Stochastic processes and their applications time dependent solutions for some queueing and inventory models

The objective of this thesis is to study the time dependent behaviour of some complex queueing and inventory models. It contains a detailed analysis of the basic stochastic processes underlying these models. In the theory of queues, analysis of time dependent behaviour is an area.very little developed compared to steady state theory. Tine dependence seems certainly worth studying from an application point of view but unfortunately, the analytic difficulties are considerable. Glosod form solutions are complicated even for such simple models as M/M /1. Outside M/>M/1, time dependent solutions have been found only in special cases and involve most often double transforms which provide very little insight into the behaviour of the queueing systems themselves. In inventory theory also There is not much results available giving the time dependent solution of the system size probabilities. Our emphasis is on explicit results free from all types of transforms and the method used may be of special interest to a wide variety of problems having regenerative structure.

Time Resolved Analysis of C2 Emission from Laser Induced Graphite Plasma in Helium Atmosphere

We report time resolved study of C2 emission from laser produced carbon plasma in presence of ambient helium gas. The 1.06µm: radiation from a Nd:YAG laser was focused onto a graphite target where it·produced a transient plasma. We observed double peak structure in the time profile of C2 species. The twin peaks were observed only after a threshold laser fluence. It is proposed that the faster velocity component in the temporal profiles originates mainly due to recombination processes. The laser fluence and ambient gas dependence of the double peak intensity distribution is also reported.

Spatial and time resolved analysis of CN bands in the laser induced plasma from graphite

Analysis of the emission bands of the CN molecules in the plasma generated from a graphite target irradiated with 1-06/~m radiation pulses from a Q-switched Nd:YAG laser has been done. Depending on the position of the sampled volume of the plasma plume, the intensity distribution in the emission spectra is found to change drastically. The vibrational temperature and population distribution in the different vibrational levels have been studied as function of distance from the target for different time delays with respect to the incidence of the laser pulse. The translational temperature calculated from time of flight is found to be higher than the observed vibrational temperature for CN molecules and the reason for this is explained.

Significance of Time Scales in Nonlinear Dynamical Analysis of Electroencephalogram Signals

We propose to show in this paper, that the time series obtained from biological systems such as human brain are invariably nonstationary because of different time scales involved in the dynamical process. This makes the invariant parameters time dependent. We made a global analysis of the EEG data obtained from the eight locations on the skull space and studied simultaneously the dynamical characteristics from various parts of the brain. We have proved that the dynamical parameters are sensitive to the time scales and hence in the study of brain one must identify all relevant time scales involved in the process to get an insight in the working of brain.

Modeling and Analysis of Some Heavy Tailed Time Series

The thesis has covered various aspects of modeling and analysis of finite mean time series with symmetric stable distributed innovations. Time series analysis based on Box and Jenkins methods are the most popular approaches where the models are linear and errors are Gaussian. We highlighted the limitations of classical time series analysis tools and explored some generalized tools and organized the approach parallel to the classical set up. In the present thesis we mainly studied the estimation and prediction of signal plus noise model. Here we assumed the signal and noise follow some models with symmetric stable innovations.We start the thesis with some motivating examples and application areas of alpha stable time series models. Classical time series analysis and corresponding theories based on finite variance models are extensively discussed in second chapter. We also surveyed the existing theories and methods correspond to infinite variance models in the same chapter. We present a linear filtering method for computing the filter weights assigned to the observation for estimating unobserved signal under general noisy environment in third chapter. Here we consider both the signal and the noise as stationary processes with infinite variance innovations. We derived semi infinite, double infinite and asymmetric signal extraction filters based on minimum dispersion criteria. Finite length filters based on Kalman-Levy filters are developed and identified the pattern of the filter weights. Simulation studies show that the proposed methods are competent enough in signal extraction for processes with infinite variance.Parameter estimation of autoregressive signals observed in a symmetric stable noise environment is discussed in fourth chapter. Here we used higher order Yule-Walker type estimation using auto-covariation function and exemplify the methods by simulation and application to Sea surface temperature data. We increased the number of Yule-Walker equations and proposed a ordinary least square estimate to the autoregressive parameters. Singularity problem of the auto-covariation matrix is addressed and derived a modified version of the Generalized Yule-Walker method using singular value decomposition.In fifth chapter of the thesis we introduced partial covariation function as a tool for stable time series analysis where covariance or partial covariance is ill defined. Asymptotic results of the partial auto-covariation is studied and its application in model identification of stable auto-regressive models are discussed. We generalize the Durbin-Levinson algorithm to include infinite variance models in terms of partial auto-covariation function and introduce a new information criteria for consistent order estimation of stable autoregressive model.In chapter six we explore the application of the techniques discussed in the previous chapter in signal processing. Frequency estimation of sinusoidal signal observed in symmetric stable noisy environment is discussed in this context. Here we introduced a parametric spectrum analysis and frequency estimate using power transfer function. Estimate of the power transfer function is obtained using the modified generalized Yule-Walker approach. Another important problem in statistical signal processing is to identify the number of sinusoidal components in an observed signal. We used a modified version of the proposed information criteria for this purpose.

