Separation index of graphs and stacked 2-spheres

In 1987, Kalai proved that stacked spheres of dimension d >= 3 are characterised by the fact that they attain equality in Barnette's celebrated Lower Bound Theorem. This result does not extend to dimension d = 2. In this article, we give a characterisation of stacked 2-spheres using what we call the separation index. Namely, we show that the separation index of a triangulated 2-sphere is maximal if and only if it is stacked. In addition, we prove that, amongst all n-vertex triangulated 2-spheres, the separation index is minimised by some n-vertex flag sphere for n >= 6. Furthermore, we apply this characterisation of stacked 2-spheres to settle the outstanding 3-dimensional case of the Lutz-Sulanke-Swartz conjecture that ``tight-neighbourly triangulated manifolds are tight''. For dimension d >= 4, the conjecture has already been proved by Effenberger following a result of Novik and Swartz. (C) 2015 Elsevier Inc. All rights reserved.

Diffractive Optical Analysis for Refractive Index Sensing using Transparent Phase Gratings

We report the implementation of a micro-patterned, glass-based photonic sensing element that is capable of label-free biosensing. The diffractive optical analyzer is based on the differential response of diffracted orders to bulk as well as surface refractive index changes. The differential read-out suppresses signal drifts and enables time-resolved determination of refractive index changes in the sample cell. A remarkable feature of this device is that under appropriate conditions, the measurement sensitivity of the sensor can be enhanced by more than two orders of magnitude due to interference between multiply reflected diffracted orders. A noise-equivalent limit of detection (LoD) of 6 x 10(-7) was achieved with this technique with scope for further improvement.

A novel index for identification of weak nodes for reactive compensation to improve voltage stability

In this study, a new reactive power loss index (RPLI) is proposed for identification of weak buses in the system. This index is further used for determining the optimal locations for placement of reactive compensation devices in the power system for additional voltage support. The new index is computed from the reactive power support and loss allocation algorithm using Y-bus method for the system under intact condition and as well as critical/severe network contingencies cases. Fuzzy logic approach is used to select the important and critical/severe line contingencies from the contingency list. The inherent characteristics of the reactive power in system operation is properly addressed while determining the reactive power loss allocation to load buses. The proposed index is tested on sample 10-bus equivalent system and 72-bus practical equivalent system of Indian southern region power grid. The validation of the weak buses identification from the proposed index with that from other existing methods in the literature is carried out to demonstrate the effectiveness of the proposed index. Simulation results show that the identification of weak buses in the system from the new RPLI is completely non-iterative, thus requires minimal computational efforts as compared with other existing methods in the literature.

Use of polydispersity index as control parameter to study melting/freezing of Lennard-Jones system: Comparison among predictions of bifurcation theory with Lindemann criterion, inherent structure analysis and Hansen-Verlet rule

Using polydispersity index as an additional order parameter we investigate freezing/melting transition of Lennard-Jones polydisperse systems (with Gaussian polydispersity in size), especially to gain insight into the origin of the terminal polydispersity. The average inherent structure (IS) energy and root mean square displacement (RMSD) of the solid before melting both exhibit quite similar polydispersity dependence including a discontinuity at solid-liquid transition point. Lindemann ratio, obtained from RMSD, is found to be dependent on temperature. At a given number density, there exists a value of polydispersity index (delta (P)) above which no crystalline solid is stable. This transition value of polydispersity(termed as transition polydispersity, delta (P) ) is found to depend strongly on temperature, a feature missed in hard sphere model systems. Additionally, for a particular temperature when number density is increased, delta (P) shifts to higher values. This temperature and number density dependent value of delta (P) saturates surprisingly to a value which is found to be nearly the same for all temperatures, known as terminal polydispersity (delta (TP)). This value (delta (TP) similar to 0.11) is in excellent agreement with the experimental value of 0.12, but differs from hard sphere transition where this limiting value is only 0.048. Terminal polydispersity (delta (TP)) thus has a quasiuniversal character. Interestingly, the bifurcation diagram obtained from non-linear integral equation theories of freezing seems to provide an explanation of the existence of unique terminal polydispersity in polydisperse systems. Global bond orientational order parameter is calculated to obtain further insights into mechanism for melting.

Evaluation of the Index-Flood Approach Related Regional Frequency Analysis Procedures

Index-flood related regional frequency analysis (RFA) procedures are in use by hydrologists to estimate design quantiles of hydrological extreme events at data sparse/ungauged locations in river basins. There is a dearth of attempts to establish which among those procedures is better for RFA in the L-moment framework. This paper evaluates the performance of the conventional index flood (CIF), the logarithmic index flood (LIF), and two variants of the population index flood (PIF) procedures in estimating flood quantiles for ungauged locations by Monte Carlo simulation experiments and a case study on watersheds in Indiana in the U.S. To evaluate the PIF procedure, L-moment formulations are developed for implementing the procedure in situations where the regional frequency distribution (RFD) is the generalized logistic (GLO), generalized Pareto (GPA), generalized normal (GNO) or Pearson type III (PE3), as those formulations are unavailable. Results indicate that one of the variants of the PIF procedure, which utilizes the regional information on the first two L-moments is more effective than the CIF and LIF procedures. The improvement in quantile estimation using the variant of PIF procedure as compared with the CIF procedure is significant when the RFD is a generalized extreme value, GLO, GNO, or PE3, and marginal when it is GPA. (C) 2015 American Society of Civil Engineers.

Electromagnetic analysis of novel class of multiple core/multiple clad step index single mode optical fiber by analytical means

General propagation properties and universal curves are given for double clad single mode fibers with inner cladding index higher or lower than the outer cladding index, using the parameter: inner cladding/core radii ratio. Mode cut-off conditions are also examined for the cases. It is shown that dispersion properties largely differ from the single clad single mode fiber case, leading to large new possibilities for extension of single mode operation for large wavelength tange. Paper demonstrates that how substantially we can extend the single mode operation range by using the raised inner cladding fiber. Throughout we have applied our own computations technique to find out the eigenvalue for a given modes. Detail derivations with all trivial mathematics for eigenmode equation are derived for each case. Paper also demonstrates that there is not much use of using depressed inner cladding fiber. We have also concluded that using the large inner cladding/inner core radius we can significantly increase the single mode operation range for the large wavelength region. (C) 2015 Elsevier GmbH. All rights reserved.

Isotopic disequilibrium in Globigerina bulloides and carbon isotope response to productivity increase in Southern Ocean

Oxygen and carbon isotope ratios in planktonic foraminifera Globigerina bulloides collected from tow samples along a transect from the equatorial Indian ocean to the Southern Ocean (45 degrees E and 80 degrees E and 10 degrees N to 53 degrees S) were analysed and compared with the equilibrium delta O-18 and delta C-13 values of calcite calculated using the temperature and isotopic composition of the water column. The results agree within similar to 0.25% for the region between 10 degrees N and 40 degrees S and 75-200 m water depth which is considered to be the habitat of Globigerina bulloides. Further south (from 40 degrees S to 55 degrees S), however, the measured delta O-18 and delta C-13 values are higher than the expected values by similar to 2% and similar to 1% respectively. These enrichments can be attributed to either a `vital effect' or a higher calcification rate. An interesting pattern of increase in the delta C-13(DIC) value of the surface water with latitude is observed between 35 degrees S and similar to 60 degrees S, with a peak at similar to 42 degrees S. This can be caused by increased organic matter production and associated removal. A simple model accounting for the increase in the delta C-13(DIC) values is proposed which fits well with the observed chlorophyll abundance as a function of latitude.