This volume emphasises studies related to classical Stefan problems. The term "Stefan problem" is generally used for heat transfer problems with phase-changes such as from the liquid to the solid. Stefan problems have some characteristics that are typical of them, but certain problems arising in fields such as mathematical physics and engineering also exhibit characteristics similar to them. The term ``classical" distinguishes the formulation of these problems from their weak formulation, in which the solution need not possess classical derivatives. Under suitable assumptions, a weak solution could be as good as a classical solution. In hyperbolic Stefan problems, the characteristic features of Stefan problems are present but unlike in Stefan problems, discontinuous solutions are allowed because of the hyperbolic nature of the heat equation. The numerical solutions of inverse Stefan problems, and the analysis of direct Stefan problems are so integrated that it is difficult to discuss one without referring to the other. So no strict line of demarcation can be identified between a classical Stefan problem and other similar problems. On the other hand, including every related problem in the domain of classical Stefan problem would require several volumes for their description. A suitable compromise has to be made. The basic concepts, modelling, and analysis of the classical Stefan problems have been extensively investigated and there seems to be a need to report the results at one place. This book attempts to answer that need.
To understand and make the practical use of the grammatical rules is a challenge poised at various competitive exams. Students preparing for various competitive exams need elucidated grammar rules that are explained in a very easy and understandable language. Practical English Grammar & Composition is the hand book and an easy guide to learn English aimed at learning and improving knowledge of grammar and its applicability. In order to make the students conversant with the practical applicability of the grammar rules, sentences depicting the right usage are also given after the rules. A number of solved exercises are also given after the chapters that enable the students test their acquired knowledge. Word Powers section is a unique feature of the book that will play a crucial role in making the students ready to face the competitions ahead.
The book, a result of extensive research on numbers is intended for the general public - even for those who are not so enthusiastic about mathematics. It conveys the message that mathematics is a very exciting and interesting subject. Numbers possess some amazing properties which will not only amaze you but also provide thrill, excitement, fun and keep you spellbound. The mathematical ideas in the book provide hours, days, and months, if not years of “entertaining numbers”. Moreover, it will also result in increasing the general knowledge of the readers. The book takes you through a thrilling, stimulating, and adventurous voyage of exploration into the realm of numbers.
This textbook, now in the second edition, offers a completely up-to-date and in-depth introduction to the principles and applications of optoelectronic devices and systems. The text gives a detailed description of optical fibre waveguides, optical fibre cables and their characteristics, manufacturing process and drawing of optical fibres. In addition, it deals with photon sources, photon detectors, fibre optics as a medium and LAN and WAN systems, short and long haul optical fibre communication systems, electro-optic modulators and their characteristics. The second edition possesses a new section on Optical Fibre Based Broadband High Speed Network in Chapter 8, thus highlighting an updated version. Apart from this, a new chapter on Intensity Dependent Refractive Index Effect has been introduced into the text that discusses the effect of focusing on spatial and temperature profiles in a non-linear crystal medium. This chapter further explains the various physical phenomena like the creation of sharp opaque filaments, irradiation induced damaging of the crystal, oscillatory waveguide propagation, saturation effects and other properties in detail. Primarily intended for the undergraduate students of electronics and communication engineering, the book should also prove extremely useful for the postgraduate students of physics. Key features • Provides comprehensive explanation of optical fibre communication with illustrations. • Gives extensive theory and experimental and holographic applications. • Discusses the applications of lasers in industry, military and medical as well as fibre optics applications. • Describes optical computing, optical gates and their applications with illustrations. • Includes solved numericals at the end of book for better understanding of topics.
The Classical Stefan Problem: Basic Concepts, Modelling and Analysis with Quasi-Analytical Solutions and Methods, New Edition, provides the fundamental theory, concepts, modeling, and analysis of the physical, mathematical, thermodynamical, and metallurgical properties of classical Stefan and Stefan-like problems as applied to heat transfer problems with phase-changes, such as from liquid to solid. This self-contained work reports and derives the results from tensor analysis, differential geometry, non-equilibrium thermodynamics, physics, and functional analysis, and is thoroughly enriched with many appropriate references for in-depth background reading on theorems. Each chapter in this fully revised and updated edition begins with basic concepts and objectives, also including direction on how the subject matter was developed. It contains more than 400 pages of new material on quasi-analytical solutions and methods of classical Stefan and Stefan-like problems.The book aims to bridge the gap between the theoretical and solution aspects of the afore-mentioned problems. Provides both the phenomenology and mathematics of Stefan problems Bridges physics and mathematics in a concrete and readable manner Presents well-organized chapters that start with proper definitions followed by explanations and references for further reading Includes both numerical and quasi-analytical solutions and methods of classical Stefan and Stefan-like problems
The book, now in its third edition, is thoroughly revised and updated as per the new syllabi of Optical Fiber Communication of various universities. The material is well-presented and designed for undergraduate and postgraduate students pursuing courses in Electrical Engineering, and Electronics and Telecommunication Engineering. The book offers a completely accessible and in-depth knowledge of the principles and applications of optical fiber communication (OFC). It deals with materials, devices, components, and systems of OFC. The coverage includes key concepts such as properties of light, evolution and elements of OFC, its benefits, along with applications in optical LAN and communication links. The attenuation loss of different types, dispersion mechanism, photon sources (LED and lasers), detectors (PIN and avalanche), analog and digital transmitter and receiver systems, connectorization, OADM, and amplifiers are described. Built-up of long haul OFC links at 8 Mb/s and 2.5 Gb/s, and optical interface are explained with illustrations. It also contains solved numerical problems for better understanding of topics. KEY FEATURES • Includes optical fiber LAN for data centres and industries • Provides detail treatment of LED, semiconductor, lasers, Tx and Rx • Discusses all optical communications links and optical networks • Includes important questions with answers • Provides practice papers and model test papers
A proverb is a short, easily memorable phrase or a saying that offers a moral lesson, explains a timeless truth and a practical word of wisdom in a very alluring form. Knowledge of Proverbs is necessary for perfect knowledge of a language. English language learners, often struggling with a limited vocabulary find these memorable proverbs easy to learn and fun to use. When used at right places they also let you express your opinions convincingly. This book, ‘A collection of Popular & Interesting Proverbs’ is a treasure trove for the students keen to enrich their English language skill. The book starts with all the interesting information on proverbs, followed by a meticulous collection of all other forms of quotes and proverbs. Also, many Illuminating Quotes about India, Popular Sayings in Different Countries are given, to make the book fascinating and valuable asset for students. Table of ContentA Unique World & Interesting Proverbs, Traditional Proverbs, Important Proverbs from Different Countries, Sayings and Quotes about India, Conflicting Proverbs, Proverbial Sayings and Quotes by Great Personalities.
Fluid Mechanics And Hydraulic Machines is designed for the course on fluid mechanics and hydraulic machines offered to the undergraduate students of mechanical and civil engineering. Written in a lucid style, the book lays emphasis on explaining the logic and physics of critical problems to develop analytical skills in the reader.
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