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Routes to fractality and entropy in Liesegang systems

Liesegang bands are formed when solutions of co-precipitate ions interdiffuse in a 1D gel matrix. In a recent study [R. F. Sultan, Acta. Mech. Sin. 27, 119 (2011)], Liesegang patterns have been characterized as fractal structures. In addition to experimentally obtained patterns, geometric Liesegang patterns were constructed in conformity with the well-known empirical laws. Both mathematical fractal dimensions and box count dimensions for images of PbF{sub 2} and PbI{sub 2} Liesegang patterns have been calculated. Liesegang patterns can also be described by the entropy state function, and categorized as more or less ordered structures. We revisit the relation between entropy and fractal dimension, and apply it to simulated geometrical Liesegang patterns. We have resort to three different routes for the estimation of the entropy of a Liesegang pattern. The HarFA software enabled the calculation of the Hausdorff dimension and the topological entropy, then the information dimension and the Shannon entropy. In a third pathway, analytical calculations were carried out by estimating the probability of occurrence of a fractal element or coverage. The product of Shannon entropy and Boltzmann constant yields the thermodynamic entropy. The values for PbF{sub 2} and PbI{sub 2} Liesegang patterns attained the order of magnitude of the reported Third Law entropies, but yet remained lower, in conformity with the more ordered Liesegang structures.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Nonlinear susceptibilities for weakly turbulent magnetized plasma: Electrostatic approximation

The plasma weak turbulence theory is a perturbative nonlinear theory, which has been proven to be quite valid in a number of applications. However, the standard weak turbulence theory found in the literature is fully developed for highly idealized unmagnetized plasmas. As many plasmas found in nature and laboratory are immersed in a background static magnetic field, it is necessary to extend the existing discussions to include the effects of ambient magnetic field. Such a task is quite formidable, however, which has prevented fundamental and significant progresses in the subject matter. The central difficulty lies in the formulation of the complete nonlinear response functions for magnetized plasmas. The present paper derives the nonlinear susceptibilities for weakly turbulent magnetized plasmas up to the third order nonlinearity, but in doing so, a substantial reduction in mathematical complexity is achieved by the use of Bessel function addition theorem (or sum rule). The present paper also constructs the weak turbulence wave kinetic equation in a formal sense. For the sake of simplicity, however, the present paper assumes the electrostatic interaction among plasma particles. Fully electromagnetic generalization is a subject of a subsequent paper.

Physics↗

WISE TF: A MID-INFRARED, 3.4 {mu}m EXTENSION OF THE TULLY-FISHER RELATION USING WISE PHOTOMETRY

We present a mid-infrared Tully-Fisher (TF) relation using photometry from the 3.4 {mu}m W1 band of the Wide-field Infrared Survey Explorer (WISE) satellite. The WISE TF relation is formed from 568 galaxies taken from the all-sky 2MASS Tully-Fisher (2MTF) galaxy catalog, spanning a range of environments including field, group, and cluster galaxies. This constitutes the largest mid-infrared TF relation constructed to date. After applying a number of corrections to galaxy magnitudes and line widths, we measure a master TF relation given by M{sub corr} = -22.24 - 10.05[log (W{sub corr}) - 2.5], with an average dispersion of {sigma}{sub WISE} = 0.686 mag. There is some tension between WISE TF and a preliminary 3.6 {mu}m relation, which has a shallower slope and almost no intrinsic dispersion. However, our results agree well with a more recent relation constructed from a large sample of cluster galaxies. We additionally compare WISE TF to the near-infrared 2MTF template relations, finding a good agreement between the TF parameters and total dispersions of WISE TF and the 2MTF K-band template. This fact, coupled with typical galaxy colors of (K - W1) {approx} 0, suggests that these two bands are tracing similar stellar populations, including the older, centrally-located stars in the galactic bulge which can (for galaxies with a prominent bulge) dominate the light profile.

