4,889 research outputs found
Light-cone coordinates based at a geodesic world line
Continuing work initiated in an earlier publication [Phys. Rev. D 69, 084007
(2004)], we construct a system of light-cone coordinates based at a geodesic
world line of an arbitrary curved spacetime. The construction involves (i) an
advanced-time or a retarded-time coordinate that labels past or future light
cones centered on the world line, (ii) a radial coordinate that is an affine
parameter on the null generators of these light cones, and (iii) angular
coordinates that are constant on each generator. The spacetime metric is
calculated in the light-cone coordinates, and it is expressed as an expansion
in powers of the radial coordinate in terms of the irreducible components of
the Riemann tensor evaluated on the world line. The formalism is illustrated in
two simple applications, the first involving a comoving world line of a
spatially-flat cosmology, the other featuring an observer placed on the axis of
symmetry of Melvin's magnetic universe.Comment: 11 pages, 1 figur
The Angstrom Exponent and Bimodal Aerosol Size Distributions
Powerlaws have long been used to describe the spectral dependence of aerosol extinction, and the wavelength exponent of the aerosol extinction powerlaw is commonly referred to as the Angstrom exponent. The Angstrom exponent is often used as a qualitative indicator of aerosol particle size, with values greater than two indicating small particles associated with combustion byproducts, and values less than one indicating large particles like sea salt and dust. In this study, we investigate the relationship between the Angstrom exponent and the mode parameters of bimodal aerosol size distributions using Mie theory calculations and Aerosol Robotic Network (AERONET) retrievals. We find that Angstrom exponents based upon seven wavelengths (0.34, 0.38, 0.44, 0.5, 0.67, 0.87, and 1.02 micrometers) are sensitive to the volume fraction of aerosols with radii less then 0.6 micrometers, but not to the fine mode effective radius. The Angstrom exponent is also known to vary with wavelength, which is commonly referred to as curvature; we show how the spectral curvature can provide additional information about aerosol size distributions for intermediate values of the Angstrom exponent. Curvature also has a significant effect on the conclusions that can be drawn about two-wavelength Angstrom exponents; long wavelengths (0.67, 0.87 micrometers) are sensitive to fine mode volume fraction of aerosols but not fine mode effective radius, while short wavelengths (0.38, 0.44 micrometers) are sensitive to the fine mode effective radius but not the fine mode volume fraction
Periodic orbits of the ensemble of Sinai-Arnold cat maps and pseudorandom number generation
We propose methods for constructing high-quality pseudorandom number
generators (RNGs) based on an ensemble of hyperbolic automorphisms of the unit
two-dimensional torus (Sinai-Arnold map or cat map) while keeping a part of the
information hidden. The single cat map provides the random properties expected
from a good RNG and is hence an appropriate building block for an RNG, although
unnecessary correlations are always present in practice. We show that
introducing hidden variables and introducing rotation in the RNG output,
accompanied with the proper initialization, dramatically suppress these
correlations. We analyze the mechanisms of the single-cat-map correlations
analytically and show how to diminish them. We generalize the Percival-Vivaldi
theory in the case of the ensemble of maps, find the period of the proposed RNG
analytically, and also analyze its properties. We present efficient practical
realizations for the RNGs and check our predictions numerically. We also test
our RNGs using the known stringent batteries of statistical tests and find that
the statistical properties of our best generators are not worse than those of
other best modern generators.Comment: 18 pages, 3 figures, 9 table
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Defect Formation in EBM Parts Built in Horizontal Orientation
EBM built parts in a horizontal orientation, particularly with bottom curved surfaces, are prone
to variations in dimensional accuracy and defect formation. These defects likely occur due to the
nature of the supports utilized and the build strategy. To understand the effect of support
structures and scan direction on these defects, a series of cylindrical parts were built using
different diameters, support structures and scan strategies. The as-built samples were
mechanically tested and sample cross sections were analyzed. Pore formation and balling effects
were observed in the lower section of some samples. The study looks at the effects of supports,
geometry and scan strategy on the minimization of these defects and improving the dimensional
accuracy of horizontally built samples.Mechanical Engineerin
Understanding complex magnetic order in disordered cobalt hydroxides through analysis of the local structure
In many ostensibly crystalline materials, unit-cell-based descriptions do not
always capture the complete physics of the system due to disruption in
long-range order. In the series of cobalt hydroxides studied here,
Co(OH)(Cl)(HO), magnetic Bragg diffraction reveals a
fully compensated N\'eel state, yet the materials show significant and open
magnetization loops. A detailed analysis of the local structure defines the
aperiodic arrangement of cobalt coordination polyhedra. Representation of the
structure as a combination of distinct polyhedral motifs explains the existence
of locally uncompensated moments and provides a quantitative agreement with
bulk magnetic measurements and magnetic Bragg diffraction
Algorithmic fault tolerance using the Lanczos method
We consider the problem of algorithm-based fault tolerance, and make two major contributions. First, we show how very general sequences of polynomials can be used to generate the checksums, so as to reduce the chance of numerical overows. Second, we show how the Lanczos process can be applied in the error location and correction steps, so as to save on the amount of work and to facilitate actual hardware implementation
Optimal Quantum States for Image Sensing in Loss
We consider a general image sensing framework that includes many quantum
sensing problems by an appropriate choice of image set, prior probabilities,
and cost function. For any such problem, in the presence of loss and a signal
energy constraint, we show that a pure input state of light with the signal
modes in a mixture of number states minimizes the cost among all
ancilla-assisted parallel strategies. Lossy binary phase discrimination with a
peak photon number constraint and general lossless image sensing are considered
as examples.Comment: 6 pages, 3 figures. The supplementary material is provided as an
appendix. The content is the same as the published versio
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Proof of concept for an innovative pump fishway design to move fish upstream over dams
Reversing worldwide declines in freshwater fish while making sustainable use of water resources will require effective and economical fishways to restore fish migrations. Mitigation of barrier effects at dams and weirs is too often impeded by poor fishway performance and high costs, so that many fish migrations continue to be obstructed. Improved and less-costly designs are urgently needed. Our innovative pump fishway concept combines fish-behaviour insights, proved fishways techniques and aquaculture’s pumping methods for safe upstream transport of living fish. We ran a series of experimental trials using several scale-model fishway designs with young, hatchery-bred fish. Our horizontal-cylinder design successfully combined volitional-passage functions of existing fishways with non-volitional transport in a conduit carrying pumped water. Several key principles of fish behaviour in fishways led to design improvements: disturbed fish often seek refuge at depth; fishes’ escape reactions strongly motivate swimming into flows; and curved structures aid passage by reducing delays. Replicated trials finally produced an average of 98% successful passage, within brief cycling periods. The pump fishway concept offers potential for effective upstream fish passage at new and existing sites \u3e~2m high, with low construction and maintenance costs and highly adaptable operation in variable flow regimes. Development beyond the concept-trial phase is now a priority
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