22,981 research outputs found
Singular inextensible limit in the vibrations of post-buckled rods: analytical derivation and role of boundary conditions
In-plane vibrations of an elastic rod clamped at both extremities are studied. The rod is modeled as an extensible planar Kirchhoff elastic rod under large displacements and rotations. Equilibrium configurations and vibrations around these configurations are computed analytically in the incipient post-buckling regime. Of particular interest is the variation of the first mode frequency as the load is increased through the buckling threshold. The loading type is found to have a crucial importance as the first mode frequency is shown to behave singularly in the zero thickness limit in case of prescribed axial displacement, whereas a regular behavior is found in the case of prescribed axial load
A new, large-scale map of interstellar reddening derived from HI emission
We present a new map of interstellar reddening, covering the 39\% of the sky
with low {\rm HI} column densities (
or ) at resolution, based on
all-sky observations of Galactic HI emission by the HI4PI Survey. In this low
column density regime, we derive a characteristic value of for gas with and find no significant reddening associated with gas at
higher velocities. We compare our HI-based reddening map with the Schlegel,
Finkbeiner, and Davis (1998, SFD) reddening map and find them consistent to
within a scatter of . Further, the differences between our
map and the SFD map are in excellent agreement with the low resolution
() corrections to the SFD map derived by Peek and Graves
(2010) based on observed reddening toward passive galaxies. We therefore argue
that our HI-based map provides the most accurate interstellar reddening
estimates in the low column density regime to date. Our reddening map is made
publicly available (http://dx.doi.org/10.7910/DVN/AFJNWJ).Comment: Re-submitted to ApJ. The reddening map is available at
http://dx.doi.org/10.7910/DVN/AFJNW
Polynomial Time corresponds to Solutions of Polynomial Ordinary Differential Equations of Polynomial Length
We provide an implicit characterization of polynomial time computation in
terms of ordinary differential equations: we characterize the class
of languages computable in polynomial time in terms of
differential equations with polynomial right-hand side.
This result gives a purely continuous (time and space) elegant and simple
characterization of . This is the first time such classes
are characterized using only ordinary differential equations. Our
characterization extends to functions computable in polynomial time over the
reals in the sense of computable analysis. This extends to deterministic
complexity classes above polynomial time.
This may provide a new perspective on classical complexity, by giving a way
to define complexity classes, like , in a very simple
way, without any reference to a notion of (discrete) machine. This may also
provide ways to state classical questions about computational complexity via
ordinary differential equations, i.e.~by using the framework of analysis
Numerical computation of the conformal map onto lemniscatic domains
We present a numerical method for the computation of the conformal map from
unbounded multiply-connected domains onto lemniscatic domains. For -times
connected domains the method requires solving boundary integral
equations with the Neumann kernel. This can be done in
operations, where is the number of nodes in the discretization of each
boundary component of the multiply connected domain. As demonstrated by
numerical examples, the method works for domains with close-to-touching
boundaries, non-convex boundaries, piecewise smooth boundaries, and for domains
of high connectivity.Comment: Minor revision; simplified Example 6.1, and changed Example 6.2 to a
set without symmetr
Hausdorff dimension of some groups acting on the binary tree
Based on the work of Abercrombie, Barnea and Shalev gave an explicit formula
for the Hausdorff dimension of a group acting on a rooted tree. We focus here
on the binary tree T. Abert and Virag showed that there exist finitely
generated (but not necessarily level-transitive) subgroups of AutT of arbitrary
dimension in [0,1].
In this article we explicitly compute the Hausdorff dimension of the
level-transitive spinal groups. We then show examples of 3-generated spinal
groups which have transcendental Hausdroff dimension, and exhibit a
construction of 2-generated groups whose Hausdorff dimension is 1.Comment: 10 pages; full revision; simplified some proof
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