Study on period search methods of variable stars: Application to ASAS and CRTS databases

Study on variable stars is an important topic of modern astrophysics. After the invention of powerful telescopes and high resolving powered CCD’s, the variable star data is accumulating in the order of peta-bytes. The huge amount of data need lot of automated methods as well as human experts. This thesis is devoted to the data analysis on variable star’s astronomical time series data and hence belong to the inter-disciplinary topic, Astrostatistics. For an observer on earth, stars that have a change in apparent brightness over time are called variable stars. The variation in brightness may be regular (periodic), quasi periodic (semi-periodic) or irregular manner (aperiodic) and are caused by various reasons. In some cases, the variation is due to some internal thermo-nuclear processes, which are generally known as intrinsic vari- ables and in some other cases, it is due to some external processes, like eclipse or rotation, which are known as extrinsic variables. Intrinsic variables can be further grouped into pulsating variables, eruptive variables and flare stars. Extrinsic variables are grouped into eclipsing binary stars and chromospheri- cal stars. Pulsating variables can again classified into Cepheid, RR Lyrae, RV Tauri, Delta Scuti, Mira etc. The eruptive or cataclysmic variables are novae, supernovae, etc., which rarely occurs and are not periodic phenomena. Most of the other variations are periodic in nature. Variable stars can be observed through many ways such as photometry, spectrophotometry and spectroscopy. The sequence of photometric observa- xiv tions on variable stars produces time series data, which contains time, magni- tude and error. The plot between variable star’s apparent magnitude and time are known as light curve. If the time series data is folded on a period, the plot between apparent magnitude and phase is known as phased light curve. The unique shape of phased light curve is a characteristic of each type of variable star. One way to identify the type of variable star and to classify them is by visually looking at the phased light curve by an expert. For last several years, automated algorithms are used to classify a group of variable stars, with the help of computers. Research on variable stars can be divided into different stages like observa- tion, data reduction, data analysis, modeling and classification. The modeling on variable stars helps to determine the short-term and long-term behaviour and to construct theoretical models (for eg:- Wilson-Devinney model for eclips- ing binaries) and to derive stellar properties like mass, radius, luminosity, tem- perature, internal and external structure, chemical composition and evolution. The classification requires the determination of the basic parameters like pe- riod, amplitude and phase and also some other derived parameters. Out of these, period is the most important parameter since the wrong periods can lead to sparse light curves and misleading information. Time series analysis is a method of applying mathematical and statistical tests to data, to quantify the variation, understand the nature of time-varying phenomena, to gain physical understanding of the system and to predict future behavior of the system. Astronomical time series usually suffer from unevenly spaced time instants, varying error conditions and possibility of big gaps. This is due to daily varying daylight and the weather conditions for ground based observations and observations from space may suffer from the impact of cosmic ray particles. Many large scale astronomical surveys such as MACHO, OGLE, EROS, xv ROTSE, PLANET, Hipparcos, MISAO, NSVS, ASAS, Pan-STARRS, Ke- pler,ESA, Gaia, LSST, CRTS provide variable star’s time series data, even though their primary intention is not variable star observation. Center for Astrostatistics, Pennsylvania State University is established to help the astro- nomical community with the aid of statistical tools for harvesting and analysing archival data. Most of these surveys releases the data to the public for further analysis. There exist many period search algorithms through astronomical time se- ries analysis, which can be classified into parametric (assume some underlying distribution for data) and non-parametric (do not assume any statistical model like Gaussian etc.,) methods. Many of the parametric methods are based on variations of discrete Fourier transforms like Generalised Lomb-Scargle peri- odogram (GLSP) by Zechmeister(2009), Significant Spectrum (SigSpec) by Reegen(2007) etc. Non-parametric methods include Phase Dispersion Minimi- sation (PDM) by Stellingwerf(1978) and Cubic spline method by Akerlof(1994) etc. Even though most of the methods can be brought under automation, any of the method stated above could not fully recover the true periods. The wrong detection of period can be due to several reasons such as power leakage to other frequencies which is due to finite total interval, finite sampling interval and finite amount of data. Another problem is aliasing, which is due to the influence of regular sampling. Also spurious periods appear due to long gaps and power flow to harmonic frequencies is an inherent problem of Fourier methods. Hence obtaining the exact period of variable star from it’s time series data is still a difficult problem, in case of huge databases, when subjected to automation. As Matthew Templeton, AAVSO, states “Variable star data analysis is not always straightforward; large-scale, automated analysis design is non-trivial”. Derekas et al. 2007, Deb et.al. 2010 states “The processing of xvi huge amount of data in these databases is quite challenging, even when looking at seemingly small issues such as period determination and classification”. It will be beneficial for the variable star astronomical community, if basic parameters, such as period, amplitude and phase are obtained more accurately, when huge time series databases are subjected to automation. In the present thesis work, the theories of four popular period search methods are studied, the strength and weakness of these methods are evaluated by applying it on two survey databases and finally a modified form of cubic spline method is intro- duced to confirm the exact period of variable star. For the classification of new variable stars discovered and entering them in the “General Catalogue of Vari- able Stars” or other databases like “Variable Star Index“, the characteristics of the variability has to be quantified in term of variable star parameters.

