Why charges go to the surface: a generalized Thomson problem

We study a generalization of a Thomson problem of n particles confined to a sphere and interacting by a 1/r^g potential. It is found that for g \le 1 the electrostatic repulsion expels all the charges to the surface of the sphere. However for g>1 and n>n_c(g) occupation of the bulk becomes energetically favorable. It is curious to note that the Coulomb law lies exactly on the interface between these two regimes

Dynamics of Black Hole Pairs II: Spherical Orbits and the Homoclinic Limit of Zoom-Whirliness

Spinning black hole pairs exhibit a range of complicated dynamical behaviors. An interest in eccentric and zoom-whirl orbits has ironically inspired the focus of this paper: the constant radius orbits. When black hole spins are misaligned, the constant radius orbits are not circles but rather lie on the surface of a sphere and have acquired the name "spherical orbits". The spherical orbits are significant as they energetically frame the distribution of all orbits. In addition, each unstable spherical orbit is asymptotically approached by an orbit that whirls an infinite number of times, known as a homoclinic orbit. A homoclinic trajectory is an infinite whirl limit of the zoom-whirl spectrum and has a further significance as the separatrix between inspiral and plunge for eccentric orbits. We work in the context of two spinning black holes of comparable mass as described in the 3PN Hamiltonian with spin-orbit coupling included. As such, the results could provide a testing ground of the accuracy of the PN expansion. Further, the spherical orbits could provide useful initial data for numerical relativity. Finally, we comment that the spinning black hole pairs should give way to chaos around the homoclinic orbit when spin-spin coupling is incorporated.Comment: 16 pages, several figure

Chaos and Order in Models of Black Hole Pairs

Chaos in the orbits of black hole pairs has by now been confirmed by several independent groups. While the chaotic behavior of binary black hole orbits is no longer argued, it remains difficult to quantify the importance of chaos to the evolutionary dynamics of a pair of comparable mass black holes. None of our existing approximations are robust enough to offer convincing quantitative conclusions in the most highly nonlinear regime. It is intriguing to note that in three different approximations to a black hole pair built of a spinning black hole and a non-spinning companion, two approximations exhibit chaos and one approximation does not. The fully relativistic scenario of a spinning test-mass around a Schwarzschild black hole shows chaos, as does the Post-Newtonian Lagrangian approximation. However, the approximately equivalent Post-Newtonian Hamiltonian approximation does not show chaos when only one body spins. It is well known in dynamical systems theory that one system can be regular while an approximately related system is chaotic, so there is no formal conflict. However,the physical question remains, Is there chaos for comparable mass binaries when only one object spins? We are unable to answer this question given the poor convergence of the Post-Newtonian approximation to the fully relativistic system. A resolution awaits better approximations that can be trusted in the highly nonlinear regime

Cell-to-cell spread of poliovirus in the spinal cord of bonnet monkeys (Macaca radiata)

In order to study the spread of poliovirus in the spinal cord of bonnet monkeys, 10(8) TCID50 Mahoney strain of poliovirus was inoculated into the ulnar nerves of monkeys that were subsequently autopsied on days 1, 2, 3, 6, 9, 12, 14, 15 and 16 postinoculation (p.i.). Virus spread in the spinal cord, the accompanying histopathological changes and paralysis occurred in a cervico-thoraco-lumbar direction. Virus reached the cervical region of the spinal cord within the first 3 days and subsequently spread to all segments of the spinal cord. In situ hybridization demonstrated viral RNA initially in the cervical neurons on day 3 p.i. and in the anterior horn neurons of lumbar segments of the spinal cord by day 6 p.i. Loss of Nissl substance in some of the anterior horn neurons was apparent on day 3 p.i. in the cervical and thoracic regions and by day 6 p.i. in the lumbar region. In the lumbar region, neuronophagia was a consistent feature which was observed on days 6-9 p.i., followed by neuronal dropouts on day 12 p.i. and thereafter. In the cervical and thoracic region, reappearance of Nissl substance was apparent from day 12 p.i. Upper limb paralysis preceded lower limb paralysis (5.5+/-1.73 vs 8.18+/-2.18, P = 0.046), further suggesting that virus spread within the spinal cord was via an intraneural route despite persistent viraemia detectable from day 2 p.i. onwards. The temporal distribution of the virus spread, distribution of viral RNA, histopathological and clinical changes indicate a cell-to-cell spread of poliovirus in the CNS, having gained access to the CNS from the peripheral nerve

