Experimental polarization encoded quantum key distribution over optical fibres with real-time continuous birefringence compensation

In this paper we demonstrate an active polarization drift compensation scheme for optical fibres employed in a quantum key distribution experiment with polarization encoded qubits. The quantum signals are wavelength multiplexed in one fibre along with two classical optical side channels that provide the control information for the polarization compensation scheme. This set-up allows us to continuously track any polarization change without the need to interrupt the key exchange. The results obtained show that fast polarization rotations of the order of 40*pi rad/s are effectively compensated for. We demonstrate that our set-up allows continuous quantum key distribution even in a fibre stressed by random polarization fluctuations. Our results pave the way for Bell-state measurements using only linear optics with parties separated by long-distance optical fibres

Similarity solutions and Conservation laws for the Bogoyavlensky-Konopelchenko Equation by Lie point symmetries

The 1 + 2 dimensional Bogoyavlensky-Konopelchenko Equation is investigated for its solution and conservation laws using the Lie point symmetry analysis. In the recent past, certain work has been done describing the Lie point symmetries for the equation and this work seems to be incomplete (Ray S (2017) Compt. Math. Appl. 74, 1157). We obtained certain new symmetries and corresponding conservation laws. The travelling-wave solution and some other similarity solutions are studied.Comment: 12 pages. Accepted for publication in Quaestiones Mathematica

Noether's Theorem and Symmetry

In Noether's original presentation of her celebrated theorm of 1918 allowance was made for the dependence of the coefficient functions of the differential operator which generated the infinitesimal transformation of the Action Integral upon the derivatives of the depenent variable(s), the so-called generalised, or dynamical, symmetries. A similar allowance is to be found in the variables of the boundary function, often termed a gauge function by those who have not read the original paper. This generality was lost after texts such as those of Courant and Hilbert or Lovelock and Rund confined attention to point transformations only. In recent decades this dimunition of the power of Noether's Theorem has been partly countered, in particular in the review of Sarlet and Cantrijn. In this special issue we emphasise the generality of Noether's Theorem in its original form and explore the applicability of even more general coefficient functions by alowing for nonlocal terms. We also look for the application of these more general symmetries to problems in which parameters or parametric functions have a more general dependence upon the independent variablesComment: 23 pages, to appear in Symmetry in the special issue "Noether's Theorem and Symmetry", dedicated for the 100 years from the publication of E. Noether's original work on the invariance of the functional of the Calculus of Variation

On the contribution of the Hall term in small-scale magnetohydrodynamic dynamo

A detailed study of small-scale Hall magnetohydrodynamic dynamo has been performed both analytically and numerically. Assuming the magnetic field and the current to be separate fields, the contribution of the Hall term has been decomposed into two parts and their individual contributions have been studied separately. Calculating the scale-separated transfer rates described in Dar \textit{et. al.} (Physica D, 157 (207), 2001), it is found that the small-scale current fields are the primary contributors in sustaining large scale magnetic fields. Furthermore, the nature of the scale-to-scale fluxes are found to be globally intact with the ion inertial scale

Comparative study on sorption characteristics of coal seams from Barakar and Raniganj formations of Damodar Valley Basin, India

The methane retention mechanism in coal seams is markedly different from those of conventional gas reservoirs. Methane remains mainly as physically adsorbed molecules on micropore surface. Chemical and petrographic compositions of coal are the measures of maturity and type of organic matter that control the methane sorption characteristics of the coal. 99% of Indian coal occurrences are contributed by lower Gondwana sequences housed in two major geologic formations, younger Raniganj and older Barakar. The Raniganj Formation is best exposed in Raniganj Sub-basin and Barakar Formation is best exposed in Jharia Sub-basin of Damodar Valley. Present work attempts a systematic investigation on comparative account of methane sorption characteristics of coals from Raniganj Formation of Raniganj Sub-basin and Barakar Formations of Jharia Sub-basin in relation to their chemical composition and petrographic makeup. Chemical analyses shows that moisture, ash, volatile matter and fixed carbon varies between 2.5 and 4.6%, 10.0–27.2%, 38.8–40.2% (dmmf) and 59.8–61.2% (dmmf), respectively for Raniganj coals and, 0.5–1.1%, 16.7–32.9%, 20.7–22.0% (dmmf) and 78.0–79.3% (dmmf), respectively for Barakar coals. Carbon content is distinct for the suites of coal, 79.2–85.4% and 85.6–92.0% for Raniganj and Barakar coals, respectively. The vitrinite reflectance for the Raniganj coals ranges 0.53–0.72% and the Barakar coals ranges 1.09–1.23%. Based on the chemical composition and vitrinite reflectance value Raniganj coals belongs to high volatile bituminous type, whereas Barakar coals belongs to high to medium volatile bituminous type. Such variation in composition and maturity is mainly attributed to the variation in precursor organic matter as well as the basinal and thermal history of the sub-basins under consideration. H/C atomic ratio of the Raniganj and Barakar coals varies between 0.65 and 0.80 and 0.51–0.72 and O/C atomic ratio varies between 0.05 and 0.13 and 0.01–0.07, respectively. Coals of both the Raniganj and Barakar formations are mostly of kerogen Type-III with Raniganj coals falling in wet gas maturity stage approaching early-thermogenic methane generation whereas Barakar coals falling in condensate gas stage approaching peakthermogenic methane generation. The Langmuir volume ranges from 9.3–21.8 cc/g (daf) for Raniganj coals and 21.1–29.1 cc/g (daf) for Barakar coals. Sorption capacity for the set of coals shows a strong rank dependency and increase with corresponding increase in rank down the stratigraphic column. Methane sorption capacity shows positive relationship with carbon content and vitrinite reflectance, and negative relationship with moisture content, ash and volatile matter. Moisture effect is more prominent in low rank Raniganj coals. The adsorption capacity shows a strong positive relation with vitrinite content and a moderate negative relation with inertinite content for both the Raniganj and Barakar coals, which may be attributed to dominancy of micropores in vitrinites with rank enhancement. The multiple regression analysis shows that the moisture is the main predictor of the VL, and the interaction of moisture with ash and reflectance mainly control the sorption capacity. A predictive model equation is developed for determination of sorption for Damodar basin coals from carbon, ash and moisture data

Control-oriented Modeling of Bend Propagation in an Octopus Arm

Bend propagation in an octopus arm refers to a stereotypical maneuver whereby an octopus pushes a bend (localized region of large curvature) from the base to the tip of the arm. Bend propagation arises from the complex interplay between mechanics of the flexible arm, forces generated by internal muscles, and environmental effects (buoyancy and drag) from of the surrounding fluid. In part due to this complexity, much of prior modeling and analysis work has relied on the use of high dimensional computational models. The contribution of this paper is to present a control-oriented reduced order model based upon a novel parametrization of the curvature of the octopus arm. The parametrization is motivated by the experimental results. The reduced order model is related to and derived from a computational model which is also presented. The results from the two sets of models are compared using numerical simulations which is shown to lead to useful qualitative insights into bend propagation. A comparison between the reduced order model and experimental data is also reported