Spectral dependence of third order nonlinear optical susceptibility of zinc phthalocyanine

Wavelength dependence of saturable absorption (SA) and reverse saturable absorption (RSA) of zinc phthalocyanine was studied using 10 Hz, 8 ns pulses from a tunable laser, in the wavelength range of 520–686 nm, which includes the rising edge of the Q band in the electronic absorption spectrum. The nonlinear response is wavelength dependent and switching from RSA to SA has been observed as the excitation wavelength changes from the low absorption window region to higher absorption regime near the Q band. The SA again changes back to RSA when we further move over to the infrared region. Values of the imaginary part of third order susceptibility are calculated for various wavelengths in this range. This study is important in identifying the spectral range over which the nonlinear material acts as RSA based optical limiter.

Spectral dependence of third order nonlinear optical susceptibility of zinc phthalocyanine

Wavelength dependence of saturable absorption (SA) and reverse saturable absorption (RSA) of zinc phthalocyanine was studied using 10 Hz, 8 ns pulses from a tunable laser, in the wavelength range of 520–686 nm, which includes the rising edge of the Q band in the electronic absorption spectrum. The nonlinear response is wavelength dependent and switching from RSA to SA has been observed as the excitation wavelength changes from the low absorption window region to higher absorption regime near the Q band. The SA again changes back to RSA when we further move over to the infrared region. Values of the imaginary part of third order susceptibility are calculated for various wavelengths in this range. This study is important in identifying the spectral range over which the nonlinear material acts as RSA based optical limiter.

Short-Term Load Forecast Of A Low Loadfactor Power System For Optimization Of Merit Order Dispatch Using Adaptive Learning Algorithm

Short term load forecasting is one of the key inputs to optimize the management of power system. Almost 60-65% of revenue expenditure of a distribution company is against power purchase. Cost of power depends on source of power. Hence any optimization strategy involves optimization in scheduling power from various sources. As the scheduling involves many technical and commercial considerations and constraints, the efficiency in scheduling depends on the accuracy of load forecast. Load forecasting is a topic much visited in research world and a number of papers using different techniques are already presented. The accuracy of forecast for the purpose of merit order dispatch decisions depends on the extent of the permissible variation in generation limits. For a system with low load factor, the peak and the off peak trough are prominent and the forecast should be able to identify these points to more accuracy rather than minimizing the error in the energy content. In this paper an attempt is made to apply Artificial Neural Network (ANN) with supervised learning based approach to make short term load forecasting for a power system with comparatively low load factor. Such power systems are usual in tropical areas with concentrated rainy season for a considerable period of the year

Concomitants of Order Statistics from Morgenstern Family

The study deals with the distribution theory and applications of concomitants from the Morgenstern family of bivariate distributions.The Morgenstern system of distributions include all cumulative distributions of the form FX,Y(X,Y)=FX(X) FY(Y)[1+α(1-FX(X))(1-FY(Y))], -1≤α≤1.The system provides a very general expression of a bivariate distributions from which members can be derived by substituting expressions of any desired set of marginal distributions.It is a brief description of the basic distribution theory and a quick review of the existing literature.The Morgenstern family considered in the present study provides a very general expression of a bivariate distribution from which several members can be derived by substituting expressions of any desired set of marginal distributions.Order statistics play a very important role in statistical theory and practice and accordingly a remarkably large body of literature has been devoted to its study.It helps to develop special methods of statistical inference,which are valid with respect to a broad class of distributions.The present study deals with the general distribution theory of Mk, [r: m] and Mk, [r: m] from the Morgenstern family of distributions and discuss some applications in inference, estimation of the parameter of the marginal variable Y in the Morgestern type uniform distributions.

