Transistor Biasing

When transistors are used as switches, they operate either in cut off or in saturation mode. Whereas, when transistors are used to amplify small signals, a quiescent operating point is selected somewhere in the middle of the conduction range. The region of the location of a quiescent point depends on the kind of amplifier. For example, an amplifier may be used for maximum voltage and/or current gain, or high input resistance, or power gain. In some applications, an amplifier ought to consume minimum power, especially when it is used with a battery-operated device. After selecting the quiescent operating point, it is also required that it remains stable. If there is some change in the operating temperature or variation in supply voltage, the operating point may change its location. Variations due to the manufacturing tolerance in component values and in transistor parameters also affect the quiescent point. Irrespective of the reason, it is required that the quiescent point should remain located within specified limits.

Three amplifier configurations are commonly used while employing either BJT or FET amplification. The configuration depends on the terminals, out of the three, that is common to the input and the output of the amplifier. These configurations are studied on the basis of their characteristics, such as voltage gain, current gain, input and output resistance, and bandwidth, i.e., the frequency range within which the amplifier operates without any significant reduction in the output waveform. The operating frequency range becomes limited as the voltage gain drops at low and high operating frequencies. Hence, the study of frequency response becomes important.

11.1 INTRODUCTION [LO1]

Stresses developed at the contact between two loaded elastic bodies are generally localized and most machine parts or structures are designed based on the stresses in the main body. However, there are many important machine members where the localized stresses developed at the contact between curved surfaces with initially limited contact area play an important role in their design. Ball or roller bearings, gears, cams, and valve tappets of internal combustion engines are some of the examples of machine parts where contact stresses must be taken into account in order to predict their failure probability.

The localized contact stresses that develop between two curved bodies as they are loaded with small deformations are often referred to as Hertzian stresses, following the work of H. Hertz (1881), who first solved these contact problems elegantly more than a century ago. Since then the topic has received a good deal of attention by the researchers due to its importance in engineering practice and science. Much work has been done on the stress distribution at the Hertzian contact surfaces and sub-surfaces. Ball bearings and gear teeth often fail by pitting. Hertzian stress analysis can precisely locate the depth at which maximum shear stress occurs where cracks may initiate and propagate leading to failure. Thus, a remedy to such failures may be prescribed in terms of limiting stresses. In many rolling contact problems, failure occurs with the initiation of a tiny crack that eventually grows due to repeated contacts. Analysis of crack initiation and growth is often based on Hertzian stress analysis. In this chapter, we shall consider the basics and application of contact stress analysis, beginning with some basic elasticity theory necessary for such analyses.

Key Concepts

• • Phenomenon of global warming and its connection with industrialization

• • Concerns and threats of global warming and climate change

• • Impact of carbon emissions on global warming

• • Initiatives towards reduction of carbon emissions and preventing global warming

• • Concepts of Earth Overshoot Day, sustainable development and net-zero emissions

• • United Nations’ sustainable development goals.

• • Link between energy demand and global warming

• • How to decarbonize the energy system

Introduction

Sustainable development, in recent years, has emerged as one of the most talked-about concepts. What does this term mean, and why has it become so important? The Industrial Revolution, which gained momentum in the 19th century, was a landmark event. It represented the culmination of human efforts of thousands of years. The revolution led to great inventions, making life better and easier. The human efforts involved in day-to-day activities have decreased continuously, and automation has resulted in increased human comfort. All sectors of our life, be it agriculture, transport, and even daily routine work at our homes, have been made easier by this revolution. But these developments have extracted a significant cost, particularly on the environment.

The effect of industrial activities on the environment has been described in a poignant way by @SDGoals. It shows that if we scale down the age of the earth from its actual value of 4.6 billion years to 46 years, then on the same scale human life has been on the earth for about 4 hours only. The Industrial Revolution, on this scale, began only a minute ago, and in that time, we have destroyed more than half of the world's forests.

Key Concepts

• • Importance of energy sector in decarbonization

• • Energy-related SDGs

• • Goal 7: Targets, indicators, progress

• • Goal 11: Targets, indicators, progress

• • Goal 13: Targets, indicators, progress

Introduction

The UN, realizing the importance of preventing damage to the climate and warming of the planet, started working in this area more than 50 years ago. But the real transformation has come after the Paris Agreement and the adoption of SDGs. The climate change challenge was largely absent from the agenda of the countries and considerations in policy formulation in even the most advanced countries in the world. Growing evidence of the threat of global warming led to a change in the approach, with a radical change seen after the declaration of the Paris Agreement and the 17 SDGs.

