Structure of Lanczos-Lovelock Lagrangians in Critical Dimensions

The Lanczos-Lovelock models of gravity constitute the most general theories of gravity in D dimensions which satisfy (a) the principle of of equivalence, (b) the principle of general co-variance, and (c) have field equations involving derivatives of the metric tensor only up to second order. The mth order Lanczos-Lovelock Lagrangian is a polynomial of degree m in the curvature tensor. The field equations resulting from it become trivial in the critical dimension $D = 2m$ and the action itself can be written as the integral of an exterior derivative of an expression involving the vierbeins, in the differential form language. While these results are well known, there is some controversy in the literature as to whether the Lanczos-Lovelock Lagrangian itself can be expressed as a total divergence of quantities built only from the metric and its derivatives (without using the vierbeins) in $D = 2m$. We settle this issue by showing that this is indeed possible and provide an algorithm for its construction. In particular, we demonstrate that, in two dimensions, $R \sqrt{-g} = \partial_j R^j$ for a doublet of functions $R^j = (R^0,R^1)$ which depends only on the metric and its first derivatives. We explicitly construct families of such R^j -s in two dimensions. We also address related questions regarding the Gauss-Bonnet Lagrangian in $D = 4$. Finally, we demonstrate the relation between the Chern-Simons form and the mth order Lanczos-Lovelock Lagrangian.Comment: 15 pages, no figure

Membrane Paradigm and Horizon Thermodynamics in Lanczos-Lovelock gravity

We study the membrane paradigm for horizons in Lanczos-Lovelock models of gravity in arbitrary D dimensions and find compact expressions for the pressure p and viscosity coefficients \eta and \zeta of the membrane fluid. We show that the membrane pressure is intimately connected with the Noether charge entropy S_Wald of the horizon when we consider a specific m-th order Lanczos-Lovelock model, through the relation pA/T=(D-2m)/(D-2)S_Wald, where T is the temperature and A is the area of the horizon. Similarly, the viscosity coefficients are expressible in terms of entropy and quasi-local energy associated with the horizons. The bulk and shear viscosity coefficients are found to obey the relation \zeta=-2(D-3)/(D-2)\eta.Comment: v1: 13 pages, no figure. (v2): refs added, typos corrected, new subsection added on the ratio \eta/s. (v3): some clarification added, typos corrected, to appear in JHE

Phase transition and scaling behavior of topological charged black holes in Horava-Lifshitz gravity

Gravity can be thought as an emergent phenomenon and it has a nice "thermodynamic" structure. In this context, it is then possible to study the thermodynamics without knowing the details of the underlying microscopic degrees of freedom. Here, based on the ordinary thermodynamics, we investigate the phase transition of the static, spherically symmetric charged black hole solution with arbitrary scalar curvature $2k$ in Ho\v{r}ava-Lifshitz gravity at the Lifshitz point $z=3$. The analysis is done using the canonical ensemble frame work; i.e. the charge is kept fixed. We find (a) for both $k=0$ and $k=1$, there is no phase transition, (b) while $k=-1$ case exhibits the second order phase transition within the {\it physical region} of the black hole. The critical point of second order phase transition is obtained by the divergence of the heat capacity at constant charge. Near the critical point, we find the various critical exponents. It is also observed that they satisfy the usual thermodynamic scaling laws.Comment: Minor corrections, refs. added, to appear in Class. Quant. Grav. arXiv admin note: text overlap with arXiv:1111.0973 by other author

Gravitational memory for uniformly accelerated observers

Recently, Hawking, Perry and Strominger described a physical process that implants supertranslational hair on a Schwarzschild black hole by an infalling matter shock wave without spherical symmetry. Using the Bondi-Metzner-Sachs-type symmetries of the Rindler horizon, we present an analogous process that implants supertranslational hair on a Rindler horizon by a matter shock wave without planar symmetry, and we investigate the corresponding memory effect on the Rindler family of uniformly linearly accelerated observers. We assume each observer to remain linearly uniformly accelerated through the wave, in the sense of the curved spacetime generalization of the Letaw-Frenet equations. Starting with a family of observers who follow the orbits of a single boost Killing vector before the wave, we find that after the wave has passed, each observer still follows the orbit of a boost Killing vector but this boost differs from trajectory to trajectory, and the trajectory dependence carries a memory of the planar inhomogeneity of the wave. We anticipate this classical memory phenomenon to have a counterpart in Rindler space quantum field theory

A Comprehensive Evaluation of Nature Inspired Routing Algorithm for Mobile Ad Hoc Network : DEA and BCA

This paper discussed about the comprehensive evaluation of nature inspired routing algorithms such as Dolphin Echolocation Algorithm (DEA) and Bee colony Algorithm (BCA) use for distance optimization. The influence of DEA and BCA algorithms on Quality of Service (QoS) performance matrices for Mobile Ad hoc Network (MANET) is analyzed. Ultimately with the help of DEA it is possible to achieve optimized routing path between source and destination nodes. Further this paper have the analysis of various results which gives the comprehensive evaluation of DEA algorithm and it is suitable for MANET for achieving good Throughput, packet delivery ratio, delay and overhand

Treatment of synthetic textile wastewater containing dye mixtures with microcosms