Characterization of Probability Distributions Using the Residual Entropy Function

The present study on the characterization of probability distributions using the residual entropy function. The concept of entropy is extensively used in literature as a quantitative measure of uncertainty associated with a random phenomenon. The commonly used life time models in reliability Theory are exponential distribution, Pareto distribution, Beta distribution, Weibull distribution and gamma distribution. Several characterization theorems are obtained for the above models using reliability concepts such as failure rate, mean residual life function, vitality function, variance residual life function etc. Most of the works on characterization of distributions in the reliability context centers around the failure rate or the residual life function. The important aspect of interest in the study of entropy is that of locating distributions for which the shannon’s entropy is maximum subject to certain restrictions on the underlying random variable. The geometric vitality function and examine its properties. It is established that the geometric vitality function determines the distribution uniquely. The problem of averaging the residual entropy function is examined, and also the truncated form version of entropies of higher order are defined. In this study it is established that the residual entropy function determines the distribution uniquely and that the constancy of the same is characteristics to the geometric distribution

Properties of Equilibrium Distributions of Order n

The present work is intended to discuss various properties and reliability aspects of higher order equilibrium distributions in continuous, discrete and multivariate cases, which contribute to the study on equilibrium distributions. At first, we have to study and consolidate the existing literature on equilibrium distributions. For this we need some basic concepts in reliability. These are being discussed in the 2nd chapter, In Chapter 3, some identities connecting the failure rate functions and moments of residual life of the univariate, non-negative continuous equilibrium distributions of higher order and that of the baseline distribution are derived. These identities are then used to characterize the generalized Pareto model, mixture of exponentials and gamma distribution. An approach using the characteristic functions is also discussed with illustrations. Moreover, characterizations of ageing classes using stochastic orders has been discussed. Part of the results of this chapter has been reported in Nair and Preeth (2009). Various properties of equilibrium distributions of non-negative discrete univariate random variables are discussed in Chapter 4. Then some characterizations of the geo- metric, Waring and negative hyper-geometric distributions are presented. Moreover, the ageing properties of the original distribution and nth order equilibrium distribu- tions are compared. Part of the results of this chapter have been reported in Nair, Sankaran and Preeth (2012). Chapter 5 is a continuation of Chapter 4. Here, several conditions, in terms of stochastic orders connecting the baseline and its equilibrium distributions are derived. These conditions can be used to rede_ne certain ageing notions. Then equilibrium distributions of two random variables are compared in terms of various stochastic orders that have implications in reliability applications. In Chapter 6, we make two approaches to de_ne multivariate equilibrium distribu- tions of order n. Then various properties including characterizations of higher order equilibrium distributions are presented. Part of the results of this chapter have been reported in Nair and Preeth (2008). The Thesis is concluded in Chapter 7. A discussion on further studies on equilib- rium distributions is also made in this chapter.

Modelling and Analysis of Some Time Series

The thesis deals with some of the non-linear Gaussian and non-Gaussian time models and mainly concentrated in studying the properties and application of a first order autoregressive process with Cauchy marginal distribution. In this thesis some of the non-linear Gaussian and non-Gaussian time series models and mainly concentrated in studying the properties and application of a order autoregressive process with Cauchy marginal distribution. Time series relating to prices, consumptions, money in circulation, bank deposits and bank clearing, sales and profit in a departmental store, national income and foreign exchange reserves, prices and dividend of shares in a stock exchange etc. are examples of economic and business time series. The thesis discuses the application of a threshold autoregressive(TAR) model, try to fit this model to a time series data. Another important non-linear model is the ARCH model, and the third model is the TARCH model. The main objective here is to identify an appropriate model to a given set of data. The data considered are the daily coconut oil prices for a period of three years. Since it is a price data the consecutive prices may not be independent and hence a time series based model is more appropriate. In this study the properties like ergodicity, mixing property and time reversibility and also various estimation procedures used to estimate the unknown parameters of the process.

