Studies on nonlinear dynamics of certain reaction systems

The nonlinear dynamics of certain important reaction systems are discussed and analysed in this thesis. The interest in the theoretical and the experimental studies of chemical reactions showing oscillatory dynamics and associated properties is increasing very rapidly. An attempt is made to study some nonlinear phenomena exhibited by the well known chemical oscillator, the BelousovZhabotinskii reaction whose mathematical properties are much in common with the properties of biological oscillators. While extremely complex, this reaction is still much simpler than biological systems at least from the modelling point of view. A suitable model [19] for the system is analysed and the researcher has studied the limit cycle behaviour of the system, for different values of the stoichiometric parameter f, by keeping the value of the reaction rate (k6) fixed at k6 = l. The more complicated three-variable model is stiff in nature.

Investigations on Stochastic Storage Systems with Positive Service Time

In this thesis the queueing-inventory models considered are analyzed as continuous time Markov chains in which we use the tools such as matrix analytic methods. We obtain the steady-state distributions of various queueing-inventory models in product form under the assumption that no customer joins the system when the inventory level is zero. This is despite the strong correlation between the number of customers joining the system and the inventory level during lead time. The resulting quasi-birth-anddeath (QBD) processes are solved explicitly by matrix geometric methods

Activated packed bed bioreactor for rapid nitrification in brackish water hatchery systems

A packed bed bioreactor (PBBR) was developed for rapid establishment of nitrification in brackish water hatchery systems in the tropics. The reactors were activated by immobilizing ammonia-oxidizing (AMONPCU- 1) and nitrite-oxidizing (NIONPCU-1) bacterial consortia on polystyrene and low-density polyethylene beads, respectively. Fluorescence in situ hybridization demonstrated the presence of autotrophic nitrifiers belong to Nitrosococcus mobilis, lineage of b ammonia oxidizers and nitrite oxidizer Nitrobacter sp. in the consortia. The activated reactors upon integration to the hatchery system resulted in significant ammonia removal (P\0.01) culminating to its undetectable levels. Consequently, a significantly higher percent survival of larvae was observed in the larval production systems. With spent water the reactors could establish nitrification with high percentage removal of ammonia (78%), nitrite (79%) and BOD (56%) within 7 days of initiation of the process. PBBR is configured in such a way to minimize the energy requirements for continuous operation by limiting the energy inputs to a single stage pumping of water and aeration to the aeration cells. The PBBR shall enable hatchery systems to operate under closed recirculating mode and pave the way for better water management in the aquaculture industry.

Characterizations of some continuous distributions using partial moments

Inthis paper,we define partial moments for a univariate continuous random variable. A recurrence relationship for the Pearson curve using the partial moments is established. The interrelationship between the partial moments and other reliability measures such as failure rate, mean residual life function are proved. We also prove some characterization theorems using the partial moments in the context of length biased models and equilibrium distributions