Connected quantized Weyl algebras and quantum cluster algebras

For an algebraically closed field K, we investigate a class of noncommutative K-algebras called connected quantized Weyl algebras. Such an algebra has a PBW basis for a set of generators {x1,…,xn} such that each pair satisfies a relation of the form xixj=qijxjxi+rij, where ⁎ qij∈K⁎ and rij∈K, with, in some sense, sufficiently many pairs for which rij≠0. For such an algebra it turns out that there is a single parameter q such that each qij=q±1. Assuming that q≠±1, we classify connected quantized Weyl algebras, showing that there are two types linear and cyclic. When q is not a root of unity we determine the prime spectra for each type. The linear case is the easier, although the result depends on the parity of n, and all prime ideals are completely prime. In the cyclic case, which can only occur if n is odd, there are prime ideals for which the factors have arbitrarily large Goldie rank. We apply connected quantized Weyl algebras to obtain presentations of two classes of quantum cluster algebras. Let n≥3 be an odd integer. We present the quantum cluster algebra of a Dynkin quiver of type An−1 as a factor of a linear connected quantized Weyl algebra by an ideal generated by a central element. We also consider the quiver Pn+1(1) identified by Fordy and Marsh in their analysis of periodic quiver mutation. When n is odd, we show that the quantum cluster algebra of this quiver is generated by a cyclic connected quantized Weyl algebra in n variables and one further generator. We also present it as the factor of an iterated skew polynomial algebra in n+2 variables by an ideal generated by a central element. For both classes, the quantum cluster algebras are simple noetherian. We establish Poisson analogues of the results on prime ideals and quantum cluster algebras. We determine the Poisson prime spectra for the semiclassical limits of the linear and cyclic connected quantized Weyl algebras and show that, when n is odd, the cluster algebras of An−1 and Pn+1(1) are simple Poisson algebras that can each be presented as a Poisson factor of a polynomial algebra, with an appropriate Poisson bracket, by a principal ideal generated by a Poisson central element

Magnetoluminescence

Pulsar Wind Nebulae, Blazars, Gamma Ray Bursts and Magnetars all contain regions where the electromagnetic energy density greatly exceeds the plasma energy density. These sources exhibit dramatic flaring activity where the electromagnetic energy distributed over large volumes, appears to be converted efficiently into high energy particles and gamma-rays. We call this general process magnetoluminescence. Global requirements on the underlying, extreme particle acceleration processes are described and the likely importance of relativistic beaming in enhancing the observed radiation from a flare is emphasized. Recent research on fluid descriptions of unstable electromagnetic configurations are summarized and progress on the associated kinetic simulations that are needed to account for the acceleration and radiation is discussed. Future observational, simulation and experimental opportunities are briefly summarized.Comment: To appear in "Jets and Winds in Pulsar Wind Nebulae, Gamma-ray Bursts and Blazars: Physics of Extreme Energy Release" of the Space Science Reviews serie

Role of spent fuel characterization in the development of safe repositories

Objective is to understand the spent fuel performance. In order to do this, we must quantify the spent fuel characteristics at various time intervals during specific field and laboratory tests. This spent fuel characterization is used to identify and describe mathematically the degradation modes experienced during the tests. Incorporation of these descriptions into the more comprehensive spent fuel performance prediction model will aid in the overall licensing of repositories for permanent disposal of the spent fuel waste form

Theoretical analysis of mechanism of photorefractive enhancement of photochromic gratings in BSO

We present the results of theoretical modelling of the increase in diffraction efficiency in photorefractive BSO under conditions of photorefractive enhancement via permanent photochromic gratings. The results are modelled using coupled wave theory, including the anisotropic nature of the secondary refractive index grating, optical activity and electric field induced birefringence. The dependence of the enhancement of the diffraction efficiency as a function of the input polarisation of the diffracted beam. and of the applied electric field is presented for two different crystal geometries

Mechanism of photorefractive enhancement of photochromic gratings in BSO - Experimental results and phenomenological modelling

We report an increase of more than a factor of 100 in the diffraction efficiency from photochromic gratings written in BSO by uniformly illuminating these gratings with 488 nm light to induce secondary photorefractive gratings. Upon application of an electric field, the phase shift between the two gratings can he varied and under appropriate conditions the diffraction efficiency can increase. The dependence of the enhanced diffraction efficiency as a function of the applied electric field and readout beam polarisation was experimentally investigated for two different crystal orientations. Phenomenological modelling is presented requiring modifications to the phase angle between the photochromic and induced photorefractive gratings in order to reproduce the experimentally observed asymmetry in the increase in the diffraction efficiency. This suggests a periodic modulation of the photorefractive donor/acceptor density, due to the presence of the photochromic grating

A new reaction pathway in organophosphorus chemistry: competing SN2- and AE'-pathways for nucleophilic attack at a phosphorus-cage compound

Competition: A combination of 31P NMR spectroscopic and calculational studies have shown that nucleophilic substitution in the phosphorus-carbon cage compound ClP3(CtBu)2 occurs through competing SN2- and AE-type reaction pathways (see scheme for model compound ClP3(CH)2). The AE mechanism results in the formation of a C2v-symmetric intermediate prior to release of the chloride ion