Geodesics in the Generalized Schwarzschild Solution

Since Schwarzshild discovered the point-mass solution to Einstein's equations that bears his name, many equivalent forms of the metric have been catalogued. Using an elementary coordinate transformation, we derive the most general form for the stationary, spherically-symmetric vacuum metric, which contains one free function. Different choices for the function correspond to common expressions for the line element. From the general metric, we obtain particle and photon trajectories, and use them to specify several time coordinates adapted to physical situations. The most general form of the metric is only slightly more complicated than the Schwarzschild form, which argues effectively for teaching the general line element in place of the diagonal metric.Comment: 7 pages, 1 figure; revised to reflect referee comments; submitted to Am. J. of Phy

Scattering, Damping, and Acoustic Oscillations: Simulating the Structure of Dark Matter Halos with Relativistic Force Carriers

We demonstrate that self-interacting dark matter models with interactions mediated by light particles can have significant deviations in the matter power-spectrum and detailed structure of galactic halos when compared to a standard cold dark matter scenario. While these deviations can take the form of suppression of small scale structure that are in some ways similar to that of warm dark matter, the self-interacting models have a much wider range of possible phenomenology. A long-range force in the dark matter can introduce multiple scales to the initial power spectrum, in the form of dark acoustic oscillations and an exponential cut-off in the power spectrum. Using simulations we show that the impact of these scales can remain observationally relevant up to the present day. Furthermore, the self-interaction can continue to modify the small-scale structure of the dark matter halos, reducing their central densities and creating a dark matter core. The resulting phenomenology is unique to this type of models.Comment: 23 pages, 11 figure

Testing the strength and direction of selection on vocal frequency using metabolic scaling theory

A major challenge for studies assessing drivers of phenotypic divergence is the statistical comparison of taxa with unique, often unknown, evolutionary histories, and for which there are no clear expected trait values. Because many traits are fundamentally constrained by energy availability, we suggest that trait values predicted by scaling theories such as the metabolic theory of ecology (MTE) can provide baseline expectations. Here, we introduce a metabolic scaling-based approach to test theory involving the direction and magnitude of ecological and sexual selection, using vocal frequency as an example target of selection. First, we demonstrate that MTE predicts the relationship between the natural log of body size and natural log of vocal frequency across 795 bird species, controlling for phylogeny. Family-wide deviations in slope and intercepts from MTE estimates reveal taxa with potentially important differences in physiology or natural history. Further, species-level frequency deviations from MTE expectations are predicted by factors related to ecological and sexual selection and, in some cases, provide evidence that differs from current understanding of the direction of selection and identity of ecological selective agents. For example, our approach lends additional support to the findings from many cross-habitat studies that suggest that dense vegetation selects for lower frequency signals. However, our analysis also suggests that birds in non-forested environments vocalize at frequencies higher than expected based on MTE, prompting intriguing questions about the selective forces in non-forest environments that may act on vocal frequency. Additionally, vocal frequency deviates more strongly from MTE expectations among species with smaller repertoires and those with low levels of sexual dichromatism, complicating the use of these common sexual selection surrogates. Broad application of our metabolic scaling approach might provide an important complementary approach to understanding how selection shapes phenotypic evolution by offering a common baseline across studies and taxa and providing the basis to explore evolutionary trade-offs within and among multicomponent and multimodal traits

Visuomotor Entrainment and the Frequency-Dependent Response of Walking Balance to Perturbations

Visuomotor entrainment, or the synchronization of motor responses to visual stimuli, is a naturally emergent phenomenon in human standing. Our purpose was to investigate the prevalence and resolution of visuomotor entrainment in walking and the frequency-dependent response of walking balance to perturbations. We used a virtual reality environment to manipulate optical flow in ten healthy young adults during treadmill walking. A motion capture system recorded trunk, sacrum, and heel marker trajectories during a series of 3-min conditions in which we perturbed a virtual hallway mediolaterally with systematic changes in the driving frequencies of perceived motion. We quantified visuomotor entrainment using spectral analyses and changes in balance control using trunk sway, gait variability, and detrended fluctuation analyses (DFA). ML kinematics were highly sensitive to visual perturbations, and instinctively synchronized (i.e., entrained) to a broad range of driving frequencies of perceived ML motion. However, the influence of visual perturbations on metrics of walking balance was frequency-dependent and governed by their proximity to stride frequency. Specifically, we found that a driving frequency nearest to subjects' average stride frequency uniquely compromised trunk sway, gait variability, and step-to-step correlations. We conclude that visuomotor entrainment is a robust and naturally emerging phenomenon during human walking, involving coordinated and frequency-dependent adjustments in trunk sway and foot placement to maintain balance at the whole-body level. These findings provide mechanistic insight into how the visuomotor control of walking balance is disrupted by visual perturbations and important reference values for the emergence of balance deficits due to age, injury, or disease

Masses, luminosities, and orbital coplanarities of the µ Orionis quadruple-star system from phases differential astrometry

μ Orionis was identified by spectroscopic studies as a quadruple-star system. Seventeen high-precision differential astrometry measurements of μ Ori have been collected by the Palomar High-precision Astrometric Search for Exoplanet Systems (PHASES). These show both the motion of the long-period binary orbit and short-period perturbations superimposed on that caused by each of the components in the long-period system being themselves binaries. The new measurements enable the orientations of the long-period binary and short-period subsystems to be determined. Recent theoretical work predicts the distribution of relative inclinations between inner and outer orbits of hierarchical systems to peak near 40 and 140 degrees. The degree of coplanarity of this complex system is determined, and the angle between the planes of the A–B and Aa–Ab orbits is found to be 136.7 ± 8.3 degrees, near the predicted distribution peak at 140 degrees; this result is discussed in the context of the handful of systems with established mutual inclinations. The system distance and masses for each component are obtained from a combined fit of the PHASES astrometry and archival radial velocity observations. The component masses have relative precisions of 5% (component Aa), 15% (Ab), and 1.4% (each of Ba and Bb). The median size of the minor axes of the uncertainty ellipses for the new measurements is 20 micro-arcseconds (μas). Updated orbits for δ Equulei, κ Pegasi, and V819 Herculis are also presented

