Parareal in time 3D numerical solver for the LWR Benchmark neutron diffusion transient model

We present a parareal in time algorithm for the simulation of neutron diffusion transient model. The method is made efficient by means of a coarse solver defined with large time steps and steady control rods model. Using finite element for the space discretization, our implementation provides a good scalability of the algorithm. Numerical results show the efficiency of the parareal method on large light water reactor transient model corresponding to the Langenbuch-Maurer-Werner (LMW) benchmark [1]

A Simflowny-based high-performance 3D code for the generalized induction equation

In the interior of neutron stars, the induction equation regulates the long-term evolution of the magnetic fields by means of resistivity, Hall dynamics and ambipolar diffusion. Despite the apparent simplicity and compactness of the equation, the dynamics it describes is not trivial and its understanding relies on accurate numerical simulations. While a few works in 2D have reached a mature stage and a consensus on the general dynamics at least for some simple initial data, only few attempts have been performed in 3D, due to the computational costs and the need for a proper numerical treatment of the intrinsic non-linearity of the equation. Here, we carefully analyze the general induction equation, studying its characteristic structure, and we present a new Cartesian 3D code, generated by the user-friendly, publicly available {\em Simflowny} platform. The code uses high-order numerical schemes for the time and spatial discretization, and relies on the highly-scalable {\em SAMRAI} architecture for the adaptive mesh refinement. We present the application of the code to several benchmark tests, showing the high order of convergence and accuracy achieved and the capabilities in terms of magnetic shock resolution and three-dimensionality. This paper paves the way for the applications to a realistic, 3D long-term evolution of neutron stars interior and, possibly, of other astrophysical sources.Comment: 23 pages, 13 figures. In pres

On the problem of the relation between phason elasticity and phason dynamics in quasicrystals

It has recently been claimed that the dynamics of long-wavelength phason fluctuations has been observed in i-AlPdMn quasicrystals. We will show that the data reported call for a more detailed development of the elasticity theory of Jaric and Nelsson in order to determine the nature of small phonon-like atomic displacements with a symmetry that follows the phason elastic constants. We also show that a simple model with a single diffusing tile is sufficient to produce a signal that (1) is situated at a "satellite position'' at a distance q from each Bragg peak, that (2) has an intensity that scales with the intensity of the corresponding Bragg peak, (3) falls off as 1/q-squared and (4) has a time decay constant that is proportional to 1/(D q-squared). It is thus superfluous to call for a picture of "phason waves'' in order to explain such data, especially as such "waves'' violate many physical principles.Comment: 36 pages, 0 figures, discussion about vacancies, fluctuating Fourier components, and difference between static and dynamical structure factors added, other addition

The AGASA/SUGAR Anisotropies and TeV Gamma Rays from the Galactic Center: A Possible Signature of Extremely High-energy Neutrons

Recent analysis of data sets from two extensive air shower cosmic ray detectors shows tantalizing evidence of an anisotropic overabundance of cosmic rays towards the Galactic Center (GC) that ``turns on'' around $10^{18}$ eV. We demonstrate that the anisotropy could be due to neutrons created at the Galactic Center through charge-exchange in proton-proton collisions, where the incident, high energy protons obey an $\sim E^{-2}$ power law associated with acceleration at a strong shock. We show that the normalization supplied by the gamma-ray signal from EGRET GC source 3EG J1746-2851 -- ascribed to pp induced neutral pion decay at GeV energies -- together with a very reasonable spectral index of 2.2, predicts a neutron flux at $\sim 10^{18}$ eV fully consistent with the extremely high energy cosmic ray data. Likewise, the normalization supplied by the very recent GC data from the HESS air-Cerenkov telescope at \~TeV energies is almost equally-well compatible with the $\sim 10^{18}$ eV cosmic ray data. Interestingly, however, the EGRET and HESS data appear to be themselves incompatible. We consider the implications of this discrepancy. We discuss why the Galactic Center environment can allow diffusive shock acceleration at strong shocks up to energies approaching the ankle in the cosmic ray spectrum. Finally, we argue that the shock acceleration may be occuring in the shell of Sagittarius A East, an unusual supernova remnant located very close to the Galactic Center. If this connection between the anisotropy and Sagittarius A East could be firmly established it would be the first direct evidence for a particular Galactic source of cosmic rays up to energies near the ankle.Comment: 57 pages, 2 figure