343 research outputs found
Particle ejection during mergers of dark matter halos
Dark matter halos are built from accretion and merging. During merging some
of the dark matter particles may be ejected with velocities higher than the
escape velocity. We use both N-body simulations and single-particle
smooth-field simulations to demonstrate that rapid changes to the mean field
potential are responsible for such ejection, and in particular that dynamical
friction plays no significant role in it. Studying a range of minor mergers, we
find that typically between 5-15% of the particles from the smaller of the two
merging structures are ejected. We also find that the ejected particles
originate essentially from the small halo, and more specifically are particles
in the small halo which pass later through the region in which the merging
occurs.Comment: 18 pages, 12 figures. Accepted for publication in JCA
Perturbation Theory for Fractional Brownian Motion in Presence of Absorbing Boundaries
Fractional Brownian motion is a Gaussian process x(t) with zero mean and
two-time correlations ~ t^{2H} + s^{2H} - |t-s|^{2H}, where H, with
0<H<1 is called the Hurst exponent. For H = 1/2, x(t) is a Brownian motion,
while for H unequal 1/2, x(t) is a non-Markovian process. Here we study x(t) in
presence of an absorbing boundary at the origin and focus on the probability
density P(x,t) for the process to arrive at x at time t, starting near the
origin at time 0, given that it has never crossed the origin. It has a scaling
form P(x,t) ~ R(x/t^H)/t^H. Our objective is to compute the scaling function
R(y), which up to now was only known for the Markov case H=1/2. We develop a
systematic perturbation theory around this limit, setting H = 1/2 + epsilon, to
calculate the scaling function R(y) to first order in epsilon. We find that
R(y) behaves as R(y) ~ y^phi as y -> 0 (near the absorbing boundary), while
R(y) ~ y^gamma exp(-y^2/2) as y -> oo, with phi = 1 - 4 epsilon + O(epsilon^2)
and gamma = 1 - 2 epsilon + O(epsilon^2). Our epsilon-expansion result confirms
the scaling relation phi = (1-H)/H proposed in Ref. [28]. We verify our
findings via numerical simulations for H = 2/3. The tools developed here are
versatile, powerful, and adaptable to different situations.Comment: 16 pages, 8 figures; revised version 2 adds discussion on spatial
small-distance cutof
Estimating surplus production and maximum sustainable yield from biomass data when catch and effort time series are not available
In order to describe a simple method of estimating maximum sustainable yield (MSY), we first demonstrate that the parameters of the two well-known surplus production models of Schaefer and Fox can be expressed in terms of fishing mortality that yields maximum sustainable yield (FMSY), annual yield and mean biomass. If FMSY is known, or alternatively, is assumed to be some specified function of a known natural mortality rate, it thereby becomes possible to estimate MSY and describe the surplus production function even when the data are limited to one year of estimates for catch and mean biomass. The method is compared to other simple methods for estimating MSY and its potential application is discussed. (Résumé d'auteur
Comment on "Mean First Passage Time for Anomalous Diffusion"
We correct a previously erroneous calculation [Phys. Rev. E 62, 6065 (2000)]
of the mean first passage time of a subdiffusive process to reach either end of
a finite interval in one dimension. The mean first passage time is in fact
infinite.Comment: To appear in Phys. Rev.
The problem of analytical calculation of barrier crossing characteristics for Levy flights
By using the backward fractional Fokker-Planck equation we investigate the
barrier crossing event in the presence of Levy noise. After shortly review
recent results obtained with different approaches on the time characteristics
of the barrier crossing, we derive a general differential equation useful to
calculate the nonlinear relaxation time. We obtain analytically the nonlinear
relaxation time for free Levy flights and a closed expression in quadrature of
the same characteristics for cubic potential.Comment: 12 pages, 2 figures, presented at 5th International Conference on
Unsolved Problems on Noise, Lyon, France, 2008, to appear in J. Stat. Mech.:
Theory and Experimen
Survival of a Diffusing Particle in a Transverse Shear Flow: A First-Passage Problem with Continuously Varying Persistence Exponent
We consider a particle diffusing in the y-direction, dy/dt=\eta(t), subject
to a transverse shear flow in the x-direction, dx/dt=f(y), where x \ge 0 and
x=0 is an absorbing boundary. We treat the class of models defined by f(y) =
\pm v_{\pm}(\pm y)^\alpha where the upper (lower) sign refers to y>0 (y<0). We
show that the particle survives with probability Q(t) \sim t^{-\theta} with
\theta = 1/4, independent of \alpha, if v_{+}=v_{-}. If v_{+} \ne v_{-},
however, we show that \theta depends on both \alpha and the ratio v_{+}/v_{-},
and we determine this dependence.Comment: 4 page
A note on the development of a new software package, the FAO-ICLARM stock assessment tools (FiSAT)
FiSAT (computer programme), Stock assessment, Computer programs
Asymptotic behavior of self-affine processes in semi-infinite domains
We propose to model the stochastic dynamics of a polymer passing through a
pore (translocation) by means of a fractional Brownian motion, and study its
behavior in presence of an absorbing boundary. Based on scaling arguments and
numerical simulations, we present a conjecture that provides a link between the
persistence exponent and the Hurst exponent of the process, thus
sheding light on the spatial and temporal features of translocation.
Furthermore, we show that this conjecture applies more generally to a broad
class of self affine processes undergoing anomalous diffusion in bounded
domains, and we discuss some significant examples.Comment: 4 pages, 3 figures; to be published in Phys. Rev. Let
Generalized persistence exponents: an exactly soluble model
It was recently realized that the persistence exponent appearing in the
dynamics of nonequilibrium systems is a special member of a continuously
varying family of exponents, describing generalized persistence properties. We
propose and solve a simplified model of coarsening, where time intervals
between spin flips are independent, and distributed according to a L\'evy law.
Both the limit distribution of the mean magnetization and the generalized
persistence exponents are obtained exactly.Comment: 4 pages, 3 figures Submitted to PR
Record statistics for biased random walks, with an application to financial data
We consider the occurrence of record-breaking events in random walks with
asymmetric jump distributions. The statistics of records in symmetric random
walks was previously analyzed by Majumdar and Ziff and is well understood.
Unlike the case of symmetric jump distributions, in the asymmetric case the
statistics of records depends on the choice of the jump distribution. We
compute the record rate , defined as the probability for the th
value to be larger than all previous values, for a Gaussian jump distribution
with standard deviation that is shifted by a constant drift . For
small drift, in the sense of , the correction to
grows proportional to arctan and saturates at the value
. For large the record rate approaches a
constant, which is approximately given by
for .
These asymptotic results carry over to other continuous jump distributions with
finite variance. As an application, we compare our analytical results to the
record statistics of 366 daily stock prices from the Standard & Poors 500
index. The biased random walk accounts quantitatively for the increase in the
number of upper records due to the overall trend in the stock prices, and after
detrending the number of upper records is in good agreement with the symmetric
random walk. However the number of lower records in the detrended data is
significantly reduced by a mechanism that remains to be identified.Comment: 16 pages, 7 figure
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