Climate change, global warming, and shifting to sustainable ways of growth are major concerns of present times. Although these issues were identified many years ago, for a long time the exact nature of these phenomena and their impact were under debate. However, recent years have seen clearly visible and regularly occurring phenomena that confirm the adverse effects and grave threat of global warming and climate change.

It is noteworthy that 17 November 2023 was an important day for climate change, as on this day the average temperature of the earth exceeded by more than 2°C compared to the pre-industrial age temperature for the first time. The Copernicus Climate Change Service of the European Union (EU) has confirmed that in 2023 the average temperature of the earth's surface was 1.48°C higher than the temperature during the pre-industrialization days. In absolute terms also, the global emissions of CO2 are rising; in 2022, for example, these emissions were at least a billion tonnes higher than in 2019.

The Conference of Parties (CoP) is the supreme decision, making body under the United Nations Framework Convention on Climate Change (UNFCC). CoP is an important annual event initiated about 30 years ago. But the increasing interest of public, over the years, in the event shows that we have come a long way in understanding the adverse impacts of climate change. From sceptics doubting the very idea of climate change to it becoming the most debated topic in the world is a major change.

Sinusoidal Oscillations

The feedback amplifiers having negative feedback are likely to become unstable because of some unavoidable phase lag at the output due to the frequency-dependent nature of the primary amplifier gain or feedback network, or due to both. The feedback becomes positive if the additional phase lag becomes 180o at a certain frequency. If the loop gain becomes unity at any frequency, the amplifier starts oscillating at this frequency. This instability and consequent oscillations are undesirable in circuits used as amplifiers. However, practically, such oscillations are generated intentionally for widespread applications also. Hence, many schemes and approaches are in use to obtain oscillations for different frequency ranges. Such circuits are known as oscillators, or signal generators.

To understand this instability and the development of oscillations, intended or otherwise, consider the basic block diagram of a negative feedback amplifier shown in Figure 6.1. Here, vin is the input signal, the net input to the amplifier is ve, the voltage gain of the amplifier is (Av) , βff is the feedback factor, and vout is the output voltage.

The voltage gain of the feedback amplifier is (vout/vin ) = Av/(1 + βf Av). When the voltage gain Av and feedback factor βf are negative (or positive) and real constants, the feedback becomes negative. However, because of the frequency-dependent nature of the primary (and/or in feedback circuit) amplifier, the loop gain has an additional phase shift of 180o at some critical frequency ωo.

10.1 INTRODUCTION [LO1]

There are many applications where structures or machine parts are subjected to significant changes in temperature, for example, turbine blades, high-speed rotating machinery, and boilers in thermal power plants. Large thermal stresses may be developed in such applications, and sometimes such stresses may exceed the yield limit. It is therefore necessary to make provisions in the design of components to avoid failure due to thermal stresses. If the ends of a rod or any other machine parts are rigidly fixed such that the expansion or compression is prevented and the temperature is changed, tensile or compressive stress would be set up, and in simple terms, these stresses are called thermal stresses. In a long steam pipe, expansion joints are sometimes inserted, and in bridges, one end may be rigidly fastened to the main structure while the other end rests on rollers to avoid thermal stresses. In simple terms, this may be demonstrated considering a rod of length l and cross-sectional area A fixed at both ends (Figure 10.1) and temperature is raised by ΔT. This would produce a thermal strain ∈t in the rod such that

where a is the coefficient of thermal expansion. Since the rod is not free to expand, a compressive stress σc would be developed in the rod, and this is given by

If the rise in temperature is significant, the rod may buckle, which is of serious consideration in the design of machine parts or structures. To avoid this, we need to find the critical force Pcr for buckling. Using the basic buckling criterion, this can be given for a column pin ended at both ends, by

where I is the least moment of inertia of the constant cross-section column (rod) and A is the cross-sectional area of the column.

6A Radiation as a photon gas

In the nineteenth century, physicists applied classical electromagnetic theory to explain the experimental results of black body radiation but were unable to provide an adequate explanation. This was a major problem to the physicists as classical theory predicted an infinite amount of energy of the radiation emitted from a black body. This gross disagreement was called the “ultraviolet catastrophe”. Max Planck presented a paper on December 14, 1900, in which he guessed the answer to this problem of black body radiation. This guess marked the very beginning of quantum mechanics.

The electromagnetic radiation inside a black body chamber exists as patterns of standing waves or modes. A single mode is like a standing wave on a guitar string and is characterized by a frequency. Planck made a bold hypothesis that the energy of such a mode is quantized, ithat is, only certain energies of these oscillation modes are allowed. Thus, the energy 𝐸𝑛 of 𝑛th mode is given by 𝐸𝑛 = (𝑛 + 12 ) ℏ𝜔 = (𝑛 + 12 ) ℎ𝜈, where 𝜈 is the oscillation frequency, ℎ is Planck's constant, and 𝑛 is an integer starting with 0. Thus, each oscillation mode can exist in any one of an infinite number of energy states whose energies are equally separated by the energy ℏ𝜔. In the discussion of the properties of the photon gas, for the time being, we shall ignore 12 in the expression for 𝐸𝑛 as it has no effect on the results we seek. Therefore, we take 𝐸𝑛 = 𝑛ℏ𝜔 as the energy of the 𝑛th mode whose (angular) frequency is 𝜔. When the energy of a mode is 𝐸𝑛, we say that there are 𝑛 photons in the mode. Each photon has energy equal to ℏ𝜔. Thus, according to the prescription of Max Planck, a black body radiation chamber consists of a number of photons in various energy states with different amounts of energy.

rystallography

The science that deals with the geometrical structure and physical properties of crystalline solids is called crystallography.

