Christopher bindhu (220 risultati)

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Paperback. Condizione: new. Paperback. Vibrations, Dispersion, and Brillouin Zone in a Monoatomic LatticeThis book presents a clear and systematic exploration of vibrational motion in a one-dimensional monoatomic crystal, emphasizing how atomic arrangements and lattice periodicity determine the vibrational properties of solids. Beginning with the concept of lattice spacing and atomic displacements, it introduces the mathematical framework required to describe phonon behaviour and wave propagation in crystals.A major focus of the book is the First Brillouin Zone, the fundamental region in reciprocal space where all distinct wave vectors lie. The book explains why all physical phonon states are contained within-p/aand how any wave vector outside this range can be mapped back into it. This provides a deep understanding of the periodicity of the dispersion relation and the redundancy of k-values outside the Brillouin zone.The phonon dispersion relation for a monoatomic chain is carefully derived, showing how atomic forces lead to the frequency-wave-vector relationw=4Cmsin(ka2).The book explains how this relation governs the allowed vibrational frequencies, why phonons have a maximum cutoff frequency, and how the dispersion curve repeats in successive Brillouin zones.A detailed discussion of the long-wavelength limit demonstrates that for small values of kkk, the dispersion becomes linear, wk, \omega \propto k,wk, revealing that low-frequency lattice vibrations behave like ordinary sound waves.The concept of group velocity, vg=dw/dk=aCmcos(ka2), is introduced as the speed at which energy is carried through the lattice. The book explains why the group velocity becomes zero at the Brillouin zone boundary and reaches its maximum at the zone center.To strengthen understanding, the book includes: Clear conceptual explanationsShort answer questionsMultiple-choice questionsSimple numerical problems with step-by-step solutionsOverall, this book provides a complete and accessible introduction to phonon dynamics, reciprocal space, and lattice wave propagation in monoatomic crystals. It serves as an excellent resource for students of solid-state physics, materials science, and condensed matter physics, offering both conceptual clarity and mathematical insight. This item is printed on demand. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.…

PAP. Condizione: New. New Book. Shipped from UK. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000.

PAP. Condizione: New. New Book. Shipped from UK. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000.

Paperback. Condizione: new. Paperback. Vibrations of Crystals with Monatomic BasisThis book provides a detailed, concept-oriented introduction to the vibrational behavior of crystals that contain one atom per primitive cell. It explains how atoms arranged in a regular lattice can oscillate collectively, forming waves that propagate through the crystal. These vibrations play a fundamental role in determining the mechanical, thermal, and electronic properties of solids.The analysis begins by defining the displacement usu_sus of the sss-th atom from its equilibrium position and describing how entire atomic planes move in phase when a vibrational wave travels through the lattice. For any wave vector kkk, the system supports three vibrational modes-one longitudinal (parallel to the wave direction) and two transverse (perpendicular to the wave direction).To determine how these vibrations behave, the book introduces the elastic restoring forces acting between neighboring atoms. Assuming a linear response and nearest-neighbour interactions, the force on any atom depends on the difference in displacement between that atom and its adjacent planes. Applying Newton's second law leads to the fundamental equation of motion for the lattice.Using a harmonic trial solution us=Ae-iwtu_s = A e^{-i\omega t}us=Ae-iwt and expressing atomic displacements in terms of a wave vector, the book derives the dispersion relation: w2=2Cm(1-coska), \omega^2 = \frac{2C}{m}(1 - \cos ka),w2=m2C(1-coska), where CCC is the force constant, mmm is the atomic mass, aaa is the lattice spacing, and kkk is the wave vector.This relation describes how the vibrational frequency varies with kkk, showing that the frequency becomes zero at k=0k = 0k=0 (all atoms move together) and reaches a maximum at the boundary of the first Brillouin zone k=p/ak = \pm \pi/ak=p/a.Using trigonometric identities, this relation is rewritten as: w=4Cmsin(ka/2), \omega = \sqrt{\frac{4C}{m}} \sin(ka/2),w=m4Csin(ka/2), revealing the periodic nature of lattice vibrations. The book explains how this dispersion curve governs the propagation of vibrational energy, the group velocity, and the behaviour of low- and high-frequency modes.Overall, this book gives a complete understanding of lattice dynamics in simple monatomic crystals. It builds the foundation for advanced topics such as phonons, thermal conductivity, heat capacity, scattering processes, and vibrations in more complex crystal structures. This item is printed on demand. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.…

PAP. Condizione: New. New Book. Shipped from UK. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000.

