigate the formation of blends by varying the branch architecture of the polymer binder and by shortening the solvent dry time using ultrasonic spray casting. The phase morphologies of the resulting blend films have been thoroughly characterized with a variety of techniques in three dimensions over multiple length scales, including AFM, energy-filtered transmission electron microscope, and neutron reflectivity, and have been correlated with electrical transport performance. From the results, we have inferred that the phase morphology is kinetically determined, limited by the inherent slow movement of polymer macromolecules. The kinetic picture, supported by molecular dynamics modeling, not only consistently explains our observations but also resolves inconsistencies in previous works. The achieved mechanistic understanding will guide further optimization of blend-based organic electronics, such as OFETs and organic photovoltaics.

36 MATERIALS SCIENCE↗

The Applicability of Nonlinear Systems Dynamics Chaos Measures to Cardiovascular Physiology Variables

Three measures of nonlinear chaos (fractal dimension, Approximate Entropy (ApEn), and Lyapunov exponents) were studied as potential measures of cardiovascular condition. It is suggested that these measures have potential in the assessment of cardiovascular condition in environments of normal cardiovascular stress (normal gravity on the Earth surface), cardiovascular deconditioning (microgravity of space), and increased cardiovascular stress (lower body negative pressure (LBNP) treatments).

Hooker, John C.↗

A hybrid multigrid technique for computing steady-state solutions to supersonic flows

Recently, Li and Sanders have introduced a class of finite difference schemes to approximate generally discontinuous solutions to hyperbolic systems of conservation laws. These equations have the form together with relevant boundary conditions. When modelling hypersonic spacecraft reentry, the differential equations above are frequently given by the compressible Euler equations coupled with a nonequilibrium chemistry model. For these applications, steady state solutions are often sought. Many tens (to hundreds) of super computer hours can be devoted to a single three space dimensional simulation. The primary difficulty is the inability to rapidly and reliably capture the steady state. In these notes, we demonstrate that a particular variant from the schemes presented can be combined with a particular multigrid approach to capture steady state solutions to the compressible Euler equations in one space dimension. We show that the rate of convergence to steady state coming from this multigrid implementation is vastly superior to the traditional approach of artificial time relaxation. Moreover, we demonstrate virtual grid independence. That is, the rate of convergence does not depend on the degree of spatial grid refinement.

Sanders, Richard↗

Advanced transportation system studies technical area 3: Alternate propulsion subsystem concepts, volume 3

The objective of this contract was to provide definition of alternate propulsion systems for both earth-to-orbit (ETO) and in-space vehicles (upper stages and space transfer vehicles). For such propulsion systems, technical data to describe performance, weight, dimensions, etc. was provided along with programmatic information such as cost, schedule, needed facilities, etc. Advanced technology and advanced development needs were determined and provided. This volume separately presents the various program cost estimates that were generated under three tasks: the F-1A Restart Task, the J-2S Restart Task, and the SSME Upper Stage Use Task. The conclusions, technical results, and the program cost estimates are described in more detail in Volume 1 - Executive Summary and in individual Final Task Reports.

Levak, Daniel↗

Advanced Transportation System Studies. Technical Area 3: Alternate Propulsion Subsystems Concepts: Program Cost Estimates - Volume 3

The objective of this contract was to provide definition of alternate propulsion systems for both earth-to-orbit (ETO) and in-space vehicles (upper stages and space transfer vehicles). For such propulsion systems, technical data to describe performance, weight, dimensions, etc. was provided along with programmatic information such as cost, schedule, needed facilities, etc. Advanced technology and advanced development needs were determined and provided. This volume separately presents the various program cost estimates that were generated under three tasks: the F- IA Restart Task, the J-2S Restart Task, and the SSME Upper Stage Use Task. The conclusions, technical results , and the program cost estimates are described in more detail in Volume I - Executive Summary and in individual Final Task Reports.

