Singular Solutions and Perturbations in Control Systems,
Modeling, simulation and analysis of chemically reacting flow systems have become very important last days due to continuously increasing demand in efficient power generators – gas turbines, power plants, internal combustion engines etc. Reducing emission of carbon dioxide, nitrogen oxides and other pollutants without significant loss of the efficiency of combustion facilities requires very sophisticated modeling and precise knowledge of governing processes of combustion. The aim of this research was to develop and implement geometrical methods for qualitative and quantitative system analysis of the combustion processes taking place in multiphase media. Combustion of a flammable spray as an auto-ignition of a cloud of fuel droplets in a hot gas and pressure driven flame - a flame propagating in a confined media were modeled and investigated. The method of singular perturbations has been used, further developed and adapted for the analysis. The results and methods present in this book would be very helpful to the researchers dealing with reacting flow modeling, asymptotic analysis and numerical simulations, to engineers and students interested in applied mathematics.
A rigorous theoretical investigation has been made on linear and nonlinear structures (solitons, shocks, double layers, etc.) associated with dust-acoustic (DA) waves in four-component dusty plasma (composed of inertialess electron and ion fluids, and negatively as well as positively charged inertial dust fluids). The results may be useful in understanding the localized electrostatic disturbances in both space environments and laboratory devices.
In this work we consider an interaction between Cold Dark Matter (CDM) and Dark Energy (DE) fluids, in which energy transfers from the CDM to the DE. Our results show changes in the evolution of the CDM. These results will be able to explain why Dark Energy only comes to dominate after galaxy formation. Future work will be to compare these results with data from galaxy surveys and the South African Square Kilometre Array (SKA).
Matrix Computations and Semiseparable Matrices – Eigenvalve and Singular Value Methods V2
Kamps (1995) suggested a new theoretical approach, which is called generalized order statistics (gos). This new model includes ordinary order statistics (oos), sequential order statistics, progressive type II censored order statistics and record values. The concept of gos enables a common approach to structural similarities and analogies. The distributional and inferential properties of oos and record values turn out to remain valid for gos (cf. Cramer and Kamps, 2001). Thus, the concept of gos provides a large class of models with many interesting and useful properties for both the description and the analysis of practical problems. Due to this reason, the question arises whether the general distribution theory of gos as well as their properties can be obtained by analogy with that for oos. The latter has been extensively investigated in the literature, e.g., see, David, 1981. The main purpose of this thesis is to investigate the asymptotic behavior of some important functions of gos, in view of theory of statistics and its applications. Some of these functions are non-linear, e.g., extremal product and extremal quotient and other are linear e.g., range and midrange.
The exact distributions of multivariate statistics used for the inference in multivariate analysis are usually not known or quite difficult to handle. The topic of this book belongs to the area of approximation of unknown distributions through classical distributions and to the related estimation problems. The methods used here are based on concepts of matrix algebra like the Kronecker product, the vec-operator and the matrix derivative. The multivariate normal distribution and the class of elliptical distributions are examined. The asymptotic variance of the sample correlation coefficient is calculated using approximate linearization. Some applications of the asymptotic distribution of the sample correlation coefficient are considered for populations with different distributions. The main term of the bias of the shape parameter of the asymmetric normal distribution and the Lauter's F-statistic was found using the Taylor expansion. Simulation experiments are described and the results of the simulation study are presented beside derivation of theoretical results.
This book studies the evolution of scalar cosmological perturbations in the 1+3 Covariant Gauge-Invariant formalism for generic f(R) theories of gravity. It provides with a complete set of equations describing the evolution of matter and curvature fluctuations for a multi-fluid cosmological medium. It also deals with a specific model of a radiation-dust fluid universe described by barotropic equations of state where the perturbation equations are applied around a background solution of a specific toy model of gravity and looks at exact solutions for scales much smaller and much larger than the Hubble radius.
River ecosystems are essential and integral part of the biosphere. Urbanization in India is taking place at a faster rate than rest of the world. The mounting population, increased economic activity, and industrialization always result in increased water demand. The Cauvery River and its tributaries are the major source of water for drinking, agriculture, and industrial needs of Karnataka and Tamil Nadu states. It flows through a densely populated area, from Western Ghats to Bay of Bengal. Rivers Noyyal, Bhavani and Amaravathi are the major contributories to Cauvery in the Tamil Nadu state. Delta regions of the Cauvery River basin are one of the significant areas of rice production in India. In spite of large-scale utilization of the river basin for irrigation and drinking purposes, the lack of appropriate water management has seemingly deteriorated the water quality due to increasing anthropogenic activities. In this context, this book focuses on environmental monitoring of River Cauvery in delta region of Southern India with emphasis on surface water chemistry.