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Books on the topic 'Symmetric tensor'

Author: Grafiati

Published: 4 June 2021

Last updated: 18 February 2022

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1

Baerheim, Reidar. Coordinate free representation of the hierarchically symmetric tensor of rank 4 in determination of symmetry. [Utrecht: Faculteit Aardwetenschappen, Universiteit Utrecht], 1998.

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2

Tensor categories. Providence, Rhode Island: American Mathematical Society, 2015.

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3

A, Lohe M., ed. Quantum group symmetry and q-tensor algebras. Singapore: World Scientific, 1995.

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4

Griffith, J. S. The irreducible tensor method for molecular symmetry groups. Mineola, NY: Dover Publications, 2006.

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5

Conference on Hopf Algebras and Tensor Categories (2011 University of Almeria). Hopf algebras and tensor categories: International conference, July 4-8, 2011, University of Almería, Almería, Spain. Edited by Andruskiewitsch Nicolás 1958-, Cuadra Juan 1975-, and Torrecillas B. (Blas) 1958-. Providence, Rhode Island: American Mathematical Society, 2013.

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6

Spherical tensor operators: Tables of matrix elements and symmetries. Singapore: World Scientific, 1990.

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7

Isett, Philip. The Divergence Equation. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691174822.003.0006.

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This chapter introduces the divergence equation. A key ingredient in the proof of the Main Lemma for continuous solutions is to find special solutions to this divergence equation, which includes a smooth function and a smooth vector field on ³, plus an unknown, symmetric (2, 0) tensor. The chapter presents a proposition that takes into account a condition relating to the conservation of momentum as well as a condition that reflects Newton's law, which states that every action must have an equal and opposite reaction. This axiom, in turn, implies the conservation of momentum in classical mechanics. In view of Noether's theorem, the constant vector fields which act as Galilean symmetries of the Euler equation are responsible for the conservation of momentum. The chapter shows proof that all solutions to the Euler-Reynolds equations conserve momentum.

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8

Cates, M. Complex fluids: the physics of emulsions. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198789352.003.0010.

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These lectures start with the mean field theory for a symmetric binary fluid mixture, addressing interfacial tension, the stress tensor, and the equations of motion (Model H). We then consider the phase separation kinetics of such a mixture: coalescence, Ostwald ripening, its prevention by trapped species, coarsening of bicontinuous states, and the role of shear flow. The third topic addressed is the stabilization of emulsions by using surfactants to reduce or even eliminate the interfacial tension between phases; the physics of bending energy, which becomes relevant in the latter case, is then presented briefly. The final topic is the creation of long-lived metastable emulsions by adsorption of colloidal particles or nanoparticles at the fluid–fluid interface; alongside spherical droplets, these methods can be used to create a range of unconventional structures with potentially interesting properties that are only now being explored.

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9

Biedenharn, L. C., and M. A. Lohe. Quantum Group Symmetry and Q-Tensor Algebras. WORLD SCIENTIFIC, 1995. http://dx.doi.org/10.1142/2815.

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10

Kachelriess, Michael. Spacetime symmetries. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198802877.003.0006.

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This chapter introduces tensor fields, covariant derivatives and the geodesic equation on a (pseudo-) Riemannian manifold. It discusses how symmetries of a general space-time can be found from the Killing equation, and how the existence of Killing vector fields is connected to global conservation laws.

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11

V, Popov S., ed. Encyclopedia of material tensors on CD. Chichester: Wiley, 1999.

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12

Mann, Peter. Classical Electromagnetism. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0027.

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In this chapter, Noether’s theorem as a classical field theory is presented and the properties of variations are again discussed for fields (i.e. field variations, space variations, time variations, spacetime variations), resulting in the Noether condition. Quasisymmetries and spontaneous symmetry breaking are discussed, as well as local symmetry and global symmetry. Following these definitions, Noether’s first theorem and Noether’s second theorem are developed. The classical Schrödinger field is investigated and the key equations of classical mechanics are summarised into a single Lagrangian. Symmetry properties of the field action and equations of motion are then compared. The chapter discusses the energy–momentum tensor, the Klein–Utiyama theorem, the Liouville equation and the Hamilton–Jacobi equation. It also discusses material science, special orthogonal groups and complex scalar fields.

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13

Steigmann, David J. Elements of plasticity theory. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198567783.003.0013.

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Chapter 13 develops the modern theory for finite elastic-plastic deformations. It covers dissipation and highlights the role of the Eshelby tensor, and recovers the classical theory for isotropic materials using material symmetry arguments. Also developed are the equations of classical slip-line theory for plane-strain deformations.

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14

Kachelriess, Michael. Spin-1 and spin-2 fields. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198802877.003.0007.

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Massive and massless spin-1 and spin-2 fields, their field equations and propagators are studied. The connection between local gauge symmetry and the coupling to a conserved current is derived in the massless case. The dynamical stress tensor is defined as source of gravity, and its local conservation is shown. The basic ideas of large extra dimensions is outlined in an appendix.

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15

Newnham, Robert E. Properties of Materials. Oxford University Press, 2004. http://dx.doi.org/10.1093/oso/9780198520757.001.0001.

