Showing papers on "Symmetry (physics) published in 1975"
TL;DR: In this paper, a mathematical framework is developed to study the mechanical behavior of material surfaces, and the tensorial nature of surface stress is established using the force and moment balance laws using a linear theory with non-vanishing residual stress.
Abstract: A mathematical framework is developed to study the mechanical behavior of material surfaces. The tensorial nature of surface stress is established using the force and moment balance laws. Bodies whose boundaries are material surfaces are discussed and the relation between surface and body stress examined. Elastic surfaces are defined and a linear theory with non-vanishing residual stress derived. The free-surface problem is posed within the linear theory and uniqueness of solution demonstrated. Predictions of the linear theory are noted and compared with the corresponding classical results. A note on frame-indifference and symmetry for material surfaces is appended.
2,641 citations
TL;DR: In this article, it was shown that when the order parameter has a continuous symmetry, the ordered state is unstable against an arbitrarily weak random field in less than four dimensions and the borderline dimensionality above which mean-field-theory results hold is six.
Abstract: Phase transitions are considered in systems where the field conjugate to the order parameter is static and random. It is demonstrated that when the order parameter has a continuous symmetry, the ordered state is unstable against an arbitrarily weak random field in less than four dimensions. The borderline dimensionality above which mean-field-theory results hold is six. (auth)
1,911 citations
1,153 citations
TL;DR: In this article, an effective medium approximation for the conductivity tensor of a randomly inhomogeneous medium is generalized to treat, in principle, materials consisting of crystallites of arbitrary shape and conductivities tensors of arbitrary symmetry.
Abstract: An old effective-medium approximation for the conductivity tensor of a randomly inhomogeneous medium is generalized to treat, in principle, materials consisting of crystallites of arbitrary shape and conductivity tensors of arbitrary symmetry. The effective-medium approximation is roughly analogous to the coherent-potential approximation (CPA) of alloy theory. The analog of the average-$t$-matrix approximation (ATA) is also formulated in a general way. The method is fully tractable analytically for ellipsoidal crystallites. Several applications are discussed. The effective conductivity of a polycrystal consisting of randomly oriented uniaxial crystallites is calculated as a function of the anisotropy of the grains. For a model polycrystal in an intense magnetic field, the CPA and ATA are compared, the former giving more accurate results.
473 citations
303 citations
TL;DR: In this article, the properties of simple estimates based on equitailed order statistics are derived, such as transformation of exponential and gamma random variables, and errors in previous work are discovered and partially corrected.
Abstract: SUMMARY Transformations to symmetry, or approximate symmetry, are considered. In particular, properties of simple estimates based on equitailed order statistics are derived. Examples include transformation of exponential and gamma random variables. Errors in previous work are discovered and partially corrected.
252 citations
TL;DR: In this article, the motion of a slender axisymmetric rod-like particle is investigated for translation through a quiescent second-order fluid and for rotation in a simple shear flow of the same material.
Abstract: The motion of a slender axisymmetric rod-like particle is investigated theoretically for translation through a quiescent second-order fluid and for rotation in a simple shear flow of the same material. The analysis consists of an asymptotic expansion about the limit of rheologically slow flow, coupled with an application of a generalized form of the reciprocal theorem of Lorentz to calculate the force and torque on the particle. It is shown that an arbitrarily oriented particle with fore-aft symmetry translates, to a first approximation, at the same rate as in an equivalent Newtonian fluid, but that the motion of particles with no fore-aft symmetry may be modified at the same level of approximation. In addition, it is found that freely translating particles with fore-aft symmetry exhibit a single stable orientation with the axis of revolution vertical. In simple shear flow at small and moderate shear rates, the non-Newtonian nature of the suspending fluid causes a drift through Jeffery orbits to the equilibrium orbit C = 0 in which the particle rotates about its axis of revolution. At larger shear rates, the particle aligns itself in the direction of flow and ceases to rotate. Comparison with the available experimental data indicates that the measured rate of orbit drift may be used to determine the second normal stress difference parameter of the second-order fluid model. Finally, in an appendix, some preliminary observations are reported of the motion of slender rod-like particles falling through a quiescent viscoelastic fluid.
217 citations
TL;DR: The consequences of assuming weak and e.m. forces constitute a gauge field theory, and there are no heavy leptons, are investigated in this article, where a particular Higgs system containing two multiplets is studied in detail.
182 citations
TL;DR: In this paper, the Yang-Mills field theory was studied in a space with more than four dimensions, and the relation of this work to recent work on gravitation theory by Yang is explored.
