Vanishing of Gravitational Particle Production in the Formation of Cosmic Strings

We consider the gravitationally induced particle production from the quantum vacuum which is defined by a free, massless and minimally coupled scalar field during the formation of a gauge cosmic string. Previous discussions of this topic estimate the power output per unit length along the string to be of the order of $10^{68}$ ergs/sec/cm in the s-channel. We find that this production may be completely suppressed. A similar result is also expected to hold for the number of produced photons.Comment: 10 pages, Plain LaTex. Minor improvements. To appear in PR

Phonon-induced quadrupolar ordering of the magnetic superconductor TmNi2_2B2_2C

We present synchrotron x-ray diffraction studies revealing that the lattice of thulium borocarbide is distorted below T_Q = 13.5 K at zero field. T_Q increases and the amplitude of the displacements is drastically enhanced, by a factor of 10 at 60 kOe, when a magnetic field is applied along [100]. The distortion occurs at the same wave vector as the antiferromagnetic ordering induced by the a-axis field. A model is presented that accounts for the properties of the quadrupolar phase and explains the peculiar behavior of the antiferromagnetic ordering previously observed in this compound.Comment: submitted to PR

High order Fuchsian equations for the square lattice Ising model: χ(6)\chi^{(6)}

This paper deals with $\tilde{\chi}^{(6)}$, the six-particle contribution to the magnetic susceptibility of the square lattice Ising model. We have generated, modulo a prime, series coefficients for $\tilde{\chi}^{(6)}$. The length of the series is sufficient to produce the corresponding Fuchsian linear differential equation (modulo a prime). We obtain the Fuchsian linear differential equation that annihilates the "depleted" series $\Phi^{(6)}=\tilde{\chi}^{(6)} - {2 \over 3} \tilde{\chi}^{(4)} + {2 \over 45} \tilde{\chi}^{(2)}$. The factorization of the corresponding differential operator is performed using a method of factorization modulo a prime introduced in a previous paper. The "depleted" differential operator is shown to have a structure similar to the corresponding operator for $\tilde{\chi}^{(5)}$. It splits into factors of smaller orders, with the left-most factor of order six being equivalent to the symmetric fifth power of the linear differential operator corresponding to the elliptic integral $E$. The right-most factor has a direct sum structure, and using series calculated modulo several primes, all the factors in the direct sum have been reconstructed in exact arithmetics.Comment: 23 page

First-principles study of the energetics of charge and cation mixing in U_{1-x} Ce_x O_2

The formalism of electronic density-functional-theory, with Hubbard-U corrections (DFT+U), is employed in a computational study of the energetics of U_{1-x} Ce_x O_2 mixtures. The computational approach makes use of a procedure which facilitates convergence of the calculations to multiple self-consistent DFT+U solutions for a given cation arrangement, corresponding to different charge states for the U and Ce ions in several prototypical cation arrangements. Results indicate a significant dependence of the structural and energetic properties on the nature of both charge and cation ordering. With the effective Hubbard-U parameters that reproduce well the measured oxidation-reduction energies for urania and ceria, we find that charge transfer between U(IV) and Ce(IV) ions, leading to the formation of U(V) and Ce(III), gives rise to an increase in the mixing energy in the range of 4-14 kJ/mol of formula unit, depending on the nature of the cation ordering. The results suggest that although charge transfer between uranium and cerium ions is disfavored energetically, it is likely to be entropically stabilized at the high temperatures relevant to the processing and service of urania-based solid solutions.Comment: 8 pages, 6 figure

Quantum Geometry and Diffusion

We study the diffusion equation in two-dimensional quantum gravity, and show that the spectral dimension is two despite the fact that the intrinsic Hausdorff dimension of the ensemble of two-dimensional geometries is very different from two. We determine the scaling properties of the quantum gravity averaged diffusion kernel.Comment: latex2e, 10 pages, 4 figure

Response of the large-scale subglacial drainage system of Northeast Greenland to surface elevation changes

