Towards gravitationally assisted negative refraction of light by vacuum

Propagation of electromagnetic plane waves in some directions in gravitationally affected vacuum over limited ranges of spacetime can be such that the phase velocity vector casts a negative projection on the time-averaged Poynting vector. This conclusion suggests, inter alia, gravitationally assisted negative refraction by vacuum.Comment: 6 page

Kramers-Kronig, Bode, and the meaning of zero

The implications of causality, as captured by the Kramers-Kronig relations between the real and imaginary parts of a linear response function, are familiar parts of the physics curriculum. In 1937, Bode derived a similar relation between the magnitude (response gain) and phase. Although the Kramers-Kronig relations are an equality, Bode's relation is effectively an inequality. This perhaps-surprising difference is explained using elementary examples and ultimately traces back to delays in the flow of information within the system formed by the physical object and measurement apparatus.Comment: 8 pages; American Journal of Physics, to appea

The Statistical Physics of Regular Low-Density Parity-Check Error-Correcting Codes

A variation of Gallager error-correcting codes is investigated using statistical mechanics. In codes of this type, a given message is encoded into a codeword which comprises Boolean sums of message bits selected by two randomly constructed sparse matrices. The similarity of these codes to Ising spin systems with random interaction makes it possible to assess their typical performance by analytical methods developed in the study of disordered systems. The typical case solutions obtained via the replica method are consistent with those obtained in simulations using belief propagation (BP) decoding. We discuss the practical implications of the results obtained and suggest a computationally efficient construction for one of the more practical configurations.Comment: 35 pages, 4 figure

Asymmetric quantum error correcting codes

The noise in physical qubits is fundamentally asymmetric: in most devices, phase errors are much more probable than bit flips. We propose a quantum error correcting code which takes advantage of this asymmetry and shows good performance at a relatively small cost in redundancy, requiring less than a doubling of the number of physical qubits for error correction

Reconstructing the massive black hole cosmic history through gravitational waves

The massive black holes we observe in galaxies today are the natural end-product of a complex evolutionary path, in which black holes seeded in proto-galaxies at high redshift grow through cosmic history via a sequence of mergers and accretion episodes. Electromagnetic observations probe a small subset of the population of massive black holes (namely, those that are active or those that are very close to us), but planned space-based gravitational-wave observatories such as the Laser Interferometer Space Antenna (LISA) can measure the parameters of ``electromagnetically invisible'' massive black holes out to high redshift. In this paper we introduce a Bayesian framework to analyze the information that can be gathered from a set of such measurements. Our goal is to connect a set of massive black hole binary merger observations to the underlying model of massive black hole formation. In other words, given a set of observed massive black hole coalescences, we assess what information can be extracted about the underlying massive black hole population model. For concreteness we consider ten specific models of massive black hole formation, chosen to probe four important (and largely unconstrained) aspects of the input physics used in structure formation simulations: seed formation, metallicity ``feedback'', accretion efficiency and accretion geometry. For the first time we allow for the possibility of ``model mixing'', by drawing the observed population from some combination of the ``pure'' models that have been simulated. A Bayesian analysis allows us to recover a posterior probability distribution for the ``mixing parameters'' that characterize the fractions of each model represented in the observed distribution. Our work shows that LISA has enormous potential to probe the underlying physics of structure formation.Comment: 24 pages, 16 figures, submitted to Phys. Rev.

Scaling of the Critical Function for the Standard Map: Some Numerical Results

The behavior of the critical function for the breakdown of the homotopically non-trivial invariant (KAM) curves for the standard map, as the rotation number tends to a rational number, is investigated using a version of Greene's residue criterion. The results are compared to the analogous ones for the radius of convergence of the Lindstedt series, in which case rigorous theorems have been proved. The conjectured interpolation of the critical function in terms of the Bryuno function is discussed.Comment: 26 pages, 3 figures, 13 table

The preparation and characterisation of monomeric and linked metal carbonyl clusters containing the closo-Si2Co4 pseudo-octahedral core

PhSiH3 reacts with [Co₄(CO)₁₂] at 50 °C in hydrocarbon solvents to give [(µ₄-SiPh)₂Co₄(CO)₁₁], 2c, shown by an X-ray crystal structure determination to have a pseudo-octahedral Si₂Co₄ core. Substituted aryl-silanes behaved similarly. Mixtures of PhSiH₃, H₃SiC₆H₄SiH₃ and [Co₄(CO)₁₂] in a ca. 2 1 2 ratio gave the dimeric cluster [{Co₄(µ₄-SiPh)(CO)₁₁Si}₂C₆H₄], 3a, which has the two Si₂Co₄ cores linked by a C₆H₄ group to give a rigid molecule which an X-ray structure analysis shows to be over 23 Å long. Related dimers linked by –(CH₂)₈– groups were isolated from mixtures of PhSiH₃, α ,ω-(H₃Si)₂(CH₂)₈ and [Co₄(CO)₁₂]. Electrochemical studies show the two cluster units in 3a do not interact electronically

