5,141 research outputs found
1-d gravity in infinite point distributions
The dynamics of infinite, asymptotically uniform, distributions of
self-gravitating particles in one spatial dimension provides a simple toy model
for the analogous three dimensional problem. We focus here on a limitation of
such models as treated so far in the literature: the force, as it has been
specified, is well defined in infinite point distributions only if there is a
centre of symmetry (i.e. the definition requires explicitly the breaking of
statistical translational invariance). The problem arises because naive
background subtraction (due to expansion, or by "Jeans' swindle" for the static
case), applied as in three dimensions, leaves an unregulated contribution to
the force due to surface mass fluctuations. Following a discussion by
Kiessling, we show that the problem may be resolved by defining the force in
infinite point distributions as the limit of an exponentially screened pair
interaction. We show that this prescription gives a well defined (finite) force
acting on particles in a class of perturbed infinite lattices, which are the
point processes relevant to cosmological N-body simulations. For identical
particles the dynamics of the simplest toy model is equivalent to that of an
infinite set of points with inverted harmonic oscillator potentials which
bounce elastically when they collide. We discuss previous results in the
literature, and present new results for the specific case of this simplest
(static) model starting from "shuffled lattice" initial conditions. These show
qualitative properties (notably its "self-similarity") of the evolution very
similar to those in the analogous simulations in three dimensions, which in
turn resemble those in the expanding universe.Comment: 20 pages, 8 figures, small changes (section II shortened, added
discussion in section IV), matches final version to appear in PR
A dynamical classification of the range of pair interactions
We formalize a classification of pair interactions based on the convergence
properties of the {\it forces} acting on particles as a function of system
size. We do so by considering the behavior of the probability distribution
function (PDF) P(F) of the force field F in a particle distribution in the
limit that the size of the system is taken to infinity at constant particle
density, i.e., in the "usual" thermodynamic limit. For a pair interaction
potential V(r) with V(r) \rightarrow \infty) \sim 1/r^a defining a {\it
bounded} pair force, we show that P(F) converges continuously to a well-defined
and rapidly decreasing PDF if and only if the {\it pair force} is absolutely
integrable, i.e., for a > d-1, where d is the spatial dimension. We refer to
this case as {\it dynamically short-range}, because the dominant contribution
to the force on a typical particle in this limit arises from particles in a
finite neighborhood around it. For the {\it dynamically long-range} case, i.e.,
a \leq d-1, on the other hand, the dominant contribution to the force comes
from the mean field due to the bulk, which becomes undefined in this limit. We
discuss also how, for a \leq d-1 (and notably, for the case of gravity, a=d-2)
P(F) may, in some cases, be defined in a weaker sense. This involves a
regularization of the force summation which is generalization of the procedure
employed to define gravitational forces in an infinite static homogeneous
universe. We explain that the relevant classification in this context is,
however, that which divides pair forces with a > d-2 (or a < d-2), for which
the PDF of the {\it difference in forces} is defined (or not defined) in the
infinite system limit, without any regularization. In the former case dynamics
can, as for the (marginal) case of gravity, be defined consistently in an
infinite uniform system.Comment: 12 pages, 1 figure; significantly shortened and focussed, additional
references, version to appear in J. Stat. Phy
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 , 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.Comment: 28 pages, 1 figure, to appear in Proceedings of 9th Course on
Astrofundamental Physics, International School D. Chalonge, Kluwer, eds N.G.
