Fast Mesh Refinement in Pseudospectral Optimal Control

Mesh refinement in pseudospectral (PS) optimal control is embarrassingly easy --- simply increase the order $N$ of the Lagrange interpolating polynomial and the mathematics of convergence automates the distribution of the grid points. Unfortunately, as $N$ increases, the condition number of the resulting linear algebra increases as $N^2$; hence, spectral efficiency and accuracy are lost in practice. In this paper, we advance Birkhoff interpolation concepts over an arbitrary grid to generate well-conditioned PS optimal control discretizations. We show that the condition number increases only as $\sqrt{N}$ in general, but is independent of $N$ for the special case of one of the boundary points being fixed. Hence, spectral accuracy and efficiency are maintained as $N$ increases. The effectiveness of the resulting fast mesh refinement strategy is demonstrated by using \underline{polynomials of over a thousandth order} to solve a low-thrust, long-duration orbit transfer problem.Comment: 27 pages, 12 figures, JGCD April 201

Stellar Collisions and Ultracompact X-ray Binary Formation

(abridged) We report the results of SPH calculations of parabolic collisions between a subgiant or slightly evolved red-giant star and a neutron star (NS). Such collisions are likely to form ultracompact X-ray binaries (UCXBs) observed today in old globular clusters. In particular, we compute collisions of a 1.4 Msun NS with realistically modelled parent stars of initial masses 0.8 and 0.9 Msun, each at three different evolutionary stages (corresponding to three different radii R). The distance of closest approach for the initial orbit varies from 0.04 R (nearly head-on) to 1.3 R (grazing). These collisions lead to the formation of a tight binary, composed of the NS and the subgiant or red-giant core, embedded in an extremely diffuse common envelope (CE) typically of mass ~0.1 to 0.3 Msun. Our calculations follow the binary for many hundreds of orbits, ensuring that the orbital parameters we determine at the end of the calculations are close to final. Some of the fluid initially in the envelope of the (sub)giant, from 0.003 to 0.023 Msun in the cases we considered, is left bound to the NS. The eccentricities of the resulting binaries range from about 0.2 for our most grazing collision to about 0.9 for the nearly head-on cases. In almost all the cases we consider, gravitational radiation alone will cause sufficiently fast orbital decay to form a UCXB within a Hubble time, and often on a much shorter timescale. Our hydrodynamics code implements the recent SPH equations of motion derived with a variational approach by Springel & Hernquist and by Monaghan. Numerical noise is reduced by enforcing an analytic constraint equation that relates the smoothing lengths and densities of SPH particles. We present tests of these new methods to help demonstrate their improved accuracy.Comment: 41 pages, 17 figures, accepted by Ap

Both Reintroduction and Recolonization Likely Contributed to the Re-establishment of a Fisher Population in East-central Alberta

Recently, Stewart et al. (2017) investigated the origins of contemporary fisher populations in the Cooking Lake Moraine (CLM) of east-central Alberta, Canada, where fishers (Pekania pennanti) from Ontario and Manitoba, Canada were reintroduced in the early 1990s. To address this objective, Stewart et al. (2017) compared microsatellite alleles from extant fisher populations in the CLM to those from Ontario, Manitoba, and other Alberta populations. They reported that the CLM population clustered with adjacent native Alberta populations, consistent with recolonization, but also that 2 of 109 microsatellite alleles in the CLM occurred only in the source populations from Ontario and Manitoba. Rather than allowing for the possibility that these alleles descended from reintroduced fishers, the authors speculated that they represented random mutations among fishers that recolonized the area naturally from nearby populations in Alberta, and concluded that the reintroduction had failed completely. We disagree with this conclusion for 2 reasons. We contend it is more likely that the 2 alleles represent a genetic signature from the individuals released during the reintroduction, rather than being the result of mutations. We further suggest that, irrespective of the genetic legacy of introduced fishers in the recovered population, the presence of reintroduced fishers in the CLM may have helped facilitate natural recolonization of the area by fishers from surrounding areas. In our view, Stewart et al.’s (2017) findings do not demonstrate conclusively that the reintroduction program failed; on the contrary, we argue that their findings indicate that reintroduced fishers likely contributed to the long-term persistence of fishers in the CLM. The uncertainty surrounding this case underscores the importance of genetic monitoring following reintroductions.https://digitalcommons.snc.edu/faculty_staff_works/1032/thumbnail.jp