Levack, Daniel J. H.↗

Drop Size Distribution Measurements Supporting the NASA Global Precipitation Measurement Mission: Infrastructure and Preliminary Results

Global Precipitation Measurement Mission (GPM) retrieval algorithm validation requires datasets that characterize the 4-D structure, variability, and correlation properties of hydrometeor particle size distributions (PSD) and accumulations over satellite fields of view (5 -- 50 km). Key to this process is the combined use of disdrometer and polarimetric radar platforms. Here the disdrometer measurements serve as a reference for up-scaling dual-polarimetric radar observations of the PSD to the much larger volumetric sampling domain of the radar. The PSD observations thus derived provide a much larger data set for assessing DSD variability, and satellite-based precipitation retrieval algorithm assumptions, in all three spatial dimensions for a range of storm types and seasons. As one component of this effort, the GPM Ground Validation program recently acquired five 3rd generation 2D Video disdrometers as part of its Disdrometer and Radar Observations of Precipitation Facility (DROP), currently hosted in northern Alabama by the NASA Marshall Space Flight Center and the University of Alabama in Huntsville. These next-generation 2DVDs were operated and evaluated in different phases of data collection under the scanning domain of the UAH ARMOR C-band dual-polarimetric radar. During this period approximately 7500 minutes of PSD data were collected and processed to create gamma size distribution parameters using a truncated method of moments approach. After creating the gamma parameter datasets the DSDs were then used as input to T-matrix code for computation of polarimetric radar moments at C-band. The combined dataset was then analyzed with two basic objectives in mind: 1) the investigation of seasonal variability in the rain PSD parameters as observed by the 2DVDs; 2) the use of combined polarimetric moments and observed gamma distribution parameters in a functional form to retrieve PSD parameters in 4-D using the ARMOR radar for precipitation occurring in different seasons and for different rain system types. Preliminary results suggest that seasonal variations in the DSD parameters do occur, but are most pronounced when comparing tropical PSDs to either winter or summer convective precipitation. For example the previously documented shift to relatively smaller drop diameters in higher number concentrations for equivalent rain rate bins was observed in tropical storm rainbands occurring over Huntsville. On a more inter seasonal basis empirical fits between parameters such as D0 and ZDR do not appear to exhibit robust seasonal biases- i.e., one fit seems to work for all seasons within acceptable standard error (O[10%]) for estimates of D0. In polarimetric retrievals of the vertical variability in PSD (rain layer) for a tropical rainband we find that the Do varies with height when partitioned by specified precipitation categories (e.g., convective or stratiform, heavy and light stratiform etc.) but this variation is of order 10-20% and is smaller than the difference in D0 observed between the basic delineation of convective and stratiform precipitation types. Currently we are expanding our analysis of the vertical structure of the PSD to include several seasonally and/or dynamically-different storm system types (e.g., winter convection and stratiform events; summer mid-latitude convective etc.) sampled by ARMOR. The study will present the results of our combined analyses.

Petersen, Walter A.↗

Indications of low dimensionality in magnetospheric dynamics

Using three separate but related approaches, the question of whether the dynamic response of the magnetosphere to the solar wind input may be described by a low-order system of equations is examined. First, it is determined that the dimension of the subset (the attractor) in the high-dimensional magnetospheric phase space associated with the westward auroral electrojet (AL) index for some of the data sets compiled by Bargatze et al. (1985) is 4.0 + or - 0.2, seemingly independent of activity level. Second, direct modeling of the magnetosphere, considering the bulk properties of the tail plasma, leads to a system of equations that is similar to those previously reported as a dripping faucet model; here, the focus is specifically on the prediction of a natural frequency in this model. Finally, a peak is identified with the predicted frequency in power spectra of AL computed for intervals with both low and high activity. Peaks at other frequencies also appear in the spectra, and such resonances would be expected for a chaotic nonlinear oscillator. Combining these approaches it is concluded that at least some aspects of magnetospheric dynamics may be meaningfully modeled by low-dimensional sets of equations.

Roberts, D. A.↗

Lower Hybrid Solitary Structures

Lower hybrid solitary structures (LHSS) have been observed by sounding rockets in the auroral ionosphere for over a decade and a half. LHSS are spatial structures embedded in space plasmas containing ambient whistler mode hiss. They are characterized by a density depletion of a few percent to several tens of percent in which electric fields near, both above and below, the lower hybrid resonance are more intense than the background fields by a factor of three to five. LHSS have dimensions across the magnetic field of a few to many thermal ion gyroradii, usually 10-100 meters and a density profile that is Gaussian and consistent with cylindrical symmetry. Along the magnetic field the dimensions are estimated to be several kilometers to several hundred kilometers. Electric field interferometry reveals that the phase fronts of LHSS electric fields rotate azimuthally within the density depletions; right-hand above the lower hybrid resonance and left-hand below the lower hybrid resonance [Pincon et al., 1997; Schuck et al., 1998; Bonnell et al., 1998; Tjulin et al., 2003; Schuck et al., 2003]. The description of this phenomena was driven by the observations the Cornell University sounding rocket program headed by the late Paul Kintner.

