Symbolic Representation for Analog Realization of A Family of Fractional Order Controller Structures via Continued Fraction Expansion

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.This paper uses the Continued Fraction Expansion (CFE) method for analog realization of fractional order differ-integrator and few special classes of fractional order (FO) controllers viz. Fractional Order Proportional-Integral-Derivative (FOPID) controller, FO[PD] controller and FO lead-lag compensator. Contemporary researchers have given several formulations for rational approximation of fractional order elements. However, approximation of the controllers studied in this paper, due to having fractional power of a rational transfer function, is not available in analog domain; although its digital realization already exists. This motivates us for applying CFE based analog realization technique for complicated FO controller structures to get equivalent rational transfer functions in terms of the controller tuning parameters. The symbolic expressions for rationalized transfer function in terms of the controller tuning parameters are especially important as ready references, without the need of running CFE algorithm every time and also helps in the synthesis of analog circuits for such FO controllers

Optimized Quality Factor of Fractional Order Analog Filters with Band-Pass and Band-Stop Characteristics

This is the author accepted manuscript. The final version is available from IEEE via the DOI in this record.Fractional order (FO) filters have been investigated in this paper, with band-pass (BP) and band-stop (BS) characteristics, which can not be achieved with conventional integer order filters with orders lesser then two. The quality factors for symmetric and asymmetric magnitude response have been optimized using real coded Genetic Algorithm (GA) for a user specified center frequency. Parametric influence of the FO filters on the magnitude response is also illustrated with credible numerical simulations

Resonant inelastic X-ray scattering in a Mott insulator

We calculate the resonant inelastic X-ray scattering (RIXS) response in a Mott insulator which is described by the Falicov-Kimball model. The model can be solved exactly within the single site dynamical mean-field theory (DMFT) approximation and the calculated RIXS response is accurate up to a local background correction. We find that on resonance the RIXS response is greatly enhanced over various other non-resonant background effects and the response systematically evolves from a single peak structure, arising due to relaxation processes within the lower Hubbard band, to a two peak structure, arising due to relaxation processes within the upper Hubbard band as well as across the Mott gap into the lower Hubbard band, as we vary the incident photon frequency to access states from the bottom of the lower Hubbard band to the top of the upper Hubbard band. The charge transfer excitations are found to disperse monotonically outwards (as a function of transfered energy) as we go from the center of the Brillouin zone towards the zone corner. These correlation induced features have been observed by Hasan {\it et. al.} (Science {\bf 288}, 1811 (2000)) and many other experimentalists in RIXS measurements over various transition metal oxide compounds and are found to be robust and survive even for large Auger lifetime broadening effects. As a comparison, we also calculate the dynamic structure factor for this model, which is proportional to the nonresonant part of the response, and does not show these specific signatures.Comment: 14 pages, 14 figures, submitted to Physical Review

Magnetic phase transitions in Eu(Co1-xNix)(2-y)As-2 single crystals

The effects of Ni doping in Eu(Co1-xNix)(2-y)As-2 single crystals with x = 0 to 1 grown out of self-flux are investigated via crystallographic, electronic transport, magnetic, and thermal measurements. All compositions adopt the body-centered-tetragonal ThCr2Si2 structure with space group I4/mmm. We also find 3%-4% of randomly distributed vacancies on the Co/Ni site. Anisotropic magnetic susceptibility chi(alpha) (alpha = ab, c) data versus temperature T show clear signatures of an antiferromagnetic (AFM) c-axis helix structure associated with the Eu+2 spins 7/2 for x = 0 and 1 as previously reported. The chi(alpha)(T) data for x = 0.03 and 0.10 suggest an anomalous 2q magnetic structure containing two helix axes along the c axis and in the ab plane, respectively, whereas for x = 0.75 and 0.82 a c-axis helix is inferred as previously found for x = 0 and 1. At intermediate compositions x = 0.2, 0.32, 0.42, 0.54, and 0.65, a magnetic structure with a large ferromagnetic (FM) c-axis component is found from magnetization versus field isotherms, suggested to be an incommensurate FM c-axis cone structure associated with the Eu spins, which consists of both AFM and FM components. In addition, the chi(T) and heat capacity C-p(T) data for x = 0.2-0.65 indicate the occurrence of itinerant FM order associated with the Co/Ni atoms with Curie temperatures from 60 to 25 K, respectively. Electrical resistivity rho(T) measurements indicate metallic character for all compositions with abrupt increases in slope on cooling below the Eu AFM transition temperatures. In addition to this panoply of magnetic transitions, Eu-151 Mossbauer measurements indicate that ordering of the Eu moments proceeds via an incommensurate sine amplitude-modulated structure with additional transition temperatures associated with this effect