Showing papers on "Symmetry (physics) published in 1982"
TL;DR: In this article, the authors investigated topological vacuum structures in models with spontaneous breaking of exact and approximate global symmetries and the cosmological evolution of the structure is discussed.
Abstract: Topological vacuum structures are investigated in models with spontaneous breaking of exact and approximate global symmetries. The cosmological evolution of the structure is discussed. A spontaneous breaking of an exact global U(1) symmetry gives rise to vacuum strings which can produce cosmological density fluctuations leading to galaxy formation. In a simplified axion model, the vacuum structures are strings connected by domain walls. They decay before they can dominate the universe.
359 citations
TL;DR: In this article, an investigation on novel lines is made into the problem of water waves according to the perfect-fluid model, with reference to wave motions in both two and three space dimensions and with allowance for surface tension.
Abstract: An investigation on novel lines is made into the problem of water waves according to the perfect-fluid model, with reference to wave motions in both two and three space dimensions and with allowance for surface tension. Attention to the Hamiltonian structure of the complete nonlinear problem and the use of methods based on infinitesimal-transformation theory provide a Systematic account of symmetries inherent to the problem and of corresponding conservation laws.The introduction includes an outline of relevant elements from Hamiltonian theory (§ 1.1) and a brief discussion of implications that the present findings may carry for the approximate mathematical modelling of water waves (§1.2). Details of the hydrodynamic problem are recalled in §2. Then in §3 questions about the regularity of solutions are put in perspective, and a general interpretation is expounded regarding the phenomenon of wave-breaking as the termination of smooth Hamil- tonian evolution. In §4 complete symmetry groups are given for several versions of the water-wave problem : easily understood forms of the main results are listed first in §4.1, and the systematic derivations of them are explained in §4.2. Conservation laws implied by the one-parameter subgroups of the full symmetry groups are worked out in §5, where a recent extension of Noether's theorem is applied relying on the Hamiltonian structure of the problem. The physical meanings of the conservation laws revealed in §5, to an extent abstractly there, are examined fully in §6 and various new insights into the water-wave problem are presented.In Appendix 1 the parameterized version of the problem is considered, covering cases where the elevation of the free surface is not a single-valued function of horizontal position. I n Appendix 2 a general method for finding the symmetry groups of free-boundary problems is explained, and the exposition includes the mathematical material underlying the particular applications in §§4 and 5.
253 citations
TL;DR: In this paper, the repulsive core of the nucleon-nucleon interaction was studied in the quark model and the resonating group equation was solved with the color Fermi-Breit interaction including a linear or quadratic confinement potential.
215 citations
TL;DR: This work focuses on axion models in which this “discrete” symmetry is embedded in the spontaneously broken continuous group of the theory, and describes how such models are constructed.
164 citations
159 citations
TL;DR: In this paper, the Kobayashi-Maskawa matrix is determined and the mass of the t quark is predicted for a six-quark-six-lepton standard model.
Abstract: We consider SU(2) x U(1) gauge models with an additional global symmetry of S/sub n/ type. In particular, we study S/sub 4/ symmetry for a six-quark--six-lepton standard model. We find that the Kobayashi-Maskawa matrix is completely determined and the mass of the t quark is predicted. Some of the results persist in S/sub n/ applied to n families. Restrictions on neutrino masses and mixings are given. Implications of CP and flavor nonconservation that arise in the neutral-Higgs-boson sector are discussed.
128 citations
TL;DR: In this article, the theory of part I is applied to prove several existence and non-existence results for special cases, such as if φ ⩾ 0 has rotational symmetry.
Abstract: The theory of part I is applied to prove several existence and non-existence results for special cases. If N = 3, a global classical solution of P° exists, if φ ⩾ 0 has rotational symmetry. If N ⩾ 4, global classical solutions of P° do not always exist.
121 citations
TL;DR: In this article, the authors considered the possibility that the family group may be a spontaneously broken continuous global symmetry, and they showed that the couplings of the associated Goldstone bosons to fermions can be sufficiently suppressed so as to satisfy the phenomenological bounds.
