7,873 research outputs found
The branching Brownian motion seen from its tip
It has been conjectured since the work of Lalley and Sellke (1987) that the
branching Brownian motion seen from its tip (e.g. from its rightmost particle)
converges to an invariant point process. Very recently, it emerged that this
can be proved in several different ways (see e.g. Brunet and Derrida, 2010,
Arguin et al., 2010, 2011). The structure of this extremal point process turns
out to be a Poisson point process with exponential intensity in which each atom
has been decorated by an independent copy of an auxiliary point process. The
main goal of the present work is to give a complete description of the limit
object via an explicit construction of this decoration point process. Another
proof and description has been obtained independently by Arguin et al. (2011).Comment: 47 pages, 3 figure
TRIZ, ASIT, CK Connections and Disconnections between Three Major Theoretical Frameworks on Creativity
This paper intend to propose a comparative analysis of three major theoretical framework engineers and creative companies frequently use. All of them propose to help users to break psychological walls hiding creative solutions. Beyond the individual preferences and the mimesis effect, studying what is the DNA, often fruit of the History of Europe, behind these theories and analyzing how they are or not connected allows us to understand how we come to the future society of knowledge
Emergence of pulled fronts in fermionic microscopic particle models
We study the emergence and dynamics of pulled fronts described by the
Fisher-Kolmogorov-Petrovsky-Piscounov (FKPP) equation in the microscopic
reaction-diffusion process A + A A$ on the lattice when only a particle is
allowed per site. To this end we identify the parameter that controls the
strength of internal fluctuations in this model, namely, the number of
particles per correlated volume. When internal fluctuations are suppressed, we
explictly see the matching between the deterministic FKPP description and the
microscopic particle model.Comment: 4 pages, 4 figures. Accepted for publication in Phys. Rev. E as a
Rapid Communicatio
Asymptotic Scaling of the Diffusion Coefficient of Fluctuating "Pulled" Fronts
We present a (heuristic) theoretical derivation for the scaling of the
diffusion coefficient for fluctuating ``pulled'' fronts. In agreement
with earlier numerical simulations, we find that as ,
approaches zero as , where is the average number of particles per
correlation volume in the stable phase of the front. This behaviour of
stems from the shape fluctuations at the very tip of the front, and is
independent of the microscopic model.Comment: Some minor algebra corrected, to appear in Rapid Comm., Phys. Rev.
A phenomenological theory giving the full statistics of the position of fluctuating pulled fronts
We propose a phenomenological description for the effect of a weak noise on
the position of a front described by the Fisher-Kolmogorov-Petrovsky-Piscounov
equation or any other travelling wave equation in the same class. Our scenario
is based on four hypotheses on the relevant mechanism for the diffusion of the
front. Our parameter-free analytical predictions for the velocity of the front,
its diffusion constant and higher cumulants of its position agree with
numerical simulations.Comment: 10 pages, 3 figure
Fluctuating "Pulled" Fronts: the Origin and the Effects of a Finite Particle Cutoff
Recently it has been shown that when an equation that allows so-called pulled
fronts in the mean-field limit is modelled with a stochastic model with a
finite number of particles per correlation volume, the convergence to the
speed for is extremely slow -- going only as .
In this paper, we study the front propagation in a simple stochastic lattice
model. A detailed analysis of the microscopic picture of the front dynamics
shows that for the description of the far tip of the front, one has to abandon
the idea of a uniformly translating front solution. The lattice and finite
particle effects lead to a ``stop-and-go'' type dynamics at the far tip of the
front, while the average front behind it ``crosses over'' to a uniformly
translating solution. In this formulation, the effect of stochasticity on the
asymptotic front speed is coded in the probability distribution of the times
required for the advancement of the ``foremost bin''. We derive expressions of
these probability distributions by matching the solution of the far tip with
the uniformly translating solution behind. This matching includes various
correlation effects in a mean-field type approximation. Our results for the
probability distributions compare well to the results of stochastic numerical
simulations. This approach also allows us to deal with much smaller values of
than it is required to have the asymptotics to be valid.Comment: 26 pages, 11 figures, to appear in Phys. rev.
