2,053 research outputs found
Granular Brownian motion
We study the stochastic motion of an intruder in a dilute driven granular
gas. All particles are coupled to a thermostat, representing the external
energy source, which is the sum of random forces and a viscous drag. The
dynamics of the intruder, in the large mass limit, is well described by a
linear Langevin equation, combining the effects of the external bath and of the
"granular bath". The drag and diffusion coefficients are calculated under few
assumptions, whose validity is well verified in numerical simulations. We also
discuss the non-equilibrium properties of the intruder dynamics, as well as the
corrections due to finite packing fraction or finite intruder mass.Comment: 19 pages, 4 figures, in press on Journal of Statistical Mechanics:
Theory and Experiment
Rank, select and access in grammar-compressed strings
Given a string of length on a fixed alphabet of symbols, a
grammar compressor produces a context-free grammar of size that
generates and only . In this paper we describe data structures to
support the following operations on a grammar-compressed string:
\mbox{rank}_c(S,i) (return the number of occurrences of symbol before
position in ); \mbox{select}_c(S,i) (return the position of the th
occurrence of in ); and \mbox{access}(S,i,j) (return substring
). For rank and select we describe data structures of size
bits that support the two operations in time. We
propose another structure that uses
bits and that supports the two queries in , where
is an arbitrary constant. To our knowledge, we are the first to
study the asymptotic complexity of rank and select in the grammar-compressed
setting, and we provide a hardness result showing that significantly improving
the bounds we achieve would imply a major breakthrough on a hard
graph-theoretical problem. Our main result for access is a method that requires
bits of space and time to extract
consecutive symbols from . Alternatively, we can achieve query time using bits of space. This matches a lower bound stated by Verbin
and Yu for strings where is polynomially related to .Comment: 16 page
Lempel-Ziv Parsing in External Memory
For decades, computing the LZ factorization (or LZ77 parsing) of a string has
been a requisite and computationally intensive step in many diverse
applications, including text indexing and data compression. Many algorithms for
LZ77 parsing have been discovered over the years; however, despite the
increasing need to apply LZ77 to massive data sets, no algorithm to date scales
to inputs that exceed the size of internal memory. In this paper we describe
the first algorithm for computing the LZ77 parsing in external memory. Our
algorithm is fast in practice and will allow the next generation of text
indexes to be realised for massive strings and string collections.Comment: 10 page
Noise Rectification and Fluctuations of an Asymmetric Inelastic Piston
We consider a massive inelastic piston, whose opposite faces have different
coefficients of restitution, moving under the action of an infinitely dilute
gas of hard disks maintained at a fixed temperature. The dynamics of the piston
is Markovian and obeys a continuous Master Equation: however, the asymmetry of
restitution coefficients induces a violation of detailed balance and a net
drift of the piston, as in a Brownian ratchet. Numerical investigations of such
non-equilibrium stationary state show that the velocity fluctuations of the
piston are symmetric around the mean value only in the limit of large piston
mass, while they are strongly asymmetric in the opposite limit. Only taking
into account such an asymmetry, i.e. including a third parameter in addition to
the mean and the variance of the velocity distribution, it is possible to
obtain a satisfactory analytical prediction for the ratchet drift velocity.Comment: 6 pages, 5 figures, to be published on Europhysics Letters; some
references have been adde
Effect of vegetation on sound fields in idealised urban open spaces
Noise pollution is a major environmental problem within the EU and during the last years vegetation was examined for its benefits in increasing health and well-being of citizens from different viewpoints, including noise control and soundscape enhancement. This work focuses on numerical simulations to investigate the effectiveness of vegetation for controlling sound fields, especially in terms of the abatement of traffic noise. Two idealised urban squares were studied, one rectangular and one octagonal. Three plant types, climbing plants (ivy), living green walls with soil substrate and plants in pots (nephrolepis exaltata), were used in this investigation, based on their measured properties in laboratory, and four aspects of the use of vegetation were evaluated: effect of the amount of vegetation, effect of changing in the scattering coefficient of vegetation, effect of vegetation in different receiver positions and effect of vegetation on different groups of receivers. Parametric studies on the determination of a line source and on the definition of sound power levels referred to traffic noise were also developed. Three simulation tools were used, namely CATT-Acoustic®, CRR (Combined Ray-tracing and Radiosity) and Odeon
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