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Crystals are sometimes called 'Flowers of the Mineral Kingdom'. In addition to their great beauty, crystals and other textured materials are enormously useful in electronics, optics, acoustics and many other engineering applications. This richly illustrated text describes the underlying principles of crystal physics and chemistry, covering a wide range of topics and illustrating numerous applications in many fields of engineering using the most important materials today. Tensors, matrices, symmetry and structure-property relationships form the main subjects of the book. While tensors and matrices provide the mathematical framework for understanding anisotropy, on which the physical and chemical properties of crystals and textured materials often depend, atomistic arguments are also needed to quantify the property coefficients in various directions. The atomistic arguments are partly based on symmetry and partly on the basic physics and chemistry of materials. After introducing the point groups appropriate for single crystals, textured materials and ordered magnetic structures, the directional properties of many different materials are described: linear and nonlinear elasticity, piezoelectricity and electrostriction, magnetic phenomena, diffusion and other transport properties, and both primary and secondary ferroic behavior. With crystal optics (its roots in classical mineralogy) having become an important component of the information age, nonlinear optics is described along with the piexo-optics, magneto-optics, and analogous linear and nonlinear acoustic wave phenomena. Enantiomorphism, optical activity, and chemical anisotropy are discussed in the final chapters of the book.

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16

Deruelle, Nathalie, and Jean-Philippe Uzan. Conservation laws. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0045.

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This chapter studies how the ‘spacetime symmetries’ can generate first integrals of the equations of motion which simplify their solution and also make it possible to define conserved quantities, or ‘charges’, characterizing the system. As already mentioned in the introduction to matter energy–momentum tensors in Chapter 3, the concepts of energy, momentum, and angular momentum are related to the invariance properties of the solutions of the equations of motion under spacetime translations or rotations. The chapter explores these in greater detail. It first turns to isometries and Killing vectors. The chapter then examines the first integrals of the geodesic equation, and Noether charges.

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17

Emam, Moataz H. Covariant Physics. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198864899.001.0001.

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This book is an introduction to the modern methods of the general theory of relativity, tensor calculus, space time geometry, the classical theory of fields, and a variety of theoretical physics oriented topics rarely discussed at the level of the intended reader (mid-college physics major). It does so from the point of view of the so-called principle of covariance; a symmetry that underlies most of physics, including such familiar branches as Newtonian mechanics and electricity and magnetism. The book is written from a minimalist perspective, providing the reader with only the most basic of notions; just enough to be able to read, and hopefully comprehend, modern research papers on these subjects. In addition, it provides a (hopefully short) preparation for the student to be able to conduct research in a variety of topics in theoretical physics; with particular emphasis on physics in curved spacetime backgrounds. The hope is that students with a minimal mathematical background in calculus and only some introductory courses in physics may be able to study this book and benefit from it.

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18

Boudreau, Joseph F., and Eric S. Swanson. Quantum field theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198708636.003.0024.

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Markov chain Monte Carlo techniques are developed to compute properties of a variety of quantum field theories. The method is introduced with a simple scalar field theory and used to evaluate the particle spectrum and phase diagram for parity symmetry breaking. The technique of micorcanonical updating is introduced to increase efficiency. The important topic of gauge theory is then introduced via the gauged Z2 model. Development of the gauge theory formalism continues with Abelian gauge theory in two dimensions. The interaction between static charges is computed and compared to the exact result. The string tension in nonableian SU(2) gauge theory is explored with the aid of the renormalization group, which gives an entrée to a discussion of the Higgs mechanism. Finally, the formalism for including fermions is briefly reviewed.

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19

Sunderkötter, Cord, and Luis Requena. Panniculitides. Oxford University Press, 2013. http://dx.doi.org/10.1093/med/9780199642489.003.0165.

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Panniculitis is an inflammation that originates primarily in the subcutaneous fatty tissue (panniculus adiposus). It is associated with rheumatological diseases and with adverse events to rheumatological therapies (e.g. poststeroid panniculitis, erythema nodosum, infective panniculitis). The panniculitides are classified histopathologically into mostly septal panniculitis and mostly lobular panniculitis, according to the major or denser localization of the infiltrate, and also into those with or without vasculitis. Additional criteria involve the composition of the inflammatory infiltrate, the cause, and an underlying or associated disease. The clinical hallmarks of panniculitis are subcutaneous nodules or plaques, often located on the lower limb. A deep excisional biopsy is often required for a more precise diagnosis, given the often sparse and monotonous clinical symptoms. Erythema nodosum is the most common form and a typical example of septal panniculitis. It occurs in response to many different provoking factors, the most common trigger in children being a 'strep throat', in adults sarcoidosis. Clinically, it presents with a sudden symmetrical appearance of painful, tender, warm, erythematous nodes or plaques, usually on the shins, which resemble bruises. Classical and cutaneous polyarteriitis nodosa present a mostly septal panniculitis associated with vasculitis. Here subcutaneous, partially ulcerating nodules are surrounded by livedo racemosa. The mostly lobular panniculitides not associated with vasculitis include lupus panniculitis (lupus erythematosus profundus, typically with ensuing lipoatrophy and predilection for the upper part of the body), panniculitis in dermatomyositis (often calcifiying), cold panniculitis, pancreatic panniculitis, panniculitis due toα‎-antitrypsin deficiency, poststeroid panniculitis (in children after rapid withdrawal of corticosteroids), calciphylaxis (with and without renal failure), and factitious panniculitis (after mechanical, physical, or chemical injuries to the subcutaneous tissue, often self-inflicted). Nodular vasculitis (formerly erythema induratum Bazin) is a lobular panniculitis with vasculitis involving mostly the small blood vessels of the fat lobule. It appears to present a (hyper)reactive response to certain infections (tuberculosis, streptococci, candida) or to cold exposure or chronic venous insufficiency in susceptible females. In conclusion, the panniculitides are a heterogenous group of diseases requiring a systematic work-up and knowledge of certain histological or clinical criteria.

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