33621420
Point processes and stochastic displacement fields.
The effect of a stochastic displacement field on a statistically independent point process is analyzed. Stochastic displacement fields can be divided into two large classes: spatially correlated and uncorrelated. For both cases exact transformation equations for the two-point correlation function and the power spectrum of the point process are found, and a detailed study of them with important paradigmatic examples is done. The results are general and in any dimension. Particular attention is devoted to the kind of large-scale correlations that can be introduced by the displacement field and to the realizability of arbitrary "superhomogeneous" point processes.
9116544
Gravitational dynamics of an infinite shuffled lattice: Particle coarse-graining, nonlinear clustering, and the continuum limit.
We study the evolution under their self-gravity of particles evolving from infinite "shuffled lattice" initial conditions. We focus here specifically on the comparison between the evolution of such a system and that of "daughter" coarse-grained particle distributions. These are sparser (i.e., lower density) particle distributions, defined by a simple coarse-graining procedure, which share the same large-scale mass fluctuations. We consider both the case that such coarse-grainings are performed (i) on the initial conditions, and (ii) at a finite time with a specific additional prescription. In numerical simulations we observe that, to a first approximation, these coarse-grainings represent well the evolution of the two-point correlation properties over a significant range of scales. We note, in particular, that the form of the two-point correlation function in the original system, when it is evolving in the asymptotic "self-similar" regime, may be reproduced well in a daughter coarse-grained system in which the dynamics are still dominated by two-body (nearest neighbor) interactions. This provides a simple physical description of the origin of the form of part of the asymptotic nonlinear correlation function. Using analytical results on the early time evolution of these systems, however, we show that small observed differences between the evolved system and its coarse-grainings at the initial time will in fact diverge as the ratio of the coarse-graining scale to the original interparticle distance increases. The second coarse-graining studied, performed at a finite time in a specified manner, circumvents this problem. It also makes it more physically transparent why gravitational dynamics from these initial conditions tends toward a self-similar evolution. We finally discuss the precise definition of a limit in which a continuum (specifically Vlasov-type) description of the observed linear and nonlinear evolution should be applicable. This requires the introduction of an additional intrinsic length scale (e.g., a physical smoothing in the force at small scales), which is kept fixed as the particle density diverges. In this limit the different coarse-grainings are equivalent and leave the evolution of the "mother" system invariant.
1069360
Fluctuations in galaxy counts: A new test for homogeneity vs. fractality
Fractal properties are usually characterized by means of various statistical tools which deal with spatial average quantities. Here we focus on the determination of fluctuations around the average counts and we develop a test for the study of galaxy distribution both in redshift and magnitude space. Fluctuations in the counts of galaxies, in a fractal distribution, are of the same order of the average number at all scales as a function of redshift and magnitude. We point out that the study of these kinds of fluctuations can be a powerful test to understand the nature of galaxy clustering at very large scales.
14466810
Basic properties of galaxy clustering in the light of recent results from the Sloan Digital Sky Survey
We discuss some of the basic implications of recent results on galaxy correlations published by the SDSS collaboration. In particular we focus on the evidence which has been recently presented for the scale and nature of the transition to homogeneity in the galaxy distribution, and results which describe the dependence of clustering on luminosity. The two questions are in fact strictly entangled, as the stability of the measure of the amplitude of the correlation function depends on the scale at which the mean density becomes well defined. We note that the recent results which indicate the convergence to well defined homogeneity in a volume equivalent to that of a sphere of radius 70 Mpc/h, place in doubt previous detections of luminosity bias from measures of the amplitude of the correlation function. We emphasize that the way to resolve these issues is to first use, in volume limited samples corresponding to different ranges of luminosity, the unnormalized two point statistics to establish the scale (and value) at which the mean density becomes well defined. We note also that the recent SDSS results for these statistics are in good agreement with those obtained by us through analyses of many previous samples, confirming in particular that the galaxy distribution is well described by a fractal dimension D 2 up to a scale of at least 20 Mpc/h. We discuss critically the agreement of this new data with current theoretical models.
14013791
Initial Conditions, Discreteness and Non-Linear Structure Formation in Cosmology
In this lecture we address three different but related aspects of the initial continuous fluctuation field in standard cosmological models. Firstly we discuss the properties of the so-called Harrison-Zeldovich like spectra. This power spectrum is a fundamental feature of all current standard cosmological models. In a simple classification of all stationary stochastic processes into three categories, we highlight with the name “super- homogeneous” the properties of the class to which models like this, with P(0) = 0, belong. In statistical physics language they are well described as glass-like. Secondly, the initial continuous density field with such small amplitude correlated Gaussian fluctuations must be discretised in order to set up the initial particle distribution used in gravitational N-body simulations. We discuss the main issues related to the effects of discretisation, particularly concerning the effect of particle induced fluctuations on the statistical properties of the initial conditions and on the dynamical evolution of gravitational clustering.
31106687
Gravitational dynamics of an infinite shuffled lattice of particles.