The most important component of the increased concern over climate change is related to energy. Energy is the dominant contributor to climate change, accounting for a minimum around 60% of total global greenhouse gas emissions, and in fact some studies have shown this share to be more than 70%. All the related key terms in vogue these days, such as ‘low-carbon system’, ‘decarbonization’, ‘net-zero system’, and ‘carbon-neutral system’, have energy at the centre. Irrespective of the solutions adopted and the timelines set by different countries, it is agreed upon by all concerned that transition to a low-carbon climate cannot be achieved without decarbonizing the energy systems.

In images, some objects in the visual scene stand outfrom their neighboring or other regions grabbingimmediate attention of a human observer. Thoseobjects are called visuallysalient objects. The distinct perceptualquality of these objects compared to other objectsin the scene is called visualsaliency. This quality is attributed tothe behavior of an observer, and hence it issubjective. The mechanism by which the visuallysalient objects are selected is called visual attention. It is akey perceptual function in human visual system (HVS)for processing information from complex naturalscenes (Pinker, 1986). The visual attentionmechanism extracts essential features from redundantdata aiding the information processing in humanbrain. Our nervous system has a limited ability forsimultaneous processing of all the incoming sensoryinformation. The attention mechanism thusaccelerates this processing by selecting andmodulating the most relevant information. Thereexist multiple perceptive and cognitive operationsunder a hierarchical control process to establishglobal priorities to highlight some locations,objects or features in the visual field. A powerfulapproach to study visual saliency is to analyze eyegaze data of a viewer of a given scene, as thevisual saliency is associated with its correspondinggaze information of human beings. In this chapter wedevelop an understanding of visual attention,saliency and cognitive processing in the HVS.

5.1 Visual cognition

The way an individual acquires and processes the visualinformation is called visualcognition. It involves interpretation ofvisual sensation and identification of object, suchas, recognition of face, scene and object, visualattention and search, recognition of visual wordsand reading, control of eye movement and activevision, short-term and long-term visual memory,visual imagery, etc.

2.1 MATHEMATICAL PRELIMINARIES [LO1]

In any scientific or engineering field of study, knowledge of some mathematical techniques and methods are essential. Solid mechanics is no exception. To develop proper formulation methods and solution techniques for elasticity problems, it is necessary to have an appropriate mathematical background. In this chapter, we shall discuss Cartesian tensors, which have a special significance in the discussion of stress, strain, and displacement fields, and their manipulation. Other mathematical details will be discussed as and when they are required in solving different problems.

Tensors may be defined in a number of ways. One simple definition is that a tensor is a physical quantity that is governed by certain transformation laws when the coordinate system is changed. A tensor is invariant under any change of coordinate system, but its components along the coordinate axes change with the changed coordinate system. Tensors of order zero are called scalars. Common examples of scalars are temperature, density, Young's modulus, or Poisson's ratio. They have a single magnitude at each point in space, and they are invariant with coordinate transformations. A typical example of scalars is often taken as temperature T at a point in space with coordinates (x, y, z) represented as T(x, y, z). Temperature at the same point does not change if we choose a different coordinate system (x′, y′, z′) represented as T′(x′, y′, z′) and we may say

T=T′. (2.1.1)

Tensors of first order are vectors, and we know that a vector has a magnitude and a direction. A typical example of a vector is a velocity vector V. It is sometimes taken as a convention to represent a vector by a bold letter. Consider the velocity vector V in (x, y, z) coordinate system.

In the single view camera geometry it is not possibleto resolve the ambiguity of depth of the scene pointfrom its image point even with a calibrated camera,whose projection matrix is known. It is onlypossible to construct the ray in the 3-dimensional(3-D) world coordinate system passing through theimage point from the center of the camera. But in anoptical image a viewer can distinguish the objectpoint which forms the image. It is the opticalenergy received from that point in a surface of theobject and their distribution over its neighborhoodthat provide the key information to a viewer ininterpreting the object point and judging thedistances from the camera. In this chapter, wediscuss how the depth ambiguity in a single viewcamera geometry can be resolved with the help ofanother additional camera. The combined setup of twocameras is called stereo camera setup and thegeometry defined by them is referred to as stereo geometry.

12.1 | Epipolar geometry

A stereo setup consists of two cameras and a scenepoint, 𝑿, whose image is captured by the cameras,as illustrated in Fig. 12.1. The first (left) andthe second (right) cameras are specified by theircamera centers, 𝑪 and 𝑪′, respectively, whichcapture the images of the scene point on theirrespective image planes. In convention, the firstcamera or left camera is considered as the referencecamera of the stereo setup. By the rule ofprojection, let the image of the scene point, 𝑿, inthe first camera be 𝒙. Similarly, the image of 𝑿in the image plane of the second camera isrepresented by 𝒙′. The two images, 𝒙 and 𝒙′,correspond to the same scene point, 𝑿. Thus, forevery scene point, there will be two image points inthe image planes of the two cameras, if the scenepoint is visible from both the cameras.

