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The paper gives two approaches to write explicit presentations for the class of Dehn quandles using presentations of their underlying groups. The first approach gives finite presentations for Dehn quandles of a class of Garside groups and Gaussian groups. The second approach is for general Dehn quandles when the centralisers of generators of their underlying groups are known. Several examples including Dehn quandles of spherical Artin groups, surface groups and mapping class groups of orientable surfaces are given to illustrate the results., Comment: 32 pages

Let $\mathrm{Mod}(S_g)$ be the mapping class group of the closed orientable surface of genus $g \geq 1$, and let $\mathrm{LMod}_{p}(X)$ be the liftable mapping class group associated with a finite-sheeted branched cover $p:S \to X$, where $X$ is a hyperbolic surface. For $k \geq 2$, let $p_k: S_{k(g-1)+1} \to S_g$ be the standard $k$-sheeted regular cyclic cover. In this paper, we show that $\{\mathrm{LMod}_{p_k}(S_g)\}_{k \geq 2}$ forms an infinite family of self-normalizing subgroups in $\mathrm{Mod}(S_g)$, which are also maximal when $k$ is prime. Furthermore, we derive explicit finite generating sets for $\mathrm{LMod}_{p_k}(S_g)$ for $g \geq 3$ and $k \geq 2$, and $\mathrm{LMod}_{p_2}(S_2)$. For $g \geq 2$, as an application of our main result, we also derive a generating set for $\mathrm{LMod}_{p_2}(S_g) \cap C_{\mathrm{Mod}(S_g)}(\iota)$, where $C_{\mathrm{Mod}(S_g)}(\iota)$ is the centralizer of the hyperelliptic involution $\iota \in \mathrm{Mod}(S_g)$. Let $\mathcal{L}$ be the infinite ladder surface, and let $q_g : \mathcal{L} \to S_g$ be the standard infinite-sheeted cover induced by $\langle h^{g-1} \rangle$ where $h$ is the standard handle shift on $\mathcal{L}$. As a final application, we derive a finite generating set for $\mathrm{LMod}_{q_g}(S_g)$ for $g \geq 3$., Comment: 16 pages, 9 figures. Added a few more results and figures, improved the exposition. Comments are welcome

Unifying various constructions of quandles including Coxeter quandles, free quandles, knot quandles of prime knots and Dehn quandles of orientable surfaces, we introduce Dehn quandles of groups with respect to their subsets. It turns out that Dehn quandles are precisely the ones that embed naturally into their enveloping groups. We prove that the enveloping group of the Dehn quandle of a given group with respect to its generating set is a central extension of that group, and that enveloping groups of Dehn quandles of Artin groups and link groups with respect to their standard generating sets are the groups themselves. We discuss orderability of Dehn quandles and prove that free involutory quandles are left orderable, whereas certain generalised Alexander quandles are bi-orderable. Specialising to surfaces, we give generating sets for Dehn quandles of orientable surfaces with punctures and compute their automorphism groups. As applications, we recover a result of Niebrzydowski and Przytycki proving that the knot quandle of the trefoil knot is isomorphic to the Dehn quandle of the torus and also extend a result of Yetter on epimorphisms of Dehn quandles of orientable surfaces onto certain involutory homological quandles., Comment: 25 pages, 4 figures

Multilayer X-ray mirrors consist of a coating of a large number of alternate layers of high Z and low Z materials with a typical thickness of 10-100 Angstrom, on a suitable substrate. Such coatings play an important role in enhancing the reflectivity of X-ray mirrors by allowing reflections at angles much larger than the critical angle of X-ray reflection for the given materials. Coating with an equal thickness of each bilayer enhances the reflectivity at discrete energies, satisfying Bragg condition. However, by systematically varying the bilayer thickness in the multilayer stack, it is possible to design X-ray mirrors having enhanced reflectivity over a broad energy range. One of the most important applications of such a depth graded multilayer mirror is to realize hard X-ray telescopes for astronomical purposes. Design of such multilayer X-ray mirrors and their characterization with X-ray reflectivity measurements require appropriate software tools. We have initiated the development of hard X-ray optics for future Indian X-ray astronomical missions, and in this context, we have developed a program, DarpanX, to calculate X-ray reflectivity for single and multilayer mirrors. It can be used as a stand-alone tool for designing multilayer mirrors with required characteristics. But more importantly, it has been implemented as a local model for the popular X-ray spectral fitting program, XSPEC, and thus can be used for accurate fitting of the experimentally measured X-ray reflectivity data. DarpanX is implemented as a Python 3 module, and an API is provided to access the underlying algorithms. Here we present details of DarpanX implementation and its validation for different type multilayer structures. We also demonstrate the model fitting capability of DarpanX for experimental X-ray reflectivity measurements of single and multilayer samples., Comment: Accepted for publication in Astronomy and Computing, 13 pages, 9 figures