79 ASTRONOMY AND ASTROPHYSICS↗

Density functional theory based neural network force fields from energy decompositions

In order to develop force fields (FF) for molecular dynamics simulations that retain the accuracy of ab initio density functional theory (DFT), in this work we developed a machine learning protocol based on an energy decomposition scheme that extracts atomic energies from DFT calculations. Our DFT to FF (DFT2FF) approach provides almost hundreds of times more data for the DFT energies, which dramatically improves accuracy with less DFT calculations. In addition, we use piecewise cosine basis functions to systematically construct symmetry invariant features into the neural network model. We illustrate this DFT2FF approach for amorphous silicon where only 800 DFT configurations are sufficient to achieve an accuracy of 1 meV/atom for energy and 0.1 eV/A for forces. We then use the resulting FF model to calculate the thermal conductivity of amorphous Si based on long molecular dynamics simulations. The dramatic speedup in training in our DFT2FF protocol allows the adoption of a simulation paradigm where an accurate and problem specific FF for a given physics phenomenon is trained on-the-spot through a quick DFT precalculation and FF training.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Parallel Algorithms for Efficient Computation of High-Order Line Graphs of Hypergraphs

This paper considers structures of systems beyond dyadic (pairwise) interactions and investigates mathematical modeling of multi-way interactions and connections as hypergraphs, where captured relationships among system entities are set-valued. To date, in most situations, entities in a hypergraph are considered connected as long as there is at least one common ``neighbor''. However, minimal commonality sometimes discards the ``strength'' of connections and interactions among groups. To this end, considering the ``width'' of a connection, referred to as the \emph{$s$-overlap} of neighbors, provides more meaningful insights into how closely the communities or entities interact with each other. In addition, $s$-overlap computation is the fundamental kernel to construct the line graph of a hypergraph, a low-order approximation of the hypergraph which can carry significant information about the original hypergraph. Subsequent stages of a data analytics pipeline then can apply highly-tuned graph algorithms on the line graph to reveal important features. Given a hypergraph, computing the $s$-overlaps by exhaustively considering all pairwise entities can be computationally prohibitive. To tackle this challenge, we develop efficient algorithms to compute $s$-overlaps and the corresponding line graph of a hypergraph. We propose several heuristics to avoid execution of redundant work and improve performance of the $s$-overlap computation. Our parallel algorithm, combined with these heuristics, is orders of magnitude (more than $10\times$) faster than the naive algorithm in all cases and the SpGEMM algorithm with filtration in most cases (especially with large $s$ value).

hypergraph algorithms, graph algorithms, parallel ↗

Constructing Neural Network Based Models for Simulating Dynamical Systems

Dynamical systems see widespread use in natural sciences like physics, biology, and chemistry, as well as engineering disciplines such as circuit analysis, computational fluid dynamics, and control. For simple systems, the differential equations governing the dynamics can be derived by applying fundamental physical laws. However, for more complex systems, this approach becomes exceedingly difficult. Data-driven modeling is an alternative paradigm that seeks to learn an approximation of the dynamics of a system using observations of the true system. In recent years, there has been an increased interest in applying data-driven modeling techniques to solve a wide range of problems in physics and engineering. Here this article provides a survey of the different ways to construct models of dynamical systems using neural networks. In addition to the basic overview, we review the related literature and outline the most significant challenges from numerical simulations that this modeling paradigm must overcome. Based on the reviewed literature and identified challenges, we provide a discussion on promising research areas.

97 MATHEMATICS AND COMPUTING↗

U M subshell X-ray emission spectroscopy of uranium dioxide: the effect of excitation energy

There are very great differences between the non-resonant U M subshell X-ray Emission Spectra of Uranium Dioxide generated with low and high-energy excitation. Additionally, these different spectra are each supported by theoretical constructs. It will be shown that the differences between these experimental spectra can be reconciled and the utility of both theoretical approaches confirmed, including the use of FEFF in the low energy and high-energy regimes.

