736 research outputs found

### Multiplicities in ultrarelativistic proton-(anti)proton collisions and negative binomial distribution fits

Likelihood ratio tests are performed for the hypothesis that charged-particle
multiplicities measured in proton-(anti)proton collisions at $\sqrt{s}$ = 0.9
and 2.36 TeV are distributed according to the negative binomial form. Results
indicate that the hypothesis should be rejected in the all cases of ALICE-LHC
measurements in the limited pseudo-rapidity windows, whereas should be accepted
in the corresponding cases of UA5 data. Possible explanations of that and of
the disagreement with the least-squares fitting method are given.Comment: 14 pages, clarified version, reference added. To appear in
International Journal of Modern Physics

### The inelastic hard dimer gas: a non-spherical model for granular matter

We study a two-dimensional gas of inelastic smooth hard dimers. Since the
collisions between dimers are dissipative, being characterized by a coefficient
of restitution $\alpha<1$, and no external driving force is present, the energy
of the system decreases in time and no stationary state is achieved. However,
the resulting non equilibrium state of the system displays several interesting
properties in close analogy with systems of inelastic hard spheres, whose
relaxational dynamics has been thoroughly explored. We generalise to inelastic
systems a recently method introduced [G.Ciccotti and G.Kalibaeva, J. Stat.
Phys. {\bf 115}, 701 (2004)] to study the dynamics of rigid elastic bodies made
up of different spheres hold together by rigid bonds. Each dimer consists of
two hard disks of diameter $d$, whose centers are separated by a fixed distance
$a$. By describing the rigid bonds by means of holonomic constraints and
deriving the appropriate collision rules between dimers, we reduce the dynamics
to a set of equations which can be solved by means of event driven simulation.
After deriving the algorithm we study the decay of the total kinetic energy,
and of the ratio between the rotational and the translational kinetic energy of
inelastic dimers. We show numerically that the celebrated Haff's homogeneous
cooling law $t^{-2}$, describing how the kinetic energy of an inelastic hard
sphere system with constant coefficient of restitution decreases in time, holds
even in the case of these non spherical particles. We fully characterize this
homogeneous decay process in terms of appropriate decay constants and confirm
numerically the scaling behavior of the velocity distributions.Comment: 21 pages, 6 figures and 2 tables, submitted to JC

### Time-averaged MSD of Brownian motion

We study the statistical properties of the time-averaged mean-square
displacements (TAMSD). This is a standard non-local quadratic functional for
inferring the diffusion coefficient from an individual random trajectory of a
diffusing tracer in single-particle tracking experiments. For Brownian motion,
we derive an exact formula for the Laplace transform of the probability density
of the TAMSD by mapping the original problem onto chains of coupled harmonic
oscillators. From this formula, we deduce the first four cumulant moments of
the TAMSD, the asymptotic behavior of the probability density and its accurate
approximation by a generalized Gamma distribution

### Information filtering via Iterative Refinement

With the explosive growth of accessible information, expecially on the
Internet, evaluation-based filtering has become a crucial task. Various systems
have been devised aiming to sort through large volumes of information and
select what is likely to be more relevant. In this letter we analyse a new
ranking method, where the reputation of information providers is determined
self-consistently.Comment: 10 pages, 3 figures. Accepted for publication on Europhysics Letter

### The Ehrenfest urn revisited: Playing the game on a realistic fluid model

The Ehrenfest urn process, also known as the dogs and fleas model, is
realistically simulated by molecular dynamics of the Lennard-Jones fluid. The
key variable is Delta z, i.e. the absolute value of the difference between the
number of particles in one half of the simulation box and in the other half.
This is a pure-jump stochastic process induced, under coarse graining, by the
deterministic time evolution of the atomic coordinates. We discuss the Markov
hypothesis by analyzing the statistical properties of the jumps and of the
waiting times between jumps. In the limit of a vanishing integration time-step,
the distribution of waiting times becomes closer to an exponential and,
therefore, the continuous-time jump stochastic process is Markovian. The random
variable Delta z behaves as a Markov chain and, in the gas phase, the observed
transition probabilities follow the predictions of the Ehrenfest theory.Comment: Accepted by Physical Review E on 4 May 200

