3,636 research outputs found
Asymptotic genealogy of a critical branching process
Consider a continuous-time binary branching process conditioned to have
population size n at some time t, and with a chance p for recording each
extinct individual in the process. Within the family tree of this process, we
consider the smallest subtree containing the genealogy of the extant
individuals together with the genealogy of the recorded extinct individuals. We
introduce a novel representation of such subtrees in terms of a point-process,
and provide asymptotic results on the distribution of this point-process as the
number of extant individuals increases. We motivate the study within the scope
of a coherent analysis for an a priori model for macroevolution.Comment: 30 page
Crescent Singularities in Crumpled Sheets
We examine the crescent singularity of a developable cone in a setting
similar to that studied by Cerda et al [Nature 401, 46 (1999)]. Stretching is
localized in a core region near the pushing tip and bending dominates the outer
region. Two types of stresses in the outer region are identified and shown to
scale differently with the distance to the tip. Energies of the d-cone are
estimated and the conditions for the scaling of core region size R_c are
discussed. Tests of the pushing force equation and direct geometrical
measurements provide numerical evidence that core size scales as R_c ~ h^{1/3}
R^{2/3}, where h is the thickness of sheet and R is the supporting container
radius, in agreement with the proposition of Cerda et al. We give arguments
that this observed scaling law should not represent the asymptotic behavior.
Other properties are also studied and tested numerically, consistent with our
analysis.Comment: 13 pages with 8 figures, revtex. To appear in PR
Auxiliary field method and analytical solutions of the Schr\"{o}dinger equation with exponential potentials
The auxiliary field method is a new and efficient way to compute approximate
analytical eigenenergies and eigenvectors of the Schr\"{o}dinger equation. This
method has already been successfully applied to the case of central potentials
of power-law and logarithmic forms. In the present work, we show that the
Schr\"{o}dinger equation with exponential potentials of the form can also be analytically solved by using the
auxiliary field method. Formulae giving the critical heights and the energy
levels of these potentials are presented. Special attention is drawn on the
Yukawa potential and the pure exponential one
A way to synchronize models with seismic faults for earthquake forecasting: Insights from a simple stochastic model
Numerical models are starting to be used for determining the future behaviour
of seismic faults and fault networks. Their final goal would be to forecast
future large earthquakes. In order to use them for this task, it is necessary
to synchronize each model with the current status of the actual fault or fault
network it simulates (just as, for example, meteorologists synchronize their
models with the atmosphere by incorporating current atmospheric data in them).
However, lithospheric dynamics is largely unobservable: important parameters
cannot (or can rarely) be measured in Nature. Earthquakes, though, provide
indirect but measurable clues of the stress and strain status in the
lithosphere, which should be helpful for the synchronization of the models. The
rupture area is one of the measurable parameters of earthquakes. Here we
explore how it can be used to at least synchronize fault models between
themselves and forecast synthetic earthquakes. Our purpose here is to forecast
synthetic earthquakes in a simple but stochastic (random) fault model. By
imposing the rupture area of the synthetic earthquakes of this model on other
models, the latter become partially synchronized with the first one. We use
these partially synchronized models to successfully forecast most of the
largest earthquakes generated by the first model. This forecasting strategy
outperforms others that only take into account the earthquake series. Our
results suggest that probably a good way to synchronize more detailed models
with real faults is to force them to reproduce the sequence of previous
earthquake ruptures on the faults. This hypothesis could be tested in the
future with more detailed models and actual seismic data.Comment: Revised version. Recommended for publication in Tectonophysic
Bethe Ansatz in the Bernoulli Matching Model of Random Sequence Alignment
For the Bernoulli Matching model of sequence alignment problem we apply the
Bethe ansatz technique via an exact mapping to the 5--vertex model on a square
lattice. Considering the terrace--like representation of the sequence alignment
problem, we reproduce by the Bethe ansatz the results for the averaged length
of the Longest Common Subsequence in Bernoulli approximation. In addition, we
compute the average number of nucleation centers of the terraces.Comment: 14 pages, 5 figures (some points are clarified
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