Analysis of Stochastic Volatility Sequences Generated by Product Autoregressive Models

The classical methods of analysing time series by Box-Jenkins approach assume that the observed series uctuates around changing levels with constant variance. That is, the time series is assumed to be of homoscedastic nature. However, the nancial time series exhibits the presence of heteroscedasticity in the sense that, it possesses non-constant conditional variance given the past observations. So, the analysis of nancial time series, requires the modelling of such variances, which may depend on some time dependent factors or its own past values. This lead to introduction of several classes of models to study the behaviour of nancial time series. See Taylor (1986), Tsay (2005), Rachev et al. (2007). The class of models, used to describe the evolution of conditional variances is referred to as stochastic volatility modelsThe stochastic models available to analyse the conditional variances, are based on either normal or log-normal distributions. One of the objectives of the present study is to explore the possibility of employing some non-Gaussian distributions to model the volatility sequences and then study the behaviour of the resulting return series. This lead us to work on the related problem of statistical inference, which is the main contribution of the thesis

Activation of Progesterone Receptor by ATP

Progesterone-receptor complex from freshly prepared hen oviduct cytosol acquired the ability to bind to isolated nuclei, DNA-cellulose and ATP-Sepharose when incubated with 5-10 mM ATP at 4°C. The extent of this ATP-dependent activation was higher when compared with heat-activation achieved by warming the progesterone- receptor complex at 23 °C. The transformation of progesterone-receptor complex which occurred in a time-dependent manner was only partially dependent on hormone presence. The ATP effect was selective in causing this transformation whereas ADP, AMP and cAMP failed to show any such effect. The non-hydrolizable analogs of ATP, adenosine 5'-[a,/3-methylene]triphosphate and adenosine 5-[/l,y-imido]triphosphate were also found to be ineffective. Presence of 10 mM sodium molybdate blocked both the ATP and the heat-activation of progesterone-receptor complex. Mn" or Mg` had no detectable effect on the receptor activation but the presence of Ca" increased the extent of ATP-activation slightly. EDTA presence (> 5 mM) decreased the extent of receptor activation by about 40 % and was, therefore, not included in the buffers used for activation studies. Divalent cations were also ineffective when tested in the presence of 1- 5 mM EDTA. The properties of progesterone-receptor complex remained intact under the above conditions when analyzed for steroid-binding specificity and Scatchard analysis. However, the ATP-activated progesterone-receptor complex lost the ability to aggregate when tested on low-salt sucrose gradients. ATP was equally effective in activating the rat-uterine estradiol-receptor complex at 4 "C and influenced the transformation of 4-S receptor form into a 5-S form when analyzed on sucrose gradients containing 0.3 M KCI. The presence of ATP also increased the rate of activation of progesterone-receptor complex at 23 °C. These findings suggest a role for ATP in receptor function and offer a convenient method of studying the process of receptor activation at low temperature and mild assay conditions.

GABAA and GABAB Receptor Gene Expression and Functional Regulation During Pancreatic Regeneration and Insulin Secretion in Rats

