3,668 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

### Field theory of self-organized fractal etching

We propose a phenomenological field theoretical approach to the chemical
etching of a disordered-solid. The theory is based on a recently proposed
dynamical etching model. Through the introduction of a set of Langevin
equations for the model evolution, we are able to map the problem into a field
theory related to isotropic percolation. To the best of the authors knowledge,
it constitutes the first application of field theory to a problem of chemical
dynamics. By using this mapping, many of the etching process critical
properties are seen to be describable in terms of the percolation
renormalization group fixed point. The emerging field theory has the
peculiarity of being ``{\it self-organized}'', in the sense that without any
parameter fine-tuning, the system develops fractal properties up to certain
scale controlled solely by the volume, $V$, of the etching solution.
In the limit $V \to \infty$ the upper cut-off goes to infinity and the system
becomes scale invariant. We present also a finite size scaling analysis and
discuss the relation of this particular etching mechanism with Gradient
Percolation.
Finally, the possibility of considering this mechanism as a new generic path
to self-organized criticality is analyzed, with the characteristics of being
closely related to a real physical system and therefore more directly
accessible to experiments.Comment: 9 pages, 3 figures. Submitted to Phys. Rev.

### 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 $x_c$, the value of the avalanche exponent $\tau$ and the
asymptotic distribution of minimal fitnesses.Comment: 4 pages, 3 figures, to be published on Physical Review Letter

### Statistical properties of fractures in damaged materials

We introduce a model for the dynamics of mud cracking in the limit of of
extremely thin layers. In this model the growth of fracture proceeds by
selecting the part of the material with the smallest (quenched) breaking
threshold. In addition, weakening affects the area of the sample neighbour to
the crack. Due to the simplicity of the model, it is possible to derive some
analytical results. In particular, we find that the total time to break down
the sample grows with the dimension L of the lattice as L^2 even though the
percolating cluster has a non trivial fractal dimension. Furthermore, we obtain
a formula for the mean weakening with time of the whole sample.Comment: 5 pages, 4 figures, to be published in Europhysics Letter

### Combination of the searches for the low-mass Standard Model Higgs boson with ATLAS detector

In this paper, a brief overview of the results, based on proton-proton collision data recorded at a centre-of-mass energy of 7TeV in 2011 and 8TeV in 2012, for the properties of a new Higgs-like particle at 125.5 GeV are presented

### 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

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