Paperback. Condizione: new. Paperback. This book presents a comprehensive study on global warming, climate change, and the influence of the transportation sector on Kerala's regional climate. It explains the scientific basis of global warming, including the greenhouse effect, major greenhouse gases, and the rapid rise of atmospheric carbon dioxide due to human activities. Historical climate data, global CO2 trends, and the enhanced greenhouse effect are examined to show how rising emissions contribute to temperature increase, humidity amplification, and climate instability.The study provides a detailed overview of transportation-related emissions at global and regional scales, highlighting Kerala's high vehicle density and fuel consumption patterns. Using scientifically accepted fuel-to-CO2 conversion factors, the book quantifies annual emissions from private vehicles and evaluates their contribution to atmospheric CO2. The results show that even small increases in CO2 levels significantly intensify warming in warm, humid regions like Kerala.The scientific links between CO2 concentration, temperature rise, water vapour increase, and heavy rainfall are discussed using principles of climate physics. The book examines how warmer air holding more moisture leads to extreme rainfall events and connects these processes to the 2018 Kerala flood. This case study demonstrates how climate change, combined with human-induced vulnerabilities such as land-use changes, can magnify the severity of natural disasters.Public transport systems are analyzed as a key solution to reducing emissions. The book evaluates Kerala's existing transport infrastructure-including buses, railways, metro, and water transport-and discusses global best practices that can support a shift toward sustainable mobility. Policy recommendations, behavioural strategies, and climate mitigation measures are provided to help reduce transportation emissions and strengthen climate resilience.The book concludes that Kerala's future climate will depend strongly on present-day choices. Reducing CO2 emissions, strengthening public transport, improving urban planning, and adopting sustainable behaviours are essential to limit warming, reduce extreme rainfall, and protect future generations. This work aims to support scientific understanding, policy development, and informed decision-making to address one of the most pressing challenges of our time. This item is printed on demand. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. …

PAP. Condizione: New. New Book. Shipped from UK. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000.

Taschenbuch. Condizione: Neu. Neuware - This book presents the concepts of polarized light-linear, circular, and elliptical polarization-explained in a simple and detailed manner based on the approach used in Griffiths' Introduction to Electrodynamics. The ideas of how the electric field behaves in different types of polarization, why the electric field alone is used to define polarization, and how light interacts with matter are broken down into easy-to-understand explanations without complicated mathematics. Each concept is supported by clear examples, step-by-step reasoning, and a question-answer method that helps students learn actively rather than passively. To reinforce understanding, the book includes short-answer questions, long-answer questions, numerical problems, and a complete set of multiple-choice questions designed to test and strengthen conceptual clarity. Overall, this book is a student-friendly guide that simplifies Griffiths' electrodynamics ideas and makes the topic of polarization easy, visual, and engaging for learners.…

Paperback. Condizione: new. Paperback. This book is particularly suitable for students because it emphasizes: Simple, student-friendly explanationsStep-by-step derivationsImportant equations highlighted clearlyDefinitions followed by physical meaningConnection between mathematical equations and physical conceptsQuestion answers and MCQ for better conceptual understandingUseful revision material for examinationsSelf-learning without requiring lengthy textbook explanations This item is printed on demand. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.…

PAP. Condizione: New. New Book. Shipped from UK. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000.

Paperback. Condizione: new. Paperback. This book introduces the fundamental principles governing the motion of particles through the laws of conservation and energy. Beginning with Newton's Second Law, it derives the law of conservation of linear momentum, demonstrating that the momentum of a particle remains constant when no external force acts on it. The concept of angular momentum is then developed, establishing the relationship between torque and the time rate of change of angular momentum, leading to the law of conservation of angular momentum in the absence of external torque.The text explains the concepts of work, kinetic energy, and the Work-Energy Theorem, showing that the work done by the net force on a particle equals the change in its kinetic energy. It further distinguishes between conservative and non-conservative forces, emphasizing that conservative forces perform path-independent work and have zero work around a closed path.Using Stokes' theorem, the book shows that a conservative force field is irrotational and can be expressed as the negative gradient of a scalar potential function, thereby introducing potential energy. The relationship between work and potential energy naturally leads to the law of conservation of mechanical energy, which states that the sum of kinetic and potential energies remains constant in a conservative force field.To reinforce conceptual understanding, the book includes: Detailed mathematical derivations.Step-by-step physical explanations.Twenty-five conceptual short-answer questions.Twenty-five multiple-choice questions with answers for self-assessment.Designed in a concise microlearning format, this book serves as a quick yet comprehensive resource for undergraduate physics students studying Mechanics of a Particle, helping them develop both conceptual clarity and problem-solving skills. This item is printed on demand. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.…