Solids are classified into two categories:

• 1. Crystalline solids

• 2. Amorphous solids

CRYSTALLINE SOLIDS

Crystalline solids are those that contain the regular repeated pattern of atoms or molecules, as shown in Figure 10.1. The physical properties of crystalline solids are different in different directions. Therefore, crystalline solids are anisotropic. Examples are rock salt, quartz, calcite, sugar, and so on.

AMORPHOUS SOLIDS

Figure 10.2 illustrates an amorphous material, which lacks the regular arrangement of atoms or molecules. The amorphous solid's physical characteristics are uniform throughout. As a result, amorphous solids are isotropic. Examples are glass, rubber, polymers, and so on.

SPACE LATTICES

A crystal is made up of identical structural units (atoms, molecules, or ions) that are infinitely repeated in space; each unit can be replaced by a geometrical point. The outcome is a pattern of dots with crystal-like geometrical characteristics. The crystal lattice or space lattice is this geometric arrangement. Lattice points are the name given to the geometrical points.

The regular pattern of points that describes the three-dimensional arrangement of points (atoms, molecules, or ions) in the crystal structure is called the crystal lattice or space lattice.

BASIS

The unit assembly of atoms, molecules, or ions identical in the composition, arrangement, and orientation is called basis. If we add the basis to every lattice point, then it forms a crystal structure, as shown in Figure 10.3.

Space lattice + Basis = Crystal structure.

Engineering physics plays a crucial role in providing the foundational knowledge necessary for the development of innovative technologies. It is an essential part of the curriculum for students in various streams of science and engineering at the undergraduate level.

The goal of this book is to develop a solid understanding of the basic principles of physics and highlight their relevance to engineering. The content is structured to progressively build the knowledge and skills necessary for further studies in both theoretical and applied sciences. Each chapter begins with the basic concepts and gradually moves to more advanced topics, supported by numerical examples, illustrations, and problem sets that reinforce learning. The problems included are designed to improve the problem-solving skills of students and provide practical insight into the engineering applications of physics.

The manuscript includes 14 chapters that were prepared in accordance with the syllabus taught in various Indian colleges and universities. In addition to core topics, the manuscript also covers advanced topics such as relativistic mechanics, quantum mechanics, optical fiber, lasers, semiconducting materials, superconducting materials, and nanomaterials. Students who want to pursue higher education and a career in research, as well as instructors who instruct postgraduate courses at universities, will find these topics helpful for building a solid foundational understanding and developing problem-solving abilities.

Preventing climate change and ensuring sustainable development is one of the most talked about concepts in recent years. The issue of climate change and global warming is closely related to carbon dioxide (CO2) emissions. The rising level of CO2 in the environment is a major concern because of the resulting global warming and its associated adverse effects. In 2015 the United Nations executed the Paris Agreement. The agreement aims to limit the global temperature rise to 2°C, and to make best efforts to keep it to 1.5°C.

This objective has an important connection with energy and, particularly, electrical energy. The most common conventional method for producing electricity is by burning coal, which leads to CO2 emissions. Electricity produced from solar energy and wind energy is considered green electricity because it does not contribute to CO2 emissions. An important component of the CO2 emission reduction initiative of the UN, therefore, is the installation of green energy sources on a large scale throughout the world.

In line with this vision, the most important part of a carbon emission reduction plan worldwide is installation of these sources on a large scale. India, for example, has committed to having 50% of the total installed capacity by 2030 from green sources of electricity generation. This push towards a shift to solar, wind, and hydro-based energy sources is happening at a very fast rate. Under this changed scenario, these technologies are set to become the main technologies in the electric power network. In the Indian grid, for example, the share of solar energy has grown from about 2.6 GW in 2014 to more than 100 GW in 2025. This shift is set to change the fundamental way in which electricity has been generated, transmitted, and utilized.

Thirteen scholars using original and thorough historical information have worked together to consider variability across thirteen cases of premodern economies representing a worldwide distribution, contrasting sociopolitical scale, and forms of organization. In Chapter 1, we defined economies as organized to extract resources, mobilize labor, and make things and distribute them for consumption. This consumption meets the ever-changing demand of human populations and their institutional formations that create the diversity of material life of human societies. With extended interactions, our comparative study probably represents the best available overall consideration of economic variability in premodern societies. We do not see our book as a final statement with evident conclusions of premodern economies, but as a substantial step forward.

