Zipf’s law and distribution of population in Indian cities

The Zipf’s law is studied here in the context of size distribution of Indian cities and the power law exponent is estimated. We have used the data from the Indian censuses of 1981,1991 and 2001. The analysis shows that the population distribution in Indian cities do follow a power law similar to the ones found in other countries. The scaling exponent are found to be 2.15 ± 0.01 for 1981, 2.11 ± 0.01 for 1991 and 2.05 ± 0.02 for 2001 from the linear fit. We have also estimated the scaling exponent from the maximum likelihood estimator technique which is found to be 2.04 ±.07 for the year 2001.     

Role of sugar in controlling reaction pathways: A study with thymine and thymidine

Magnetic field effect in conjunction with laser flash photolysis have been used for studying interactions of 9,10-anthraquinone and 2-methyl 1,4-naphthoquinone (menadione) with a DNA base, thymine (Thy) and its nucleoside, thymidine (dThd). Irrespective of medium Thy has been found to support both electron transfer (ET) and hydrogen abstraction with the quinones while dThd has exhibited a complete reluctance towards ET. This unique behavior of dThd has been attributed to a failure in attaining aromaticity by virtue of keto-enol tautomerism upon addition of a sugar moiety. Electron withdrawing effect of sugar unit is also considered responsible for reduction of ET from dThd. Again both Thy and dThd have exhibited hydrogen abstraction in homogeneous medium, which is normally unexpected. The above behaviors of the bases have been explained on the basis of their chemical structures.     

Change point estimation in non-monotonic aging models

The problem of estimating change points in various non-monotonic aging models is considered. A general methodology for consistent estimation of the change point is developed and applied to non-monotonic aging models based on the hazard rate function as well as on the mean residual life function.     

Mitigation of edgewise vibrations in wind turbine blades by means of roller dampers

Edgewise vibrations in wind turbine blades are lightly damped, and large amplitude vibrations induced by the turbulence may significantly shorten the fatigue life of the blade. This paper investigates the performance of roller dampers for mitigation of edgewise vibrations in rotating wind turbine blades. Normally, the centrifugal acceleration of the rotating blade can reach to a magnitude of 7–8g, which makes it possible to use this kind of damper with a relatively small mass ratio for suppressing edgewise vibrations effectively. The parameters of the damper to be optimized are the mass ratio, the frequency ratio, the coefficient of rolling friction and the position of the damper in the blade. The optimization of these parameters has been carried out on a reduced 2-DOF nonlinear model of the rotating wind turbine blade equipped with a roller damper in terms of a ball or a cylinder, ignoring the coupling with other degrees of freedom of the wind turbine. The edgewise modal loading on the blade has been calculated from a more sophisticated 13-DOF aeroelastic wind turbine model with due consideration to the indicated couplings, the turbulence and the aerodynamic damping. Various turbulence intensities and mean wind speeds have been considered to evaluate the effectiveness of the roller damper in reducing edgewise vibrations when the working conditions of the wind turbine are changed. Further, the optimized roller damper is incorporated into the 13-DOF wind turbine model to verify the application of the decoupled optimization. The results indicate that the proposed damper can effectively improve the structural response of wind turbine blades.     

In-Situ Intrinsic Interface Strength Measurement at Elevated Temperatures and its Relationship to Interfacial Structure

A previously developed laser spallation technique has been modified to measure the tensile strength of thin film interfaces in-situ at temperatures up to 1100°C. Tensile strengths of Nb/A-plane sapphire, FeCrAl/A-plane sapphire and FeCrAlY/A-plane sapphire were measured up to 950°C. The measured strengths at high temperatures were substantially lower compared with their corresponding strengths at ambient temperature. For example, at 850°C, the interface tensile strength for the Nb/sapphire (151 ± 17 MPa), FeCrAl/sapphire (62 ± 8 MPa) and FeCrAlY/sapphire (82 ± 11 MPa) interface systems were lower by factors of approximately, 3, 5, and 8, respectively, over their corresponding ambient values. These results underscore the importance of using such in-situ measured values under operating conditions as the failure criterion in any life prediction or reliability models of such coated systems where local interface temperature excursions are expected. The results on alloy film interfaces also demonstrate that the presence of Y increases the strength of FeCrAl/Al₂O₃ interfaces.     

Velocity and rotation measurements in acoustically levitated droplets

The velocity scale inside an acoustically levitated droplet depends on the levitator and liquid properties. Using Particle Imaging Velocimetry (PIV), detailed velocity measurements have been made in a levitated droplet of different diameters and viscosity. The maximum velocity and rotation are normalized using frequency and amplitude of acoustic levitator, and droplet viscosity. The non-dimensional data are fitted for micrometer- and millimeter-sized droplets levitated in different levitators for different viscosity fluids. It is also shown that the rotational speed of nanosilica droplets at an advanced stage of vaporization compares well with that predicted by exponentially fitted parameters.     

Minimal cut-generating functions are nearly extreme

We study continuous (strongly) minimal cut generating functions for the model where all variables are integer. We consider both the original Gomory–Johnson setting as well as a recent extension by Y?ld?z and Cornuéjols (Math Oper Res 41:1381–1403, 2016). We show that for any continuous minimal or strongly minimal cut generating function, there exists an extreme cut generating function that approximates the (strongly) minimal function as closely as desired. In other words, the extreme functions are “dense” in the set of continuous (strongly) minimal functions.     

Characterization of collagen fibers in Bruch’s membrane using chemical force microscopy

Bruch’s membrane is a layer composed of collagen fibers located just beneath the retina. This study validates a strategy used to map the morphological and adhesion characteristics of collagen fibers in Bruch’s membrane. Atomic force microscopy tips were functionalized with different chemical groups and used to map the hydrophilic and hydrophobic regions on the surface of the eye tissue. The largest adhesion forces were observed when tips functionalized with NH₂ groups were used. The trend in the adhesion forces was rationalized based on the distribution of different functional groups in the triple-helical structure of the collagen fibers. The results of this study can be used to design more effective strategies to treat eye diseases such as age-related macular degeneration.