A Random Multifractal Tilling

We develop a multifractal random tilling that fills the square. The multifractal is formed by an arrangement of rectangular blocks of different sizes, areas and number of neighbors. The overall feature of the tilling is an heterogeneous and anisotropic random self-affine object. The multifractal is constructed by an algorithm that makes successive sections of the square. At each $n$-step there is a random choice of a parameter $\rho_i$ related to the section ratio. For the case of random choice between $\rho_1$ and $\rho_2$ we find analytically the full spectrum of fractal dimensions

Are Neutron-Rich Elements Produced in the Collapse of Strange Dwarfs ?

The structure of strange dwarfs and that of hybrid stars with same baryonic number is compared. There is a critical mass (M~0.24M_sun) in the strange dwarf branch, below which configurations with the same baryonic number in the hybrid star branch are more stable. If a transition occurs between both branches, the collapse releases an energy of about of 3x10^{50} erg, mostly under the form of neutrinos resulting from the conversion of hadronic matter onto strange quark matter. Only a fraction (~4%) is required to expel the outer neutron-rich layers. These events may contribute significantly to the chemical yield of nuclides with A>80 in the Galaxy, if their frequency is of about one per 1500 years.Comment: Accepted for publication in IJMP

The unpolarized two-loop massive pure singlet Wilson coefficients for deep-inelastic scattering

We calculate the massive two--loop pure singlet Wilson coefficients for heavy quark production in the unpolarized case analytically in the whole kinematic region and derive the threshold and asymptotic expansions. We also recalculate the corresponding massless two--loop Wilson coefficients. The complete expressions contain iterated integrals with elliptic letters. The contributing alphabets enlarge the Kummer-Poincar\'e letters by a series of square-root valued letters. A new class of iterated integrals, the Kummer-elliptic integrals, are introduced. For the structure functions $F_2$ and $F_L$ we also derive improved asymptotic representations adding power corrections. Numerical results are presented.Comment: 42, pages Latex, 8 Figure

Gravitational Model of High Energy Particles in a Collimated Jet

Observations suggest that relativistic particles play a fundamental role in the dynamics of jets emerging from active galactic nuclei as well as in their interaction with the intracluster medium. However, no general consensus exists concerning the acceleration mechanism of those high energy particles. A gravitational acceleration mechanism is here proposed, in which particles leaving precise regions within the ergosphere of a rotating supermassive black hole produce a highly collimated flow. These particles follow unbound geodesics which are asymptotically parallel to the spin axis of the black hole and are characterized by the energy $E$, the Carter constant ${\cal Q}$ and zero angular momentum of the component $L_z$. If environmental effects are neglected, the present model predicts at distances of about 140 kpc from the ergosphere the presence of electrons with energies around 9.4 GeV. The present mechanism can also accelerate protons up to the highest energies observed in cosmic rays by the present experiments.Comment: 27 pages and 5 figures. Accepted for publication in Astrophysical Journal. arXiv admin note: text overlap with arXiv:1011.654

The O(α2)O(\alpha^2) Initial State QED Corrections to e+e−e^+e^- Annihilation to a Neutral Vector Boson Revisited

We calculate the non-singlet, the pure singlet contribution, and their interference term, at $O(\alpha^2)$ due to electron-pair initial state radiation to $e^+ e^-$ annihilation into a neutral vector boson in a direct analytic computation without any approximation. The correction is represented in terms of iterated incomplete elliptic integrals. Performing the limit $s \gg m_e^2$ we find discrepancies with the earlier results of Ref.~\cite{Berends:1987ab} and confirm results obtained in Ref.~\cite{Blumlein:2011mi} where the effective method of massive operator matrix elements has been used, which works for all but the power corrections in $m^2/s$. In this way, we also confirm the validity of the factorization of massive partons in the Drell-Yan process. We also add non-logarithmic terms at $O(\alpha^2)$ which have not been considered in \cite{Berends:1987ab}. The corrections are of central importance for precision analyzes in $e^+e^-$ annihilation into $\gamma^*/Z^*$ at high luminosity.Comment: 4 pages Latex, 2 Figures, several style file

Anisotropy and percolation threshold in a multifractal support

Recently a multifractal object, $Q_{mf}$, was proposed to study percolation properties in a multifractal support. The area and the number of neighbors of the blocks of $Q_{mf}$ show a non-trivial behavior. The value of the probability of occupation at the percolation threshold, $p_{c}$, is a function of $\rho$, a parameter of $Q_{mf}$ which is related to its anisotropy. We investigate the relation between $p_{c}$ and the average number of neighbors of the blocks as well as the anisotropy of $Q_{mf}$