The cosmological simulation code GADGET-2

We discuss the cosmological simulation code GADGET-2, a new massively parallel TreeSPH code, capable of following a collisionless fluid with the N-body method, and an ideal gas by means of smoothed particle hydrodynamics (SPH). Our implementation of SPH manifestly conserves energy and entropy in regions free of dissipation, while allowing for fully adaptive smoothing lengths. Gravitational forces are computed with a hierarchical multipole expansion, which can optionally be applied in the form of a TreePM algorithm, where only short-range forces are computed with the `tree'-method while long-range forces are determined with Fourier techniques. Time integration is based on a quasi-symplectic scheme where long-range and short-range forces can be integrated with different timesteps. Individual and adaptive short-range timesteps may also be employed. The domain decomposition used in the parallelisation algorithm is based on a space-filling curve, resulting in high flexibility and tree force errors that do not depend on the way the domains are cut. The code is efficient in terms of memory consumption and required communication bandwidth. It has been used to compute the first cosmological N-body simulation with more than 10^10 dark matter particles, reaching a homogeneous spatial dynamic range of 10^5 per dimension in a 3D box. It has also been used to carry out very large cosmological SPH simulations that account for radiative cooling and star formation, reaching total particle numbers of more than 250 million. We present the algorithms used by the code and discuss their accuracy and performance using a number of test problems. GADGET-2 is publicly released to the research community.Comment: submitted to MNRAS, 31 pages, 20 figures (reduced resolution), code available at http://www.mpa-garching.mpg.de/gadge

Convolutional Codes in Rank Metric with Application to Random Network Coding

Random network coding recently attracts attention as a technique to disseminate information in a network. This paper considers a non-coherent multi-shot network, where the unknown and time-variant network is used several times. In order to create dependencies between the different shots, particular convolutional codes in rank metric are used. These codes are so-called (partial) unit memory ((P)UM) codes, i.e., convolutional codes with memory one. First, distance measures for convolutional codes in rank metric are shown and two constructions of (P)UM codes in rank metric based on the generator matrices of maximum rank distance codes are presented. Second, an efficient error-erasure decoding algorithm for these codes is presented. Its guaranteed decoding radius is derived and its complexity is bounded. Finally, it is shown how to apply these codes for error correction in random linear and affine network coding.Comment: presented in part at Netcod 2012, submitted to IEEE Transactions on Information Theor

GADGET: A code for collisionless and gasdynamical cosmological simulations

We describe the newly written code GADGET which is suitable both for cosmological simulations of structure formation and for the simulation of interacting galaxies. GADGET evolves self-gravitating collisionless fluids with the traditional N-body approach, and a collisional gas by smoothed particle hydrodynamics. Along with the serial version of the code, we discuss a parallel version that has been designed to run on massively parallel supercomputers with distributed memory. While both versions use a tree algorithm to compute gravitational forces, the serial version of GADGET can optionally employ the special-purpose hardware GRAPE instead of the tree. Periodic boundary conditions are supported by means of an Ewald summation technique. The code uses individual and adaptive timesteps for all particles, and it combines this with a scheme for dynamic tree updates. Due to its Lagrangian nature, GADGET thus allows a very large dynamic range to be bridged, both in space and time. So far, GADGET has been successfully used to run simulations with up to 7.5e7 particles, including cosmological studies of large-scale structure formation, high-resolution simulations of the formation of clusters of galaxies, as well as workstation-sized problems of interacting galaxies. In this study, we detail the numerical algorithms employed, and show various tests of the code. We publically release both the serial and the massively parallel version of the code.Comment: 32 pages, 14 figures, replaced to match published version in New Astronomy. For download of the code, see http://www.mpa-garching.mpg.de/gadget (new version 1.1 available

The stellar atmosphere simulation code Bifrost

Context: Numerical simulations of stellar convection and photospheres have been developed to the point where detailed shapes of observed spectral lines can be explained. Stellar atmospheres are very complex, and very different physical regimes are present in the convection zone, photosphere, chromosphere, transition region and corona. To understand the details of the atmosphere it is necessary to simulate the whole atmosphere since the different layers interact strongly. These physical regimes are very diverse and it takes a highly efficient massively parallel numerical code to solve the associated equations. Aims: The design, implementation and validation of the massively parallel numerical code Bifrost for simulating stellar atmospheres from the convection zone to the corona. Methods: The code is subjected to a number of validation tests, among them the Sod shock tube test, the Orzag-Tang colliding shock test, boundary condition tests and tests of how the code treats magnetic field advection, chromospheric radiation, radiative transfer in an isothermal scattering atmosphere, hydrogen ionization and thermal conduction. Results: Bifrost completes the tests with good results and shows near linear efficiency scaling to thousands of computing cores

Stable quantum memories with limited measurement

We demonstrate the existence of a finite temperature threshold for a 1D stabilizer code under an error correcting protocol that requires only a fraction of the syndrome measurements. Below the threshold temperature, encoded states have exponentially long lifetimes, as demonstrated by numerical and analytical arguments. We sketch how this algorithm generalizes to higher dimensional stabilizer codes with string-like excitations, like the toric code.Comment: 11 Pages, 7 Figure