478 research outputs found
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
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