Fast Rise of "Neptune-Size" Planets (4−8REarth4-8 R_{\rm Earth}) from P∼10P\sim10 to ∼250\sim250 days -- Statistics of Kepler Planet Candidates Up to ∼0.75AU\sim 0.75 {\rm AU}

We infer the period ($P$) and size ($R_p$) distribution of Kepler transiting planet candidates with $R_p\ge 1 R_{\rm Earth}$ and $P < 250$ days hosted by solar-type stars. The planet detection efficiency is computed by using measured noise and the observed timespans of the light curves for $\sim 120,000$ Kepler target stars. We focus on deriving the shape of planet period and radius distribution functions. We find that for orbital period $P>10$ days, the planet frequency d$N_p$/d$\log$P for "Neptune-size" planets ($R_p = 4-8 R_{\rm Earth}$) increases with period as $\propto P^{0.7\pm0.1}$. In contrast, d$N_p$/d$\log$P for "super-Earth-size" ($2-4 R_{\rm Earth}$) as well as "Earth-size" ($1-2 R_{\rm Earth}$) planets are consistent with a nearly flat distribution as a function of period ($\propto P^{0.11\pm0.05}$ and $\propto P^{-0.10\pm0.12}$, respectively), and the normalizations are remarkably similar (within a factor of $\sim 1.5$ at $50$ days). Planet size distribution evolves with period, and generally the relative fractions for big planets ($\sim 3-10 R_{\rm Earth}$) increase with period. The shape of the distribution function is not sensitive to changes in selection criteria of the sample. The implied nearly flat or rising planet frequency at long period appears to be in tension with the sharp decline at $\sim 100$ days in planet frequency for low mass planets (planet mass $m_p < 30 M_{\rm Earth}$) recently suggested by HARPS survey. Within $250$ days, the cumulative frequencies for Earth-size and super-Earth-size planets are remarkably similar ($\sim 28$ and $25$), while Neptune-size and Jupiter-size planets are $\sim 7$, and $\sim 3$, respectively. A major potential uncertainty arises from the unphysical impact parameter distribution of the candidates.Comment: Accepted by Ap

Grain refinement control in TIG arc welding

A method for controlling grain size and weld puddle agitation in a tungsten electrode inert gas welding system to produce fine, even grain size and distribution is disclosed. In the method the frequency of dc welding voltage pulses supplied to the welding electrode is varied over a preselected frequency range and the arc gas voltage is monitored. At some frequency in the preselected range the arc gas voltage will pass through a maximum. By maintaining the operating frequency of the system at this value, maximum weld puddle agitation and fine grain structure are produced

Effect of rotational disruption on the size-frequency distribution of the Main Belt asteroid population

The size distribution of small asteroids in the Main Belt is assumed to be determined by an equilibrium between the creation of new bodies out of the impact debris of larger asteroids and the destruction of small asteroids by collisions with smaller projectiles. However, for a diameter less than 6 km we find that YORP-induced rotational disruption significantly contributes to the erosion even exceeding the effects of collisional fragmentation. Including this additional grinding mechanism in a collision evolution model for the asteroid belt, we generate size-frequency distributions from either an accretional (Weidenschilling, 2011) or an "Asteroids were born big" (Morbidelli, 2009) initial size-frequency distribution that are consistent with observations reported in Gladman et al. (2009). Rotational disruption is a new mechanism that must be included in all future collisional evolution models of asteroids.Comment: 5 pages, 3 figures, accepted in MNRAS letter

Microcraters in aluminum foils exposed by Stardust

We will present preliminary results on the nature and size frequency distribution of microcraters that formed in aluminum foils during the flyby of comet Wild 2 by the Stardust spacecraft

Spatial modelling of claim frequency and claim size in insurance

In this paper models for claim frequency and claim size in non-life insurance are considered. Both covariates and spatial random e ects are included allowing the modelling of a spatial dependency pattern. We assume a Poisson model for the number of claims, while claim size is modelled using a Gamma distribution. However, in contrast to the usual compound Poisson model going back to Lundberg (1903), we allow for dependencies between claim size and claim frequency. Both models for the individual and average claim sizes of a policyholder are considered. A fully Bayesian approach is followed, parameters are estimated using Markov Chain Monte Carlo (MCMC). The issue of model comparison is thoroughly addressed. Besides the deviance information criterion suggested by Spiegelhalter et al. (2002), the predictive model choice criterion (Gelfand and Ghosh (1998)) and proper scoring rules (Gneiting and Raftery (2005)) based on the posterior predictive distribution are investigated. We give an application to a comprehensive data set from a German car insurance company. The inclusion of spatial e ects significantly improves the models for both claim frequency and claim size and also leads to more accurate predictions of the total claim sizes. Further we quantify the significant number of claims e ects on claim size

The frequency spectrum of finite samples from the intermittent silence process

It has been argued that the actual distribution of word frequencies could be reproduced or explained by generating a random sequence of letters and spaces according to the so-called intermittent silence process. The same kind of process could reproduce or explain the counts of other kinds of units from a wide range of disciplines. Taking the linguistic metaphor, we focus on the frequency spectrum, i.e., the number of words with a certain frequency, and the vocabulary size, i.e., the number of different words of text generated by an intermittent silence process. We derive and explain how to calculate accurately and efficiently the expected frequency spectrum and the expected vocabulary size as a function of the text size.Peer ReviewedPostprint (author's final draft