Generalized Variational Problems and Euler–Lagrange equations

This paper introduces three new operators and presents some of their properties. It defines a new class of variational problems (called Generalized Variational Problems, or GVPs) in terms of these operators and derives Euler–Lagrange equations for this class of problems. It is demonstrated that the left and the right fractional Riemann–Liouville integrals, and the left and the right fractional Riemann–Liouville, Caputo, Riesz–Riemann–Liouville and Riesz–Caputo derivatives are special cases of these operators, and they are obtained by considering a special kernel. Further, the Euler–Lagrange equations developed for functional defined in terms of the left and the right fractional Riemann–Liouville, Caputo, Riesz–Riemann–Liouville and Riesz–Caputo derivatives are special cases of the Euler–Lagrange equations developed here. Examples are considered to demonstrate the applications of the new operators and the new Euler–Lagrange equations. The concepts of adjoint differential operators and adjoint differential equations defined in terms of the new operators are introduced. A new class of generalized Lagrangian, Hamiltonian, and action principles are presented. In special cases, these formulations lead to fractional adjoint differential operators and adjoint differential equations, and fractional Lagrangian, Hamiltonian, and action principle. Thus, the new operators introduce a generalized approach to many problems in classical mechanics in general and variational calculus in particular. Possible extensions of the subject and the concepts discussed here are also outlined.     

Functionalization of conducting polymer with novel Co(II) complex: Electroanalysis of ascorbic acid

We report for the first time the functionalization of a conducting polymer with a metal complex in order to develop a new type of catalytic material exhibiting better electronic communication through their delocalized π electrons. The Co(II) complex having hydroxyl group as functional moiety is chemically coupled with carboxyl group of polyanthranilic acid which itself is a self doped conducting polymer. The covalent linkage between Co(II) and –OH group is confirmed using UV–vis, FT-IR and NMR spectroscopic techniques. The Co(II) complex functionalized polymer does exhibit excellent redox behavior and stability with mixed properties of Co(II) complex and π-conjugated polymer. The material possesses potential benefits in sensors/biosensor applications and it is demonstrated for the electroanalysis of ascorbic acid at a level of nano molar concentration.     

Hybrid connection algorithm: A strategy for efficient restoration in WDM optical networks

In present communication, we propose a modified resource allocation strategy, namely, hybrid connection algorithm, for achieving efficient restoration in WDM optical networks. The main theme of the algorithm is that, while attempting connection establishment, a wavelength is reserved in advance for providing resources for backup lightpaths. The analysis and the comparison of the proposed strategy with other existing strategies has been undertaken using metrics such as, restoration efficiency, number of wavelength links used by primary and backup lightpaths, and the percent link utilization. The proposed strategy provides 100% restoration efficiency and much better performance than the existing techniques.     

Iron(III)-mediated ATRP systems of n-docosyl acrylate with AIBN and BPO

Well-defined poly(n-docosyl acrylate) (PDA) with narrow molecular weight distribution has been synthesized by atom transfer radical polymerization (ATRP) and reverse ATRP of n-docosyl acrylate (DA) at 80 °C in N,N-dimethylformamide using the carbon tetrabromide/FeCl₃/2,2′-bipyridine (bpy) initiation system in the presence of 2,2′-azobisisobutyronitrile (AIBN) and benzoyl peroxide (BPO) as the source of reducing agent. The rates of polymerization for both the systems exhibit first-order kinetics with respect to the monomer, however, peroxide-initiated system shows slow rate of polymerization as compared to the azo-system. The effect of various reaction parameters on number average molecular weight (M _n ) and molecular weight distribution (M _w/M _n ) have been investigated. The resulting PDA that obtained in presence of AIBN and BPO systems has been compared for both the conventional and reverse ATRP. The reverse ATRP initiated by peroxides behaves differently than that of the azo initiators. In reverse ATRP with BPO, the rate of polymerization (R _p) has been significantly increased with the increase of BPO resulting higher M _n and broader M _w/M _n . The reverse ATRP of DA did not exhibit living characteristics with BPO system. PDA has been characterized by GPC, FTIR, and NMR spectroscopy.     

Modelling of start-up time for high temperature polymer electrolyte fuel cells

Start-up time is one of the important factors that limit the application of high temperature polymer electrolyte fuel cells in several areas. Present work involves the analysis of different warm-up methodologies to analyse the start-up time for phosphoric acid doped PBI membrane based fuel cells. With this objective a number of three dimensional thermal models have been developed. Different heating methodologies such as reactant heating, coolant heating and combined heating (reactant and ohmic) are simulated. The ohmic heating is implemented for generating heat in the membrane itself at high current densities. Hence, combining it with other heating techniques is found effective in reducing start-up times significantly.     

Effect of Zr on dielectric, ferroelectric and impedance properties of BaTiO3 ceramic

A polycrystalline sample of Zr-doped barium titanate (BaTiO₃) was prepared by conventional solid state reaction method. The effect of Zr (0·15) on the structural and microstructural properties of BaTiO₃ was investigated by XRD and SEM. The electrical properties (dielectric, ferroelectric and impedance spectroscopy) were measured in wide range of frequency and temperature. With substitutions of Zr, the structure of BaTiO₃ changes from tetragonal to rhombohedral. Lattice parameters were found to increase with substitution. The room temperature dielectric constant increases from ～ 1675 to ～ 10586 and peak dielectric constant value increases from ～ 13626 to ～ 21023 with diffuse phase transition. Impedance spectroscopy reveals the formation of grain and grain boundary in the material and found to decrease with increase in temperature.     

Structural and ferroelectric properties of lanthanum modified BPZT ceramics

Lanthanum modified Ba_0.80Pb_0.20Ti_0.90Zr_0.10O₃ (BPZT) ceramics with composition Ba_0.80−xLa_x Pb_0.20Ti_0.90Zr_0.10O₃; x = 0–0.01 in steps of 0.0025 were prepared by conventional solid state method. All the samples were sintered at 1325 °C after compacting in circular discs. Detailed structural and ferroelectric properties were carried out for sintered specimens. X-ray diffraction analysis for all the sintered specimens shows tetragonal structure with perovskite. Coercive field (E_c) and remanent polarization (P_r) to spontaneous polarization (P_s) ratio (P_r/P_s) was found to decrease with increase in temperature. P_r/P_s ratio was found to decrease with increase in x, except x = 0.0025.     

Peat swamps at Giral lignite field of Barmer basin,Rajasthan, Western India: understanding the evolution through petrological modelling

International Journal of Coal Science & Technology - The lignite samples collected from Giral lignite field of Barmer basin have been subjected to petrological investigation. The data generated...