Retrial Queues with Orbital Search

Queueing system in which arriving customers who find all servers and waiting positions (if any) occupied many retry for service after a period of time are retrial queues or queues with repeated attempts. This study deals with two objectives one is to introduce orbital search in retrial queueing models which allows to minimize the idle time of the server. If the holding costs and cost of using the search of customers will be introduced, the results we obtained can be used for the optimal tuning of the parameters of the search mechanism. The second one is to provide insight of the link between the corresponding retrial queue and the classical queue. At the end we observe that when the search probability Pj = 1 for all j, the model reduces to the classical queue and when Pj = 0 for all j, the model becomes the retrial queue. It discusses the performance evaluation of single-server retrial queue. It was determined by using Poisson process. Then it discuss the structure of the busy period and its analysis interms of Laplace transforms and also provides a direct method of evaluation for the first and second moments of the busy period. Then it discusses the M/ PH/1 retrial queue with disaster to the unit in service and orbital search, and a multi-server retrial queueing model (MAP/M/c) with search of customers from the orbit. MAP is convenient tool to model both renewal and non-renewal arrivals. Finally the present model deals with back and forth movement between classical queue and retrial queue. In this model when orbit size increases, retrial rate also correspondingly increases thereby reducing the idle time of the server between services

Studies of stability of fluid flowa using variational methods

The study of stability problems is relevant to the study of structure of a physical system. It 1S particularly important when it is not possible to probe into its interior and obtain information on its structure by a direct method. The thesis states about stability theory that has become of dominant importance in the study of dynamical systems. and has many applications in basic fields like meteorology, oceanography, astrophysics and geophysics- to mention few of them. The definition of stability was found useful 1n many situations, but inadequate in many others so that a host of other important concepts have been introduced in past many years which are more or less related to the first definition and to the common sense meaning of stability. In recent years the theoretical developments in the studies of instabilities and turbulence have been as profound as the developments in experimental methods. The study here Points to a new direction for stability studies based on Lagrangian formulation instead of the Hamiltonian formulation used by other authors.

Catalysis by Modified Pillared Clays and Porous Clay Heterostructures

In this venture three distinct class of catalysts such as, pillared clays and transition metal loaded pillared clays , porous clay heterostructures and their transition metal loaded analogues and DTP supported on porous clay heterostructures etc. were prepared and characterized by various physico chemical methods. The catalytic activities of prepared catalysts were comparatively evaluated for the industrially important alkylation, acetalization and oxidation reactions.The general conclusions drawn from the present investigation are  Zirconium, iron - aluminium pillared clays were synthesized by ion exchange method and zirconium-silicon porous heterostructures were Summary and conclusions 259 prepared by intergallery template method. Transition metals were loaded in PILCs and PCHs by wet impregnation method.  Textural and acidic properties of the clays were modified by pillaring and post pillaring modifications.  The shift in 2θ value to lower range and increase in d (001) spacing indicate the success of pillaring process.  Surface area, pore volume, average pore size etc. increased dramatically as a result of pillaring process.  Porous clay heterostructures have higher surface area, pore volume, average pore diameter and narrow pore size distribution than that of pillared clays.  The IR spectrum of PILCs and PCHs are in accordance with literature without much variation compared to parent montmorillonite which indicate that basic clay structure is retained even after modification.  The silicon NMR of PCHs materials have intense peaks corresponding to Q4 environment which indicate that mesoporous silica is incorporated between clay layers.  Thermo gravimetric analysis showed that thermal stability is improved after the pillaring process. PCH materials have higher thermal stability than PILCs.  In metal loaded pillared clays, up to 5% metal species were uniformly dispersed (with the exception of Ni) as evident from XRD and TPR analysis. Chapter 9 260  Impregnation of transition metals in PILCs and PCHs enhanced acidity of catalysts as evident from TPD of ammonia and cumene cracking reactions.  For porous clay heterostructures the acidic sites have major contribution from weak and medium acid sites which can be related to the Bronsted sites as evident from TPD of ammonia.  Pillared clays got more Lewis acidity than PCHs as inferred from α- methyl styrene selectivity in cumene cracking reaction.  SEM images show that layer structure is preserved even after modification. Worm hole like morphology is observed in TEM image of PCHs materials  In ZrSiPCHS, Zr exists as Zr 4+ and is incorporated to silica pillars in the intergallary of clay layers as evident from XPS analysis.  In copper loaded zirconium pillared clays, copper exists as isolated species with +2 oxidation state at lower loading. At higher loading, Cu exists as clusters as evident from reduction peak at higher temperatures in TPR.  In vanadium incorporated PILCs and PCHs, vanadium exist as isolated V5+ in tetrahedral coordination which is confirmed from TPR and UVVis DRS analysis.  In cobalt loaded PCHs, cobalt exists as CoO with 2+ oxidation state as confirmed from XPS.  Cerium incorporated iron aluminium pillared clay was found to be the best catalyst for the hydroxylation of phenol in aqueous media due to the additional surface area provided by ceria mesopores and its redox properties. Summary and conclusions 261  Cobalt loaded zirconium porous clay heterostructures were found to be promising catalyst for the tertiary butylation of phenol due to higher surface area and acidic properties.  Copper loaded pillared clays were found to be good catalyst for the direct hydroxylation of benzene to phenol.  Vanadium loaded PCHs catalysts were found to be efficient catalysts for oxidation of benzyl alcohol.  DTP was firmly fixed on the mesoporous channels of PCHs by Direct method and functionalization method.  DTP supported PCHs catalyst were found to be good catalyst for acetalization of cyclohexanone with more than 90% conversion.

Development of a Fully Automated Image Analysis Method for High Density cDNA and array CGH Microarray Based Genomic Studies

In this thesis, different techniques for image analysis of high density microarrays have been investigated. Most of the existing image analysis techniques require prior knowledge of image specific parameters and direct user intervention for microarray image quantification. The objective of this research work was to develop of a fully automated image analysis method capable of accurately quantifying the intensity information from high density microarrays images. The method should be robust against noise and contaminations that commonly occur in different stages of microarray development.