Spray Pyrolysed Zinc Oxide Thin Films : Effects of Doping and Ion Beam Irradiation

In recent years scientists have made rapid and significant advances in the field of semiconductor physics. One of the most important fields of current interest in materials science is the fundamental aspects and applications of conducting transparent oxide thin films (TCO). The characteristic properties of such coatings are low electrical resistivity and high transparency in the visible region. The first semitransparent and electrically conducting CdO film was reported as early as in 1907 [1]. Though early work on these films was performed out of purely scientific interest, substantial technological advances in such films were made after 1940. The technological interest in the study of transparent semiconducting films was generated mainly due to the potential applications of these materials both in industry and research. Such films demonstrated their utility as transparent electrical heaters for windscreens in the aircraft industry. However, during the last decade, these conducting transparent films have been widely used in a variety of other applications such as gas sensors [2], solar cells [3], heat reflectors [4], light emitting devices [5] and laser damage resistant coatings in high power laser technology [6]. Just a few materials dominate the current TCO industry and the two dominant markets for TCO’s are in architectural applications and flat panel displays. The architectural use of TCO is for energy efficient windows. Fluorine doped tin oxide (FTO), deposited using a pyrolysis process is the TCO usually finds maximum application. SnO2 also finds application ad coatings for windows, which are efficient in preventing radiative heat loss, due to low emissivity (0.16). Pyrolitic tin oxide is used in PV modules, touch screens and plasma displays. However indium tin oxide (ITO) is mostly used in the majority of flat panel display (FPD) applications. In FPDs, the basic function of ITO is as transparent electrodes. The volume of FPD’s produced, and hence the volume of ITO coatings produced, continues to grow rapidly. But the current increase in the cost of indium and the scarcity of this material created the difficulty in obtaining low cost TCOs. Hence search for alternative TCO materials has been a topic of active research for the last few decades. This resulted in the development of binary materials like ZnO, SnO2, CdO and ternary materials like II Zn2SnO4, CdSb2O6:Y, ZnSO3, GaInO3 etc. The use of multicomponent oxide materials makes it possible to have TCO films suitable for specialized applications because by altering their chemical compositions, one can control the electrical, optical, chemical and physical properties. But the advantages of using binary materials are the easiness to control the chemical compositions and depositions conditions. Recently, there were reports claiming the deposition of CdO:In films with a resistivity of the order of 10-5 ohm cm for flat panel displays and solar cells. However they find limited use because of Cd-Toxicity. In this regard, ZnO films developed in 1980s, are very useful as these use Zn, an abundant, inexpensive and nontoxic material. Resistivity of this material is still not very low, but can be reduced through doping with group-III elements like In, Al or Ga or with F [6]. Hence there is a great interest in ZnO as an alternative of ITO. In the present study, we prepared and characterized transparent and conducting ZnO thin films, using a cost effective technique viz Chemical Spray Pyrolysis (CSP). This technique is also suitable for large area film deposition. It involves spraying a solution, (usually aqueous) containing soluble salts of the constituents of the desired compound, onto a heated substrate.

A Variational Calculation of TE and TM Cutoff Wavenumbers in Circular Eccentric Guides by Conformal Mapping

The cutoff wavenumbers of higher order modes in circular eccentric guides are computed with the variational analysis combined with a conformal mapping. A conformal mapping is applied to the variational formulation, and the variational equation is solved by the finite-element method. Numerical results for TE and TM cutoff wavenumbers are presented for different distances between the centers and ratio of the radii. Comparisons with numerical results found in the literature validate the presented method

A fibre optic evanescent wave sensor used for the detection of trace nitrites in water

A fibre optic technique for detecting trace amounts of nitrite compounds in water is described. The off-line fibre optic sensor outlined here is based on evanescent field absorption in a test solution formed by the reaction of nitrite compounds in water with suitable chemical reagents. A short unclad portion of a plastic clad silica fibre acts as the sensing region. The experimental results clearly establish the usefulness of the present technique for detecting very low concentrations of the order of 1 ppb (parts per billion) of nitrite compounds with a large dynamic range of 1–1000 ppb. Such a high sensitivity enables the present device to be used for measuring the nitrite content in drinking water.

Fibre optic sensor for the detection of adulterant traces in coconut oil

The design and development of a fibre optic evanescent wave refractometer for the detection of trace amounts of paraffin oil and palm oil in coconut oil is presented. This sensor is based on a side-polished plastic optical fibre. At the sensing region, the cladding and a small portion of the core are removed and the fibre nicely polished. The sensing region is fabricated in such a manner that it sits perfectly within a bent mould. This bending of the sensing region enhances its sensitivity. The oil mixture of different mix ratios is introduced into the sensing region and we observed a sharp decrease in the output intensity. The observed variation in the intensity is found to be linear and the detection limit is 2% (by volume) paraffin oil/palm oil in coconut oil. The resolution of this refractometric sensor is of the order of 10−3. Since coconut oil is consumed in large volumes as edible oil in south India, this fibre optic sensor finds great relevance for the detection of adulterants such as paraffin oil or palm oil which are readily miscible in coconut oil. The advantage of this type of sensor is that it is inexpensive and easy to set up. Another attraction of the side-polished fibre is that only a very small amount of analyte is needed and its response time is only 7 s.

