Counting constraints in flat array fragments

We identify a fragment of Presburger arithmetic enriched with free function symbols and cardinality constraints for interpreted sets, which is amenable to automated analysis. We establish decidability and complexity results for such a fragment and we implement our algorithms. The experiments run in discharging proof obligations coming from invariant checking and bounded model-checking benchmarks show the practical feasibility of our decision procedure

Counting Constraints in Flat Array Fragments

We identify a fragment of Presburger arithmetic enriched with free function symbols and cardinality constraints for interpreted sets, which is amenable to automated analysis. We establish decidability and complexity results for such a fragment and we implement our algorithms. The experiments run in discharging proof obligations coming from invariant checking and bounded model-checking benchmarks show the practical feasibility of our decision procedure

Correlated Prompt Fission Data in Transport Simulations

Detailed information on the fission process can be inferred from the observation, modeling and theoretical understanding of prompt fission neutron and $\gamma$-ray~observables. Beyond simple average quantities, the study of distributions and correlations in prompt data, e.g., multiplicity-dependent neutron and \gray~spectra, angular distributions of the emitted particles, $n$-$n$, $n$-$\gamma$, and $\gamma$-$\gamma$~correlations, can place stringent constraints on fission models and parameters that would otherwise be free to be tuned separately to represent individual fission observables. The FREYA~and CGMF~codes have been developed to follow the sequential emissions of prompt neutrons and $\gamma$-rays~from the initial excited fission fragments produced right after scission. Both codes implement Monte Carlo techniques to sample initial fission fragment configurations in mass, charge and kinetic energy and sample probabilities of neutron and $\gamma$~emission at each stage of the decay. This approach naturally leads to using simple but powerful statistical techniques to infer distributions and correlations among many observables and model parameters. The comparison of model calculations with experimental data provides a rich arena for testing various nuclear physics models such as those related to the nuclear structure and level densities of neutron-rich nuclei, the $\gamma$-ray~strength functions of dipole and quadrupole transitions, the mechanism for dividing the excitation energy between the two nascent fragments near scission, and the mechanisms behind the production of angular momentum in the fragments, etc. Beyond the obvious interest from a fundamental physics point of view, such studies are also important for addressing data needs in various nuclear applications. (See text for full abstract.)Comment: 39 pages, 57 figure files, published in Eur. Phys. J. A, reference added this versio

Validation of techniques to mitigate copper surface contamination in CUORE

In this article we describe the background challenges for the CUORE experiment posed by surface contamination of inert detector materials such as copper, and present three techniques explored to mitigate these backgrounds. Using data from a dedicated test apparatus constructed to validate and compare these techniques we demonstrate that copper surface contamination levels better than 10E-07 - 10E-08 Bq/cm2 are achieved for 238U and 232Th. If these levels are reproduced in the final CUORE apparatus the projected 90% C.L. upper limit on the number of background counts in the region of interest is 0.02-0.03 counts/keV/kg/y depending on the adopted mitigation technique.Comment: 10 pages, 6 figures, 6 table

Fission decay of N = Z nuclei at high angular momentum: 60^{60}Zn

Using a unique two-arm detector system for heavy ions (the BRS, binary reaction spectrometer) coincident fission events have been measured from the decay of $^{60}$Zn compound nuclei formed at 88MeV excitation energy in the reactions with $^{36}$Ar beams on a $^{24}$Mg target at $E_{lab}(^{36}$Ar) = 195 MeV. The detectors consisted of two large area position sensitive (x,y) gas telescopes with Bragg-ionization chambers. From the binary coincidences in the two detectors inclusive and exclusive cross sections for fission channels with differing losses of charge were obtained. Narrow out-of-plane correlations corresponding to coplanar decay are observed for two fragments emitted in binary events, and in the data for ternary decay with missing charges from 4 up to 8. After subtraction of broad components these narrow correlations are interpreted as a ternary fission process at high angular momentum through an elongated shape. The lighter mass in the neck region consists dominantly of two or three-particles. Differential cross sections for the different mass splits for binary and ternary fission are presented. The relative yields of the binary and ternary events are explained using the statistical model based on the extended Hauser-Feshbach formalism for compound nucleus decay. The ternary fission process can be described by the decay of hyper-deformed states with angular momentum around 45-52 $hbar$.Comment: 23 pages, 25 figure

Small crater populations on Vesta

The NASA Dawn mission has extensively examined the surface of asteroid Vesta, the second most massive body in the main belt. The high quality of the gathered data provides us with an unique opportunity to determine the surface and internal properties of one of the most important and intriguing main belt asteroids (MBAs). In this paper, we focus on the size frequency distributions (SFDs) of sub-kilometer impact craters observed at high spatial resolution on several selected young terrains on Vesta. These small crater populations offer an excellent opportunity to determine the nature of their asteroidal precursors (namely MBAs) at sizes that are not directly observable from ground-based telescopes (i.e., below ~100 m diameter). Moreover, unlike many other MBA surfaces observed by spacecraft thus far, the young terrains examined had crater spatial densities that were far from empirical saturation. Overall, we find that the cumulative power-law index (slope) of small crater SFDs on Vesta is fairly consistent with predictions derived from current collisional and dynamical models down to a projectile size of ~10 m diameter (Bottke et al., 2005a,b). The shape of the impactor SFD for small projectile sizes does not appear to have changed over the last several billions of years, and an argument can be made that the absolute number of small MBAs has remained roughly constant (within a factor of 2) over the same time period. The apparent steady state nature of the main belt population potentially provides us with a set of intriguing constraints that can be used to glean insights into the physical evolution of individual MBAs as well as the main belt as an ensemble.Comment: Accepted by PSS, to appear on Vesta cratering special issu

Multiband photometry of a Patroclus-Menoetius mutual event: Constraints on surface heterogeneity

We present the first complete multiband observations of a binary asteroid mutual event. We obtained high-cadence, high-signal-to-noise photometry of the UT 2018 April 9 inferior shadowing event in the Jupiter Trojan binary system Patroclus-Menoetius in four Sloan bands $-$ $g'$, $r'$, $i'$, and $z'$. We use an eclipse lightcurve model to fit for a precise mid-eclipse time and estimate the minimum separation of the two eclipsing components during the event. Our best-fit mid-eclipse time of $2458217.80943^{+0.00057}_{-0.00050}$ is 19 minutes later than the prediction of Grundy et al. (2018); the minimum separation between the center of Menoetius' shadow and the center of Patroclus is $72.5\pm0.7$ km $-$ slightly larger than the predicted 69.5 km. Using the derived lightcurves, we find no evidence for significant albedo variations or large-scale topographic features on the Earth-facing hemisphere and limb of Patroclus. We also apply the technique of eclipse mapping to place an upper bound of $\sim$0.15 mag on wide-scale surface color variability across Patroclus.Comment: 5 pages, 3 figures, accepted for publication in A