Static Structural Signatures of Nearly Jammed Disordered and Ordered Hard-Sphere Packings: Direct Correlation Function

Dynamical signatures are known to precede jamming in hard-particle systems, but static structural signatures have proven more elusive. The observation that compressing hard-particle packings towards jamming causes growing hyperuniformity has paved the way for the analysis of jamming as an "inverted critical point" in which the direct correlation function $c(r)$ diverges. We establish quantitative relationships between various singularities in $c(r)$ and the total correlation function $h(r)$ that provide a concrete means of identifying features that must be expressed in $c(r)$ if one hopes to reproduce details in the pair correlation function accurately. We also analyze systems of three-dimensional monodisperse hard-spheres of diameter $D$ as they approach ordered and disordered jammed configurations. For the latter, we use the Lubachevsky-Stillinger (LS) and Torquato-Jiao (TJ) packing algorithms, which both generate disordered packings, but can show perceptible structural differences. We identify a short-ranged scaling $c(r) \propto -1/r$ as $r \rightarrow 0$ and show that this, along with the developing delta function at $c(D)$, is a consequence of the growing long-rangedness in $c(r)$. Near the freezing density, we identify qualitative differences in the structure factor $S(k)$ as well as $c(r)$ between TJ- and LS-generated configurations and link them to differences in the protocols' packing dynamics. Configurations from both algorithms have structure factors that approach zero in the low-wavenumber limit as jamming is approached and are shown to exhibit a corresponding power-law decay in $c(r)$ for large $r$ as a consequence. Our work advances the notion that static signatures are exhibited by hard-particle packings as they approach jamming and underscores the utility of the direct correlation function as a means of monitoring for an incipient rigid network

Critical slowing down and hyperuniformity on approach to jamming

Hyperuniformity characterizes a state of matter that is poised at a critical point at which density or volume-fraction fluctuations are anomalously suppressed at infinite wavelengths. Recently, much attention has been given to the link between strict jamming and hyperuniformity in frictionless hard-particle packings. Doing so requires one to study very large packings, which can be difficult to jam properly. We modify the rigorous linear programming method of Donev et al. [J. Comp. Phys. 197, 139 (2004)] in order to test for jamming in putatively jammed packings of hard-disks in two dimensions. We find that various standard packing protocols struggle to reliably create packings that are jammed for even modest system sizes; importantly, these packings appear to be jammed by conventional tests. We present evidence that suggests that deviations from hyperuniformity in putative maximally random jammed (MRJ) packings can in part be explained by a shortcoming in generating exactly-jammed configurations due to a type of "critical slowing down" as the necessary rearrangements become difficult to realize by numerical protocols. Additionally, various protocols are able to produce packings exhibiting hyperuniformity to different extents, but this is because certain protocols are better able to approach exactly-jammed configurations. Nonetheless, while one should not generally expect exact hyperuniformity for disordered packings with rattlers, we find that when jamming is ensured, our packings are very nearly hyperuniform, and deviations from hyperuniformity correlate with an inability to ensure jamming, suggesting that strict jamming and hyperuniformity are indeed linked. This raises the possibility that the ideal MRJ packings have no rattlers. Our work provides the impetus for the development of packing algorithms that produce large disordered strictly jammed packings that are rattler-free.Comment: 15 pages, 11 figures. Accepted for publication in Phys. Rev.

Uncertainties in Atmospheric Muon-Neutrino Fluxes Arising from Cosmic-Ray Primaries

We present an updated calculation of the uncertainties on the atmospheric muon-neutrino flux arising from cosmic-ray primaries. For the first time, we include recent measurements of the cosmic-ray primaries collected since 2005. We apply a statistical technique that allows the determination of correlations between the parameters of the GSHL primary-flux parametrisation and the incorporation of these correlations into the uncertainty on the muon-neutrino flux. We obtain an uncertainty related to the primary cosmic rays of around $(5\text{--}15)\%$, depending on energy, which is about a factor of two smaller than the previously determined uncertainty. The hadron production uncertainty is added in quadrature to obtain the total uncertainty on the neutrino flux, which is reduced by $\approx 5\%$. To take into account an unexpected hardening of the spectrum of primaries above energies of $100$ $\text{GeV}$ observed in recent measurements, we propose an alternative parametrisation and discuss its impact on the neutrino flux uncertainties

Transition Probabilities in Generalized Quantum Search Hamiltonian Evolutions

A relevant problem in quantum computing concerns how fast a source state can be driven into a target state according to Schr\"odinger's quantum mechanical evolution specified by a suitable driving Hamiltonian. In this paper, we study in detail the computational aspects necessary to calculate the transition probability from a source state to a target state in a continuous time quantum search problem defined by a multi-parameter generalized time-independent Hamiltonian. In particular, quantifying the performance of a quantum search in terms of speed (minimum search time) and fidelity (maximum success probability), we consider a variety of special cases that emerge from the generalized Hamiltonian. In the context of optimal quantum search, we find it is possible to outperform, in terms of minimum search time, the well-known Farhi-Gutmann analog quantum search algorithm. In the context of nearly optimal quantum search, instead, we show it is possible to identify sub-optimal search algorithms capable of outperforming optimal search algorithms if only a sufficiently high success probability is sought. Finally, we briefly discuss the relevance of a tradeoff between speed and fidelity with emphasis on issues of both theoretical and practical importance to quantum information processing.Comment: 17 pages, 6 figures, 3 tables. Online ready in Int. J. Geometric Methods in Modern Physics (2020