Sanchez and Y.M. Pariiski, uses crckapb.st pages, 3 figure, ro appear in
Proceedings of 9th Course on Astrofundamental Physics, International School
D. Chalonge, Kluwer, Eds. N.G. Sanchez and Y.M. Pariiski, uses crckapb.st
Force distribution in a randomly perturbed lattice of identical particles with pair interaction
We study the statistics of the force felt by a particle in the class of
spatially correlated distribution of identical point-like particles,
interacting via a pair force (i.e. gravitational or Coulomb), and
obtained by randomly perturbing an infinite perfect lattice. In the first part
we specify the conditions under which the force on a particle is a well defined
stochastic quantity. We then study the small displacements approximation,
giving both the limitations of its validity, and, when it is valid, an
expression for the force variance. In the second part of the paper we extend to
this class of particle distributions the method introduced by Chandrasekhar to
study the force probability density function in the homogeneous Poisson
particle distribution. In this way we can derive an approximate expression for
the probability distribution of the force over the full range of perturbations
of the lattice, i.e., from very small (compared to the lattice spacing) to very
large where the Poisson limit is recovered. We show in particular the
qualitative change in the large-force tail of the force distribution between
these two limits. Excellent accuracy of our analytic results is found on
detailed comparison with results from numerical simulations. These results
provide basic statistical information about the fluctuations of the
interactions (i) of the masses in self-gravitating systems like those
encountered in the context of cosmological N-body simulations, and (ii) of the
charges in the ordered phase of the One Component Plasma.Comment: 23 pages, 10 figure
Fluctuations in galaxy counts: a new test for homogeneity versus 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 kind of fluctuations can be a
powerful test to understand the nature of galaxy clustering at very large
scales.Comment: 7 pages, corrected to match the published versio
Hough Transform Proposal and Simulations for Particle Track Recognition for LHC Phase-II Upgrade
In the near future, LHC experiments will continue future upgrades by overcoming the technological obsolescence of the detectors and the readout capabilities. Therefore, after the conclusion of a data collection period, CERN will have to face a long shutdown to improve overall performance, by updating the experiments, and implementing more advanced technologies and infrastructures. In particular, the largest LHC experiment, i.e., ATLAS, will upgrade parts of the detector, the trigger, and the data acquisition system. In addition, the ATLAS experiment will complete the implementation of new strategies, algorithms for data handling, and transmission to the final storage apparatus. This paper presents an overview of an upgrade planned for the second half of this decade for the ATLAS experiment. In particular, we show a study of a novel pattern recognition algorithm used in the trigger system, which is a device designed to provide the information needed to select physical events from unnecessary background data. The idea is to use a well known mathematical transform, the Hough transform, as the algorithm for the detection of particle trajectories. The effectiveness of the algorithm has already been validated in the past, regardless of particle physics applications, to recognize generic shapes within images. On the contrary, here, we first propose a software emulation tool, and a subsequent hardware implementation of the Hough transform, for particle physics applications. Until now, the Hough transform has never been implemented on electronics in particle physics experiments, and since a hardware implementation would provide benefits in terms of overall Latency, we complete the studies by comparing the simulated data with a physical system implemented on a Xilinx hardware accelerator (FELIX-II card). In more detail, we have implemented a low-abstraction RTL design of the Hough transform on Xilinx UltraScale+ FPGAs as target devices for filtering applications
Recent neutronics developments for reactor safety studies with SIMMER code at KIT
The SIMMER family of codes is applied for safety studies of sodium fast reactors and reactors of other types. Both neutronics and fluid-dynamics parts of SIMMER are under development. In the paper new neutronics capabilities are presented. In particular developments for neutron transport solvers and a new technique for taking into account thermal expansion effects are described. These new capabilities facilitate 3D simulations and improve accuracy of modelling for the initiation transient phase during a hypothetical severe accident
Modeling Heterogeneous Materials via Two-Point Correlation Functions: II. Algorithmic Details and Applications
In the first part of this series of two papers, we proposed a theoretical
formalism that enables one to model and categorize heterogeneous materials
(media) via two-point correlation functions S2 and introduced an efficient
heterogeneous-medium (re)construction algorithm called the "lattice-point"
algorithm. Here we discuss the algorithmic details of the lattice-point
procedure and an algorithm modification using surface optimization to further
speed up the (re)construction process. The importance of the error tolerance,
which indicates to what accuracy the media are (re)constructed, is also
emphasized and discussed. We apply the algorithm to generate three-dimensional
digitized realizations of a Fontainebleau sandstone and a boron
carbide/aluminum composite from the two- dimensional tomographic images of
their slices through the materials. To ascertain whether the information
contained in S2 is sufficient to capture the salient structural features, we
compute the two-point cluster functions of the media, which are superior
signatures of the micro-structure because they incorporate the connectedness
information. We also study the reconstruction of a binary laser-speckle pattern
in two dimensions, in which the algorithm fails to reproduce the pattern
accurately. We conclude that in general reconstructions using S2 only work well
for heterogeneous materials with single-scale structures. However, two-point
information via S2 is not sufficient to accurately model multi-scale media.
Moreover, we construct realizations of hypothetical materials with desired
structural characteristics obtained by manipulating their two-point correlation
functions.Comment: 35 pages, 19 figure
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