The present study demonstrate the functional alterations of the GABAA and GABAB receptors and the gene expression during the regeneration of pancreas following partial pancreatectomy. The role of these receptors in insulin secretion and pancreatic DNA synthesis using the specific agonists and antagonists also are studied in vitro. The alterations of GABAA and GABAR receptor function and gene expression in the brain stem, crebellum and hypothalamus play an important role in the sympathetic regulation of insulin secretion during pancreatic regeneration. Previous studies have given much information linking functional interaction between GABA and the peripheral nervous system. The involvement of specific receptor subtypes functional regulation during pancreatic regeneration has not given emphasis and research in this area seems to be scarce. We have observed a decreased GABA content, down regulation of GABAA receptors and an up regulation of GABAB receptors in the cerebral cortex, brain stem and hypothalamus. Real Time-PCR analysis confirmed the receptor data in the brain regions. These alterations in the GABAA and GABAB receptors of the brain are suggested to govern the regenerative response and growth regulation of the pancreas through sympathetic innervation. In addition, receptor binding studies and Real Time-PCR analysis revealed that during pancreatic regeneration GABAA receptors were down regulated and GABAB receptors were up regulated in pancreatic islets. This suggests an inhibitory role for GABAA receptors in islet cell proliferation i.e., the down regulation of this receptor facilitates proliferation. Insulin secretion study during 1 hour showed GABA has inhibited the insulin secretion in a dose dependent manner in normal and hyperglycaemic conditions. Bicuculline did not antagonize this effect. GABAA agonist, muscimol inhibited glucose stimulated insulin secretion from pancreatic islets except in the lowest concentration of 1O-9M in presence of 4mM glucose.Musclmol enhanced insulin secretion at 10-7 and 10-4M muscimol in presence of 20mM glucose- 4mM glucose represents normal and 20mM represent hyperglycaemic conditions. GABAB agonist, baclofen also inhibited glucose induced insulin secretion and enhanced at the concentration of 1O-5M at 4mM glucose and at 10-9M baclofen in presence of 20mM glucose. This shows a differential control of the GABAA and GABAB receptors over insulin release from the pancreatic islets. During 24 hours in vitro insulin secretion study it showed that low concentration of GABA has inhibited glucose stimulated insulin secretion from pancreatic islets. Muscimol, the GABAA agonist, inhibited the insulin secretion but, gave an enhanced secretion of insulin in presence of 4mM glucose at 10-7 , 10-5 and 1O-4M muscimol. But in presence of 20mM glucose muscimol significantly inhibited the insulin secretion. GABAB agonist, baclofen also inhibited glucose induced insulin secretion in presence of both 4mM and 20mM glucose. This shows the inhibitory role of GABA and its specific receptor subtypes over insulin synthesis from pancreatic bete-islets. In vitro DNA synthesis studies showed that activation of GABAA receptor by adding muscimol, a specific agonist, inhibited islet DNA synthesis. Also, the addition of baclofen, a specific agonist of GABAB receptor resulted in the stimulation of DNA synthesis.Thus the brain and pancreatic GABAA and GABAB receptor gene expression differentially regulates pancreatic insulin secretion and islet cell proliferation during pancreatic regeneration. This will have immense clinical significance in therapeutic applications in the management of Diabetes mellitus.

Recurrence Quantification Analysis of System Signals for Detecting Tool and Chatter in Turning

In this thesis, the applications of the recurrence quantification analysis in metal cutting operation in a lathe, with specific objective to detect tool wear and chatter, are presented.This study is based on the discovery that process dynamics in a lathe is low dimensional chaotic. It implies that the machine dynamics is controllable using principles of chaos theory. This understanding is to revolutionize the feature extraction methodologies used in condition monitoring systems as conventional linear methods or models are incapable of capturing the critical and strange behaviors associated with the metal cutting process.As sensor based approaches provide an automated and cost effective way to monitor and control, an efficient feature extraction methodology based on nonlinear time series analysis is much more demanding. The task here is more complex when the information has to be deduced solely from sensor signals since traditional methods do not address the issue of how to treat noise present in real-world processes and its non-stationarity. In an effort to get over these two issues to the maximum possible, this thesis adopts the recurrence quantification analysis methodology in the study since this feature extraction technique is found to be robust against noise and stationarity in the signals.The work consists of two different sets of experiments in a lathe; set-I and set-2. The experiment, set-I, study the influence of tool wear on the RQA variables whereas the set-2 is carried out to identify the sensitive RQA variables to machine tool chatter followed by its validation in actual cutting. To obtain the bounds of the spectrum of the significant RQA variable values, in set-i, a fresh tool and a worn tool are used for cutting. The first part of the set-2 experiments uses a stepped shaft in order to create chatter at a known location. And the second part uses a conical section having a uniform taper along the axis for creating chatter to onset at some distance from the smaller end by gradually increasing the depth of cut while keeping the spindle speed and feed rate constant.The study concludes by revealing the dependence of certain RQA variables; percent determinism, percent recurrence and entropy, to tool wear and chatter unambiguously. The performances of the results establish this methodology to be viable for detection of tool wear and chatter in metal cutting operation in a lathe. The key reason is that the dynamics of the system under study have been nonlinear and the recurrence quantification analysis can characterize them adequately.This work establishes that principles and practice of machining can be considerably benefited and advanced from using nonlinear dynamics and chaos theory.

