Small distance expansion for radiative heat transfer between curved objects

We develop a small distance expansion for the radiative heat transfer between gently curved objects, in terms of the ratio of distance to radius of curvature. A gradient expansion allows us to go beyond the lowest order proximity transfer approximation. The range of validity of such expansion depends on temperature as well as material properties. Generally, the expansion converges faster for the derivative of the transfer than for the transfer itself, which we use by introducing a near-field adjusted plot. For the case of a sphere and a plate, the logarithmic correction to the leading term has a very small prefactor for all materials investigated.Comment: 5 pages, 3 figure

Statistical Mechanics of Quantum-Classical Systems with Holonomic Constraints

The statistical mechanics of quantum-classical systems with holonomic constraints is formulated rigorously by unifying the classical Dirac bracket and the quantum-classical bracket in matrix form. The resulting Dirac quantum-classical theory, which conserves the holonomic constraints exactly, is then used to formulate time evolution and statistical mechanics. The correct momentum-jump approximation for constrained system arises naturally from this formalism. Finally, in analogy with what was found in the classical case, it is shown that the rigorous linear response function of constrained quantum-classical systems contains non-trivial additional terms which are absent in the response of unconstrained systems.Comment: Submitted to Journal of Chemical Physic

The Relation between Solar Eruption Topologies and Observed Flare Features I: Flare Ribbons

In this paper we present a topological magnetic field investigation of seven two-ribbon flares in sigmoidal active regions observed with Hinode, STEREO, and SDO. We first derive the 3D coronal magnetic field structure of all regions using marginally unstable 3D coronal magnetic field models created with the flux rope insertion method. The unstable models have been shown to be a good model of the flaring magnetic field configurations. Regions are selected based on their pre-flare configurations along with the appearance and observational coverage of flare ribbons, and the model is constrained using pre-flare features observed in extreme ultraviolet and X-ray passbands. We perform a topology analysis of the models by computing the squashing factor, Q, in order to determine the locations of prominent quasi-separatrix layers (QSLs). QSLs from these maps are compared to flare ribbons at their full extents. We show that in all cases the straight segments of the two J-shaped ribbons are matched very well by the flux-rope-related QSLs, and the matches to the hooked segments are less consistent but still good for most cases. In addition, we show that these QSLs overlay ridges in the electric current density maps. This study is the largest sample of regions with QSLs derived from 3D coronal magnetic field models, and it shows that the magnetofrictional modeling technique that we employ gives a very good representation of flaring regions, with the power to predict flare ribbon locations in the event of a flare following the time of the model

Evidence for the Gompertz Curve in the Income Distribution of Brazil 1978-2005

This work presents an empirical study of the evolution of the personal income distribution in Brazil. Yearly samples available from 1978 to 2005 were studied and evidence was found that the complementary cumulative distribution of personal income for 99% of the economically less favorable population is well represented by a Gompertz curve of the form $G(x)=\exp [\exp (A-Bx)]$, where $x$ is the normalized individual income. The complementary cumulative distribution of the remaining 1% richest part of the population is well represented by a Pareto power law distribution $P(x)= \beta x^{-\alpha}$. This result means that similarly to other countries, Brazil's income distribution is characterized by a well defined two class system. The parameters $A$, $B$, $\alpha$, $\beta$ were determined by a mixture of boundary conditions, normalization and fitting methods for every year in the time span of this study. Since the Gompertz curve is characteristic of growth models, its presence here suggests that these patterns in income distribution could be a consequence of the growth dynamics of the underlying economic system. In addition, we found out that the percentage share of both the Gompertzian and Paretian components relative to the total income shows an approximate cycling pattern with periods of about 4 years and whose maximum and minimum peaks in each component alternate at about every 2 years. This finding suggests that the growth dynamics of Brazil's economic system might possibly follow a Goodwin-type class model dynamics based on the application of the Lotka-Volterra equation to economic growth and cycle.Comment: 22 pages, 15 figures, 4 tables. LaTeX. Accepted for publication in "The European Physical Journal B

Structural anisotropy and orientation-induced Casimir repulsion in fluids

In this work we theoretically consider the Casimir force between two periodic arrays of nanowires (both in vacuum, and on a substrate separated by a fluid) at separations comparable to the period. Specifically, we compute the dependence of the exact Casimir force between the arrays under both lateral translations and rotations. Although typically the force between such structures is well-characterized by the Proximity Force Approximation (PFA), we find that in the present case the microstructure modulates the force in a way qualitatively inconsistent with PFA. We find instead that effective-medium theory, in which the slabs are treated as homogeneous, anisotropic dielectrics, gives a surprisingly accurate picture of the force, down to separations of half the period. This includes a situation for identical, fluid-separated slabs in which the exact force changes sign with the orientation of the wire arrays, whereas PFA predicts attraction. We discuss the possibility of detecting these effects in experiments, concluding that this effect is strong enough to make detection possible in the near future.Comment: 12 pages, 9, figure. Published version with expanded discussio

Structural anisotropy and orientation-induced Casimir repulsion in fluids

In this work we theoretically consider the Casimir force between two periodic arrays of nanowires (both in vacuum, and on a substrate separated by a fluid) at separations comparable to the period. Specifically, we compute the dependence of the exact Casimir force between the arrays under both lateral translations and rotations. Although typically the force between such structures is well-characterized by the Proximity Force Approximation (PFA), we find that in the present case the microstructure modulates the force in a way qualitatively inconsistent with PFA. We find instead that effective-medium theory, in which the slabs are treated as homogeneous, anisotropic dielectrics, gives a surprisingly accurate picture of the force, down to separations of half the period. This includes a situation for identical, fluid-separated slabs in which the exact force changes sign with the orientation of the wire arrays, whereas PFA predicts attraction. We discuss the possibility of detecting these effects in experiments, concluding that this effect is strong enough to make detection possible in the near future.Comment: 12 pages, 9, figure. Published version with expanded discussio

Neutrinos from Accreting Neutron Stars

The magnetospheres of accreting neutron stars develop electrostatic gaps with huge potential drops. Protons and ions, accelerated in these gaps along the dipolar magnetic field lines to energies greater than 100 TeV, can impact onto a surrounding accretion disc. A proton-induced cascade so develops, and $\nu$-emission is produced from charged pion decays. Using GEANT4, a computer code that tracks particles produced in high energy collisions, we have calculated the resulting $\nu$-spectrum with extensive disc shower simulations. We show that the $\nu$-spectrum produced out of the proton beam is a power law. We use this result to propose accretion-powered X-ray binaries (with highly magnetized neutron stars) as a new population of point-like $\nu$-sources for km-scale detectors, such as ICECUBE. As a particular example we discuss the case of A0535+26. We show that ICECUBE should find A0535+26 to be a periodic $\nu$-source: one for which the formation and loss of its accretion disc can be fully detected. Finally, we briefly comment on the possibility that smaller telescopes, like AMANDA, could also detect A0535+26 by folding observations with the orbital period.Comment: 7 pages, 5 figures. Updates to match accepted version in Astrophys.