Large-Scale Simulations of Reionization

We use cosmological simulations to explore the large-scale effects of reionization. Since reionization is a process that involves a large dynamic range - from galaxies to rare bright quasars - we need to be able to cover a significant volume of the universe in our simulation without losing hte important small scale effects from galaxies. Here we have taken an approach that uses clumping factors derived from small scale simulations to approximate the radiative transfer on the sub-cell scales. Using this technique, we can cover a simulation size up to $1280 h^{-1} Mpc$ with $10 h^{-1} Mpc$ cells. This allows us to construct synthetic spectra of quasars similar to observed spectra of SDSS quasars at high reshifts and compare them to the observational data. These spectra can then be analyzed for HII region sizes, the presence of the Gunn-Peterson trough and the Lyman-$\alpha$ forest.Comment: 25 page

Fast Large-Scale Reionization Simulations

We present an efficient method to generate large simulations of the Epoch of Reionization (EoR) without the need for a full 3-dimensional radiative transfer code. Large dark-matter-only simulations are post-processed to produce maps of the redshifted 21cm emission from neutral hydrogen. Dark matter haloes are embedded with sources of radiation whose properties are either based on semi-analytical prescriptions or derived from hydrodynamical simulations. These sources could either be stars or power-law sources with varying spectral indices. Assuming spherical symmetry, ionized bubbles are created around these sources, whose radial ionized fraction and temperature profiles are derived from a catalogue of 1-D radiative transfer experiments. In case of overlap of these spheres, photons are conserved by redistributing them around the connected ionized regions corresponding to the spheres. The efficiency with which these maps are created allows us to span the large parameter space typically encountered in reionization simulations. We compare our results with other, more accurate, 3-D radiative transfer simulations and find excellent agreement for the redshifts and the spatial scales of interest to upcoming 21cm experiments. We generate a contiguous observational cube spanning redshift 6 to 12 and use these simulations to study the differences in the reionization histories between stars and quasars. Finally, the signal is convolved with the LOFAR beam response and its effects are analyzed and quantified. Statistics performed on this mock data set shed light on possible observational strategies for LOFAR.Comment: 18 pages, 21 figures, submitted to MNRAS For high-resolution images follow "http://www.astro.rug.nl/~thomas/eormap.pdf

Large-Scale Simulations of Clusters of Galaxies

We discuss some of the computational challenges encountered in simulating the evolution of clusters of galaxies. Eulerian adaptive mesh refinement (AMR) techniques can successfully address these challenges but are currently being used by only a few groups. We describe our publicly available AMR code, FLASH, which uses an object-oriented framework to manage its AMR library, physics modules, and automated verification. We outline the development of the FLASH framework to include collisionless particles, permitting it to be used for cluster simulation.Comment: 3 pages, 3 figures, to appear in Proceedings of the VII International Workshop on Advanced Computing and Analysis Techniques in Physics Research (ACAT 2000), Fermilab, Oct. 16-20, 200

Large scale ab-initio simulations of dislocations

We present a novel methodology to compute relaxed dislocations core configurations, and their energies in crystalline metallic materials using large-scale ab-intio simulations. The approach is based on MacroDFT, a coarse-grained density functional theory method that accurately computes the electronic structure with sub-linear scaling resulting in a tremendous reduction in cost. Due to its implementation in real-space, MacroDFT has the ability to harness petascale resources to study materials and alloys through accurate ab-initio calculations. Thus, the proposed methodology can be used to investigate dislocation cores and other defects where long range elastic effects play an important role, such as in dislocation cores, grain boundaries and near precipitates in crystalline materials. We demonstrate the method by computing the relaxed dislocation cores in prismatic dislocation loops and dislocation segments in magnesium (Mg). We also study the interaction energy with a line of Aluminum (Al) solutes. Our simulations elucidate the essential coupling between the quantum mechanical aspects of the dislocation core and the long range elastic fields that they generate. In particular, our quantum mechanical simulations are able to describe the logarithmic divergence of the energy in the far field as is known from classical elastic theory. In order to reach such scaling, the number of atoms in the simulation cell has to be exceedingly large, and cannot be achieved with the state-of-the-art density functional theory implementations

The Alignment of Clusters using Large Scale Simulations

The alignment of clusters of galaxies with their nearest neighbours and between clusters within a supercluster is investigated using simulations of 512^{3} dark matter particles for \LambdaCDM and \tauCDM cosmological models. Strongly significant alignments are found for separations of up to 15h^{-1}Mpc in both cosmologies, but for the \LambdaCDM model the alignments extend up to separations of 30h^{-1}Mpc. The effect is strongest for nearest neighbours, but is not significant enough to be useful as an observational discriminant between cosmologies. As a check of whether this difference in alignments is present in other cosmologies, smaller simulations with 256^{3} particles are investigated for 4 different cosmological models. Because of poor number statistics, only the standard CDM model shows indications of having different alignments from the other models.Comment: 6 pages, 5 figures Submitted to MNRA

