Integrability of the Minimal Strain Equations for the Lapse and Shift in 3+1 Numerical Relativity

Brady, Creighton and Thorne have argued that, in numerical relativity simulations of the inspiral of binary black holes, if one uses lapse and shift functions satisfying the ``minimal strain equations'' (MSE), then the coordinates might be kept co-rotating, the metric components would then evolve on the very slow inspiral timescale, and the computational demands would thus be far smaller than for more conventional slicing choices. In this paper, we derive simple, testable criteria for the MSE to be strongly elliptic, thereby guaranteeing the existence and uniqueness of the solution to the Dirichlet boundary value problem. We show that these criteria are satisfied in a test-bed metric for inspiraling binaries, and we argue that they should be satisfied quite generally for inspiraling binaries. If the local existence and uniqueness that we have proved holds globally, then, for appropriate boundary values, the solution of the MSE exhibited by Brady et. al. (which tracks the inspiral and keeps the metric evolving slowly) will be the unique solution and thus should be reproduced by (sufficiently accurate and stable) numerical integrations.Comment: 6 pages; RevTeX; submitted to Phys. Rev. D15. Technical issue of the uniqueness of the solution to the Dirichlet problem clarified. New subsection on the nature of the boundary dat

No-horizon theorem for spacetimes with spacelike G1 isometry groups

We consider four-dimensional spacetimes $(M,{\mathbf g})$ which obey the Einstein equations ${\mathbf G}={\mathbf T}$, and admit a global spacelike $G_{1}={\mathbb R}$ isometry group. By means of dimensional reduction and local analyis on the reduced (2+1) spacetime, we obtain a sufficient condition on ${\mathbf T}$ which guarantees that $(M,{\mathbf g})$ cannot contain apparent horizons. Given any (3+1) spacetime with spacelike translational isometry, the no-horizon condition can be readily tested without the need for dimensional reduction. This provides thus a useful and encompassing apparent horizon test for $G_{1}$-symmetric spacetimes. We argue that this adds further evidence towards the validity of the hoop conjecture, and signals possible violations of strong cosmic censorship.Comment: 8 pages, LaTeX, uses IOP package; published in Class. Quantum Gra

Nuclear shadowing from exclusive quarkonium photoproduction at the BNL RHIC and CERN LHC

The photonuclear production of vector mesons in ultraperipheral heavy ion collisions is investigated within the collinear approach using different parameterizations for the nuclear gluon distribution. The integrated cross section and the rapidity distribution for the $AA \to V AA$ ($V = J/\Psi, \Upsilon$) process are computed for energies of RHIC and LHC. A comparison with the recent PHENIX data on coherent production of $J/\Psi$ mesons is also presented. We demonstrate that the study of the exclusive quarkonium photoproduction can be used to constrain the nuclear effects in the gluon distribution.Comment: 8 pages, 4 figures, 2 tables. Version to be published in Physical Review

On the exact Foldy-Wouthuysen transformation for a Dirac spinor in torsion and other CPT and Lorentz violating backgrounds

We discuss the possibility to perform and use the exact Foldy-Wouthuysen transformation (EFWT) for the Dirac spinor coupled to different CPT and Lorentz violating terms. The classification of such terms is performed, selecting those of them which admit EFWT. For the particular example of an axial vector field, which can be associated with the completely antisymmetric torsion, we construct an explicit EFWT in the case when only a timelike component of this axial vector is present. In the cases when EFWT is not possible, one can still use the corresponding technique for deriving the perturbative Foldy-Wouthuysen transformation, as is illustrated in a particular example in the Appendix

The ground state properties of the spin-1/2 transverse Ising chain with periodically varying bonds and fields

Using continued fractions we study the ground state properties of the spin-1/2 Ising chain in a transverse field with periodically varying interaction strengths and external fields. We consider in detail the chain having the period of modulation of interactions equals 2 and compare the results obtained with those corresponding to the spin-1/2 isotropic XY chain in a transverse field. In contrast to the behaviour of the transverse XY chain, the transverse Ising chain does not exhibit a step-like magnetization vs. field dependence caused by the alternation of bonds, its susceptibility exhibits a logarithmic singularity at the field determined by interaction strengths, and it is stable with respect to spin-Peierls dimerization.Comment: 11 pages, latex, 4 figure

Caracterização físico-química e reológicas da polpa de cupuaçu congelada (Theobroma grandiflorum Schum).

Cupuaçu, uma das principais e mais consumidas frutas da região amazônica brasileira, pertence à família Sterculiacea, cuja denominação binomial é Theobroma grandiflorum schum. É uma fruta típica da Amazônia, sendo cultivada nos estados do Pará, Maranhão e Tocantins. Esta fruta apresenta crescente utilização no Brasil para o mercado interno e externo, sendo comumente comercializada como polpa congelada. Apesar de sua importância, há poucos dados de caracterização e contaminação da polpa de cupuaçu. Amostras de polpa de cupuaçu foram avaliadas quanto à viscosidade aparente, tensão de cisalhamento, umidade, cinzas, nitrogênio total, extrato etéreo, acidez, sólidos solúveis e pH. Os resultados demonstram a necessidade de aprimorar as boas práticas agrícolas e de fabricação e implantação de sistemas de controle de qualidade para minimização dos riscos associados à contaminação por micro-organismos

Geometric Scaling in Inclusive Charm Production

We show that the cross section for inclusive charm production exhibits geometric scaling in a large range of photon virtualities. In the HERA kinematic domain the saturation momentum $Q_{sat}^2(x)$ stays below the hard scale $\mu_c^2=4m_c^2$, implying charm production probing mostly the color transparency regime and unitarization effects being almost negligible. We derive our results considering two saturation models which are able to describe the DESY ep collider HERA data for the proton structure function at small values of the Bjorken variable $x$. A striking feature is the scaling on $\tau=Q_2^2/Q_{sat}^2(x)$ above saturation limit, corroborating recent theoretical studies.Comment: 4 pages, 2 figures. Version to be published in Physical Review Letter

A comparative study of the neutrino-nucleon cross section at ultra high energies

The high energy neutrino cross section is a crucial ingredient in the calculation of the event rate in high energy neutrino telescopes. Currently there are several approaches which predict different behaviours for its magnitude for ultrahigh energies. In this paper we present a comparison between the predictions based on linear DGLAP dynamics, non-linear QCD and in the imposition of a Froissart-like behaviour at high energies. In particular, we update the predictions based on the Color Glass Condensate, presenting for the first time the results for $\sigma_{\nu N}$ using the solution of the running coupling Balitsky-Kovchegov equation. Our results demonstrate that the current theoretical uncertainty for the neutrino-nucleon cross section reaches a factor three for neutrinos energies around $10^{11}$ GeV and increases to a factor five for $10^{13}$ GeV.Comment: 6 pages, 3 figure