Gravity Waves, Chaos, and Spinning Compact Binaries

Spinning compact binaries are shown to be chaotic in the Post-Newtonian expansion of the two body system. Chaos by definition is the extreme sensitivity to initial conditions and a consequent inability to predict the outcome of the evolution. As a result, the spinning pair will have unpredictable gravitational waveforms during coalescence. This poses a challenge to future gravity wave observatories which rely on a match between the data and a theoretical template.Comment: Final version published in PR

Towards a solution of the charmonium production controversy: k_t-factorization versus color octet mechanism

The cross section of \chi_{cJ} hadroproduction is calculated in the k_t-factorization approach. We find a significant contribution of the \chi_{c1} state due to non-applicability of the Landau-Yang theorem because of off-shell gluons. The results are in agreement with data and, in contrast to the collinear factorization, show a dominance of the color singlet part and a strong suppression of the color octet contribution. Our results could therefore lead to a solution of the longstanding controversy between the color singlet model and the color octet mechanism.Comment: 4 pages, 5 figures, final PRL versio

High-temperature environments of human evolution in East Africa based on bond ordering in paleosol carbonates

Many important hominid-bearing fossil localities in East Africa are in regions that are extremely hot and dry. Although humans are well adapted to such conditions, it has been inferred that East African environments were cooler or more wooded during the Pliocene and Pleistocene when this region was a central stage of human evolution. Here we show that the Turkana Basin, Kenya—today one of the hottest places on Earth—has been continually hot during the past 4 million years. The distribution of ^(13)C-^(18)O bonds in paleosol carbonates indicates that soil temperatures during periods of carbonate formation were typically above 30 °C and often in excess of 35 °C. Similar soil temperatures are observed today in the Turkana Basin and reflect high air temperatures combined with solar heating of the soil surface. These results are specific to periods of soil carbonate formation, and we suggest that such periods composed a large fraction of integrated time in the Turkana Basin. If correct, this interpretation has implications for human thermophysiology and implies a long-standing human association with marginal environments

A Neutral Polyampholyte in an ionic solution

The behavior of a neutral polyampholyte ($PA$) chain with $N$ monomers, in an ionic solution, is analyzed in the framework of the full Debye-H$\ddot u$ckel-Bjerrum-Flory $(DHBjF)$ theory. A $PA$ chain, that in addition to the neutral monomers, also contains an equal number of positively and negatively charged monomers, is dissolved in an ionic solution. For \underline{high} concentrations of salt and at high temperatures, the $PA$ exists in an extended state. As the temperature is decreased, the electrostatic energy becomes more relevant and at a $T=T_{\theta}$ the system collapses into a dilute globular state, or microelectrolyte. This state contains a concentration of salt higher than the surrounding medium. As the temperature is decreased even further, association between the monomers of the polymer and the ions of the salt becomes relevant and there is a crossover from this globular state to a low temperature extended state. For \underline{low} densities of salt, the system is collapsed for almost all temperatures and exhibits a first-order phase transition to an extended state at an unphysical low temperature.Comment: 10 pages, Revtex with epsf, 9 Postscript figures. Submitted to PR

Sine-Gordon mean field theory of a Coulomb Gas

Sine-Gordon field theory is used to investigate the phase diagram of a neutral Coulomb gas. A variational mean field free energy is constructed and the corresponding phase diagrams in two (2d) and three dimensions (3d) are obtained. When analyzed in terms of chemical potential, the Sine-Gordon theory predicts the phase diagram topologically identical with the Monte Carlo simulations and a recently developed Debye-H\"uckel-Bjerrum (DHBj) theory. In 2d we find that the infinite order Kosterlitz-Thouless line terminates in a tricritical point, after which the metal-insulator transition becomes first order. However, when the transformation from chemical potential to the density is made the whole of the insulating phase is mapped onto zero density.Comment: 5 pages, Revtex with twocolumn style, 2 Postscript figures. Submitted to PR

Chemical composition of the decaying glasma

The the initial stage of a relativistic heavy ion collision can be described by a classical color field configuration known as the Glasma. The production of quark pairs from this background field is then computed nonperturbatively by numerically solving the Dirac equation in the classical background. The result seems to point towards an early chemical equilibration of the plasma.Comment: 8 pages, 5 figures, invited talk at Stangeness in Quark Matter 2006 (SQM06), UCLA, March 200