Nonlinear optical characteristics of self-assembled films of ZnO

In the present work, we have investigated the nonlinear optical properties of self-assembled films formed from ZnO colloidal spheres by z-scan technique. The sign of the nonlinear component of refractive index of the material remains the same; however, a switching from reverse saturable absorption to saturable absorption has been observed as the material changes from colloid to self-assembled film. These different nonlinear characteristics can be mainly attributed to ZnO defect states and electronic effects when the colloidal solution is transformed into self-assembled monolayers. We investigated the intensity, wavelength and size dependence of saturable and reverse saturable absorption of ZnO self-assembled films and colloids. Values of the imaginary part of third-order susceptibility are calculated for particles of size in the range 20–300 nm at different intensity levels ranging from 40 to 325MW/cm2 within the wavelength range of 450–650 nm.

Investigations on Eco-friendly Natural Insecticides

Instead of developing easily degradable, and low-priced insecticides, we are going after highly sophisticated chemicals. Here, an attempt is being made to develop safer formulations of insecticides of botanical origin. Different parts of the plants were chosen based on their use in countryside and villages The dried plant materials were extracted with petroleum ether, and were applied on Tribolium castaneum. The results were statistically analysed. The active principles from Croton tigilium and Leea sambucina, the most potential plants, were isolated using Column Chromatography, TLC, and Hydrolysis. The isolated principles were analysed spectroscopically ( UV-Vis., IR, NMR, and MS ) to identify their chemical nature. The active principles from Leea and Croton were identified as a cholisterate derivative and a phorbol derivative respectively. In order to ascertain the environmental combatibility of the principles, degradation by soil bacteria was studied. The isolated principles were made into three type of formulations using stabilizers .The formulations were applied on Snake gourd semilooper, Pulse beetle, and mosquito larvae. Also the biocidal activity of the formulations was studied. Both Leea derivative and Croton derivative could be formulated effectively and were effective against a variety of pests. They are eco-friendly, as there is no artificial chemicals involved.

Studies on some Metal Complexes of Dithio Ligands

The thesis deals with our studies on the synthesis and elucidation of structure of some metal complexes of dithio ligands, such as the dithiocarbamates, xanthates and 2-aminocyclopent-1-ene-1-dithiocarboxylate and its N-alkyl derivatives.2-Aminocyclopent-1-ene-1-dithiocarboxylate (ACDA) is an interesting ligand, because of its potential dual capability of bonding between the metal and the ligand. Since the earlier reports on the complexes of ACDA contain contradictory ideas on the nature of its bonding, it was thought worthwhile to undertake a detailed and systematic study of these type of complexes. As the ACDA complexes have very low solubilities in solvents like chloroform, we have used the isopropyl derivative of ACDA as the ligand. The increased solubility of these complexes have made it possible to investigate their NMR and solution electronic spectra.The complexes of this ligand have not yet been reported in the literature.We have synthesised some new mixed ligand complexes of dithiocarbamates by reacting bis(dithiocarbamato)-µ-dichloro dicopper complexes (obtained by the reaction of mixed benzoic dithiocarbamic anhydride and copper(II) chloride) with ACDA or its N-alkyl derivatives.Interactions of metal halides with the mixed anhydrides formed from benzoylchloride and xanthates have also been investigated. Novel complexes of the type, [Cu2(RXant)CI] (R=i-Bu, i-Pr, n-Bu or n-Pr)) have been isolated from the reaction of copper(II) chloride and the mixed anhydride, and these reactions appear to be like the clock reactions reported in the literature.It also deal with the characterisation of the complexes of the type [Hg(R2d t c )X] (X=Cl, Br or 1),[Cu3(R2dtc)6][Cu2Br6] and [Cu(R2dtc)Cl2](R2=Me2,Et2,Pip,Morph or Pyrr)respectively, synthesised by simple and novel routes, different from those reported earlier.