36 MATERIALS SCIENCE↗

Prethermalization in coupled one-dimensional quantum gases

We consider the problem of the development of steady states in one-dimensional Bose gas tubes that are weakly coupled to one another through a density-density interaction. We analyze this development through a Boltzmann collision integral approach. We argue that when the leading order of the collision integral, where single particle-hole excitations are created in individual gases, is dominant, the state of the gas evolves first to a non-thermal fixed point, i.e. a prethermalization plateau. This order is dominant when a pair of tubes are inequivalent with, say, different temperatures or different effective interaction parameters, \gamma γ . When both tubes are in the strongly interacting regime we additionally characterize this non-thermal prethermalization plateau by constructing the quasi-conserved quantities that control the existence of this plateau as well as the associated generalized Gibbs ensemble.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

University of Arizona High Energy Physics Program

The High Energy Physics Group at the University of Arizona has conducted forefront research in elementary particle physics. Our theorists have developed new ideas in lattice QCD, SUSY phenomenology, string theory phenomenology, extra spatial dimensions, dark matter, and neutrino astrophysics. The experimentalists produced significant physics results on the ATLAS experiment at CERN's Large Hadron Collider and on the D0 experiment at the Fermilab Tevatron. In addition, the experimentalists were leaders in detector development and construction, and on service roles in these experiments.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Microgrid Preliminary Design Specification

The following document provides guidance for developing a microgrid preliminary design specification. Development of a microgrid preliminary design specification takes previous analysis has been done in coordination with key stakeholders to scope out and perform analysis on a microgrid conceptual design to be further developed into a preliminary design. The microgrid preliminary design specification outlines the functional requirements and recommendations for the preliminary design that can be put into request for information (RFI) or request for quote (RFQ) process in order to select a microgrid integrator to oversee the final design and construction process of the microgrid to be implemented. In addition to requirements, the RFI/RFQ needs to specify of the responsibilities of the microgrid integrator as well as the microgrid owner/operator of the completed microgrid as part of the microgrid preliminary design specification as well as procurement process to evaluate the bidders applying to be the microgrid integrators.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Finding Electronic Structure Machine Learning Surrogates without Training

A myriad of phenomena in materials science and chemistry rely on quantum-level simulations of the electronic structure in matter. While moving to larger length and time scales has been a pressing issue for decades, such large-scale electronic structure calculations are still challenging despite modern software approaches and advances in high-performance computing. The silver lining in this regard is the use of machine learning to accelerate electronic structure calculations – this line of research has recently gained growing attention. The grand challenge therein is finding a suitable machine-learning model during a process called hyperparameter optimization. This, however, causes a massive computational overhead in addition to that of data generation. We accelerate the construction of machine-learning surrogate models by roughly two orders of magnitude by circumventing excessive training during the hyperparameter optimization phase. We demonstrate our workflow for Kohn-Sham density functional theory, the most popular computational method in materials science and chemistry.

36 MATERIALS SCIENCE↗

Japanese Legacy Cohorts: The Life Span Study Atomic Bomb Survivor Cohort and Survivors’ Offspring

Cohorts of atomic bomb survivors—including those exposed in utero —and children conceived after parental exposure were established to investigate late health effects of atomic bomb radiation and its transgenerational effects by the Atomic Bomb Casualty Commission (ABCC) in the 1950s. ABCC was reorganized to the Radiation Effects Research Foundation (RERF) in 1975, and all work has been continued at RERF. The Life Span Study, the cohort of survivors, consists of about 120,000 subjects and has been followed since 1950. Cohorts of in utero survivors and the survivors’ children include about 3,600 and 77,000 subjects, respectively, and have been followed since 1945. Atomic bomb radiation dose was estimated for each subject based on location at the time of the bombing and shielding conditions from exposure, which were obtained through enormous efforts of investigators and cooperation of subjects. Outcomes include vital status, cause of death, and cancer incidence. In addition, sub-cohorts of these three cohorts were constructed to examine clinical features of late health effects, and the subjects have been invited to periodic health examinations at clinics of ABCC and RERF. They were also asked to donate biosamples for biomedical investigations. Epidemiological studies have observed increased radiation risks for malignant diseases among survivors, including those exposed in utero , and possible risks for some non-cancer diseases. In children of survivors, no increased risks due to parental exposure to radiation have been observed for malignancies or other diseases, but investigations are continuing, as these cohorts are still relatively young.