Medical imaging mostly deals with the visualization ofinternal organs, tissues, etc., using noninvasive orsemi-invasive methods. The primary motive is tounderstand any anomalies in the anatomies and theirfunctions. The signals are acquired inone-dimensional (1-D), two-dimensional (2-D),three-dimensional (3-D), or as videos, depending onthe purpose and mode of imaging. There are variousmodalities in medical imaging. The major modalitiesare as follows.

• • Projection X-ray (radiography)

• • X-ray computed tomography (CT scan)

• • Nuclear medicine images (emissiontomographies like, single photon emission computedtomography (SPECT) and positron emissiontomography (PET))

• • Magnetic resonance imaging (MRI)

• • Ultrasound

There are also several other modalities of medicalimaging. In this chapter, only the above mentionedtechniques are discussed.

14.1 | Projection X-ray imaging

The X-ray imaging technique was discovered by WilhelmConrad Rontgen (inaugural Nobel Prize, 1901) in 1895in Wurzburg, Germany. In its basic form, themechanism for generation of X-ray consists of avacuum tube with a cathode and an anodeappropriately placed as illustrated in Fig. 14.1(a). A beam of electron that emanates from thecathode hits the anode at a very high speed.Depending upon the material of the surface in theanode, there are sub-atomic interactions due to thestriking of sub-atomic particles, which releaseenergy in the form of electromagnetic waves of acertain wavelength band, called X-rays.

QUEUES FEATURE IN our daily lives like never before. From the checkout counter in the community grocery store to customer support over the phone, queues are theatres of great social and engineering drama. Entire business operations of many leading companies are geared towards providing hassle-free customer support and experience – timely and effective resolution of client queries about services on a regular basis. Alternatively, it could be effective traffic management and resource optimization for a multiplex cinema operator involved in ticket sales. Sometimes it may not involve humans at all, like in the case of a database query to a computer server for specific information that may be routed through a job queue. How a queue moves in time and how services are offered over epochs determine how businesses will be able to make profit or how efficiently computer servers will execute tasks. All these have a huge technological and economical impact. No wonder we have seen huge investments by concerned stakeholders to upgrade and upscale hardware and software infrastructure to re-engineer queues towards greater system efficiency and profitability. The mathematical technology of queues is crafted out of models that investigate and replicate stochastic behavior of engineering systems. This is the subject of our study in this chapter.

DIFFRACTION

Diffraction is a phenomenon in which a light beam bends around the corner of an obstacle and spreads into the geometric shadow of that obstacle.

FRESNEL AND FRAUNHOFER DIFFRACTION

Diffraction can be classified into two categories:

• 1. Fresnel diffraction

• 2. Fraunhofer diffraction

The distinction between these two categories is as follows:

• a. In Fresnel diffraction, the screen and source are at a finite distance from an obstacle. The distances are important in this class. In Fraunhofer diffraction, the source and screen are at an infinite distance from an obstacle. Therefore, inclination is important.

• b. The incident wavefront in Fresnel diffraction is either spherical or cylindrical, whereas the incident wavefront in Fraunhofer diffraction is planar.

• c. In Fresnel diffraction, the central point of the screen is either bright or dark depending on the number of zones, whereas in Fraunhofer diffraction, the central point of the screen is always bright.

FRAUNHOFER DIFFRACTION DUE TO SINGLE SLIT

Let us consider a monochromatic light source of wavelength ƛ placed at the focus of convex lens L1. The collimated rays of plane wavefront are incident on a single-slit AB of width “e.” The un-deviated rays from the slit reaches at point O, and the rays diffracted by an angle θ reach at P on the screen, as shown in Figure 12.1.

The subject, Computer Vision, deals with the science ofimparting to a machine or a computer the capabilityof seeing and understanding the environment as wehumans are able to do, and seeks to apply itstheories and models in various applications of ourlife and society. From the late sixties of the lastcentury, there have been efforts in analyzingdigital images captured by a scanner or a camera.Initially, it was the 2-D digital geometry in adiscrete grid of integral coordinate space whichdrew primary attention of the researchers. Inparticular, Prof. Azriel Rosenfeld (1931–2004) ofthe University of Maryland, USA, took a leading andpioneering role in developing theories of digitalpicture processing. Subsequently, the area wasstrengthened by the development and application oftheories of mathematical morphology, textureprocessing, pattern recognition techniques, etc.However, the major development in the theory ofcomputer vision, following the psycho-physiologicalmodels of human vision, happened in the seventies ofthe last century, when Prof. David Marr (1945–1980)of the Massachusetts Institute of Technology (MIT),Cambridge, USA, hypothesized three stages ofprocessing and representation of images by primalsketches consisting of edges, regions, 2.5-Dsketches of the scene, and finally 3-D models.

Over the years, theories of computer vision have beendeveloped from different areas of mathematical andphysical sciences, such as digital geometry,projective geometry, differential geometry, linearand nonlinear systems, human cognition andpsycho-visual perception, color representation andprocessing, computational learning, patternrecognition, etc. As we see, the theoreticalfoundation of the subject has been built fromdifferent domains, and it requires to learn thefundamentals across these disciplines in asystematic and organized manner in the context ofcore agenda of computer vision, which is to solveproblems related to the understanding of a 3-Dscene, static or dynamic, given visual inputs fromimaging systems.