5,063 research outputs found
A perturbative approach to the Bak-Sneppen Model
We study the Bak-Sneppen model in the probabilistic framework of the Run Time
Statistics (RTS). This model has attracted a large interest for its simplicity
being a prototype for the whole class of models showing Self-Organized
Criticality. The dynamics is characterized by a self-organization of almost all
the species fitnesses above a non-trivial threshold value, and by a lack of
spatial and temporal characteristic scales. This results in {\em avalanches} of
activity power law distributed. In this letter we use the RTS approach to
compute the value of , the value of the avalanche exponent and the
asymptotic distribution of minimal fitnesses.Comment: 4 pages, 3 figures, to be published on Physical Review Letter
Onsager reciprocity relations without microscopic reversibility
In this paper we show that Onsager--Machlup time reversal properties of
thermodynamic fluctuations and Onsager reciprocity relations for transport
coefficients can hold also if the microscopic dynamics is not reversible. This
result is based on the explicit construction of a class of conservative models
which can be analysed rigorously.Comment: revtex, no figure
Non perturbative renormalization group approach to surface growth
We present a recently introduced real space renormalization group (RG)
approach to the study of surface growth.
The method permits us to obtain the properties of the KPZ strong coupling
fixed point, which is not accessible to standard perturbative field theory
approaches. Using this method, and with the aid of small Monte Carlo
calculations for systems of linear size 2 and 4, we calculate the roughness
exponent in dimensions up to d=8. The results agree with the known numerical
values with good accuracy. Furthermore, the method permits us to predict the
absence of an upper critical dimension for KPZ contrarily to recent claims. The
RG scheme is applied to other growth models in different universality classes
and reproduces very well all the observed phenomenology and numerical results.
Intended as a sort of finite size scaling method, the new scheme may simplify
in some cases from a computational point of view the calculation of scaling
exponents of growth processes.Comment: Invited talk presented at the CCP1998 (Granada
Invasion Percolation with Temperature and the Nature of SOC in Real Systems
We show that the introduction of thermal noise in Invasion Percolation (IP)
brings the system outside the critical point. This result suggests a possible
definition of SOC systems as ordinary critical systems where the critical point
correspond to set to 0 one of the parameters. We recover both IP and EDEN
model, for , and respectively. For small we find a
dynamical second order transition with correlation length diverging when .Comment: 4 pages, 2 figure
Fluctuations in Stationary non Equilibrium States
In this paper we formulate a dynamical fluctuation theory for stationary non
equilibrium states (SNS) which covers situations in a nonlinear hydrodynamic
regime and is verified explicitly in stochastic models of interacting
particles. In our theory a crucial role is played by the time reversed
dynamics. Our results include the modification of the Onsager-Machlup theory in
the SNS, a general Hamilton-Jacobi equation for the macroscopic entropy and a
non equilibrium, non linear fluctuation dissipation relation valid for a wide
class of systems
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
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
Combinatorics of lattice paths with and without spikes
We derive a series of results on random walks on a d-dimensional hypercubic
lattice (lattice paths). We introduce the notions of terse and simple paths
corresponding to the path having no backtracking parts (spikes). These paths
label equivalence classes which allow a rearrangement of the sum over paths.
The basic combinatorial quantities of this construction are given. These
formulas are useful when performing strong coupling (hopping parameter)
expansions of lattice models. Some applications are described.Comment: Latex. 25 page
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
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