Biases in the determination of dynamical parameters of star clusters: today and in the Gaia era
The structural and dynamical properties of star clusters are generally
derived by means of the comparison between steady-state analytic models and the
available observables. With the aim of studying the biases of this approach, we
fitted different analytic models to simulated observations obtained from a
suite of direct N-body simulations of star clusters in different stages of
their evolution and under different levels of tidal stress to derive mass, mass
function and degree of anisotropy. We find that masses can be
under/over-estimated up to 50% depending on the degree of relaxation reached by
the cluster, the available range of observed masses and distances of radial
velocity measures from the cluster center and the strength of the tidal field.
The mass function slope appears to be better constrainable and less sensitive
to model inadequacies unless strongly dynamically evolved clusters and a
non-optimal location of the measured luminosity function are considered. The
degree and the characteristics of the anisotropy developed in the N-body
simulations are not adequately reproduced by popular analytic models and can be
detected only if accurate proper motions are available. We show how to reduce
the uncertainties in the mass, mass-function and anisotropy estimation and
provide predictions for the improvements expected when Gaia proper motions will
be available in the near future.Comment: 14 pages, 8 figures, accepted for publication by MNRA
Deterministic reaction models with power-law forces
We study a one-dimensional particles system, in the overdamped limit, where
nearest particles attract with a force inversely proportional to a power of
their distance and coalesce upon encounter. The detailed shape of the
distribution function for the gap between neighbouring particles serves to
discriminate between different laws of attraction. We develop an exact
Fokker-Planck approach for the infinite hierarchy of distribution functions for
multiple adjacent gaps and solve it exactly, at the mean-field level, where
correlations are ignored. The crucial role of correlations and their effect on
the gap distribution function is explored both numerically and analytically.
Finally, we analyse a random input of particles, which results in a stationary
state where the effect of correlations is largely diminished
From the stress response function (back) to the sandpile `dip'
We relate the pressure `dip' observed at the bottom of a sandpile prepared by
successive avalanches to the stress profile obtained on sheared granular layers
in response to a localized vertical overload. We show that, within a simple
anisotropic elastic analysis, the skewness and the tilt of the response profile
caused by shearing provide a qualitative agreement with the sandpile dip
effect. We conclude that the texture anisotropy produced by the avalanches is
in essence similar to that induced by a simple shearing -- albeit tilted by the
angle of repose of the pile. This work also shows that this response function
technique could be very well adapted to probe the texture of static granular
packing.Comment: 8 pages, 8 figures, accepted version to appear in Eur. Phys. J.
Changes in psychological need satisfaction
Abstract: Objective: (a) Examine longitudinal measurement invariance of scores from psychological need satisfaction (PNS) scales and (b) examine if changes in PNS were associated with change in moderate-to-vigorous physical activity (MVPA). Methods: Adolescents (N=842, Mage = 10.8, SD = .6) enrolled in the Monitoring Activities of Teenagers to Comprehend their Habits (MATCH) study completed measures of PNS and MVPA every 4 months over a 3 year period (2011-14) for a total of nine times. Results: PNS scores demonstrated strong longitudinal measurement invariance (i.e., invariant factor loadings and intercepts). Latent growth curve modeling indicated that a factor representing perceptions of all three PNS variables was positively associated with MVPA at Time 1 (β = .566, p<.05), and that increases in the common PNS factor were associated with increases in MVPA (β = .545, p<.05) with a large effect size (R2initial MVPA=.316; R2change in MVPA=.301). In an alternative model, MVPA at Time 1 was associated with perceived common PNS at Time 1 (β=.602, p<.001), and increases in MVPA were associated with increases in common PNS (β=.667, p<.001) with a large effect size (R2initial PNS=.363 of the R2change in PNS=.426). Conclusions: Longitudinal measurement invariance was supported, and therefore PNS scores could be used to study change over time. Further, two equally well fitting models were found suggesting that change in PNS can be both an antecedent and an outcome of MVPA. As such, both PNS and MVPA could be targeted in interventions aimed at increasing need satisfaction or MVPA
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