Congenital muscular dystrophy, cardiomyopathy, and peripheral neuropathy due to merosin deficiency: Peripheral nerve histology of cauda equina

AbstractPeripheral neuropathy, white matter abnormalities, and cardiomyopathy are associated findings with merosin-deficient congenital muscular dystrophy. Although characterization of the neuropathy with nerve conduction studies has been well documented, limited research has been able to correlate histopathology with nerve biopsy in humans. Our understanding of the mechanism, described as a demyelinating neuropathy, is mainly derived from mouse model studies. We report a 23-year-old male who succumbed to respiratory failure and ultimately cardiac arrhythmia in the setting of an uncharacterized end stage progressive muscular disease complicated by cardiomyopathy and severe scoliosis. Autopsy revealed extensive muscular atrophy and replacement by fibroadipose tissue throughout the skeletal muscle and myocardium. Immunohistochemical analysis of the muscle biopsy showed a complete loss of merosin. Thus, the cause for both his muscular disease and demyelinating neuropathy was established with the diagnosis of merosin-deficient muscular dystrophy. Nerve biopsy obtained from the cauda equina showed clear evidence of segmental demyelination and remyelination, providing a better understanding of the proximal peripheral nerve histopathological changes in this disease entity

Superlensing properties of one-dimensional dielectric photonic crystals

We present the experimental observation of the superlensing effect in a slab of a one-dimensional photonic crystal made of tilted dielectric elements. We show that this flat lens can achieve subwavelength resolution in different frequency bands. We also demonstrate that the introduction of a proper corrugation on the lens surface can dramatically improve both the transmission and the resolution of the imaged signal.Comment: 9 pages, 9 figure

Miniaturized High-Speed Modulated X-Ray Source

A miniaturized high-speed modulated X-ray source (MXS) device and a method for rapidly and arbitrarily varying with time the output X-ray photon intensities and energies. The MXS device includes an ultraviolet emitter that emits ultraviolet light, a photocathode operably coupled to the ultraviolet light-emitting diode that emits electrons, an electron multiplier operably coupled to the photocathode that multiplies incident electrons, and an anode operably coupled to the electron multiplier that is configured to produce X-rays. The method for modulating MXS includes modulating an intensity of an ultraviolet emitter to emit ultraviolet light, generating electrons in response to the ultraviolet light, multiplying the electrons to become more electrons, and producing X-rays by an anode that includes a target material configured to produce X-rays in response to impact of the more electrons

Global Assimilation of Loon Stratospheric Balloon Observations

Project Loon has an overall goal of providing worldwide internet coverage using a network of long-durationsuper-pressure balloons. Since 2013, Loon has launched over 1600 balloons from multiple tropical and middlelatitude locations. These GPS tracked balloon trajectories provide lower stratospheric wind information overthe oceans and remote land areas where traditional radiosonde soundings are sparse, thus providing uniquecoverage of lower stratospheric winds. To fully investigate these Loon winds we: 1) compare the Loon windsto winds produced by a global data assimilation system (DAS: NASA GEOS) and 2) assimilate the Loon windsinto the same comprehensive DAS. Results show that in middle latitudes the Loon winds and DAS winds agreewell, and the Loon wind assimilation has only a minor impact on the forecasts. However, in the Tropics, thereis often a substantial difference between the assimilated winds and the observed Loon winds, of 8 m/s or morein magnitude. In these cases, assimilating the Loon winds significantly improves the meteorological analysesand subsequently the forecasts of the Loon winds. By highlighting cases where the Loon and DAS winds differ,these results can lead to improved understanding of stratospheric winds, especially in the tropics, as well asaiding analyses of the representation of dynamical forcing mechanisms in the GEOS model

Physical Optics Solution for the Scattering of a Partially-coherent Wave from a Statistically Rough Material Surface

The scattering of a partially-coherent wave from a statistically rough material surface is investigated via derivation of the scattered field cross-spectral density function. Two forms of the cross-spectral density are derived using the physical optics approximation. The first is applicable to smooth-to-moderately rough surfaces and is a complicated expression of source and surface parameters. Physical insight is gleaned from its analytical form and presented in this work. The second form of the cross-spectral density function is applicable to very rough surfaces and is remarkably physical. Its form is discussed at length and closed-form expressions are derived for the angular spectral degree of coherence and spectral density radii. Furthermore, it is found that, under certain circumstances, the cross-spectral density function maintains a Gaussian Schell-model form. This is consistent with published results applicable only in the paraxial regime. Lastly, the closed-form cross-spectral density functions derived here are rigorously validated with scatterometer measurements and full-wave electromagnetic and physical optics simulations. Good agreement is noted between the analytical predictions and the measured and simulated results. © 2013 Optical Society of Americ