The Mellin Transform Technique for the Extraction of the Gluon Density

A new method is presented to determine the gluon density in the proton from jet production in deeply inelastic scattering. By using the technique of Mellin transforms not only for the solution of the scale evolution equation of the parton densities but also for the evaluation of scattering cross sections, the gluon density can be extracted in next-to-leading order QCD. The method described in this paper is, however, more general, and can be used in situations where a repeated fast numerical evaluation of scattering cross sections for varying parton distribution functions is required.Comment: 13 pages (LaTeX); 2 figures are included via epsfig; the corresponding postscript files are uuencode

Hunting Local Mixmaster Dynamics in Spatially Inhomogeneous Cosmologies

Heuristic arguments and numerical simulations support the Belinskii et al (BKL) claim that the approach to the singularity in generic gravitational collapse is characterized by local Mixmaster dynamics (LMD). Here, one way to identify LMD in collapsing spatially inhomogeneous cosmologies is explored. By writing the metric of one spacetime in the standard variables of another, signatures for LMD may be found. Such signatures for the dynamics of spatially homogeneous Mixmaster models in the variables of U(1)-symmetric cosmologies are reviewed. Similar constructions for U(1)-symmetric spacetimes in terms of the dynamics of generic $T^2$-symmetric spacetime are presented.Comment: 17 pages, 5 figures. Contribution to CQG Special Issue "A Spacetime Safari: Essays in Honour of Vincent Moncrief

Constructing compact 8-manifolds with holonomy Spin(7) from Calabi-Yau orbifolds

Compact Riemannian 7- and 8-manifolds with holonomy G(2) arid Spin(7) were first constructed by the author in 1994-5, by resolving orbifolds T-7/Gamma and T-8/Gamma. This paper describes a new construction of compact 8-manifolds with holonomy Spin(7). We start with a Calabi-Yau 4-orbifold Y with isolated singularities of a special kind. We divide by an antiholomorphic involution a of Y to get a real 8-orbifold Z = Y/. Then we resolve tire singularities of Z to get a compact 8-manifold M, which has metrics with holonomy Spin(7). Manifolds constructed in this way typically have large fourth Betti number b(4)(M).</sigma

The Singularity in Generic Gravitational Collapse Is Spacelike, Local, and Oscillatory

A longstanding conjecture by Belinskii, Khalatnikov, and Lifshitz that the singularity in generic gravitational collapse is spacelike, local, and oscillatory is explored analytically and numerically in spatially inhomogeneous cosmological spacetimes. With a convenient choice of variables, it can be seen analytically how nonlinear terms in Einstein's equations control the approach to the singularity and cause oscillatory behavior. The analytic picture requires the drastic assumption that each spatial point evolves toward the singularity as an independent spatially homogeneous universe. In every case, detailed numerical simulations of the full Einstein evolution equations support this assumption.Comment: 7 pages includes 4 figures. Uses Revtex and psfig. Received "honorable mention" in 1998 Gravity Research Foundation essay contest. Submitted to Mod. Phys. Lett.

Slow magnetic dynamics and hysteresis loops of a bulk ferromagnet

Magnetic dynamics of a bulk ferromagnet, a new single crystalline compound Co7(TeO3)4Br6, was studied by ac susceptibility and the related techniques. Very large Arrhenius activation energy of 17.2 meV (201 K) and long attempt time (2x10^(-4)s) span the full spectrum of magnetic dynamics inside a convenient frequency window, offering a rare opportunity for general studies of magnetic dynamics. Within the experimental window the ac susceptibility data build almost ideally semicircular Cole-Cole plots. Comprehensive study of experimental dynamic hysteresis loops of the compound is presented and interpreted within a simple thermal-activation-assisted spin lattice relaxation model for spin reversal. Quantitative agreement between the experimental results and the model's prediction for dynamic coercive field is achieved by assuming the central physical quantity, the Debye relaxation rate, to depend on frequency, as well as on the applied field strength and sample temperature. Cross-over between minor- to major hysteresis loops is carefully analyzed. Low-frequency limitations of the model, relying on domain wall pinning effects, are experimentally detected and appropriately discussed.Comment: A paragraph on dynamical-hysteresis assymetry added, text partially revised; Accepted in Physical Review

Optical properties of periodic systems within the current-current response framework: pitfalls and remedies

We compare the optical absorption of extended systems using the density-density and current-current linear response functions calculated within many-body perturbation theory. The two approaches are formally equivalent for a finite momentum $\mathbf{q}$ of the external perturbation. At $\mathbf{q}=\mathbf{0}$, however, the equivalence is maintained only if a small $q$ expansion of the density-density response function is used. Moreover, in practical calculations this equivalence can be lost if one naively extends the strategies usually employed in the density-based approach to the current-based approach. Specifically we discuss the use of a smearing parameter or of the quasiparticle lifetimes to describe the finite width of the spectral peaks and the inclusion of electron-hole interaction. In those instances we show that the incorrect definition of the velocity operator and the violation of the conductivity sum rule introduce unphysical features in the optical absorption spectra of three paradigmatic systems: silicon (semiconductor), copper (metal) and lithium fluoride (insulator). We then demonstrate how to correctly introduce lifetime effects and electron-hole interactions within the current-based approach.Comment: 17 pages, 6 figure

A new route towards uniformly functionalized single-layer graphene

It is shown, by DFT calculations, that the uniform functionalization of upper layer of graphite by hydrogen or fluorine does not change essentially its bonding energy with the underlying layers, whereas the functionalization by phenyl groups decreases the bonding energy by a factor of approximately ten. This means that the functionalized monolayer in the latter case can be easily separated by mild sonication. According to our computational results, such layers can be cleaned up to pure graphene, as well as functionalized further up to 25% coverage, without essential difficulties. The energy gap within the interval from 0.5 to 3 eV can be obtained by such one-side funtionalization using different chemical species.Comment: 15 pages, 3 figures, to appear in J. Phys. D: Applied Physic

The groupoidal analogue Theta~ to Joyal's category Theta is a test category

We introduce the groupoidal analogue \tilde\Theta to Joyal's cell category \Theta and we prove that \tilde\Theta is a strict test category in the sense of Grothendieck. This implies that presheaves on \tilde\Theta model homotopy types in a canonical way. We also prove that the canonical functor from \Theta to \tilde\Theta is aspherical, again in the sense of Grothendieck. This allows us to compare weak equivalences of presheaves on \tilde\Theta to weak equivalences of presheaves on \Theta. Our proofs apply to other categories analogous to \Theta.Comment: 41 pages, v2: references added, Remark 7.3 added, v3: metadata update