The influence of subglacial water on the dynamics of ice flow has been the object of increasing interest in the past decade. In this study we focus on large-scale, long-term changes in surface elevation over Northeast Greenland and the corresponding changes in subglacial water routeways. Our results show that over timescales ranging from decades to millennia the area may experience redistribution of and fluctuation in subglacial water outflux under the main glacier outlets. The fluctuations in subglacial water routing occur even in the absence of external forcing. Based on these results we conclude that changes in the subglacial water routeways are an intrinsic part of the drainage basin dynamics, where the subglacial system is likely always in a transient state. The results also imply that fluctuations at the margins observed at present might originate from changes several hundred kilometres upstream. Since surface elevation changes may propagate upstream over timescales much longer than the observational period, the cause of the fluctuations may not be present in current observational records

Perimeter Generating Functions For The Mean-Squared Radius Of Gyration Of Convex Polygons

We have derived long series expansions for the perimeter generating functions of the radius of gyration of various polygons with a convexity constraint. Using the series we numerically find simple (algebraic) exact solutions for the generating functions. In all cases the size exponent $\nu=1$.Comment: 8 pages, 1 figur

The Tully-Fisher relation of intermediate redshift field and cluster galaxies from Subaru spectroscopy

We have carried out spectroscopic observations in 4 cluster fields using Subaru's FOCAS multi-slit spectrograph and obtained spectra for 103 bright disk field and cluster galaxies at $0.06 \le z \le 1.20$. Seventy-seven of these show emission lines, and 33 provide reasonably-secure determinations of the galaxies' rotation velocity. The rotation velocities, luminosities, colours and emission-line properties of these galaxies are used to study the possible effects of the cluster environment on the star-formation history of the galaxies. Comparing the Tully-Fisher relations of cluster and field galaxies at similar reshifts we find no measurable difference in rest-frame $B$-band luminosity at a given rotation velocity (the formal difference is $0.18\pm0.33$mag). The colours of the cluster emission line galaxies are only marginally redder in rest-frame $B-V$ (by $0.06\pm0.04$mag) than the field galaxies in our sample. Taken at face value, these results seem to indicate that bright star-forming cluster spirals are similar to their field counterparts in their star-formation properties. However, we find that the fraction of disk galaxies with absorption-line spectra (i.e., with no current star formation) is larger in clusters than in the field by a factor of $\sim3$--5. This suggests that the cluster environment has the overall effect of switching off star formation in (at least) some spiral galaxies. To interpret these observational results, we carry out simulations of the possible effects of the cluster environment on the star-formation history of disk galaxies and thus their photometric and spectroscopic properties. Finally, we evaluate the evolution of the rest-frame absolute $B$-band magnitude per unit redshift at fixed rotation velocity.Comment: 21 pages, 13 figures, accepted for publication in MNRA

A new transfer-matrix algorithm for exact enumerations: Self-avoiding polygons on the square lattice

We present a new and more efficient implementation of transfer-matrix methods for exact enumerations of lattice objects. The new method is illustrated by an application to the enumeration of self-avoiding polygons on the square lattice. A detailed comparison with the previous best algorithm shows significant improvement in the running time of the algorithm. The new algorithm is used to extend the enumeration of polygons to length 130 from the previous record of 110.Comment: 17 pages, 8 figures, IoP style file

Self-avoiding walks and polygons on the triangular lattice

We use new algorithms, based on the finite lattice method of series expansion, to extend the enumeration of self-avoiding walks and polygons on the triangular lattice to length 40 and 60, respectively. For self-avoiding walks to length 40 we also calculate series for the metric properties of mean-square end-to-end distance, mean-square radius of gyration and the mean-square distance of a monomer from the end points. For self-avoiding polygons to length 58 we calculate series for the mean-square radius of gyration and the first 10 moments of the area. Analysis of the series yields accurate estimates for the connective constant of triangular self-avoiding walks, $\mu=4.150797226(26)$, and confirms to a high degree of accuracy several theoretical predictions for universal critical exponents and amplitude combinations.Comment: 24 pages, 6 figure