1,796 research outputs found
Stochasticity in halo formation and the excursion set approach
The simplest stochastic halo formation models assume that the traceless part
of the shear field acts to increase the initial overdensity (or decrease the
underdensity) that a protohalo (or protovoid) must have if it is to form by the
present time. Equivalently, it is the difference between the overdensity and
(the square root of the) shear that must be larger than a threshold value. To
estimate the effect this has on halo abundances using the excursion set
approach, we must solve for the first crossing distribution of a barrier of
constant height by the random walks associated with the difference, which is
now (even for Gaussian initial conditions) a non-Gaussian variate. The
correlation properties of such non-Gaussian walks are inherited from those of
the density and the shear, and, since they are independent processes, the
solution is in fact remarkably simple. We show that this provides an easy way
to understand why earlier heuristic arguments about the nature of the solution
worked so well. In addition to modelling halos and voids, this potentially
simplifies models of the abundance and spatial distribution of filaments and
sheets in the cosmic web.Comment: 5 pages, 1 figure. Matches published versio
The excursion set approach in non-Gaussian random fields
Insight into a number of interesting questions in cosmology can be obtained
from the first crossing distributions of physically motivated barriers by
random walks with correlated steps. We write the first crossing distribution as
a formal series, ordered by the number of times a walk upcrosses the barrier.
Since the fraction of walks with many upcrossings is negligible if the walk has
not taken many steps, the leading order term in this series is the most
relevant for understanding the massive objects of most interest in cosmology.
This first term only requires knowledge of the bivariate distribution of the
walk height and slope, and provides an excellent approximation to the first
crossing distribution for all barriers and smoothing filters of current
interest. We show that this simplicity survives when extending the approach to
the case of non-Gaussian random fields. For non-Gaussian fields which are
obtained by deterministic transformations of a Gaussian, the first crossing
distribution is simply related to that for Gaussian walks crossing a suitably
rescaled barrier. Our analysis shows that this is a useful way to think of the
generic case as well. Although our study is motivated by the possibility that
the primordial fluctuation field was non-Gaussian, our results are general. In
particular, they do not assume the non-Gaussianity is small, so they may be
viewed as the solution to an excursion set analysis of the late-time, nonlinear
fluctuation field rather than the initial one. They are also useful for models
in which the barrier height is determined by quantities other than the initial
density, since most other physically motivated variables (such as the shear)
are usually stochastic and non-Gaussian. We use the Lognormal transformation to
illustrate some of our arguments.Comment: 14 pages, new sections and figures describing new results, discussion
and references adde
The importance of stepping up in the excursion set approach
Recently, we provided a simple but accurate formula which closely
approximates the first crossing distribution associated with random walks
having correlated steps. The approximation is accurate for the wide range of
barrier shapes of current interest and is based on the requirement that, in
addition to having the right height, the walk must cross the barrier going
upwards. Therefore, it only requires knowledge of the bivariate distribution of
the walk height and slope, and is particularly useful for excursion set models
of the massive end of the halo mass function. However, it diverges at lower
masses. We show how to cure this divergence by using a formulation which
requires knowledge of just one other variable. While our analysis is general,
we use examples based on Gaussian initial conditions to illustrate our results.
Our formulation, which is simple and fast, yields excellent agreement with the
considerably more computationally expensive Monte-Carlo solution of the first
crossing distribution, for a wide variety of moving barriers, even at very low
masses.Comment: 10 pages, 5 figure
An analysis on health care costs due to accidents involving powered two wheelers to increase road safety
Powered Two Wheelers (PTWs) provide a convenient mode for a large portion of population in many cities. At the same time PTWs present serious system problems, the most important being poorer safety if compared to other motorized modes. But even when lower safety levels are acknowledged, problems behind are far from being solved. Rome is an example: although PTWs accidents rates are not negligible, the need for a specific safety policy is still unmet. Therefore the local Mobility Agency appointed the authors of this paper for a study of PTWs accidents occurring in the urban area. An assessment of the associated health care costs was also required. The objective of the paper is to report the main outcomes of this study highlighting recurring features of PTWs accidents, the high health care costs and how to quantify the economic resources to improve safety. The methodology was based on three steps: i) an analysis of the causes of PTWs accidents, which resulted into the location of black spots and assessment of the severity of the events; ii) the estimation of health care costs after a scientific literature review; iii) the association of health care costs to black spots and accidents severity to rank interventions to improve PTWs safety. This led to a final list of roads where PTWs accidents of the highest severity occurred and the required economic resources to improve their safety level. This stressed, for the first time, the unaffordable expenditures due to PTWs accidents. In conclusion, the issue whether the awareness of such costs can be used as leverage for more mindful behaviors among the riders is addressed
One step beyond: The excursion set approach with correlated steps
We provide a simple formula that accurately approximates the first crossing
distribution of barriers having a wide variety of shapes, by random walks with
a wide range of correlations between steps. Special cases of it are useful for
estimating halo abundances, evolution, and bias, as well as the nonlinear
counts in cells distribution. We discuss how it can be extended to allow for
the dependence of the barrier on quantities other than overdensity, to
construct an excursion set model for peaks, and to show why assembly and scale
dependent bias are generic even at the linear level.Comment: 5 pages, 1 figure. Uses mn2e class styl
Getting in shape with minimal energy. A variational principle for protohaloes
In analytical models of structure formation, protohalos are routinely assumed
to be peaks of the smoothed initial density field, with the smoothing filter
being spherically symmetric. This works reasonably well for identifying a
protohalo's center of mass, but not its shape. To provide a more realistic
description of protohalo boundaries, one must go beyond the spherical picture.