Numerical Investigations on Soil Structure Interaction of Multistorey Frames

Frames are the most widely used structural system for multistorey buildings. A building frame is a three dimensional discrete structure consisting of a number of high rise bays in two directions at right angles to each other in the vertical plane. Multistorey frames are a three dimensional lattice structure which are statically indeterminate. Frames sustain gravity loads and resist lateral forces acting on it. India lies at the north westem end of the Indo-Australian tectonic plate and is identified as an active tectonic area. Under horizontal shaking of the ground, horizontal inertial forces are generated at the floor levels of a multistorey frame. These lateral inertia forces are transferred by the floor slab to the beams, subsequently to the columns and finally to the soil through the foundation system. There are many parameters that affect the response of a structure to ground excitations such as, shape, size and geometry of the structure, type of foundation, soil characteristics etc. The Soil Structure Interaction (SS1) effects refer to the influence of the supporting soil medium on the behavior of the structure when it is subjected to different types of loads. Interaction between the structure and its supporting foundation and soil, which is a complete system, has been modeled with finite elements. Numerical investigations have been carried out on a four bay, twelve storeyed regular multistorey frame considering depth of fixity at ground level, at characteristic depth of pile and at full depth. Soil structure interaction effects have been studied by considering two models for soil viz., discrete and continuum. Linear static analysis has been conducted to study the interaction effects under static load. Free vibration analysis and further shock spectrum analysis has been conducted to study the interaction effects under time dependent loads. The study has been extended to four types of soil viz., laterite, sand, alluvium and layered.The structural responses evaluated in the finite element analysis are bending moment, shear force and axial force for columns, and bending moment and shear force for beams. These responses increase with increase in the founding depth; however these responses show minimal increase beyond the characteristic length of pile. When the soil structure interaction effects are incorporated in the analysis, the aforesaid responses of the frame increases upto the characteristic depth and decreases when the frame has been analysed for the full depth. It has been observed that shock spectrum analysis gives wide variation of responses in the frame compared to linear elastic analysis. Both increase and decrease in responses have been observed in the interior storeys. The good congruence shown by the two finite element models viz., discrete and continuum in linear static analysis has been absent in shock spectrum analysis.

Analysis of System Signals Based on Cross Recurrence Method for System Dynamics Characterization

Natural systems are inherently non linear. Recurrent behaviours are typical of natural systems. Recurrence is a fundamental property of non linear dynamical systems which can be exploited to characterize the system behaviour effectively. Cross recurrence based analysis of sensor signals from non linear dynamical system is presented in this thesis. The mutual dependency among relatively independent components of a system is referred as coupling. The analysis is done for a mechanically coupled system specifically designed for conducting experiment. Further, cross recurrence method is extended to the actual machining process in a lathe to characterize the chatter during turning. The result is verified by permutation entropy method. Conventional linear methods or models are incapable of capturing the critical and strange behaviours associated with the dynamical process. Hence any effective feature extraction methodologies should invariably gather information thorough nonlinear time series analysis. The sensor signals from the dynamical system normally contain noise and non stationarity. In an effort to get over these two issues to the maximum possible extent, this work adopts the cross recurrence quantification analysis (CRQA) methodology since it is found to be robust against noise and stationarity in the signals. The study reveals that the CRQA is capable of characterizing even weak coupling among system signals. It also divulges the dependence of certain CRQA variables like percent determinism, percent recurrence and entropy to chatter unambiguously. The surrogate data test shows that the results obtained by CRQA are the true properties of the temporal evolution of the dynamics and contain a degree of deterministic structure. The results are verified using permutation entropy (PE) to detect the onset of chatter from the time series. The present study ascertains that this CRP based methodology is capable of recognizing the transition from regular cutting to the chatter cutting irrespective of the machining parameters or work piece material. The results establish this methodology to be feasible for detection of chatter in metal cutting operation in a lathe.