Large scale simulations of the jet-IGM interaction

In a parameter study extending to jet densities of $10^{-5}$ times the ambient one, I have recently shown that light large scale jets start their lives in a spherical bow shock phase. This allows an easy description of the sideways bow shock propagation in that phase. Here, I present new, bipolar, simulations of very light jets in 2.5D and 3D, reaching the observationally relevant scale of $>200$ jet radii. Deviations from the early bow shock propagation law are expected because of various effects. The net effect is, however, shown to remain small. I calculate the X-ray appearance of the shocked cluster gas and compare it to Cygnus A and 3C 317. Rings, bright spots and enhancements inside the radio cocoon may be explained.Comment: 8 pages, 5 figures, ApSS accepted, proceedings of the virtual jets 2003 conference in Dogliani/Italy, v3: funny and unimportant bug corrected, one reference adde

Robustness of Cosmological Simulations I: Large Scale Structure

The gravitationally-driven evolution of cold dark matter dominates the formation of structure in the Universe over a wide range of length scales. While the longest scales can be treated by perturbation theory, a fully quantitative understanding of nonlinear effects requires the application of large-scale particle simulation methods. Additionally, precision predictions for next-generation observations, such as weak gravitational lensing, can only be obtained from numerical simulations. In this paper, we compare results from several N-body codes using test problems and a diverse set of diagnostics, focusing on a medium resolution regime appropriate for studying many observationally relevant aspects of structure formation. Our conclusions are that -- despite the use of different algorithms and error-control methodologies -- overall, the codes yield consistent results. The agreement over a wide range of scales for the cosmological tests is test-dependent. In the best cases, it is at the 5% level or better, however, for other cases it can be significantly larger than 10%. These include the halo mass function at low masses and the mass power spectrum at small scales. While there exist explanations for most of the discrepancies, our results point to the need for significant improvement in N-body errors and their understanding to match the precision of near-future observations. The simulation results, including halo catalogs, and initial conditions used, are publicly available.Comment: 32 pages, 53 figures, data from the simulations is available at http://t8web.lanl.gov/people/heitmann/arxiv, accepted for publication in ApJS, several minor revisions, reference added, main conclusions unchange

Large-scale Ferrofluid Simulations on Graphics Processing Units

We present an approach to molecular-dynamics simulations of ferrofluids on graphics processing units (GPUs). Our numerical scheme is based on a GPU-oriented modification of the Barnes-Hut (BH) algorithm designed to increase the parallelism of computations. For an ensemble consisting of one million of ferromagnetic particles, the performance of the proposed algorithm on a Tesla M2050 GPU demonstrated a computational-time speed-up of four order of magnitude compared to the performance of the sequential All-Pairs (AP) algorithm on a single-core CPU, and two order of magnitude compared to the performance of the optimized AP algorithm on the GPU. The accuracy of the scheme is corroborated by comparing the results of numerical simulations with theoretical predictions

Entropic effects in large-scale Monte Carlo simulations

The efficiency of Monte Carlo samplers is dictated not only by energetic effects, such as large barriers, but also by entropic effects that are due to the sheer volume that is sampled. The latter effects appear in the form of an entropic mismatch or divergence between the direct and reverse trial moves. We provide lower and upper bounds for the average acceptance probability in terms of the Renyi divergence of order 1/2. We show that the asymptotic finitude of the entropic divergence is the necessary and sufficient condition for non-vanishing acceptance probabilities in the limit of large dimensions. Furthermore, we demonstrate that the upper bound is reasonably tight by showing that the exponent is asymptotically exact for systems made up of a large number of independent and identically distributed subsystems. For the last statement, we provide an alternative proof that relies on the reformulation of the acceptance probability as a large deviation problem. The reformulation also leads to a class of low-variance estimators for strongly asymmetric distributions. We show that the entropy divergence causes a decay in the average displacements with the number of dimensions n that are simultaneously updated. For systems that have a well-defined thermodynamic limit, the decay is demonstrated to be n^{-1/2} for random-walk Monte Carlo and n^{-1/6} for Smart Monte Carlo (SMC). Numerical simulations of the LJ_38 cluster show that SMC is virtually as efficient as the Markov chain implementation of the Gibbs sampler, which is normally utilized for Lennard-Jones clusters. An application of the entropic inequalities to the parallel tempering method demonstrates that the number of replicas increases as the square root of the heat capacity of the system.Comment: minor corrections; the best compromise for the value of the epsilon parameter in Eq. A9 is now shown to be log(2); 13 pages, 4 figures, to appear in PR