We have used Rietveld refinement technique to determine the extent of intergrowth of Bi$_{2}$Sr$_{2}$CuO$_{6+x}$ phase and co-crystallization of competing phases in a high temperature superconductor Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+x}$ (Bi-2212). The refinement was done on powder diffractograms obtained on powders of Bi-2212 made by grinding single crystals of Bi-2212 grown using two different self-flux techniques, namely pressure technique (PT) and regrowth technique(RG). JANA and FullPROF programs were used for refinement, both of which gave consistent results. Bi and Sr atom's positions were refined in the average structure of centrosymmetric space group $Bbmb$. To incorporate for Bi atoms modulation and modulation vector, refinement was done in centrosymmetric space group N$^{Bbmb}_{1\bar{1}1}$(Bbmb(0$\gamma$1)). It was found that the b* component of the modulation vector decreased with a decrease in the superconducting transition temperature in PT sample compared to the RG sample, suggesting a better alignment of the CuO$_2$ planes with respect to Bi-O planes in PT sample. All the samples were also found to exhibit strong preferred orientation effect. Values of March-Dollase parameters corresponding to the preferred orientation function were obtained. We also calculated Brindley absorption contrast factors \textit{t}$_{\phi}$ and the effect of micro-absorption on the quantity of phases present in each sample. A Rietveld refinement incorporating all the factors resulted in exceptional values of goodness of fit parameters for all the samples with the lowest value of 2.08 found for the PT sample ground for 2 minutes. Additionally, the powders corresponding to the PT crystals were found to have no co-crystallising phase and $\sim$ 94$\%$ Bi-2212 phase, suggesting that crystals grown by pressure technique are of extremely good quality, much better than those grown by RG flux technique.

This work reports on a novel and simple synthetic route for the growth of metal-organic crystal [Cu(C2O4)(4-aminopyridine)2(H2O)]n of large size using the technique of liquid-liquid diffusion or layer diffusion. Single crystal X-ray diffraction measurements revealed a very good quality of the grown single crystals with a small value 1.101 of goodness of fit R. Rietveld refinement done on powder X-ray diffractogram obtained on few single crystals crushed together revealed a very small value of R as 3.45, indicating very good crystal quality in a batch of crystals. Density functional theory with three different basis sets generated the optimized geometry of a monomeric unit as well as its vibrational spectra. Comparison between experimentally obtained bond lengths, bond angles, IR frequencies etc. suggest (B3LYP/LanL2DZ, B3LYP/6-311++ G(d,p) basis set to describe the properties the best. Magnetic susceptibility measurements confirm the metal-organic crystal [Cu(C2O4)(4-aminopyridine)2(H2O)]n to be a very good representation of a spin 1/2 Heisenberg antiferromagnet., Comment: Accepted for publication in Crystal Research And Technology

Let $\text{Mod}(S_g)$ be the mapping class group of the closed orientable surface $S_g$ of genus $g \geq 1$. In this paper, we develop various methods for factoring periodic mapping classes into Dehn twists, up to conjugacy. As applications, we develop methods for factoring certain roots of Dehn twists as words in Dehn twists. We will also show the existence of conjugates of periodic maps of order $4g$ and $4g+2$, for $g\geq 2$, whose product is pseudo-Anosov.

The intentional yaw misalignment of leading, upwind turbines in a wind farm, termed wake steering, has demonstrated potential as a collective control approach for wind farm power maximization. The optimal control strategy, and resulting effect of wake steering on wind farm power production, are in part dictated by the power degradation of the upwind yaw misaligned wind turbines. In the atmospheric boundary layer, the wind speed and direction may vary significantly over the wind turbine rotor area, depending on atmospheric conditions and stability, resulting in freestream turbine power production which is asymmetric as a function of the direction of yaw misalignment and which varies during the diurnal cycle. In this study, we propose a model for the power production of a wind turbine in yaw misalignment based on aerodynamic blade elements which incorporates the effects of wind speed and direction changes over the turbine rotor area in yaw misalignment. A field experiment is performed using multiple utility-scale wind turbines to characterize the power production of yawed freestream operating turbines depending on the wind conditions, and the model is validated using the experimental data. The resulting power production of a yaw misaligned variable speed wind turbine depends on a nonlinear interaction between the yaw misalignment, the atmospheric conditions, and the wind turbine control system., Comment: 37 pages, 15 figures

Let $\mathrm{Mod}(S_g)$ be the mapping class group of the closed orientable surface $S_g$ of genus $g\geq 2$. In this paper, we derive necessary and sufficient conditions under which two torsion elements in $\mathrm{Mod}(S_g)$ will have conjugates that generate a finite split non-abelian metacyclic subgroup of $\mathrm{Mod}(S_g)$. As applications of the main result, we give a complete characterization of the finite dihedral and the generalized quaternionic subgroups of $\mathrm{Mod}(S_g)$ up to a certain equivalence that we will call weak conjugacy. Furthermore, we show that any finite-order mapping class whose corresponding orbifold is a sphere, has a conjugate that lifts under certain finite-sheeted regular cyclic covers of $S_g$. Moreover, for $g \geq 5$, we show the existence of an infinite dihedral subgroup of $\mathrm{Mod}(S_g)$ that is generated by an involution and a root of a bounding pair map of degree $3$. Finally, we provide a complete classification of the weak conjugacy classes of the non-abelian finite split metacyclic subgroups of $\mathrm{Mod}(S_3)$ and $\mathrm{Mod}(S_5)$. We also describe nontrivial geometric realizations of some of these actions., Comment: 31 pages, 12 figures, and 2 tables