### Generalized Master Equations for Non-Poisson Dynamics on Networks

The traditional way of studying temporal networks is to aggregate the
dynamics of the edges to create a static weighted network. This implicitly
assumes that the edges are governed by Poisson processes, which is not
typically the case in empirical temporal networks. Consequently, we examine the
effects of non-Poisson inter-event statistics on the dynamics of edges, and we
apply the concept of a generalized master equation to the study of
continuous-time random walks on networks. We show that the equation reduces to
the standard rate equations when the underlying process is Poisson and that the
stationary solution is determined by an effective transition matrix whose
leading eigenvector is easy to calculate. We discuss the implications of our
work for dynamical processes on temporal networks and for the construction of
network diagnostics that take into account their nontrivial stochastic nature

### The effect of discrete vs. continuous-valued ratings on reputation and ranking systems

When users rate objects, a sophisticated algorithm that takes into account
ability or reputation may produce a fairer or more accurate aggregation of
ratings than the straightforward arithmetic average. Recently a number of
authors have proposed different co-determination algorithms where estimates of
user and object reputation are refined iteratively together, permitting
accurate measures of both to be derived directly from the rating data. However,
simulations demonstrating these methods' efficacy assumed a continuum of rating
values, consistent with typical physical modelling practice, whereas in most
actual rating systems only a limited range of discrete values (such as a 5-star
system) is employed. We perform a comparative test of several co-determination
algorithms with different scales of discrete ratings and show that this
seemingly minor modification in fact has a significant impact on algorithms'
performance. Paradoxically, where rating resolution is low, increased noise in
users' ratings may even improve the overall performance of the system.Comment: 6 pages, 2 figure

### Dephasing by a Continuous-Time Random Walk Process

Stochastic treatments of magnetic resonance spectroscopy and optical
spectroscopy require evaluations of functions like ,
where t is time, Q(s) is the value of a stochastic process at time s, and the
angular brackets denote ensemble averaging. This paper gives an exact
evaluation of these functions for the case where Q is a continuous-time random
walk process. The continuous time random walk describes an environment that
undergoes slow, step-like changes in time. It also has a well-defined Gaussian
limit, and so allows for non-Gaussian and Gaussian stochastic dynamics to be
studied within a single framework. We apply the results to extract
qubit-lattice interaction parameters from dephasing data of P-doped Si
semiconductors (data collected elsewhere), and to calculate the two-dimensional
spectrum of a three level harmonic oscillator undergoing random frequency
modulations.Comment: 25 pages, 4 figure

### The Keck Planet Search: Detectability and the Minimum Mass and Orbital Period Distribution of Extrasolar Planets

We analyze 8 years of precise radial velocity measurements from the Keck
Planet Search, characterizing the detection threshold, selection effects, and
completeness of the survey. We carry out a systematic search for planets by
assessing the false alarm probability associated with Keplerian orbit fits to
the data. This allows us to understand the detection threshold for each star in
terms of the number and time baseline of the observations, and size of
measurement errors and stellar jitter. We show that all planets with orbital
periods 20 m/s, and eccentricities <0.6 have
been announced, and summarize the candidates at lower amplitudes and longer
orbital periods. For the remaining stars, we calculate upper limits on the
velocity amplitude of a companion, typically 10 m/s, and use the non-detections
to derive completeness corrections at low amplitudes and long orbital periods.
We give the fraction of stars with a planet as a function of planet mass and
orbital period, and extrapolate to long period orbits and low planet masses. A
power law fit for planet masses >0.3 Jupiter masses and periods <2000 days
gives a mass-period distribution dN=C M^\alpha P^\beta dlnM dlnP with
\alpha=-0.31 \pm 0.2, \beta=0.26\pm 0.1, and the normalization constant C such
that 10.5% of solar type stars have a planet with mass in the range 0.3-10
Jupiter masses and orbital period 2-2000 days. The orbital period distribution
shows an increase in the planet fraction by a factor of 5 for orbital periods
beyond 300 days. Extrapolation gives 17-20% of stars having gas giant planets
within 20 AU. Finally, taking into account differences in detectability, we
find that M dwarfs are 3 to 10 times less likely to harbor a Jupiter mass
planet than solar type stars.Comment: 20 pages, 17 figures, accepted for publication in PAS

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