The Effect of Using Exoskeleton of Blue Crab (Callinectes sapidus) as a Dietary Calcium Source on the Egg Characteristics of Layer Hens (Gallus gallus domesticus)

The study focuses on the ability to use the exoskeleton of blue crab as alternative calcium and carotenoid supplement for layer hens and its effects on egg characteristics. Three groups of eighty layer hens each were fed a base feed formulation following the standards of the University of the Philippines Los Baños. The feeds were base feed as negative control (NG), a base feed with natural egg yolk colorants (capsorubin and lutein) as positive control (PG), and a base feed with 1% ground blue crab exoskeletons, as experimental (EG). The feeding lasted four weeks before egg collection. The eggs were weighed for their albumen, yolk, shell, and egg weight. The egg yolk color was determined using a DSM Fan and a digital Chroma meter, and the shell thickness using digital calipers. Statistical treatment was done through Kruskal Wallis test using SPSS software. Results showed that eggs of EG had significantly heavier shells with a mean of 5.93±0.11g, compared to 5.83±0.08g of the NG and 5.55±0.08g of the PG. Eggshell thickness was not significantly different among the three groups. Egg yolk color was significantly different in PG with a mean DSM gradient value of 11.96±0.11, compared to 5.92±0.14 of the NG and 6.48±0.20 of EG. Ground blue crab exoskeleton as a calcium supplement may increase the weight of the eggshells but may not intensify the egg yolk color

Molecular Mechanics Simulations and Improved Tight-binding Hamiltonians for Artificial Light Harvesting Systems: Predicting Geometric Distributions, Disorder, and Spectroscopy of Chromophores in a Protein Environment

We present molecular mechanics {and spectroscopic} calculations on prototype artificial light harvesting systems consisting of chromophores attached to a tobacco mosaic virus (TMV) protein scaffold. These systems have been synthesized and characterized spectroscopically, but information about the microscopic configurations and geometry of these TMV-templated chromophore assemblies is largely unknown. We use a Monte Carlo conformational search algorithm to determine the preferred positions and orientations of two chromophores, Coumarin 343 together with its linker, and Oregon Green 488, when these are attached at two different sites (104 and 123) on the TMV protein. The resulting geometric information shows that the extent of disorder and aggregation properties, and therefore the optical properties of the TMV-templated chromophore assembly, are highly dependent on the choice of chromophores and protein site to which they are bound. We used the results of the conformational search as geometric parameters together with an improved tight-binding Hamiltonian to simulate the linear absorption spectra and compare with experimental spectral measurements. The ideal dipole approximation to the Hamiltonian is not valid since the distance between chromophores can be very small. We found that using the geometries from the conformational search is necessary to reproduce the features of the experimental spectral peaks

The Phases Differential Astrometry Data Archive. IV. The Triple Star Systems 63 Gem A and HR 2896

Differential astrometry measurements from the Palomar High-precision Astrometric Search for Exoplanet Systems (PHASES) are used to constrain the astrometric orbit of the previously known ≾2 day subsystem in the triple system 63 Gem A and have detected a previously unknown two-year Keplerian wobble superimposed on the visual orbit of the much longer period (213 years) binary system HR 2896. 63 Gem A was already known to be triple from spectroscopic work, and absorption lines from all three stars can be identified and their individual Doppler shifts measured; new velocities for all three components are presented to aid in constraining the orbit and measuring the stellar masses. In fact, 63 Gem itself is a sextuple system: the hierarchical triple (Aa1-Aa2)-Ab (in which Aa1 and Aa2 orbit each other with a rapid period just under 2 days, and Ab orbits these every two years), plus three distant common proper motion companions. The very small astrometric perturbation caused by the inner pair in 63 Gem A stretches the limits of current astrometric capabilities, but PHASES observations are able to constrain the orientation of the orbit. The two bright stars comprising the HR 2896 long-period (213 year) system have a combined spectral type of K0III and the newly detected object's mass estimate places it in the regime of being an M dwarf. The motion of the stars are slow enough that their spectral features are always blended, preventing Doppler studies. The PHASES measurements and radial velocities (when available) have been combined with lower precision single-aperture measurements covering a much longer time frame (from eyepiece measurements, speckle interferometry, and adaptive optics) to improve the characterization of the long-period orbits in both binaries. The visual orbits of the short- and long-period systems are presented for both systems and used to calculate two possible values of the mutual inclinations between inner and outer orbits of 152° ± 12° or a less likely value of 31° ± 11° for 63 Gem A and 10.°2 ± 2.°4 or 171.°2 ± 2.°8 for HR 2896. The first is not coplanar, whereas the second is either nearly coplanar or anti-coplanar

Control via electron count of the competition between magnetism and superconductivity in cobalt and nickel doped NaFeAs

Using a combination of neutron, muon and synchrotron techniques we show how the magnetic state in NaFeAs can be tuned into superconductivity by replacing Fe by either Co or Ni. Electron count is the dominant factor, since Ni-doping has double the effect of Co-doping for the same doping level. We follow the structural, magnetic and superconducting properties as a function of doping to show how the superconducting state evolves, concluding that the addition of 0.1 electrons per Fe atom is sufficient to traverse the superconducting domain, and that magnetic order coexists with superconductivity at doping levels less than 0.025 electrons per Fe atom.Comment: 4 pages, 6 figure