63 RADIATION, THERMAL, AND OTHER ENVIRON. POLLUTAN↗

INTERFERENCE OF THE RUNNING WAVES AT LIGHT BRIDGES OF A SUNSPOT

The observations of chromospheric oscillations of two umbral light bridges (LBs) within a sunspot from NOAA Active Region 12127 are presented. It was found that the running umbral waves with periods of 2.2–2.6 minutes underwent very fast damping before approaching umbral boundaries, while those with higher periods (>2.6 minutes) could propagate outside umbrae. On two sides of each LB adjacent to umbrae, the cross-wavelet spectra displayed that the oscillations on them had a common significant power region with dominant frequencies of 2–6 minutes and phase differences of ∼90°. A counterstream of two running umbral waves in the 2–6 minute frequency range propagated toward the LBs, where they encountered each other and gave rise to constructive or even destructive interference on the LBs. In addition, the velocity and density perturbations on the LBs were found in opposite phases suggesting that the perturbations were caused by the downward propagating waves.

79 ASTRONOMY AND ASTROPHYSICS↗

A design of an all digital FM discriminator.

This paper describes the design of an all digital FM discriminator. The system can be easily constructed using ordinary commercially available, digital IC's. In addition, the output SNR above threshold is computed. It is shown that the output noise consists of two terms: the first being the expected output gaussian noise having a parabolic power spectral density and the second being a quantization noise produced by the finite-level detection process used in the receiver.

Garodnick, J.↗

Preliminary study of the reliability of imaging charge coupled devices

Imaging CCDs are capable of low light level response and high signal-to-noise ratios. In space applications they offer the user the ability to achieve extremely high resolution imaging with minimum circuitry in the photo sensor array. This work relates the CCD121H Fairchild device to the fundamentals of CCDs and the representative technologies. Several failure modes are described, construction is analyzed and test results are reported. In addition, the relationship of the device reliability to packaging principles is analyzed and test data presented. Finally, a test program is defined for more general reliability evaluation of CCDs.

Beall, J. R.↗

Investigation of fuselage acoustic treatment for a twin-engine turboprop aircraft in flight and laboratory tests

A flight and laboratory study of sidewall acoustic treatment for cabin noise control is described. In flight, cabin noise levels were measured at six locations with three treatment configurations. Noise levels from narrow-band analysis are reduced to one-third octave format and used to calculate insertion loss, IL, defined as the reduction of interior noise associated with the addition of a treatment. Laboratory tests used a specially constructed structural panel modeled after the propeller plane section of the aircraft sidewall, and acoustic treatments representing those used in flight. Lab measured transmission loss and absorption values were combined using classical acoustic procedures to obtain a prediction of IL. Comparison with IL values measured in flight for the boundary layer component of the noise indicated general agreement.

Mixson, J. S.↗

Space Shuttle mission extension capability

Space Shuttle missions are currently limited to 11 days, primarily due to depletion of the power reactants (hydrogen and oxygen). A power system Mission Extension Kit (MEK) is described which could provide the capability to stay on orbit 10 additional days. These extra days would benefit Space Station construction and missions such as materials processing, earth and celestial observation, and life science studies (Spacelab). Other constraints to longer missions which may dictate minor Orbiter modifications will be discussed. The power system MEK is particularly desirable because of its existing flight qualified hardware which can be delivered within 3 to 4 years.

Fraser, W. M., Jr.↗

Procedural knowledge

Much of commonsense knowledge about the real world is in the form of procedures or sequences of actions for achieving particular goals. In this paper, a formalism is presented for representing such knowledge using the notion of process. A declarative semantics for the representation is given, which allows a user to state facts about the effects of doing things in the problem domain of interest. An operational semantics is also provided, which shows how this knowledge can be used to achieve particular goals or to form intentions regarding their achievement. Given both semantics, the formalism additionally serves as an executable specification language suitable for constructing complex systems. A system based on this formalism is described, and examples involving control of an autonomous robot and fault diagnosis for NASA's Space Shuttle are provided.

Georgeff, Michael P.↗