Centralizers of maximal regular subgroups in simple Lie groups and relative congruence classes of representations

In the paper we present a new, uniform and comprehensive description of centralizers of the maximal regular subgroups in compact simple Lie groups of all types and ranks. The centralizer is either a direct product of finite cyclic groups, a continuous group of rank 1, or a product, not necessarily direct, of a continuous group of rank 1 with a finite cyclic group. Explicit formulas for the action of such centralizers on irreducible representations of the simple Lie algebras are given.Comment: 27 page

Reconciliation of generalized refraction with diffraction theory

When an electromagnetic wave is obliquely incident on the interface between two homogeneous media with different refractive indices, the requirement of phase continuity across the interface generally leads to a shift in the trajectory of the wave. When a linearly position dependent phase shift is imposed at the interface, the resulting refraction may be described using a generalized version of Snell's law. In this Letter, we establish a formal equivalence between generalized refraction and blazed diffraction gratings, further discussing the relative merits of the two approaches.Comment: Submitted to Optics Letter

MODELLING THE COMBUSTION CHAMBER OF AN ALUMINIUM CASTING FURNACE: A METHODOLOGY

Mathematical modelling of the phenomena occurring in a combustion chamber is a very difficult task. Recently, computational methods have been developed allowing the simulation of all the processes involved in a more elaborate and reliable manner than ever before. These methods however often present weaknesses originating from their lack of gener- ality and prohibitive computation time. Our aim was to come up with a technique that could be applied to rectangular furnaces of any size and characteristics, and that would require a reasonable computation time. The technique is based on combining the PHOENICS code (used for velocity and combustion fields) with a new radiation method, the so-called imaginary planes method. Results are presented for an aluminium melter/holder furnace. Comparison between the imaginary planes method and the zone method illustrates the excellent agree- ment obtained for the radiative transfer. The technique used for the coupling of PHOENICS with the radiative part is explained. Provisions are made to take care of the unsteady state regime often encountered in such furnaces where several different operations are performed in a row. The simulation of a transient operation is presented and it is found that a single determination of the velocity pattern on the basis of a steady state assumption is sufficient to simulate adequately time dependent gas temperature and heat flux distributions

The origin of the E+ transition in GaAsN alloys

Optical properties of GaAsN system with nitrogen concentrations in the range of 0.9-3.7% are studied by full-potential LAPW method in a supercell approach. The E+ transition is identified by calculating the imaginary part of the dielectric function. The evolution of the energy of this transition with nitrogen concentration is studied and the origin of this transition is identified by analyzing the contributions to the dielectric function from different band combinations. The L_1c-derived states are shown to play an important role in the formation of the E+ transition, which was also suggested by recent experiments. At the same time the nitrogen-induced modification of the first conduction band of the host compound are also found to contribute significantly to the E+ transition. Further, the study of several model supercells demonstrated the significant influence of the nitrogen potential on the optical properties of the GaAsN system.Comment: 5 pages, 3 figure

The rings of n-dimensional polytopes

Points of an orbit of a finite Coxeter group G, generated by n reflections starting from a single seed point, are considered as vertices of a polytope (G-polytope) centered at the origin of a real n-dimensional Euclidean space. A general efficient method is recalled for the geometric description of G- polytopes, their faces of all dimensions and their adjacencies. Products and symmetrized powers of G-polytopes are introduced and their decomposition into the sums of G-polytopes is described. Several invariants of G-polytopes are found, namely the analogs of Dynkin indices of degrees 2 and 4, anomaly numbers and congruence classes of the polytopes. The definitions apply to crystallographic and non-crystallographic Coxeter groups. Examples and applications are shown.Comment: 24 page

Effect of major life events on travel behaviours: a scoping review

Open access article. Creative Commons Attribution License (CC BY) applies.The transportation sector accounts for about a quarter of global greenhouse gas emissions. Previous research suggests that major life events may be “windows of opportunity” for travel behaviour change. Our scoping review examined the effects of seven events (transitions to secondary school, post-secondary studies, labour market, marriage, parenthood, retirement, and relocation) on travel behaviours. Five databases were searched (MEDLINE, APA PsycINFO, Web of Science, SportDISCUS, and ProQuest Dissertations and Theses) and 80 articles met inclusion criteria. Relocation was the most commonly examined event (with 51studies). Findings illustrate that moving to compact neighbourhoods (with shorter commute distance/traveltime, greater walkability/access to destinations) was associated with shifts towards sustainable travel modes (e.g., walking, cycling, and transit). Relocation might be particularly conducive to implementing scalable sustainable transportation interventions, as all six interventions with appropriate statistical power were effective. Entry into the labour market was generally associated with increased car use and declines in sustainable transportation. Qualitative studies suggested that attitudes towards cycling may become negative during adolescence, while attitudes towards driving improve, highlighting a need for concerted action. Evidence for other events was less consistent. Research in developing countries remain scarce and further intervention research is needed to enhance quality of evidence.Ye

Nonlinear magnetoinductive transmission lines

Power transmission in one-dimensional nonlinear magnetic metamaterials driven at one end is investigated numerically and analytically in a wide frequency range. The nonlinear magnetic metamaterials are composed of varactor-loaded split-ring resonators which are coupled magnetically through their mutual inductances, forming thus a magnetoiductive transmission line. In the linear limit, significant power transmission along the array only appears for frequencies inside the linear magnetoinductive wave band. We present analytical, closed form solutions for the magnetoinductive waves transmitting the power in this regime, and their discrete frequency dispersion. When nonlinearity is important, more frequency bands with significant power transmission along the array may appear. In the equivalent circuit picture, the nonlinear magnetoiductive transmission line driven at one end by a relatively weak electromotive force, can be modeled by coupled resistive-inductive-capacitive (RLC) circuits with voltage-dependent capacitance. Extended numerical simulations reveal that power transmission along the array is also possible in other than the linear frequency bands, which are located close to the nonlinear resonances of a single nonlinear RLC circuit. Moreover, the effectiveness of power transmission for driving frequencies in the nonlinear bands is comparable to that in the linear band. Power transmission in the nonlinear bands occurs through the linear modes of the system, and it is closely related to the instability of a mode that is localized at the driven site.Comment: 11 pages, 11 figures, submitted to International Journal of Bifurcation and Chao

Asymmetric total synthesis of (+)-virosine a via sequential nucleophilic cyclizations onto an activated formamide

Abstract: The first synthesis of tetracyclic alkaloid virosine A is reported. The natural alkaloid was prepared in only 13 steps, in an enantioenriched form. The azabicyclo[2.2.2]octane core was efficiently assembled using a key Vilsmeier–Haack and Mannich cyclizations sequence performed in one pot