Content based imageretrieval (CBIR) is a search techniquethat uses similarity of visual features to compareimages. It is also known as image based searchprocess, where, given a query image (with or withoutan accompanying text), the system provides a set ofimages that are similar to the query. This provisionis made available in most of the search engines,which enable us to search through the internet usinga query image and get several images that arerelevant to the query. The CBIR system has a lot ofapplications in various sectors, like education,research, tourism, health care, remote sensing, etc.In CBIR systems, while retrieving the resultsagainst a query, some domain specific information,like keywords, may also be provided to improve thequality of retrieval. The scope of such retrievalsystems could be extended to videos and multimediadocuments, which include text, audio, video,graphics, and images, as well.

Challenges and issues in building a CBIRsystem

Developing efficient CBIR systems is hurdled by severalchallenges. The image similarity computed forretrieving relevant images may not always satisfythe user's search intent. Often, objective criteriamay not fill the semantic gap in the representationof similar images. Some images, that are similar tohuman understanding, may be outright rejected asdissimilar images by a computational model. Manyobjective models are sensitive to noise and thepresence of a few outlier features may disturb thedecision by rejecting seemingly similar images oraccepting dissimilar images. In such cases ofsimilarity, thesystem does not explain why a pair of images aresimilar. Such sparingly occurring instances may beacceptable in some domains, but there are variousareas, like medicine and health care, where theverdict of a system is not acceptable without aproper explanation. Also, two images may be globallysimilar or they may have some local similaritybetween them. Capturing and localizing the localsimilarities for declaring a match between twoimages are also challenging. However, most of theCBIR systems work on global similarity.

Intensity images are limited in capturing surfacegeometry. Range imaging refers to an aggregation oftechniques to capture the surface topology as acollection of points that represent depths usingdifferent kinds of range sensors. Range images forma special class of digital images that requiredifferent processing techniques in their analysis.This chapter provides an overview of range imagingand processing.

13.1 | Range image

A range image is a 21/2-D or 3-D representation of the scene. It issometimes called 21/2 -D representation because itcaptures only the surface information of an objector scene as discretized points to represent it as animage. A range image, 𝑓(𝑖, 𝑗), records thedistance, d, to the corresponding scene point at(𝑥, 𝑦, 𝑧) for each image pixel, (𝑖, 𝑗), asshown in Fig. 13.1. In the array representation of arange image, the pixel values correspond to thedistances of the surface points, unlike conventionalRGB camera image pixels that represent intensities.The distribution of all the recorded values of dforms the functional distribution of the surfacepoints over the discretized space of the image,which is known as range data or depth data. Thisdepth information may also be represented as a setof 3-D scene points, also called a point cloud. Fora given functional value, 𝑓(𝑖, 𝑗), of an imagearray at an index position of (𝑖, 𝑗), thecorresponding pixel value of a scene point (𝑥, 𝑦,𝑧) in the discrete 3-D space is represented as (𝑖,𝑗, 𝑓(𝑖, 𝑗)). An example of a range image isshown in Fig. 13.2, where the intensity image iscaptured as an RGB color image and its correspondingrange image is captured using Microsoft™ Kinectsensor.

The world of graph theory owes its birth to Leonhard Euler (1707–1782) who employed a new strategy to settle a then-unsolved problem called the K¨onigsberg Bridge problem. There were two islands in the middle of the Pregel river, which were connected to each other and also to the mainland by means of seven bridges. The structure of K¨onigsberg and the bridges are described in Figure 1.1.

The question was, “Can a person start at any one of the land masses, walk across each bridge exactly once, touch all land masses and return to the land mass where the person started?” In 1735, Euler correctly identified that there were 4 landmasses and each land mass was connected to the other landmass by means of seven bridges. He intuitively decided that he would model the land masses as “vertices” or “dots” and the seven bridges as “edges” or “lines” connecting the vertices.

