Quantum integrability of the Alday-Arutyunov-Frolov model

We investigate the quantum integrability of the Alday-Arutyunov-Frolov (AAF) model by calculating the three-particle scattering amplitude at the first non-trivial order and showing that the S-matrix is factorizable at this order. We consider a more general fermionic model and find a necessary constraint to ensure its integrability at quantum level. We then show that the quantum integrability of the AAF model follows from this constraint. In the process, we also correct some missed points in earlier works.Comment: 40 pages; Replaced with published version. Appendix and comments adde

Decomposition analysis of LTREs may facilitate the design of short-term ecotoxicological tests

This study compared two methods, based on re-analyzed data from a partly published life table response experiment (LTRE), to help determine the optimal approach for designing ecotoxicological assessments. The 36-day LTRE data recorded the toxic effects of cadmium (Cd) and imidacloprid, alone and in combination, on the reproduction and survivorship of aphids (Acyrthosiphon pisum Harris). We used this data to construct an age-classified matrix model (six age classes, each 6 days long) to estimate aphid population growth rate (λ) under each treatment. For each treatment, an elasticity analysis and a demographic decomposition analysis were performed, and results were compared. Despite different results expected from the two toxicants, the elasticity values were very similar. The elasticity of λ with respect to survival was highest in the first age class, and that with respect to fertility was highest in the second age class. The demographic decomposition analysis examined how changes in life-history traits contributed to differences in λ between control and treated populations (Δλ). This indicated that the most important contributors to Δλ were the differences in survival (resulting from both demographic sensitivity and toxicity) in the first and the second age classes of aphids and differences in fertility in the third and the fourth age classes. Additionally, the toxicants acted differently. Cd reduced Δλ by impairing fertility at third age class and reducing survivorship from the second to the third age class. Imidacloprid mostly reduced survivorship at the first and second age classes. The elasticity and decomposition analyses showed different results, because these methods addressed different questions about the interaction of organism life history and sensitivity to toxicants. This study indicated that the LTRE may be useful for designing individual-level ecotoxicological experiments that account for both the effects of the toxicant and the demographic sensitivity of the organism

Controlled enhancement of spin-current emission by three-magnon splitting

Spin currents—the flow of angular momentum without the simultaneous transfer of electrical charge—play an enabling role in the field of spintronics1, 2, 3, 4, 5, 6, 7, 8. Unlike the charge current, the spin current is not a conservative quantity within the conduction carrier system. This is due to the presence of the spin–orbit interaction that couples the spin of the carriers to angular momentum in the lattice. This spin–lattice coupling9 acts also as the source of damping in magnetic materials, where the precessing magnetic moment experiences a torque towards its equilibrium orientation; the excess angular momentum in the magnetic subsystem flows into the lattice. Here we show that this flow can be reversed by the three-magnon splitting process and experimentally achieve the enhancement of the spin current emitted by the interacting spin waves. This mechanism triggers angular momentum transfer from the lattice to the magnetic subsystem and modifies the spin-current emission. The finding illustrates the importance of magnon–magnon interactions for developing spin-current based electronics

Parallel Unsmoothed Aggregation Algebraic Multigrid Algorithms on GPUs

We design and implement a parallel algebraic multigrid method for isotropic graph Laplacian problems on multicore Graphical Processing Units (GPUs). The proposed AMG method is based on the aggregation framework. The setup phase of the algorithm uses a parallel maximal independent set algorithm in forming aggregates and the resulting coarse level hierarchy is then used in a K-cycle iteration solve phase with a $\ell^1$-Jacobi smoother. Numerical tests of a parallel implementation of the method for graphics processors are presented to demonstrate its effectiveness.Comment: 18 pages, 3 figure