The aim was to assess the ability of microcosms (laboratory-scale shallow ponds) as a post polishing stage for the remediation of artificial textile wastewater comprising two commercial dyes (basic red 46 (BR46) and reactive blue 198 (RB198)) as a mixture. The objectives were to evaluate the impact of Lemna minor L. (common duckweed) on the water quality outflows; the elimination of dye mixtures, organic matter, and nutrients; and the impact of synthetic textile wastewater comprising dye mixtures on the L. minor plant growth. Three mixtures were prepared providing a total dye concentration of 10 mg/l. Findings showed that the planted simulated ponds possess a significant (p < 0.05) potential for improving the outflow characteristics and eliminate dyes, ammonium-nitrogen (NH4-N), and nitrate-nitrogen (NO3-N) in all mixtures compared with the corresponding unplanted ponds. The removal of mixed dyes in planted ponds was mainly due to phyto-transformation and adsorption of BR46 with complete aromatic amine mineralisation. For ponds containing 2 mg/l of RB198 and 8 mg/l of BR46, removals were around 53%, which was significantly higher than those for other mixtures: 5 mg/l of RB198 and 5 mg/l of BR46 and 8 mg/l of RB198 and 2 mg/l of BR46 achieved only 41 and 26% removals, respectively. Dye mixtures stopped the growth of L. minor, and the presence of artificial wastewater reduced their development

Comparative study of Performance of RCC Multi-Storey Building for Koyna and Bhuj Earthquakes

The recent history of earthquakes have indicated that if the structures are not properly designed and constructed with required quality may cause great damage to structures. This fact has resulted in to ensure safety against earthquake forces of tall structures hence, there is need to determine seismic responses of such building for designing earthquake resistant structures by carrying seismic analysis of structure. In the present work dynamic analysis of G+12 RC multi-storied framed building considering for Koyna and Bhuj earthquake is carried out by response spectrum analysis and time history analysis and responses of such building are comparatively studied with the help of SAP2000 software. Two time histories (i.e. koyna and Bhuj) have been used to develop different acceptable criteria (base shear, storey displacement, storey drift). From the results it is recommended that time history analysis should be performed as it predicts the structural response more accurately than the response spectrum analysis. Pushover Analysis is also performed for the same building and from results it is found that building is seismically safe

Study on Morbidity and Mortality Rates in Buffaloes in Pune Division of Maharashtra State in India

The present study was carried out to analyse morbidity and mortality rate in buffaloes and its associated factors in Pune division of Maharashtra state in India. Stratified two stages random sampling design was adopted & the data of total 564 buffaloes were collected through pre-tested modified schedule from 157 buffalo owners. The data were analysed statistically by SAS 9.3 software for evaluation of Chi-square and Logistic regression analysis. Overall morbidity (28.01%) and mortality (7.98%) rates were recorded in study area. Digestive diseases and respiratory diseases are major cause of the higher morbidity and mortality in buffaloes, respectively. Statistically, there wasn't significant association of overall disease incidence with age or sex. However, the Chi-square analysis of overall mortality rate showed significance (p<0.01) difference among age and sex. Logistic regression analysis also suggested the same results. Mortality rates were recorded higher in calves and male buffaloes as compared to their respective counterparts. It is suggested that digestive and respiratory problems may be reduced by improving feeding and management practices. This study provides the important tool for determining the health status of buffaloes and has special importance in planning of prevention and control strategies designed to reduce the incidences of diseases in livestock and therefore economic status of farmers

SATELLITE BASED DROUGHT ASSESSMENT OVER LATUR, INDIA USING SOIL MOISTURE DERIVED FROM SMOS

Climatological variables such as rainfall, temperature have been extensively used by researchers for drought monitoring at a larger spatial region. These variables have a direct influence on the soil moisture which in turn extends the application of soil moisture in drought assessment. With the advancement of technology, various satellites provide soil moisture data at different spatio-temporal resolutions. In this article, soil moisture obtained from Soil Moisture Ocean Salinity (SMOS) is used to analyze the drought condition over Latur district in Maharashtra, India. The monthly soil moisture derived by averaging the daily data for the years 2010 to 2015 is compared with two drought indices, i.e. Standardized Precipitation Index (SPI) calculated for years 2010 to 2015 and Standardized Precipitation-Evapotranspiration Index (SPEI) calculated for years 2010 to 2013. Even though the overall correlation among the indices with the soil moisture is not significant, the seasonal (summer) correlation is significant. From the results, it is identified that SMOS derived soil moisture can be used as a potential parameter in drought assessment

Synthesis and Pharmacological Evaluation of Pyrazoline and Pyrimidine Analogs of Combretastatin-A4 as Anticancer, Anti-inflammatory and Antioxidant Agents

A library of 3,5-diaryl-1-carbothioamide-pyrazoline (5a–j), N1-phenyl sulfonyl pyrazoline (6a–e) and pyrimidine (7a) analogs of combretastatin-A4 were synthesized and evaluated for their in vitro anticancer, anti-inflammatory and antioxidant activity. Results of in vitro assay against human breast cancer cell line (MCF-7) showed several compounds endowed with significant cytotoxicity compared to the adriamycin, a standard anticancer drug. Among the compounds synthesized, 7a was found to possess significant antiproliferative activity (GI50 < 0.1 µM) against the MCF-7 cell line as good as adriamycin (GI50 < 0.1 µM) whereas, compounds 6c, 5j and 5g also displayed good cytotoxicity (GI50 = 25.3–42.6 µM). Besides this, most active compound 7a was also evaluated against human myeloid leukemia cell line K562 and the remarkable result was obtained with GI50 < 0.1 µM, comparable to that of adriamycin (GI50 < 0.1 µM). In addition, all the synthesized compounds were evaluated for their anti-inflammatory and antioxidant activity. The percent inhibition studies revealed that most of the compounds were found to possess substantial anti-inflammatory and antioxidant activities. This work is licensed under a Creative Commons Attribution 4.0 International License