47,712 research outputs found
Limit curves for zeros of sections of exponential integrals
We are interested in studying the asymptotic behavior of the zeros of partial
sums of power series for a family of entire functions defined by exponential
integrals. The zeros grow on the order of O(n), and after rescaling we
explicitly calculate their limit curve. We find that the rate that the zeros
approach the curve depends on the order of the singularities/zeros of the
integrand in the exponential integrals. As an application of our findings we
derive results concerning the zeros of partial sums of power series for Bessel
functions of the first kind.Comment: 19 pages, 5 figures. arXiv admin note: text overlap with
arXiv:1208.518
Cusp Anomalous dimension and rotating open strings in AdS/CFT
In the context of AdS/CFT we provide analytical support for the proposed
duality between a Wilson loop with a cusp, the cusp anomalous dimension, and
the meson model constructed from a rotating open string with high angular
momentum. This duality was previously studied using numerical tools in [1]. Our
result implies that the minimum of the profile function of the minimal area
surface dual to the Wilson loop, is related to the inverse of the bulk
penetration of the dual string that hangs from the quark--anti-quark pair
(meson) in the gauge theory.Comment: enhanced text, fixed tipos, reference added. Same results and
conclusions. arXiv admin note: text overlap with arXiv:1405.7388 by other
author
Exact Solution of an Irreversible One-Dimensional Model with Fully Biased Spin Exchanges
We introduce a model with conserved dynamics, where nearest neighbor pairs of
spins can exchange to assume the
configuration , with rate , through energy decreasing moves only. We report exact solution for
the case when one of the rates, or , is zero. The
irreversibility of such dynamics results in strong dependence on the initial
conditions. Domain wall arguments suggest that for more general models with
steady states the dynamical critical exponent for the anisotropic spin exchange
is different from the isotropic value.Comment: 16 pages, plain TeX fil
Shape-from-shading using the heat equation
This paper offers two new directions to shape-from-shading, namely the use of the heat equation to smooth the field of surface normals and the recovery of surface height using a low-dimensional embedding. Turning our attention to the first of these contributions, we pose the problem of surface normal recovery as that of solving the steady state heat equation subject to the hard constraint that Lambert's law is satisfied. We perform our analysis on a plane perpendicular to the light source direction, where the z component of the surface normal is equal to the normalized image brightness. The x - y or azimuthal component of the surface normal is found by computing the gradient of a scalar field that evolves with time subject to the heat equation. We solve the heat equation for the scalar potential and, hence, recover the azimuthal component of the surface normal from the average image brightness, making use of a simple finite difference method. The second contribution is to pose the problem of recovering the surface height function as that of embedding the field of surface normals on a manifold so as to preserve the pattern of surface height differences and the lattice footprint of the surface normals. We experiment with the resulting method on a variety of real-world image data, where it produces qualitatively good reconstructed surfaces
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