2,461 research outputs found
A scaling law for accretion zone sizes
Current theories of runaway planetary accretion require small random velocities of the accreted particles. Two body gravitational accretion cross sections which ignore tidal perturbations of the Sun are not valid for the slow encounters which occur at low relative velocities. Wetherill and Cox have studied accretion cross sections for rocky protoplanets orbiting at 1 AU. Using analytic methods based on Hill's lunar theory, one can scale these results for protoplanets that occupy the same fraction of their Hill sphere as does a rocky body at 1 AU. Generalization to bodies of different sizes is achieved here by numerical integrations of the three-body problem. Starting at initial positions far from the accreting body, test particles are allowed to encounter the body once, and the cross section is computed. A power law is found relating the cross section to the radius of the accreting body (of fixed mass)
Error-Correcting Codes for Automatic Control
Systems with automatic feedback control may consist of several remote devices, connected only by unreliable communication channels. It is necessary in these conditions to have a method for accurate, real-time state estimation in the presence of channel noise. This problem is addressed, for the case of polynomial-growth-rate state spaces, through a new type of error-correcting code that is online and computationally efficient. This solution establishes a constructive analog, for some applications in estimation and control, of the Shannon coding theorem
More Flavor SU(3) Tests for New Physics in CP Violating B Decays
The recent LHCb measurements of the and
rates and CP asymmetries are in agreement with U-spin expectations from and results. We derive the complete set of
isospin, U-spin, and SU(3) relations among the CP asymmetries in two-body
charmless and decays, some of which are novel. To go
beyond the unbroken SU(3) limit, we present relations which are properly
defined and normalized to allow incorporation of SU(3) breaking in the simplest
manner. We show that there are no CP relations beyond first order in SU(3) and
isospin breaking. We also consider the corresponding relations for charm
decays. Comparing parametrizations of the leading order sum rules with data can
shed light on the applicability and limitations of both the flavor symmetry and
factorization-based descriptions of SU(3) breaking. Two factorization relations
can already be tested, and we show they agree with current data.Comment: 30 pages, 1 figur
Cutoff for the noisy voter model
Given a continuous time Markov Chain on a finite set , the
associated noisy voter model is the continuous time Markov chain on
, which evolves in the following way: (1) for each two sites and
in , the state at site changes to the value of the state at site
at rate ; (2) each site rerandomizes its state at rate 1. We show that
if there is a uniform bound on the rates and the corresponding
stationary distributions are almost uniform, then the mixing time has a sharp
cutoff at time with a window of order 1. Lubetzky and Sly proved
cutoff with a window of order 1 for the stochastic Ising model on toroids; we
obtain the special case of their result for the cycle as a consequence of our
result. Finally, we consider the model on a star and demonstrate the surprising
phenomenon that the time it takes for the chain started at all ones to become
close in total variation to the chain started at all zeros is of smaller order
than the mixing time.Comment: Published at http://dx.doi.org/10.1214/15-AAP1108 in the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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