An isothermal equation of state for solids

An isothermal equation of state (EOS) for solids, recently suggested by the authors in the realistic form, V/V₀=f(P), with relative volume as the dependent and the pressure as the independent variable, was shown to have an advantage for some close-packed materials in that it allows B′_∞=(∂B_s/∂P)_s(P→∞) to be fitted, and this is where the usual standard equations fail. In the present study, our EOS is applied to a number of inorganic as well as organic solids, including alloys, glasses, rubbers and plastics; varying widely in their bonding and structural characteristics, as well as in their bulk modulus values. A very good agreement is observed between the data and fits. The results obtained are compared with those from two well-known equations, expressible in the realistic form, proposed by Murnaghan and Luban. Further, the results are also compared with those from the widely used two- and three-parameter EOSs, expressible in the unrealistic form only, P=f(V/V₀), proposed by Birch—and also with those from the EOS model of Keane in which B′_∞ is explicitly expressed as an equation of state parameter. The results obtained from our model compare well to these EOSs. Our EOS, in general, yields the smallest mean-squared deviations between data and fits. The values of B′_∞calculated from our EOS are compared with those from Keane's model. Further, we have studied the variation of B′_∞with temperature using the experimental isotherms of Mo and W at 10 different temperatures ranging from 100 to 1000 K, and observed that the values of B′_∞ yielded by our model and that of Keane vary, as expected, within a narrow range. Furthermore, our EOS is applied to study the stability of the fit parameters with variation in the pressure ranges with reference to the isothermal compression data on Mo and W—and also to study the variation of isothermal bulk modulus with pressure, with reference to the ultrasonic data on NaCl and noted a very good agreement with experiment. In addition, our model is applied, with B₀ and B′₀ constrained to the theoretical values, to the five theoretical isotherms of MgO at 300, 500, 1000, 1500 and 2000 K obtained on the basis of a first principles approach—a good agreement is observed with the predictions, and the values of B′_∞ inferred at different temperatures tend to converge to a constant value.     

Study of fiber optic sugar sensor

Over the last two decades, the fiber optic technology has passed through many analytical stages. Some commercially available fiber optic sensors, though in a small way, are being used for automation in mechanical and industrial environments. They are also used for instrumentation and controls. In the present work, an intensity-modulated intrinsic fiber optic sugar sensor is presented. This type of sensor, with slight modification, can be used for on-line determination of the concentration of sugar content in sugarcane juice in sugar industry. In the present set-up, a plastic fiber made of polymethylmethacrylate is used. A portion of the cladding (1 cm, 2 cm, 3 cm) at the mid-point along the length of the fiber is removed. This portion is immersed in sugar solution of known concentration and refractive index. At one end of the fiber an 850 nm source is used and at the other end a power meter is connected. By varying the concentration of sugar solution, the output power is noted. These studies are made due to the change in refractive index of the fluid. The device was found to be very sensitive which is free from EMI and shock hazards, stable and repeatable and they can be remotely interfaced with a computer to give on-line measurements and thus become useful for application in sugar industries.     

ENSTAR detector forη- mesic studies

We have initiated a search for a new type of nuclear matter, theη-mesic nucleus, using beams from the multi-GeV hadron facility, COSY at Juelich, Germany. A large acceptance scintillator detector, ENSTAR has been designed and built at BARC, Mumbai and fully assembled and tested at COSY. A test run for calibration and evaluation has been completed. In this contribution we present the design and technical details of the ENSTAR detector and how it will be used to detect protons and pions (the decay products ofη-mesic bound state). The detector is made of plastic scintillators arranged in three concentric cylindrical layers. The readout of the detectors is by means of optical fibres. The layers are used to generate ΔE –E spectra for particle identification and total energy information of stopped particles. The granularity of the detector allows for position (θ and ?ø determination making the event reconstruction kinematically complete     

Flow-injection spectrophotometric determination of residual free chlorine and chloramine

2,4-Dinitrophenylhydrazine has been suggested as a new reagent for the flow-injection spectrophotometric determination of residual chlorine based on its oxidation to 2,4-dinitrophenyldiazonium ion. The measurement of the decrease in colour intensity under reversed flow-injection (reagent injection) conditions has been used for the determination of 0.1–10 mg/l Cl present as free or combined chlorine, and for its speciation. The limit of detection was 0.05 mg/l Cl. Copper (II), iron (III) and many other ions have been found not to vitiate the results.     

Absolutely continuous spectrum for sparse potentials

In this paper we show that bounded perturbation of the discrete laplacian with a potential that is sparsely supported (a notion made precise in the paper) produces absolutely continuous spectrum in the interval [?2ν, 2ν] for large dimension ν. We note that the potential need not give rise to a compact operator, let alone have decay at infinity.     

Painlevé analysis and hamiltonian structure of a new space-dependent KdV equation

We deduce the Lax pair for a new space-dependent KdV equation, , via the technique of Painlevé analysis. From it, infinitely many conservation laws are deduced and the symplectic structure is obtained.