Why charges go to the surface: a generalized Thomson problem

We study a generalization of a Thomson problem of n particles confined to a sphere and interacting by a 1/r^g potential. It is found that for g \le 1 the electrostatic repulsion expels all the charges to the surface of the sphere. However for g>1 and n>n_c(g) occupation of the bulk becomes energetically favorable. It is curious to note that the Coulomb law lies exactly on the interface between these two regimes

Simulation of Ultra-High Energy Photon Propagation in the Geomagnetic Field

The identification of primary photons or specifying stringent limits on the photon flux is of major importance for understanding the origin of ultra-high energy (UHE) cosmic rays. We present a new Monte Carlo program allowing detailed studies of conversion and cascading of UHE photons in the geomagnetic field. The program named PRESHOWER can be used both as an independent tool or together with a shower simulation code. With the stand-alone version of the code it is possible to investigate various properties of the particle cascade induced by UHE photons interacting in the Earth's magnetic field before entering the Earth's atmosphere. Combining this program with an extensive air shower simulation code such as CORSIKA offers the possibility of investigating signatures of photon-initiated showers. In particular, features can be studied that help to discern such showers from the ones induced by hadrons. As an illustration, calculations for the conditions of the southern part of the Pierre Auger Observatory are presented.Comment: 41 pages, 9 figures, added references in introduction, corrected energy in row 1 of Table 3, extended caption of Table

Crystalline Order on a Sphere and the Generalized Thomson Problem

We attack generalized Thomson problems with a continuum formalism which exploits a universal long range interaction between defects depending on the Young modulus of the underlying lattice. Our predictions for the ground state energy agree with simulations of long range power law interactions of the form 1/r^{gamma} (0 < gamma < 2) to four significant digits. The regime of grain boundaries is studied in the context of tilted crystalline order and the generality of our approach is illustrated with new results for square tilings on the sphere.Comment: 4 pages, 5 eps figures Fig. 2 revised, improved Fig. 3, reference typo fixe

On a possible photon origin of the most-energetic AGASA events

In this work the ultra high energy cosmic ray events recorded by the AGASA experiment are analysed. With detailed simulations of the extensive air showers initiated by photons, the probabilities are determined of the photonic origin of the 6 AGASA events for which the muon densities were measured and the reconstructed energies exceeded 10^20 eV. On this basis a new, preliminary upper limit on the photon fraction in cosmic rays above 10^20 eV is derived and compared to the predictions of exemplary top-down cosmic-ray origin models.Comment: 3 pages, 1 figure, 2 tables; presented at XIII ISVHECRI, Pylos, Greec

Characteristics of geomagnetic cascading of ultra-high energy photons at the southern and northern sites of the Pierre Auger Observatory

Cosmic-ray photons above 10^19 eV can convert in the geomagnetic field and initiate a preshower, i.e. a particle cascade before entering the atmosphere. We compare the preshower characteristics at the southern and northern sites of the Pierre Auger Observatory. In addition to a shift of the preshower patterns on the sky due to the different pointing of the local magnetic field vectors, the fact that the northern Auger site is closer to the geomagnetic pole results in a different energy dependence of the preshower effect: photon conversion can start at smaller energies, but large conversion probabilitites (>90%) are reached for the whole sky at higher energies compared to the southern Auger site. We show how the complementary preshower features at the two sites can be used to search for ultra-high energy photons among cosmic rays. In particular, the different preshower characteristics at the northern Auger site may provide an elegant and unambiguous confirmation if a photon signal is detected at the southern site.Comment: 25 pages, 14 figures, minor changes, conclusions unchanged, Appendix A replaced, accepted by Astroparticle Physic

Plasma Magnetosphere Formation Around Oscillating Magnetized Neutron Stars

The notion of death line of rotating pulsars is applied to model of oscillating neutron stars. It is shown that the magnetosphere of typical non-rotating oscillating stars may not contain secondary plasma to support the generation of radio emission in the region of open field lines of plasma magnetosphere.Comment: Accepted for publication in Astrophysics & Space Scienc

Euler configurations and quasi-polynomial systems

In the Newtonian 3-body problem, for any choice of the three masses, there are exactly three Euler configurations (also known as the three Euler points). In Helmholtz' problem of 3 point vortices in the plane, there are at most three collinear relative equilibria. The "at most three" part is common to both statements, but the respective arguments for it are usually so different that one could think of a casual coincidence. By proving a statement on a quasi-polynomial system, we show that the "at most three" holds in a general context which includes both cases. We indicate some hard conjectures about the configurations of relative equilibrium and suggest they could be attacked within the quasi-polynomial framework.Comment: 21 pages, 6 figure

Dysregulation of the intrinsic apoptotic pathway mediates megakaryocytic hyperplasia in myeloproliferative neoplasms

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Limits on models of the ultrahigh energy cosmic rays based on topological defects

An erratum exists for this article. Please see the description link below for details.Using the propagation of ultrahigh energy nucleons, photons, and electrons in the universal radiation backgrounds, we obtain limits on the luminosity of topological defect scenarios for the origin of the highest energy cosmic rays. The limits are set as a function of the mass of the X particles emitted by the cosmic strings or other defects, the cosmological evolution of the topological defects, and the strength of the extragalactic magnetic fields. The existing data on the cosmic ray spectrum and on the isotropic 100 MeV gamma-ray background limit significantly the parameter space in which topological defects can generate the flux of the highest energy cosmic rays, and rule out models with the standard X-particle mass of 10¹⁶GeV and higher.R. J. Protheroe and Todor Stane

Radiation in Lorentz violating electrodynamics

Synchrotron radiation is analyzed in the classical effective Lorentz invariance violating model of Myers-Pospelov. Within the full far-field approximation we compute the electric and magnetic fields, the angular distribution of the power spectrum and the total emitted power in the m-th harmonic, as well as the polarization. We find the appearance of rather unexpected and large amplifying factors, which go together with the otherwise negligible naive expansion parameter. This opens up the possibility of further exploring Lorentz invariance violations by synchrotron radiation measurements in astrophysical sources where these amplifying factors are important.Comment: Presented at the Second Mexican Meeting on Theoretical and Experimental Physics, El Colegio Nacional, Mexico City, 6-10 September 200