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In den WarenkorbZustand: New. pp. 200.
Zustand: New. pp. 200.
Zustand: New. pp. 200.
Anbieter: Revaluation Books, Exeter, Vereinigtes Königreich
EUR 9,11
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In den WarenkorbPaperback. Zustand: Brand New. 104 pages. 8.50x5.50x0.24 inches. In Stock.
EUR 6,31
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In den WarenkorbPaperback. Zustand: Brand New. 88 pages. 8.50x5.50x0.20 inches. In Stock.
Anbieter: Revaluation Books, Exeter, Vereinigtes Königreich
EUR 9,37
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In den WarenkorbPaperback. Zustand: Brand New. B, Tharun (illustrator). 41 pages. 8.00x5.25x0.10 inches. In Stock.
Sprache: Englisch
Verlag: Printed at catholic press Fatima road Kottamukku p o,kollam Pin 691013,published by A K Publications ,Mangadu P O,Kollam,Pin 691015, 2018
ISBN 10: 9352675487 ISBN 13: 9789352675487
Anbieter: Revaluation Books, Exeter, Vereinigtes Königreich
EUR 7,04
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In den WarenkorbPaperback. Zustand: Brand New. 57 pages. 11.00x8.50x0.13 inches. In Stock.
EUR 11,85
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In den WarenkorbPaperback. Zustand: Brand New. 59 pages. 8.50x5.50x0.14 inches. In Stock.
Sprache: Englisch
Verlag: Medtech Science Press, New Delhi, 2019
ISBN 10: 9388716272 ISBN 13: 9789388716277
Anbieter: Books in my Basket, New Delhi, Indien
Soft cover. Zustand: New. ISBN:9789388716277.
Zustand: New.
Anbieter: Revaluation Books, Exeter, Vereinigtes Königreich
EUR 15,23
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In den WarenkorbPaperback. Zustand: Brand New. 106 pages. 8.50x5.50x0.27 inches. In Stock.
Zustand: New. pp. 140.
Anbieter: Revaluation Books, Exeter, Vereinigtes Königreich
EUR 18,08
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In den WarenkorbPaperback. Zustand: Brand New. 108 pages. 8.50x5.50x0.25 inches. In Stock.
Anbieter: Biblios, Frankfurt am main, HESSE, Deutschland
Zustand: New. pp. 140.
Sprache: Englisch
Verlag: Shipra Publications, Delhi, 2022
ISBN 10: 9391978290 ISBN 13: 9789391978297
Anbieter: Books in my Basket, New Delhi, Indien
Hardcover. Zustand: New. ISBN:9789391978297,viii+132pp.
Sprache: Malayalam
Verlag: Notion Press Media Pvt Ltd, 2021
ISBN 10: 1684947618 ISBN 13: 9781684947614
Anbieter: California Books, Miami, FL, USA
Zustand: New.
Zustand: New.
Anbieter: Revaluation Books, Exeter, Vereinigtes Königreich
EUR 23,06
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In den WarenkorbPaperback. Zustand: Brand New. 79 pages. 8.50x5.50x0.18 inches. In Stock.
Anbieter: Vedams eBooks (P) Ltd, New Delhi, Indien
Hardcover. Zustand: New. 'Alternative Education' concept is a contemporary one and is a continuation of non-formal education and its branches. The subject matter related to Alternative Education is scattered. This book attempts to consolidate the needed information and focuses on getting a comprehensive idea about Alternative Education, its concept, philosophy, agencies involved, curriculum, systems of education etc. Thus the book conceptualise all the factors involved in Alternative Education. This book is suitable for learning Alternative Education for scholars, teacher educators and students of Education.
Verlag: Mittal Publications
ISBN 10: 9390692156 ISBN 13: 9789390692156
Anbieter: Majestic Books, Hounslow, Vereinigtes Königreich
EUR 11,82
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In den WarenkorbZustand: New. pp. 300.
Verlag: Mittal Publications
ISBN 10: 9390692156 ISBN 13: 9789390692156
Anbieter: Books Puddle, New York, NY, USA
Zustand: New. pp. 300.
Verlag: Ess Ess Publications
ISBN 10: 9392594348 ISBN 13: 9789392594342
Anbieter: Majestic Books, Hounslow, Vereinigtes Königreich
EUR 13,08
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In den WarenkorbZustand: New.
Verlag: Ess Ess Publications
ISBN 10: 9392594348 ISBN 13: 9789392594342
Anbieter: Books Puddle, New York, NY, USA
Zustand: New.
Verlag: Mittal Publications
ISBN 10: 9390692156 ISBN 13: 9789390692156
Anbieter: Biblios, Frankfurt am main, HESSE, Deutschland
Zustand: New. pp. 300.
Verlag: Ess Ess Publications
ISBN 10: 9392594348 ISBN 13: 9789392594342
Anbieter: Biblios, Frankfurt am main, HESSE, Deutschland
Zustand: New.
Anbieter: Grand Eagle Retail, Bensenville, IL, USA
Paperback. Zustand: 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. Zustand: New. New Book. Shipped from UK. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000.
Anbieter: Grand Eagle Retail, Bensenville, IL, USA
Paperback. Zustand: 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.
Anbieter: PBShop.store US, Wood Dale, IL, USA
PAP. Zustand: New. New Book. Shipped from UK. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000.
Anbieter: Revaluation Books, Exeter, Vereinigtes Königreich
EUR 18,26
Anzahl: 2 verfügbar
In den WarenkorbPaperback. Zustand: Brand New. 82 pages. Malayalm language. 5.50x0.20x8.50 inches. In Stock.