Collisional formation of massive exomoons of super-terrestrial exoplanets

Exomoons orbiting terrestrial or super-terrestrial exoplanets have not yet been discovered; their possible existence and properties are therefore still an unresolved question. Here we explore the collisional formation of exomoons through giant planetary impacts. We make use of smooth particle hydrodynamical (SPH) collision simulations and survey a large phase-space of terrestrial/super-terrestrial planetary collisions. We characterize the properties of such collisions, finding one rare case in which an exomoon forms through a graze&capture scenario, in addition to a few graze&merge or hit&run scenarios. Typically however, our collisions form massive circumplanetary discs, for which we use follow-up N-body simulations in order to derive lower-limit mass estimates for the ensuing exomoons. We investigate the mass, long-term tidal-stability, composition and origin of material in both the discs and the exomoons. Our giant-impact models often generate relatively iron-rich moons, that form beyond the synchronous radius of the planet, and would thus tidally evolve outward with stable orbits, rather than be destroyed. Our results suggest that it is extremely difficult to collisionally form currently-detectable exomoons orbiting super-terrestrial planets, through single giant impacts. It might be possible to form massive, detectable exomoons through several mergers of smaller exomoons, formed by multiple impacts, however more studies are required in order to reach a conclusion. Given the current observational initiatives, the search should focus primarily on more massive planet categories. However, about a quarter of the exomoons predicted by our models are approximately Mercury-mass or more, and are much more likely to be detectable given a factor 2 improvement in the detection capability of future instruments, providing further motivation for their development

Stochastic finite differences and multilevel Monte Carlo for a class of SPDEs in finance

In this article, we propose a Milstein finite difference scheme for a stochastic partial differential equation (SPDE) describing a large particle system. We show, by means of Fourier analysis, that the discretisation on an unbounded domain is convergent of first order in the timestep and second order in the spatial grid size, and that the discretisation is stable with respect to boundary data. Numerical experiments clearly indicate that the same convergence order also holds for boundary-value problems. Multilevel path simulation, previously used for SDEs, is shown to give substantial complexity gains compared to a standard discretisation of the SPDE or direct simulation of the particle system. We derive complexity bounds and illustrate the results by an application to basket credit derivatives

Absence of superconductivity in iron polyhydrides at high pressures

Recently, C. M. Pépin et al. [Science 357, 382 (2017)] reported the formation of several new iron polyhydrides FeHx at pressures in the megabar range and spotted FeH5, which forms above 130 GPa, as a potential high-Tc superconductor because of an alleged layer of dense metallic hydrogen. Shortly after, two studies by A. Majumdar et al. [Phys. Rev. B 96, 201107 (2017)] and A. G. Kvashnin et al. [J. Phys. Chem. C 122, 4731 (2018)] based on ab initio Migdal-Eliashberg theory seemed to independently confirm such a conjecture. We conversely find, on the same theoretical-numerical basis, that neither FeH5 nor its precursor, FeH3, shows any conventional superconductivity and explain why this is the case. We also show that superconductivity may be attained by transition-metal polyhydrides in the FeH3 structure type by adding more electrons to partially fill one of the Fe-H hybrid bands (as, e.g., in NiH3). Critical temperatures, however, will remain low because the d-metal bonding, and not the metallic hydrogen, dominates the behavior of electrons and phonons involved in the superconducting pairing in these compounds

Evolution of swarming behavior is shaped by how predators attack

Animal grouping behaviors have been widely studied due to their implications for understanding social intelligence, collective cognition, and potential applications in engineering, artificial intelligence, and robotics. An important biological aspect of these studies is discerning which selection pressures favor the evolution of grouping behavior. In the past decade, researchers have begun using evolutionary computation to study the evolutionary effects of these selection pressures in predator-prey models. The selfish herd hypothesis states that concentrated groups arise because prey selfishly attempt to place their conspecifics between themselves and the predator, thus causing an endless cycle of movement toward the center of the group. Using an evolutionary model of a predator-prey system, we show that how predators attack is critical to the evolution of the selfish herd. Following this discovery, we show that density-dependent predation provides an abstraction of Hamilton's original formulation of ``domains of danger.'' Finally, we verify that density-dependent predation provides a sufficient selective advantage for prey to evolve the selfish herd in response to predation by coevolving predators. Thus, our work corroborates Hamilton's selfish herd hypothesis in a digital evolutionary model, refines the assumptions of the selfish herd hypothesis, and generalizes the domain of danger concept to density-dependent predation.Comment: 25 pages, 11 figures, 5 tables, including 2 Supplementary Figures. Version to appear in "Artificial Life

Formulation and optimization of the energy-based blended quasicontinuum method

We formulate an energy-based atomistic-to-continuum coupling method based on blending the quasicontinuum method for the simulation of crystal defects. We utilize theoretical results from Van Koten and Luskin [32] and Ortner and Van Koten [24] to derive optimal choices of approximation parameters (blending function and finite element grid) for microcrack and di-vacancy test problems and confirm our analytical predictions in numerical tests

Heavy Majorana neutrinos in e^-e^- collisions

We discuss the process $e^-e^- \to W^- W^-$ mediated by heavy Majorana neutrino exchange in the t- and u channel. In our model the cross section for this reaction is a function of the masses (m_N) of the heavy Majorana neutrinos and mixing parameters (U_{eN}) originating from mixing between the ordinary left-handed standard model neutrinos and additional singlet right-handed neutrino fields. Taking into account the standard model background and contraints from low energy measurements, we present discovery limits in the (m_N,U_{eN}^2) plane. We also discuss how to measure in principle the CP violating phases, i.e., the relative phases between the mixing parameters.Comment: 18 pages with 7 postscript figures included, uses epsfig.st