Photon orbital angular momentum and torque metrics for single telescopes and interferometers

Context. Photon orbital angular momentum (POAM) is normally invoked in a quantum mechanical context. It can, however, also be adapted to the classical regime, which includes observational astronomy. Aims. I explain why POAM quantities are excellent metrics for describing the end-to-end behavior of astronomical systems. To demonstrate their utility, I calculate POAM probabilities and torques from holography measurements of EVLA antenna surfaces. Methods. With previously defined concepts and calculi, I present generic expressions for POAM spectra, total POAM, torque spectra, and total torque in the image plane. I extend these functional forms to describe the specific POAM behavior of single telescopes and interferometers. Results. POAM probabilities of spatially uncorrelated astronomical sources are symmetric in quantum number. Such objects have zero intrinsic total POAM on the celestial sphere, which means that the total POAM in the image plane is identical to the total torque induced by aberrations within propagation media & instrumentation. The total torque can be divided into source- independent and dependent components, and the latter can be written in terms of three illustrative forms. For interferometers, complications arise from discrete sampling of synthesized apertures, but they can be overcome. POAM also manifests itself in the apodization of each telescope in an array. Holography of EVLA antennas observing a point source indicate that ~ 10% of photons in the n = 0 state are torqued to n != 0 states. Conclusions. POAM quantities represent excellent metrics for characterizing instruments because they are used to simultaneously describe amplitude and phase aberrations. In contrast, Zernike polynomials are just solutions of a differential equation that happen to ~ correspond to specific types of aberrations and are typically employed to fit only phases

On the (2,3)-generation of the finite symplectic groups

This paper is a new important step towards the complete classification of the finite simple groups which are $(2,3)$-generated. In fact, we prove that the symplectic groups $Sp_{2n}(q)$ are $(2,3)$-generated for all $n\geq 4$. Because of the existing literature, this result implies that the groups $PSp_{2n}(q)$ are $(2,3)$-generated for all $n\geq 2$, with the exception of $PSp_4(2^f)$ and $PSp_4(3^f)$

More on regular subgroups of the affine group

This paper is a new contribution to the study of regular subgroups of the affine group $AGL_n(F)$, for any field $F$. In particular we associate to any partition $\lambda\neq (1^{n+1})$ of $n+1$ abelian regular subgroups in such a way that different partitions define non-conjugate subgroups. Moreover, we classify the regular subgroups of certain natural types for $n\leq 4$. Our classification is equivalent to the classification of split local algebras of dimension $n+1$ over $F$. Our methods, based on classical results of linear algebra, are computer free

Scott's formula and Hurwitz groups

This paper continues previous work, based on systematic use of a formula of L. Scott, to detect Hurwitz groups. It closes the problem of determining the finite simple groups contained in $PGL_n(F)$ for $n\leq 7$ which are Hurwitz, where $F$ is an algebraically closed field. For the groups $G_2(q)$, $q\geq 5$, and the Janko groups $J_1$ and $J_2$ it provides explicit $(2,3,7)$-generators

The simple classical groups of dimension less than 6 which are (2,3)-generated

In this paper we determine the classical simple groups of dimension r=3,5 which are (2,3)-generated (the cases r = 2, 4 are known). If r = 3, they are PSL_3(q), q 4, and PSU_3(q^2), q^2 9, 25. If r = 5 they are PSL_5(q), for all q, and PSU_5(q^2), q^2 >= 9. Also, the soluble group PSU_3(4) is not (2,3)-generated. We give explicit (2,3)-generators of the linear preimages, in the special linear groups, of the (2,3)-generated simple groups.Comment: 12 page

The (2,3)(2,3)-generation of the finite unitary groups

In this paper we prove that the unitary groups $SU_n(q^2)$ are $(2,3)$-generated for any prime power $q$ and any integer $n\geq 8$. By previous results this implies that, if $n\geq 3$, the groups $SU_n(q^2)$ and $PSU_n(q^2)$ are $(2,3)$-generated, except when $(n,q)\in\{(3,2),(3,3),(3,5),(4,2), (4,3),(5,2)\}$.Comment: In this version, we obtained a complete classification of the finite simple unitary groups which are (2,3)-generated; some proofs have been semplifie

The (2,3)-generation of the special unitary groups of dimension 6

In this paper we give explicit (2,3)-generators of the unitary groups SU_6(q^ 2), for all q. They fit into a uniform sequence of likely (2,3)-generators for all n>= 6

Turbulent heat transfer in spacer-filled channels: Experimental and computational study and selection of turbulence models

Heat transfer in spacer-filled channels of the kind used in Membrane Distillation was studied in the Reynolds number range 100–2000, encompassing both steady laminar and early-turbulent flow conditions. Experimental data, including distributions of the local heat transfer coefficient h, were obtained by Liquid Crystal Thermography and Digital Image Processing. Alternative turbulence models, both of first order (k-ε, RNG k-ε, k-ω, BSL k-ω, SST k-ω) and of second order (LRR RS, SSG RS, ω RS, BSL RS), were tested for their ability to predict measured distributions and mean values of h. The best agreement with the experimental results was provided by first-order ω-based models able to resolve the viscous/conductive sublayer, while all other models, and particularly ε-based models using wall functions, yielded disappointing predictions

Storming Majorana's Tower with OAM states of light in a plasma

We extend the relationship between mass and spin angular momentum, described by the bosonic spectrum of positive definite mass particles of the Majorana solution to the Dirac equation, to photons that acquire an effective Proca mass through the Anderson-Higgs mechanism when they propagate in a plasma. In an earlier paper we showed that if the plasma is structured, it can impart orbital angular momentum (OAM) to the photons that reduces the total Proca photon mass. Here we show, through a generalisation of Majorana's solution, that photons with OAM in a plasma cannot assume negative squared mass states. This means that there exist interesting analogies with Quantum Gravity or General Relativity models involving a modified action of the Lorentz group.Comment: 4 pages; Corrected, updated versio