PAP. Condizione: New. New Book. Shipped from UK. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000.

Paperback. Condizione: new. Paperback. This book provides a clear and systematic introduction to Virtual Displacement, the Principle of Virtual Work, and D'Alembert's Principle, which form the foundation of analytical mechanics. It explains the concept of virtual displacement, its mathematical representation, and its formulation using generalized coordinates. The text then develops the Principle of Virtual Work and presents its derivation, emphasizing its application to systems in equilibrium. The book further introduces D'Alembert's Principle by incorporating inertia forces, demonstrating how dynamic problems can be transformed into equivalent equilibrium problems, thereby laying the groundwork for the formulation of Lagrange's equations of motion.To support effective learning and university examination preparation, the book includes: Detailed conceptual explanations with mathematical derivations.Step-by-step derivations of the Principle of Virtual Work and D'Alembert's Principle.Conceptual learning questions with answers.Five-mark descriptive questions with answers.Multiple-choice questions (MCQs) for self-assessment.Designed in a concise microlearning format, this book serves as an effective learning resource for undergraduate and postgraduate students studying Classical Mechanics, Engineering Physics, and Analytical Mechanics. This item is printed on demand. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.…

PAP. Condizione: New. New Book. Shipped from UK. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000.

Paperback. Condizione: new. Paperback. This book presents a comprehensive introduction to Lagrange's equations of motion, one of the fundamental formulations of analytical mechanics. Starting from D'Alembert's principle, the derivation systematically introduces holonomic constraints, generalized coordinates, virtual displacement, and generalized force, leading to the formulation of the Lagrangian function.The book explains the derivation of Lagrange's equations for both conservative and non-conservative systems and highlights their interpretation as the generalized form of Newton's second law. Special emphasis is given to the physical meaning of generalized momentum, generalized force, and the advantages of the Lagrangian approach in analyzing constrained mechanical systems.To reinforce learning, the book includes: A step-by-step derivation of Lagrange's equations.Conceptual learning questions with answers.Multiple-choice questions (MCQs).Five-mark, eight-mark, and ten-mark university examination questions.Clear explanations suitable for undergraduate and postgraduate students.This concise microlearning resource serves as a valuable guide for mastering the principles of Lagrangian mechanics and preparing for university examinations. This item is printed on demand. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.…

PAP. Condizione: New. New Book. Shipped from UK. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000.

Paperback. Condizione: new. Paperback. This book is particularly suitable for students because it emphasizes: Simple, student-friendly explanationsStep-by-step derivationsImportant equations highlighted clearlyDefinitions followed by physical meaningConnection between mathematical equations and physical conceptsQuestion answers and MCQ for better conceptual understandingUseful revision material for examinationsSelf-learning without requiring lengthy textbook explanations This item is printed on demand. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.…

PAP. Condizione: New. New Book. Shipped from UK. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000.

Paperback. Condizione: new. Paperback. This book provides a clear and simple understanding of light reflection and mirrors, starting from basic concepts to real-life applications.It explains how light behaves when it strikes different surfaces and how mirrors form images. The content gradually builds from plane mirrors tocurved mirrors, making it easy for students to understand.Key Highlights of the Book: Simple explanations with real-life examplesClear distinction between concave and convex mirrorsStep-by-step understanding of image formationHands-on learning through the spoon experimentConcept reinforcement using question banks and MCQsPractical applications in daily life and technologyWhat Students Will Learn: Laws of reflection and types of reflectionHow images are formed in mirrorsDifferences between real and virtual imagesBehaviour of light (convergence & divergence)Applications of mirrors in everyday lifeOverall, this book connects theory + experiment + real life, making learning physics easy and interesting. This item is printed on demand. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.…