Multi-site breathers in Klein-Gordon lattices: stability, resonances, and bifurcations

We prove the most general theorem about spectral stability of multi-site breathers in the discrete Klein-Gordon equation with a small coupling constant. In the anti-continuum limit, multi-site breathers represent excited oscillations at different sites of the lattice separated by a number of "holes" (sites at rest). The theorem describes how the stability or instability of a multi-site breather depends on the phase difference and distance between the excited oscillators. Previously, only multi-site breathers with adjacent excited sites were considered within the first-order perturbation theory. We show that the stability of multi-site breathers with one-site holes change for large-amplitude oscillations in soft nonlinear potentials. We also discover and study a symmetry-breaking (pitchfork) bifurcation of one-site and multi-site breathers in soft quartic potentials near the points of 1:3 resonance.Comment: 34 pages, 12 figure

Global-Scale Consequences of Magnetic-Helicity Injection and Condensation on the Sun

In the recent paper of Antiochos, a new concept for the injection of magnetic helicity into the solar corona by small-scale convective motions and its condensation onto polarity inversion lines (PILs) has been developed. We investigate this concept through global simulations of the Sun's photospheric and coronal magnetic fields and compare the results with the hemispheric pattern of solar filaments. Assuming that the vorticity of the cells is predominately counter-clockwise/clockwise in the northern/southern hemisphere, the convective motions inject negative/positive helicity into each hemisphere. The simulations show that: (i) On a north-south orientated PIL, both differential rotation and convective motions inject the same sign of helicity which matches that required to reproduce the hemispheric pattern of filaments. (ii) On a high latitude east-west orientated polar crown or sub-polar crown PIL, the vorticity of the cells has to be approximately 2-3 times greater than the local differential rotation gradient in order to overcome the incorrect sign of helicity injection from differential rotation. (iii) In the declining phase of the cycle, as a bipole interacts with the polar field, in some cases helicity condensation can reverse the effect of differential rotation along the East-West lead arm, but not in all cases. The results show that this newly developed concept of magnetic helicity injection and condensation is a viable method to explain the hemispheric pattern of filaments in conjunction with the mechanisms used in Yeates et al. (2008). Future observational studies should focus on determining the vorticity component within convective motions to determine, both its magnitude and latitudinal variation relative to the differential rotation gradient on the Sun

Milk consumption after exercise decreases electrolyte excretion.

La rehidratación es fundamental para la correcta recuperación posterior al ejercicio físico y el deporte. Las bebidas lácteas parecen ser una buena opción como bebidas rehidratantes después del ejercicio, pero aún los mecanismos no están completamente dilucidados. El presente estudio tiene por objetivo medir los efectos en la excreción de electrolitos en la orina al rehidratar con una bebida láctea baja en grasa o una bebida isotónica tras la realización de una sesión de ejercicio intermitente. 14 sujetos físicamente activos (23 ± 4 años), se dividieron en dos grupos: 1) rehidratación con bebida isotónica (ISO) y 2) rehidratación con bebida láctea baja en grasa (LBG). Se evaluó la gravedad específica de la orina (GEO), electrolitos (Na+ y K+) en orina y retención de fluidos, después del ejercicio y 4 horas posterior a la rehidratación. Se encontraron diferencias significativas en la GEO y en la excreción de K+ en el grupo LBG (p<0.005), ambos grupos muestran diferencias significativas en la excreción de Na+. Los resultados muestran que la rehidratación con bebida láctea mejora la GEO y disminuyen la excreción de K+ de forma más eficiente que la bebida isotónica posterior al ejercicioRehydration is essential for post-exercise and sport recovery. Milk seems to be a good option like sport drinks after exercise, yet the rehydration mechanisms are still not fully understood. The aim of this study was to measure the effect of drinking low-fat milk and an isotonic beverage after intermittent exercise on urine electrolytes. 14 physically active men (23 ± 4 y) were split into two groups: 1) rehydration with isotonic drink (ISO), and 2) rehydration with low-fat milk (LBG). Specific gravity (GEO) and electrolytes (Na+ and K+) were measured in urine before and after exercise with rehydration. Significant differences were found for the GEO and in K+ excretion in the LBG group (p <0.05). Both groups showed significant differences for Na+ excretion concentrations. We conclude that drinking low fat milk after exercise when compared to an isotonic drink, improves GEO and K excretio