We study, using numerical simulations, the dynamical evolution of self-gravitating point particles in static Euclidean space, starting from a simple class of infinite "shuffled lattice" initial conditions. These are obtained by applying independently to each particle on an infinite perfect lattice a small random displacement, and are characterized by a power spectrum (structure factor) of density fluctuations which is quadratic in the wave number k, at small k. For a specified form of the probability distribution function of the "shuffling" applied to each particle, and zero initial velocities, these initial configurations are characterized by a single relevant parameter: the variance delta(2) of the "shuffling" normalized in units of the lattice spacing l. The clustering, which develops in time starting from scales around l, is qualitatively very similar to that seen in cosmological simulations, which begin from lattices with applied correlated displacements and incorporate an expanding spatial background. From very soon after the formation of the first nonlinear structures, a spatiotemporal scaling relation describes well the evolution of the two-point correlations. At larger times the dynamics of these correlations converges to what is termed "self-similar" evolution in cosmology, in which the time dependence in the scaling relation is specified entirely by that of the linearized fluid theory. Comparing simulations with different delta, different resolution, but identical large scale fluctuations, we are able to identify and study features of the dynamics of the system in the transient phase leading to this behavior. In this phase, the discrete nature of the system explicitly plays an essential role.
121134571
Procedures and results of the measurements on large area photomultipliers for the NEMO project
Abstract The selection of the photomultiplier plays a crucial role in the R&D activity related to a large-scale underwater neutrino telescope. This paper illustrates the main procedures and facilities used to characterize the performances of 72 large area photomultipliers, Hamamatsu model R7081 sel. The voltage to achieve a gain of 5×10 7 , dark count rate and single photoelectron time and charge properties of the overall response were measured with a properly attenuated 410 nm pulsed laser. A dedicated study of the spurious pulses was also performed. The results prove that the photomultipliers comply with the general requirements imposed by the project.
109076725
The IBL readout system
The first upgrade for the ATLAS Pixel Detector will be an additional layer, which is called IBL (Insertable B-Layer). To readout this new layer, built from new electronics, an update of the readout electronics is necessary. The aim is to develop a system which is capable to read out at a higher bandwidth, but also compatible with the existing system to be integrated into it. This paper describes the necessary development to reach a new readout system, concentrating on the requirements of a newly designed Back of Crate card as the optical interface in the counting room.
110682003
High efficiency readout circuits for large matrices of pixels
Abstract In future collider experiments the increasing luminosity and center of mass energy are rising challenges in the research field of tracking systems where it is crucial to have very fast sensors with efficient readout in order to sustain the high particle flux. In this context we propose a high-efficiency digital readout architecture for large binary pixel matrices that is meant to cope with high hit-rates, up to 100 MHz/cm 2 , foreseen in the innermost tracker layer of the new generation particle accelerators. We modelled and designed several readout circuits to be integrated in the periphery of hybrid detectors. In this work we focus on a particular solution, to be interconnected to a 200 × 256 ‐ pixel matrix covering an area of 1.3 cm 2 . The hits are latched at pixel level, and the matrix provides a digital interface to the peripheral digital readout. The architecture is highly paralleled in order to reduce the pixels dead time introduced by readout which can be operated in data-push or triggered mode. In addition, a cluster compression algorithm, exploiting also the time sorted hit extraction, has been developed to reduce the output bandwidth. The architecture has been modelled in a hardware description language, to be synthesized in a net-list of foundry standard-cells. A Monte Carlo hit generator has been attached to simulations to evaluate the readout efficiency, both in data-push and triggered working mode. Simulation results will be presented, pointing out beside the efficiency results, the benefits introduced by the compression algorithm.
110239538
Development and simulation results of a sparsification and readout circuit for wide pixel matrices
In future collider experiments, the increasing luminosity and centre of mass energy are rising challenging problems in the design of new inner tracking systems. In this context we develop high-efficiency readout architectures for large binary pixel matrices that are meant to cope with the high-stressing conditions foreseen in the innermost layers of a tracker [The SuperB Conceptual Design Report, INFN/AE-07/02, SLAC-R-856, LAL 07-15, Available online at: http://www.pi.infn.it/SuperB ]. We model and design digital readout circuits to be integrated on VLSI ASICs. These architectures can be realized with different technology processes and sensors: they can be implemented on the same silicon sensor substrate of a CMOS MAPS devices (Monolithic Active Pixel Sensor), on the CMOS tier of a hybrid pixel sensor or in a 3D chip where the digital layer is stacked on the sensor and the analog layers [V. Re et al., Nuc. Instr. and Meth. in Phys. Res. A, doi:10.1016/j.nima.2010.05.039 ]. In the presented work, we consider a data-push architecture designed for a sensor matrix of an area of about 1.3 cm 2 with a pitch of 50 microns. The readout circuit tries to take great advantage of the high density of in-pixel digital logic allowed by vertical integration. We aim at sustaining a rate density of 100 Mtrack ⋅ s −1 ⋅ cm −2 with a temporal resolution below 1 μs . We show how this architecture can cope with these stressing conditions presenting the results of Monte Carlo simulations.
61680556
Realization and test of a 0.25$\mu$m rad-hard chip for ALICE ITS data acquisition chain