We suggest that this can be done by looking for regions of fixed volume, but
arbitrary shape, that minimize the enclosed energy. Such regions are surrounded
by surfaces over which (a slightly modified version of) the gravitational
potential is constant. We show that these equipotential surfaces provide an
excellent description of protohalo shapes, orientations and associated torques.Comment: 5 pages, 6 figure
Peaks theory and the excursion set approach
We describe a model of dark matter halo abundances and clustering which
combines the two most widely used approaches to this problem: that based on
peaks and the other based on excursion sets. Our approach can be thought of as
addressing the cloud-in-cloud problem for peaks and/or modifying the excursion
set approach so that it averages over a special subset, rather than all
possible walks. In this respect, it seeks to account for correlations between
steps in the walk as well as correlations between walks. We first show how the
excursion set and peaks models can be written in the same formalism, and then
use this correspondence to write our combined excursion set peaks model. We
then give simple expressions for the mass function and bias, showing that even
the linear halo bias factor is predicted to be k-dependent as a consequence of
the nonlocality associated with the peak constraint. At large masses, our model
has little or no need to rescale the variable delta_c from the value associated
with spherical collapse, and suggests a simple explanation for why the linear
halo bias factor appears to lie above that based on the peak-background split
at high masses when such a rescaling is assumed. Although we have concentrated
on peaks, our analysis is more generally applicable to other traditionally
single-scale analyses of large-scale structure.Comment: 10 pages, 4 figures; v2 -- minor changes, added discussion in sec2.2,
fixed a typo. Accepted in MNRA
Classical Dynamical Systems from q-algebras:"cluster" variables and explicit solutions
A general procedure to get the explicit solution of the equations of motion
for N-body classical Hamiltonian systems equipped with coalgebra symmetry is
introduced by defining a set of appropriate collective variables which are
based on the iterations of the coproduct map on the generators of the algebra.
In this way several examples of N-body dynamical systems obtained from
q-Poisson algebras are explicitly solved: the q-deformed version of the sl(2)
Calogero-Gaudin system (q-CG), a q-Poincare' Gaudin system and a system of
Ruijsenaars type arising from the same (non co-boundary) q-deformation of the
(1+1) Poincare' algebra. Also, a unified interpretation of all these systems as
different Poisson-Lie dynamics on the same three dimensional solvable Lie group
is given.Comment: 19 Latex pages, No figure
Scale dependent halo bias in the excursion set approach
If one accounts for correlations between scales, then nonlocal, k-dependent
halo bias is part and parcel of the excursion set approach, and hence of halo
model predictions for galaxy bias. We present an analysis that distinguishes
between a number of different effects, each one of which contributes to
scale-dependent bias in real space. We show how to isolate these effects and
remove the scale dependence, order by order, by cross-correlating the halo
field with suitably transformed versions of the mass field. These
transformations may be thought of as simple one-point, two-scale measurements
that allow one to estimate quantities which are usually constrained using
n-point statistics. As part of our analysis, we present a simple analytic
approximation for the first crossing distribution of walks with correlated
steps which are constrained to pass through a specified point, and demonstrate
its accuracy. Although we concentrate on nonlinear, nonlocal bias with respect
to a Gaussian random field, we show how to generalize our analysis to more
general fields.Comment: 16 pages, 10 figures; v2 -- minor changes, typos fixed, references
added, accepted in MNRA
Towards uncertainty in dimensional metrology of surface features for advanced manufacturing
In previous work, an original approach was developed for the dimensional characterisation of surface features on parts and test artefacts, aimed at supporting researchers involved in the study of advanced manufacturing processes. In the approach, methods and algorithms from image processing, coordinate metrology, surface metrology and reverse engineering are merged into an original framework for feature identification, extraction and dimensional characterisation, starting from areal topography data. With the ultimate goal of associating uncertainty to the results obtained in dimensional characterisation, this paper focuses on specifically investigating reproducibility and repeatability of dimensional characterisation results obtained on a test dataset consisting of a step-like feature manufactured by material jetting
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