A topological space, in general, can have a complex structure. To study such topological spaces, one of the main techniques is to identify such a space, by a homeomorphism, to a space defined in a better way or whose properties are known. We asked relevant questions in the beginning of Chapter 2 of sets (now topological spaces for us) being “same” (now homeomorphic for us), and we also remarked that topology is called “rubber-sheet geometry”. Thus, a topological space need not have a definite geometrical shape or a specific structure, but rather, it can be given by a complex structure. If two topological spaces are homeomorphic, they share certain common properties, which we call “topological properties” or “topological invariants”, which are preserved under a homeomorphism. Therefore, rather than identifying spaces, we can easily distinguish them if such a property is found in one space but not the other. In what follows, till the end of the course of this book, we are going to see many such topological properties and their applications in classifying many topological spaces and answer the questions that we started with in Chapter 2. For instance, we know that ℝ with the usual topology has a countable basis (see Example 2.3.14). This is a topological property called the second countability. That is, a space that does not have a countable basis cannot be homeomorphic to a space with a countable basis. We begin our discussion with the first countability below.

6.1 Local Base and First Countable Spaces

6.1.1 Local base

We have defined neighborhood of a point and neighborhood system at a point in Section 2.6 of Chapter 2. Before we state the first countability axiom, we define local base at a point.

Solid mechanics, compared to mechanics of materials or strength of materials, is generally considered to be a higher level course. It is usually offered in higher semester to senior students. There are many textbooks available on solid mechanics, but they generally include a large part of theory of elasticity with in depth mathematical formulations. The usual prerequisites are one or two semester course on elementary strength of materials and a thorough mathematical background, including scalar, vector, and tensor field theory and cartesian and curvilinear index notation. The difference in levels between these books and elementary texts on strength of materials is generally formidable. However, in our experience of teaching this course for many years at premier institutes like IIT Kharagpur and Jadavpur University, despite its complexity, senior students generally cope well with the course using the readily available textbooks.

However, there is a vast student population pursuing mechanical, civil, or allied engineering disciplines across the country in colleges where AICTE curriculum is followed. Through several years of interaction with this group of students, we have found that there is no suitable textbook that suits their requirements. The book is primarily aimed at this group of students, attempting to bridge the gap between complex formulations in the theory of elasticity and elementary strength of materials in a simplified manner for better understanding. Index notations have been avoided, and the mathematical derivations are restricted to second-order differential equations, their solution methodologies, and only a few special functions, such as stress function and Laplacian operators.

The text follows more or less the AICTE guidelines and consists of twelve chapters. The first five chapters introduce the engineering aspects of solid mechanics and establish the basic theorems of elasticity, governing equations, and their solution methodologies. The next four chapters discuss thick cylinders, rotating disks, torsion of members with both circular and noncircular cross-sections, and stress concentration in some depth using the elasticity approaches. Thermoelasticity is an important issue in the design of high-speed machinery and many other engineering applications. This is dealt with in some detail in the tenth chapter. Problems on contact between curved bodies in two-dimensional and three-dimensional situations can be challenging, and they have wide applications in mechanical engineering such as in bearing and gear technology.

Ideals, in modern algebra, are subrings of a mathematical ring with certain absorption properties. The concept of an ideal was first defined and developed by German mathematician Richard Dedekind in 1871. In particular, he used ideals to translate ordinary properties of arithmetic into properties of sets.

The origin of the notion of ideals in a ring lies in the idea of “ideal numbers”, numbers which are missing but are really ought to be there. Ernst Kummer invented the concept of ideal numbers to serve as the “missing” factors in number rings in which unique factorization fails; here the word “ideal” is in the sense of existing in imagination only.

In this chapter, the abstraction of ideals is explored through various examples. The study is examined through various problems to enable students to apprehend the notion of the ideals.

Key Concepts

• • Steps involved for developing sustainable organizations

• • Case study on a university campus

• • Integration of green sources of energy

• • Implementation of energy efficiency measures

• • Ensuring participation of stakeholders for energy conservation

Introduction

The achievement of SDGs defined under the Paris Agreement requires concerted efforts at the international, national, state, organization, and individual levels. The organizations which follow the principles of sustainable development can serve as a role model for others to follow.

Colleges for higher education and the universities also have an important role to play in achieving the SDGs in general and in the adoption and promotion of green sources of electricity in particular. Goal 4 of SDGs, although, is specific to the availability of quality education to all, but these institutions can play a much broader role in realizing the wide-ranging SDGs. For example, Goal 9: Industry, infrastructure and innovation; Goal 12: Responsible production and consumption; and Goal 13: Climate Action cannot possibly be achieved without the mindful and positive influence of higher education institutions.

More importantly, these institutes need to work on the creation of awareness about the need for sustainable development and SDGs, a crucial requirement for their achievement. The institutes should also make sustainable development an integral part of their future plans. Green and renewable sources of energy like solar PV should be adopted for existing buildings, and these should be made mandatory for the new buildings. The academic institutes, more importantly, should practice on their campuses what they are preaching in the class.