Abstract: Gauge invariance is obtained as a consequence of the spontaneous breaking of a larger symmetry. The Yang--Mills gauge fields are the corresponding Nambu--Goldstone fields. This involves the study of field theories in a space with more than four dimensions. In a ''cylindrical'' sector these field theories reduce to new non-Abelian generalizations of Jordan--Brans--Dicke theory. The nonobservability of the excess dimensions (while a difficulty for theories in which these dimensions are bosonic) should cause no problems if the higher dimensions are fermionic. In the latter case, field theories in which all basic fields are at the same time Nambu--Goldstone and Yang--Mills fields become possible. The relation of this work to recent work on gravitation theory by Yang is explored.
169 citations
TL;DR: The application of symmetry analysis to uniform waveguides is discussed in this paper, where the minimum waveguide sectors which are necessary and sufficient to completely determine the modes of the various mode classes are presented.
Abstract: The application of symmetry analysis to uniform waveguides is discussed. Symmetry analysis provides exact information concerning mode classification, mode degeneracy, modal electromagnetic-field symmetries, and the minimum waveguide sectors which completely determine the modes in each mode class. Tables are presented which list the possible mode classes and their degeneracies for the two general symmetry families, C/sub n/ and C/sub nv/, of uniform waveguides. Tables showing the azimuthal dependence of the longitudinal components of the electric and magnetic fields for each mode class are given. Based on this azimuthal dependence, figures showing the minimum waveguide sectors which are necessary and sufficient to completely determine the modes of the various mode classes are presented. The application of symmetry analysis is illustrated by considering uniform waveguides with C/sub 4/ and C/sub 6v/ symmetry.
TL;DR: In this article, one-loop effective potentials for elementary systems placed in a strong magnetic or a laser-produced electromagnetic environment are computed for the case where the system can make transitions from a spontaneously broken asymmetric phase to restored symmetry.
TL;DR: In this article, a simple theorem is stated which gives conditions under which pseudo-Goldstone particles may occur in the context of gauge theories with spontaneous symmetry breakdown induced by the Higgs phenomenon, and these conditions are broader than the occurrence of accidental symmetry and contain the latter case as a special instance.
Abstract: In the context of gauge theories with spontaneous symmetry breakdown induced by the Higgs phenomenon, a simple theorem is stated which gives conditions under which pseudo-Goldstone particles may occur. These conditions are broader than the occurrence of accidental symmetry and contain the latter case as a special instance. We analyze an example in which the gross features of the vector- and the scalar-meson mass spectra are determined by quantum effects.
TL;DR: The particle motion of surface waves in a medium with a horizontal plane of symmetry has been observed on seismograms and used to indicate the presence of such anisotropy within the Upper Mantle as discussed by the authors.
Abstract: Summary Surface waves propagating along particular directions in anisotropic media may have one of three distinctive particle motions indicating orientations of planes of anisotropic symmetry with respect to the direction of propagation and the free surface. The particle motion of surface waves in a medium with a horizontal plane of symmetry has been observed on seismograms and used to indicate the presence of such anisotropy within the Upper Mantle.
TL;DR: In this paper, a method for the numerical calculation of the hydrodynamic evolution of a self-gravitating configuration in two space dimensions with assumed axial symmetry is described.
Abstract: A method is described for the numerical calculation of the hydrodynamic evolution of a self-gravitating configuration in two space dimensions with assumed axial symmetry. The calculation is formulated in cylindrical coordinates with respect to a moving Eulerian grid and is solved using explicit hydrodynamics combined with implicit radiative transfer. The physics included is appropriate for calculation of the collapse of a rotating protostellar cloud. The gravitational field is obtained by means of an alternating-direction iterative technique. Numerical tests to demonstrate the correctness of the method are presented for special cases.
TL;DR: In this article, the first-, second-and higher-order elastic constants of a crystalline solid were derived using homogeneous deformations, in which the energy density can be separated into contributions from many-body interactions of different order.
Abstract: The method of homogeneous deformations is used to derive expressions for the first-, second- and higher-order elastic constants of a crystalline solid in which the energy density can be separated into contributions from many-body interactions of different order. Volume-dependent terms in the energy density such as those due to the conduction electrons in a metal are also considered. Emphasis is laid on casting all results into a form which is manifestly rotationally invariant and on treating the structure-dependent and structure-independent terms on the same footing. A comparison is made between the results obtained using Lagrangian and infinitesimal strain with particular reference to the symmetry properties of the elastic constants. A new and general condition for the Cauchy relation to hold is obtained.
