Possible Solutions to the Radius Anomalies of Transiting Giant Planets

We calculate the theoretical evolution of the radii of all fourteen of the known transiting extrasolar giant planets (EGPs) for a variety of assumptions concerning atmospheric opacity, dense inner core masses, and possible internal power sources. We incorporate the effects of stellar irradiation and customize such effects for each EGP and star. Looking collectively at the family as a whole, we find that there are in fact two radius anomalies to be explained. Not only are the radii of a subset of the known transiting EGPs larger than expected from previous theory, but many of the other objects are smaller than the default theory would allow. We suggest that the larger EGPs can be explained by invoking enhanced atmospheric opacities that naturally retain internal heat. This explanation might obviate the necessity for an extra internal power source. We explain the smaller radii by the presence in perhaps all the known transiting EGPs of dense cores, such as have been inferred for Saturn and Jupiter. Importantly, we derive a rough correlation between the masses of our "best-fit" cores and the stellar metallicity that seems to buttress the core-accretion model of their formation. Though many caveats and uncertainties remain, the resulting comprehensive theory that incorporates enhanced-opacity atmospheres and dense cores is in reasonable accord with all the current structural data for the known transiting giant planets.Comment: 22 pages in emulateapj format, including 10 figures (mostly in color), accepted to the Astrophysical Journal (February 9, 2007); to appear in volume 661, June 200

An Investigation Into the Electrical Activity of Tender, Resting Paraspinal Muscles Using Surface Electromyography: A Pilot Study

Abnormal resting paraspinal muscle activity has been claimed to be responsible for changes in spinal tissue texture which are detectible by manual palpation. This pilot study investigated whether there was significant electrical activity in paraspinal musculature that was tender and that appeared to have altered tissue texture on palpation. Sixteen healthy volunteers between 18 and 35 years of age had their thoracic erector spinae mass palpated bilaterally from spinal levels T3 to T10 to identify paraspinal regions exhibiting altered tissue texture relative to the contralateral muscle mass. Surface electromyography (sEMG) was used to measure electrical activity in the muscle mass at the selected levels. No significant differences in electrical activity were observed between the tender and non-tender muscle masses, although a large difference existed in the one symptomatic subject. All muscle sites displayed EMG activity at rest, although the source of activity is not clear. A number of methodological problems with the EMG recording were encountered and are discussed. Future research is recommended using symptomatic participants

Effect of Particle-Hole Asymmetry on the Mott-Hubbard Metal-Insulator Transition

The Mott-Hubbard metal-insulator transition is one of the most important problems in correlated electron systems. In the past decade, much progress has been made on examining a particle-hole symmetric form of the transition in the Hubbard model with dynamical mean field theory where it was found that the electronic self energy develops a pole at the transition. We examine the particle-hole asymmetric metal-insulator transition in the Falicov-Kimball model, and find that a number of features change when the noninteracting density of states has a finite bandwidth. Since, generically particle-hole symmetry is broken in real materials, our results have an impact on understanding the metal-insulator transition in real materials.Comment: 5 pages, 3 figure

Ferromagnetism in two band metals: Combined effect of Coulomb correlation, hybridization and band widths

We study the possibility of ferromagnetism in metals. The metal is described by two hybridized bands one of which includes Hubbard correlation whereas the other is uncorrelated. We parametrize the ratio of the band widths and their centers as well. The original Hamiltonian is transformed in an effective and simpler one. Only one site retains the full correlation (U) while in the others acts as an internal field, the self-energy, in the framework of an alloy analogy approximation. This field, in turn, is self-consistently determined by imposing the translational invariance of the problem. For several total electronic occupation numbers (n_{total}) we compare the spin dependent free energies with the corresponding paramagnetic ones. We present several results pointing out the mechanism by which the self-consistency introduces a sort of constraints, for given values of band width and band shift .Comment: 6 pages, 7 figure

Sequence composition and environment effects on residue fluctuations in protein structures

The spectrum and scale of fluctuations in protein structures affect the range of cell phenomena, including stability of protein structures or their fragments, allosteric transitions and energy transfer. The study presents a statistical-thermodynamic analysis of relationship between the sequence composition and the distribution of residue fluctuations in protein-protein complexes. A one-node-per residue elastic network model accounting for the nonhomogeneous protein mass distribution and the inter-atomic interactions through the renormalized inter-residue potential is developed. Two factors, a protein mass distribution and a residue environment, were found to determine the scale of residue fluctuations. Surface residues undergo larger fluctuations than core residues, showing agreement with experimental observations. Ranking residues over the normalized scale of fluctuations yields a distinct classification of amino acids into three groups. The structural instability in proteins possibly relates to the high content of the highly fluctuating residues and a deficiency of the weakly fluctuating residues in irregular secondary structure elements (loops), chameleon sequences and disordered proteins. Strong correlation between residue fluctuations and the sequence composition of protein loops supports this hypothesis. Comparing fluctuations of binding site residues (interface residues) with other surface residues shows that, on average, the interface is more rigid than the rest of the protein surface and Gly, Ala, Ser, Cys, Leu and Trp have a propensity to form more stable docking patches on the interface. The findings have broad implications for understanding mechanisms of protein association and stability of protein structures.Comment: 8 pages, 4 figure

Shapes of Polynomial Julia Sets

Any Jordan curve in the complex plane can be approximated arbitrarily well in the Hausdorff topology by Julia sets of polynomials. Finite collections of disjoint Jordan domains can be approximated by the basins of attraction of rational maps.Comment: 13 pages, 3 figure

Cumulant expansion of the periodic Anderson model in infinite dimension

The diagrammatic cumulant expansion for the periodic Anderson model with infinite Coulomb repulsion ($U=\infty$) is considered here for an hypercubic lattice of infinite dimension ($d=\infty$). The same type of simplifications obtained by Metzner for the cumulant expansion of the Hubbard model in the limit of $d=\infty$, are shown to be also valid for the periodic Anderson model.Comment: 13 pages, 7 figures.ps. To be published in J. Phys. A: Mathematical and General (1997

A model for the phase separation controlled by doping and the internal chemical pressure in different cuprate superconductors

In the framework of a two-band model, we study the phase separation regime of different kinds of strongly correlated charge carriers as a function of the energy splitting between the two sets of bands. The narrow (wide) band simulates the more localized (more delocalized) type of charge carriers. By assuming that the internal chemical pressure on the CuO$_2$ layer due to interlayer mismatch controls the energy splitting between the two sets of states, the theoretical predictions are able to reproduce the regime of phase separation at doping higher than 1/8 in the experimental pressure-doping-$T_c$ phase diagram of cuprates at large microstrain as it appears in overoxygenated La$_2$CuO$_4$.Comment: 8 pages, 5 figures, submitted to Phys. Rev.