Parallel Mechanisms for Visual Search in Zebrafish

This research was funded by project grant G1000053 from the National Centre for the Replacement, Reduction and Refinement of animals in research (NC3Rs; UK) and by the Medical Research Council (MRC; UK). CHB is a Royal Society (UK) Research Fellow

Learning Mechanics and Game Mechanics Under the Perspective of Self-Determination Theory to Foster Motivation in Digital Game Based Learning

Background: Using digital games for educational purposes has been associated with higher levels of motivation among learners of different educational levels. However, the underlying psychological factors involved in digital game based learning (DGBL) have been rarely analyzed considering self-determination theory (SDT, Ryan \& Deci, 2000b); the relation of SDT with the flow experience (Csikszentmihalyi, 1990) has neither been evaluated in the context of DGBL

Digital play and the actualisation of the consumer imagination

In this article, the authors consider emerging consumer practices in digital virtual spaces. Building on constructions of consumer behavior as both a sense-making activity and a resource for the construction of daydreams, as well as anthropological readings of performance, the authors speculate that many performances during digital play are products of consumer fantasy. The authors develop an interpretation of the relationship between the real and the virtual that is better equipped to understand the movement between consumer daydreams and those practices actualized in the material and now also in digital virtual reality. The authors argue that digital virtual performances present opportunities for liminoid transformations through inversions, speculations, and playfulness acted out in aesthetic dramas. To illustrate, the authors consider specific examples of the theatrical productions available to consumers in digital spaces, highlighting the consumer imagination that feeds them, the performances they produce, and the potential for transformation in consumer-players

Gln-tRNAGln synthesis in a dynamic transamidosome from Helicobacter pylori, where GluRS2 hydrolyzes excess Glu-tRNAGln

In many bacteria and archaea, an ancestral pathway is used where asparagine and glutamine are formed from their acidic precursors while covalently linked to tRNAAsn and tRNAGln, respectively. Stable complexes formed by the enzymes of these indirect tRNA aminoacylation pathways are found in several thermophilic organisms, and are called transamidosomes. We describe here a transamidosome forming Gln-tRNAGln in Helicobacter pylori, an ε-proteobacterium pathogenic for humans; this transamidosome displays novel properties that may be characteristic of mesophilic organisms. This ternary complex containing the non-canonical GluRS2 specific for Glu-tRNAGln formation, the tRNA-dependent amidotransferase GatCAB and tRNAGln was characterized by dynamic light scattering. Moreover, we observed by interferometry a weak interaction between GluRS2 and GatCAB (KD = 40 ± 5 µM). The kinetics of Glu-tRNAGln and Gln-tRNAGln formation indicate that conformational shifts inside the transamidosome allow the tRNAGln acceptor stem to interact alternately with GluRS2 and GatCAB despite their common identity elements. The integrity of this dynamic transamidosome depends on a critical concentration of tRNAGln, above which it dissociates into separate GatCAB/tRNAGln and GluRS2/tRNAGln complexes. Ester bond protection assays show that both enzymes display a good affinity for tRNAGln regardless of its aminoacylation state, and support a mechanism where GluRS2 can hydrolyze excess Glu-tRNAGln, ensuring faithful decoding of Gln codons

Multiphoton detachment of electrons from negative ions

A simple analytical solution for the problem of multiphoton detachment from negative ions by a linearly polarized laser field is found. It is valid in the wide range of intensities and frequencies of the field, from the perturbation theory to the tunneling regime, and is applicable to the excess-photon as well as near-threshold detachment. Practically, the formulae are valid when the number of photons is greater than two. They produce the total detachment rates, relative intensities of the excess-photon peaks, and photoelectron angular distributions for the hydrogen and halogen negative ions, in agreement with those obtained in other, more numerically involved calculations in both perturbative and non-perturbative regimes. Our approach explains the extreme sensitivity of the multiphoton detachment probability to the asymptotic behaviour of the bound-state wave function. Rapid oscillations in the angular dependence of the $n$-photon detachment probability are shown to arise due to interference of the two classical trajectories which lead to the same final state after the electron emerges at the opposite sides of the atom when the field is close to maximal.Comment: 27 pages, Latex, and PostScript figures fig1.ps, fig2.ps, fig3.ps, accepted for publication in Phys. Rev.