4,783 research outputs found
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
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
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
Source to tap investigation of natural organic matter in non-disinfected drinking water distribution systems
Despite being reduced by treatment, natural organic matter (NOM) is ubiquitous in drinking water distribution systems (DWDSs) from sources to consumers' taps where it can potentially have negative impacts on drinking water quality. While a few studies have investigated its behaviour in disinfected and NOM-rich DWDSs, its dynamics in non-disinfected systems, characterized by low NOM content, have not yet been explored. In this study, we monitored the NOM variations occurring between groundwater sources and consumers' taps of a non-disinfected DWDS, including three drinking water treatment plants, using both fluorescence and absorbance, selected due to their increasing adoption by water utilities. PARAFAC analysis of fluorescence data, combined with absorbance indices, highlighted how NOM characteristics in groundwater vary due to the combination of multiple factors (e.g., well depth, pumping rate), especially in the case of shallower aquifers. The treatment processes display different effects on NOM when monitored by fluorescence and absorbance, due to the differences among fluorophores and between fluorescent and chromophoric molecules. Variations of the NOM characteristics between the treatment plant outlets and sampling locations within the network were detected only in few locations, suggesting the importance of the processes occurring in specific sections of the network and the last meter before consumption. These findings highlight the overall stability of water quality within non- disinfected NOM-poor DWDSs, but they stress the importance of (i) properly selecting the analytical method to be used for monitoring and (ii) localized water quality variations mainly related to pipe materials, suggesting several implications for DWDS monitoring and management
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
Strongly coupled N=1 SYM theory on the lattice
We propose a strong coupling expansion as a possible tool to obtain
qualitative and quantitative informations about N=1 SYM theory. We point out
the existence of a mapping between strongly coupled lattice N=1 SYM theory and
a generalized SO(4) antiferromagnetic spin system.Comment: Lattice2002(spin), 3 pages, no figure
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
Diffusion, super-diffusion and coalescence from single step
From the exact single step evolution equation of the two-point correlation
function of a particle distribution subjected to a stochastic displacement
field \bu(\bx), we derive different dynamical regimes when \bu(\bx) is
iterated to build a velocity field. First we show that spatially uncorrelated
fields \bu(\bx) lead to both standard and anomalous diffusion equation. When
the field \bu(\bx) is spatially correlated each particle performs a simple
free Brownian motion, but the trajectories of different particles result to be
mutually correlated. The two-point statistical properties of the field
\bu(\bx) induce two-point spatial correlations in the particle distribution
satisfying a simple but non-trivial diffusion-like equation. These
displacement-displacement correlations lead the system to three possible
regimes: coalescence, simple clustering and a combination of the two. The
existence of these different regimes, in the one-dimensional system, is shown
through computer simulations and a simple theoretical argument.Comment: RevTeX (iopstyle) 19 pages, 5 eps-figure
Laplacian Fractal Growth in Media with Quenched Disorder
We analyze the combined effect of a Laplacian field and quenched disorder for
the generation of fractal structures with a study, both numerical and
theoretical, of the quenched dielectric breakdown model (QDBM). The growth
dynamics is shown to evolve from the avalanches of invasion percolation (IP) to
the smooth growth of Laplacian fractals, i. e. diffusion limited aggregation
(DLA) and the dielectric breakdown model (DBM). The fractal dimension is
strongly reduced with respect to both DBM and IP, due to the combined effect of
memory and field screening. This implies a specific relation between the
fractal dimension of the breakdown structures (dielectric or mechanical) and
the microscopic properties of disordered materials.Comment: 11 pages Latex (revtex), 3 postscript figures included. Submitted to
PR
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