Schuck, Peter W.↗

A study of Space Shuttle approach and landing navigation with conventional navaids

Four candidate navigation systems for the Space Shuttle Orbiter approach and landing phase are evaluated in detail. These include three conventional navaid systems and a single-station one-way Doppler system. In each case a Kalman filter is assumed to be mechanized in the onboard computer, blending the navaid data with IMU and altimeter data. Filter state dimensions ranging from 6 to 24 are involved in the candidate systems. Comprehensive truth models with state dimensions ranging from 63 to 82 are formulated and used to generate detailed performance projections. The detailed results are summarized, compared, and interpreted, the filter designs are reviewed, and suggestions are made concerning possible software improvements.

Crawford, B. S.↗

Space shuttle post-entry and landing analysis. Volume 2: Appendices

Four candidate navigation systems for the space shuttle orbiter approach and landing phase are evaluated in detail. These include three conventional navaid systems and a single-station one-way Doppler system. In each case, a Kalman filter is assumed to be mechanized in the onboard computer, blending the navaid data with IMU and altimeter data. Filter state dimensions ranging from 6 to 24 are involved in the candidate systems. Comprehensive truth models with state dimensions ranging from 63 to 82 are formulated and used to generate detailed error budgets and sensitivity curves illustrating the effect of variations in the size of individual error sources on touchdown accuracy. The projected overall performance of each system is shown in the form of time histories of position and velocity error components.

Crawford, B. S.↗

Path Toward a Unifid Geometry for Radiation Transport

The Direct Accelerated Geometry for Radiation Analysis and Design (DAGRAD) element of the RadWorks Project under Advanced Exploration Systems (AES) within the Space Technology Mission Directorate (STMD) of NASA will enable new designs and concepts of operation for radiation risk assessment, mitigation and protection. This element is designed to produce a solution that will allow NASA to calculate the transport of space radiation through complex computer-aided design (CAD) models using the state-of-the-art analytic and Monte Carlo radiation transport codes. Due to the inherent hazard of astronaut and spacecraft exposure to ionizing radiation in low-Earth orbit (LEO) or in deep space, risk analyses must be performed for all crew vehicles and habitats. Incorporating these analyses into the design process can minimize the mass needed solely for radiation protection. Transport of the radiation fields as they pass through shielding and body materials can be simulated using Monte Carlo techniques or described by the Boltzmann equation, which is obtained by balancing changes in particle fluxes as they traverse a small volume of material with the gains and losses caused by atomic and nuclear collisions. Deterministic codes that solve the Boltzmann transport equation, such as HZETRN [high charge and energy transport code developed by NASA Langley Research Center (LaRC)], are generally computationally faster than Monte Carlo codes such as FLUKA, GEANT4, MCNP(X) or PHITS; however, they are currently limited to transport in one dimension, which poorly represents the secondary light ion and neutron radiation fields. NASA currently uses HZETRN space radiation transport software, both because it is computationally efficient and because proven methods have been developed for using this software to analyze complex geometries. Although Monte Carlo codes describe the relevant physics in a fully three-dimensional manner, their computational costs have thus far prevented their widespread use for analysis of complex CAD models, leading to the creation and maintenance of toolkit-specific simplistic geometry models. The work presented here builds on the Direct Accelerated Geometry Monte Carlo (DAGMC) toolkit developed for use with the Monte Carlo N-Particle (MCNP) transport code. The workflow for achieving radiation transport on CAD models using MCNP and FLUKA has been demonstrated and the results of analyses on realistic spacecraft/habitats will be presented. Future work is planned that will further automate this process and enable the use of multiple radiation transport codes on identical geometry models imported from CAD. This effort will enhance the modeling tools used by NASA to accurately evaluate the astronaut space radiation risk and accurately determine the protection provided by as-designed exploration mission vehicles and habitats

Lee, Kerry↗

Free stream capturing in fluid conservation law for moving coordinates in three dimensions

The free-stream capturing technique for both the finite-volume (FV) and finite-difference (FD) framework is summarized. For an arbitrary motion of the grid, the FV analysis shows that volumes swept by all six surfaces of the cell have to be computed correctly. This means that the free-stream capturing time-metric terms should be calculated not only from a surface vector of a cell at a single time level, but also from a volume swept by the cell surface in space and time. The FV free-stream capturing formulation is applicable to the FD formulation by proper translation from an FV cell to an FD mesh.