Numerical instability of the Akhmediev breather and a finite-gap model of it

In this paper we study the numerical instabilities of the NLS Akhmediev breather, the simplest space periodic, one-mode perturbation of the unstable background, limiting our considerations to the simplest case of one unstable mode. In agreement with recent theoretical findings of the authors, in the situation in which the round-off errors are negligible with respect to the perturbations due to the discrete scheme used in the numerical experiments, the split-step Fourier method (SSFM), the numerical output is well-described by a suitable genus 2 finite-gap solution of NLS. This solution can be written in terms of different elementary functions in different time regions and, ultimately, it shows an exact recurrence of rogue waves described, at each appearance, by the Akhmediev breather. We discover a remarkable empirical formula connecting the recurrence time with the number of time steps used in the SSFM and, via our recent theoretical findings, we establish that the SSFM opens up a vertical unstable gap whose length can be computed with high accuracy, and is proportional to the inverse of the square of the number of time steps used in the SSFM. This neat picture essentially changes when the round-off error is sufficiently large. Indeed experiments in standard double precision show serious instabilities in both the periods and phases of the recurrence. In contrast with it, as predicted by the theory, replacing the exact Akhmediev Cauchy datum by its first harmonic approximation, we only slightly modify the numerical output. Let us also remark, that the first rogue wave appearance is completely stable in all experiments and is in perfect agreement with the Akhmediev formula and with the theoretical prediction in terms of the Cauchy data.Comment: 27 pages, 8 figures, Formula (30) at page 11 was corrected, arXiv admin note: text overlap with arXiv:1707.0565

Vortices in (2+1)d Conformal Fluids

We study isolated, stationary, axially symmetric vortex solutions in (2+1)-dimensional viscous conformal fluids. The equations describing them can be brought to the form of three coupled first order ODEs for the radial and rotational velocities and the temperature. They have a rich space of solutions characterized by the radial energy and angular momentum fluxes. We do a detailed study of the phases in the one-parameter family of solutions with no energy flux. This parameter is the product of the asymptotic vorticity and temperature. When it is large, the radial fluid velocity reaches the speed of light at a finite inner radius. When it is below a critical value, the velocity is everywhere bounded, but at the origin there is a discontinuity. We comment on turbulence, potential gravity duals, non-viscous limits and non-relativistic limits.Comment: 39 pages, 10 eps figures, v2: Minor changes, refs, preprint numbe

Polariton Condensation and Lasing

The similarities and differences between polariton condensation in microcavities and standard lasing in a semiconductor cavity structure are reviewed. The recent experiments on "photon condensation" are also reviewed.Comment: 23 pages, 6 figures; Based on the book chapter in Exciton Polaritons in Microcavities, (Springer Series in Solid State Sciences vol. 172), V. Timofeev and D. Sanvitto, eds., (Springer, 2012

Young children's cognitive achievement: home learning environment, language and ethnic background

For decades, research has shown differences in cognitive assessment scores between White and minority ethnic group(s) learners as well as differences across different minority ethnic groups. More recent data have indicated that the home learning environment and languages spoken can impact cognitive assessment and other corollary outcomes. This study uses the Millennium Cohort Study to jointly assess how minority ethnic group, home learning environment and home languages predict child cognitive assessment scores. Regression analyses were conducted using two assessment measures. The following is hypothesised: (1) cognitive achievement scores vary by minority ethnic group, (2) more home learning environment in early childhood leads to higher cognitive development scores and (3) English only in the home yields the highest cognitive scores while no English in the home yields the lowest. Findings reveal that there are differences in cognitive scores along ethnic group categories although there are also some unexpected findings. Home learning environment does not play as large a role as was predicted in raising the assessment scores overall for learners while speaking English in the home does, irrespective of ethnic background

Fractional Zaslavsky and Henon Discrete Maps

This paper is devoted to the memory of Professor George M. Zaslavsky passed away on November 25, 2008. In the field of discrete maps, George M. Zaslavsky introduced a dissipative standard map which is called now the Zaslavsky map. G. Zaslavsky initialized many fundamental concepts and ideas in the fractional dynamics and kinetics. In this paper, starting from kicked damped equations with derivatives of non-integer orders we derive a fractional generalization of discrete maps. These fractional maps are generalizations of the Zaslavsky map and the Henon map. The main property of the fractional differential equations and the correspondent fractional maps is a long-term memory and dissipation. The memory is realized by the fact that their present state evolution depends on all past states with special forms of weights.Comment: 26 pages, LaTe