TL;DR: The requirement of total axial symmetry for a system of electromagnetic fields and dust in a spatially homogeneous space-time leads uniquely to a vector cosmology of Bianchi type VII/sub h/, for which the solution is found and analyzed as mentioned in this paper.
Abstract: The requirement of total (extrinsic and intrinsic) axial symmetry for a system of electromagnetic fields and dust in a spatially homogeneous space-time leads uniquely to a vector cosmology of Bianchi type VII/sub h/, for which the solution is found and analyzed. The model is a natural generalization of the standard Friedmann model. 14 references. (auth)
TL;DR: In this paper, the methods of Dashen, Hasslacher, and Neveu were applied to quantum field theories with continuous global symmetries, and it was shown that it is possible to project out a subspace of fixed charge, and to reformulate the theory as one with internal symmetry, but with centrifugal terms arising from rotation in the internal symmetry space.
Abstract: We apply the methods of Dashen, Hasslacher, and Neveu to quantum field theories with continuous global symmetries. With a U(1) symmetry we show that it is possible to project out a subspace of fixed charge, and to reformulate the theory as one with internal symmetry, but with centrifugal terms arising from rotation in the internal-symmetry space; in the weak-coupling regime, static solutions of this equivalent problem determine the energies of the bound states. Within a particular model in one spatial dimension we demonstrate the existence of such bound states and examine the dependence of their energies upon the charge. The extension of the method to non-Abelian groups is illustrated with SU(2) examples.
TL;DR: In this paper, symmetry rules are derived for relating convergent-beam electron-diffraction pattern symmetries to the three-dimensional symmetry of the structure of 2M biotite.
Abstract: Symmetry rules are derived for relating the convergent-beam electron-diffraction pattern symmetries to the three-dimensional symmetry of the structure. These rules are applied to a study of 2M biotite. As a result the space group is determined as C2, or number 5 in International Tables for X-ray Crystallography, whereas it was previously held, in the absence of accurate data, to belong to C2/c or number 15. In addition, a method is described for uniquely determining the centrosymmetry of a crystal independently of space group, hence resolving the ambiguity between a centre of symmetry and a twofold axis present when approximations to dynamic electron scattering are used which take into accoufit only the symmetry of the projection.
TL;DR: In this paper, parentage amplitudes for transfer of a (1p) 3 group with spatial symmetry are given for 1p shell targets with initial and final states represented by intermediate-coupling wave functions.
TL;DR: Chichester as mentioned in this paper describes a book on symmetry in a spectrum running from the gold mine to the jeweller's shop, where the goal is not to interest the reader in group theory, but to teach him how to apply it in realistic detail to nontrivial physical problems.
Abstract: Melvin Lax Chichester: J Wiley 1974 pp xi + 499 price £10.55 (cased) £6.80 (paperback) If good books on symmetry were assigned to a spectrum running from the gold mine to the jeweller's shop, then this one would definitely appear in the somewhat sparsely populated region right next to the gold mine. The title is to be taken literally, the realized aim being not to interest the reader in group theory, (several crucial theorems are quoted but not proved), but lo teach him by precept and example how to apply it in realistic detail to nontrivial physical problems.
05 Oct 1975
TL;DR: In this article, a linearized kinetic theory is outlined which leads to an integral expression for the general form of the relativistic plasma dispersion function, which provides important information on the expected symmetry of irradiation of fusion targets by focused electron beams.
Abstract: Equilibrium and monoenergetic distribution functions in the laboratory frame are derived from first principles. Thermodynamically consistent macroscopic properties of relativistic beam systems are defined and discussed as a foundation for specific applications. Characteristics of superpinched relativistic electron beams such as isotropy in the lab frame, rms cone angle of the electrons with respect to the beam axis, and the energy flux across a unit surface at an arbitrary angle to the beam axis are obtained. These properties provide important information on the expected symmetry of irradiation of fusion targets by focused electron beams. A linearized kinetic theory is outlined which leads to an integral expression for the general form of the relativistic plasma dispersion function.
TL;DR: In this paper, two-body absorptive parts generated by unitarity from multi-regge particle production models are tested with respect to duality and symmetry structure (suppression of exotics and exchange degeneracy in output).
TL;DR: In this article, the power spectral density of a laser subjected to a symmetry breaking injected signal is calculated via the quantum noise operator approach, and the resulting spectrum is sharpened in a manner reminiscent of the line narrowing which occurs in the Lamb-Mossbauer effect.