9,683 research outputs found
Random-bit optimal uniform sampling for rooted planar trees with given sequence of degrees and Applications
In this paper, we redesign and simplify an algorithm due to Remy et al. for
the generation of rooted planar trees that satisfies a given partition of
degrees. This new version is now optimal in terms of random bit complexity, up
to a multiplicative constant. We then apply a natural process
"simulate-guess-and-proof" to analyze the height of a random Motzkin in
function of its frequency of unary nodes. When the number of unary nodes
dominates, we prove some unconventional height phenomenon (i.e. outside the
universal square root behaviour.)Comment: 19 page
Weak gravitational lensing of finite beams
The standard theory of weak gravitational lensing relies on the infinitesimal
light beam approximation. In this context, images are distorted by convergence
and shear, the respective sources of which unphysically depend on the
resolution of the distribution of matter---the so-called Ricci-Weyl problem. In
this letter, we propose a strong-lensing-inspired formalism to describe the
lensing of finite beams. We address the Ricci-Weyl problem by showing
explicitly that convergence is caused by the matter enclosed by the beam,
regardless of its distribution. Furthermore, shear turns out to be
systematically enhanced by the finiteness of the beam. This implies, in
particular, that the Kaiser-Squires relation between shear and convergence is
violated, which could have profound consequences on the interpretation of weak
lensing surveys.Comment: 6 pages, 2 figures, v2: matches published version, some typos
correcte
Modeling the shortening history of a fault tip fold using structural and geomorphic records of deformation
We present a methodology to derive the growth history of a fault tip fold above a basal detachment. Our approach is based on modeling the stratigraphic and geomorphic records of deformation, as well as the finite structure of the fold constrained from seismic profiles. We parameterize the spatial deformation pattern using a simple formulation of the displacement field derived from sandbox experiments. Assuming a stationary spatial pattern of deformation, we simulate the gradual warping and uplift of stratigraphic and geomorphic markers, which provides an estimate of the cumulative amounts of shortening they have recorded. This approach allows modeling of isolated terraces or growth strata. We apply this method to the study of two fault tip folds in the Tien Shan, the Yakeng and Anjihai anticlines, documenting their deformation history over the past 6–7 Myr. We show that the modern shortening rates can be estimated from the width of the fold topography provided that the sedimentation rate is known, yielding respective rates of 2.15 and 1.12 mm/yr across Yakeng and Anjihai, consistent with the deformation recorded by fluvial and alluvial terraces. This study demonstrates that the shortening rates across both folds accelerated significantly since the onset of folding. It also illustrates the usefulness of a simple geometric folding model and highlights the importance of considering local interactions between tectonic deformation, sedimentation, and erosion
The theory of stochastic cosmological lensing
On the scale of the light beams subtended by small sources, e.g. supernovae,
matter cannot be accurately described as a fluid, which questions the
applicability of standard cosmic lensing to those cases. In this article, we
propose a new formalism to deal with small-scale lensing as a diffusion
process: the Sachs and Jacobi equations governing the propagation of narrow
light beams are treated as Langevin equations. We derive the associated
Fokker-Planck-Kolmogorov equations, and use them to deduce general analytical
results on the mean and dispersion of the angular distance. This formalism is
applied to random Einstein-Straus Swiss-cheese models, allowing us to: (1) show
an explicit example of the involved calculations; (2) check the validity of the
method against both ray-tracing simulations and direct numerical integrations
of the Langevin equation. As a byproduct, we obtain a
post-Kantowski-Dyer-Roeder approximation, accounting for the effect of tidal
distortions on the angular distance, in excellent agreement with numerical
results. Besides, the dispersion of the angular distance is correctly
reproduced in some regimes.Comment: 37+13 pages, 8 figures. A few typos corrected. Matches published
versio
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