Obayashi, Shigeru↗

A fast Fourier transform-based solver for elastic micropolar composites

This work presents a spectral micromechanical formulation for obtaining the full-field and homogenized response of elastic micropolar composites. The algorithm relies on a coupled set of convolution integral equations for the micropolar strains, where periodic Green’s operators associated with a linear homogeneous reference medium are convolved with functions of the Cauchy and couple stress fields that encode the material’s heterogeneity, as well as any potential material nonlinearity. Such convolution integral equations take an algebraic form in the reciprocal Fourier space that can be solved iteratively. In this vein, the fast Fourier transform (FFT) algorithm is leveraged to accelerate the numerical solution, resulting in a mesh-free formulation in which the periodic unit cell representing the heterogeneous material can be discretized by a regular grid of pixels in two dimensions (or voxels in three dimensions). For verification, the numerical solutions obtained with the micropolar FFT solver are compared with analytical solutions for a matrix with a dilute circular inclusion subjected to plane strain loading. The developed computational framework is then used to study length-scale effects and effective (micropolar) moduli of composites with various topological configurations.

97 MATHEMATICS AND COMPUTING↗

Analysis of differences between seating positions in simulators and orbiters

Crew comments indicate that Space Shuttle simulator seats place crewmembers in a position different from that of the actual Orbiter seats. The crew feel that they launch in a different position, and with a different reach and visibility, from that in which they had trained. This study examined three factors in differences between training and flight positions. Key dimensions, which were considered important to spatial orientation, were compared in the Orbiters and simulators. These were dimensions such as seat back to glare shield and seat pan to overhead. The differences between flight and training crew equipment, and how these differences may contribute to the problem were discussed with engineers and technicians responsible for the equipment. Eye position measurements were taken on subjects to assess any differences that could be attributed to different ingress methods in the Orbiters and the simulators. This report presents the data, analysis, and recommendations.

Mongan, Philip T.↗

Analytic soliton solutions of nonlinear extensions of the Schrödinger equation

A method is presented to construct analytic solitary wave solutions in nonlinear extensions of the Schrödinger equation starting from analytic solutions of the ordinary Schrödinger equation. We provide several examples illustrating the method. We rederive three well-known soliton solutions including the N-dimensional non-relativistic Gausson as well as the one-dimensional 1 / cosh-soliton and a theory with a power-like nonlinearity proportional to |ψ| 2λ with λ > 0. We also find several new solutions in different nonlinear theories in various space dimensions which, to the best of our knowledge, have not yet been discussed in literature. Our method can be used to construct further nonlinear theories and generalized to relativistic soliton theories, and may have many applications.

Analytical soliton solutions↗

Universal L - 3 finite-size effects in the viscoelasticity of amorphous systems

We present a theory of viscoelasticity of amorphous media, which takes into account the effects of confinement along one of three spatial dimensions. The framework is based on the nonaffine extension of lattice dynamics to amorphous systems, or nonaffine response theory. The size effects due to the confinement are taken into account via the nonaffine part of the shear storage modulus G'. The nonaffine contribution is written as a sum over modes in k-space. With a rigorous argument based on the analysis of the k-space integral over modes, it is shown that the confinement size L in one spatial dimension, e.g., the z axis, leads to a infrared cutoff for the modes contributing to the nonaffine (softening) correction to the modulus that scales as L -3 . Corrections for finite sample size D in the two perpendicular dimensions scale as ~(L/D) 4 , and are negligible for L«D. For liquids it is predicted that G'~L -3 is in agreement with a previous more approximate analysis, whereas for amorphous materials G'~G' bulk +βL -3 . For the case of liquids, four different experimental systems are shown to be very well described by the L-3 law. The theory can also explain previous simulation data of confined jammed granular packings.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Experimental investigation of the relationship between impact crater morphology and impacting particle velocity and direction

Interpretation of the wealth of impact data available from the Long Duration Exposure Facility, in terms of the absolute and relative populations of space debris and natural micrometeoroids, requires three dimensional models of the distribution of impact directions, velocities and masses of such particles, as well as understanding of the impact processes. Although the stabilized orbit of LDEF provides limited directional information, it is possible to determine more accurate impact directions from detailed crater morphology. The applicability of this technique has already been demonstrated but the relationship between crater shape and impactor direction and velocity has not been derived in detail. We present the results of impact experiments and simulations: (1) impacts at micron dimensions using the Unit's 2MV Van de Graaff accelerator; (2) impacts at mm dimensions using a Light Gas Gun; and (3) computer simulations using AUTODYN-3D from which an empirical relationship between crater shape and impactor velocity, direction and particle properties we aim to derive. Such a relationship can be applied to any surface exposed to space debris or micrometeoroid particles for which a detailed pointing history is available.

Mackay, N. G.↗