106 citations
TL;DR: In this article, the symmetry of the hydrogen-atom degeneracy is exploited to obtain an exact separation of the quadratic Zeeman interaction on the Fock hypersphere in momentum space, and hence a complete classification of levels in the weak field limit.
Abstract: The $O(4)$ symmetry of the hydrogen-atom degeneracy is exploited to obtain an exact separation of the quadratic Zeeman interaction on the Fock hypersphere in momentum space, and hence a complete classification of levels in the weak-field limit. The separation constant includes a double-minimum potential, and levels below the top of the barrier have an approximate $O(2)\ifmmode\times\else\texttimes\fi{}O(2)$ symmetry and vibrational structure. Levels above the top of the barrier have an approximate $O(3)$ symmetry, and a structure similar to that of an oblate symmetric top. The crossover between the two types of levels becomes sharper at high $n$, and is related to two different types of collective coupling of angular momentum and the Runge-Lenz vector.
92 citations
TL;DR: In this article, the scattering of waves by a circular crack in an elastic medium is solved by a direct integral equation method based on expansion of stresses and displacements on the crack surface in terms of trigonometric functions and orthogonal polynomials.
Abstract: The scattering of waves by a circular crack in an elastic medium is solved by a direct integral equation method. The solution method is based on expansion of stresses and displacements on the crack surface in terms of trigonometric functions and orthogonal polynomials. The expansion coefficients are related through an infinite matrix, and by contour integration the matrix elements are expressed in terms of finite integrals. The scattered far field is expressed explicitly in terms of simple functions and the displacement expansion coefficients. The system of equations is solved numerically, and extensive results are given both in the form of maps of the scattered far field and as scattering cross sections. Neither the method nor the specific results are restricted by any assumptions of symmetry.
TL;DR: In this paper, the analysis of preferred patterns of convection in spherical shells is extended to include the case of odd degrees l of spherical harmonics, and the preferred solution among I existing ones is determined for 1≥2 by a stability analysis.
Abstract: The analysis by Busse (1975) of preferred patterns of convection in spherical shells is extended to include the case of odd degrees l of spherical harmonics. In the general part of the paper only the property of spherical symmetry of the basic state is used. The results are thus applicable to all bifurcation problems with spherical symmetry. Except in the case 1 = 1 a pattern degeneracy of the linear problem exists, which is partly removed by the solvability conditions that are generated when nonlinear terms are taken into account as perturbations. In each of the cases 1 considered so far, at least 1 physically different solutions have been found. The preferred solution among I existing ones is determined for 1≥2 by a stability analysis. In the case l = 3 emphasized in this paper the axisymmetric solution is found to be always unstable, and the solution of tetrahedronal symmetry appears to be generally preferred. The latter result is rigorously established in the special case of a thin layer with nearly insulating boundaries treated in the second part of the paper.
TL;DR: In this article, four molecular organic crystals were proposed for applications in nonlinear optics (three-wave-mixing and electrooptic effects) : methyl - (2,4 - dinitrophenyl) - aminopropanoate (MAP), 2 - methyl - 4 - nitroaniline (MNA), 3 - methyl-4 - nitropyridine - 1 - oxyde (POM), and urea.
Abstract: We present four molecular organic crystals which were recently proposed for applications in nonlinear optics (three-wave-mixing and electrooptic effects) : methyl - (2,4 - dinitrophenyl) - aminopropanoate (MAP), 2 - methyl - 4 - nitroaniline (MNA), 3 - methyl - 4 - nitropyridine - 1 - oxyde (POM) and urea. The nonlinear efficiency of molecular organic crystals is seen to depend on the molecular hyperpolarizability and on the crystalline geometry. Both features are discussed and shown to lead, for crystal point groups of lower symmetry, to new structural relations between crystalline non linear coefficients. Each of the four molecular crystals discussed here are shown to have specific properties connected to different types of applications.
TL;DR: In this article, a new method is presented for the general solution of variational equations after projection onto eigenspaces of symmetry operators, where the minimum of the projected energy surface is found following a path in the direction of the steepest descent.
TL;DR: In this paper, the absorption spectrum of benzene vapor between 3020 and 3125 cm −1 was recorded at 297 and 204 K with Doppler-limited resolution using a difference-frequency laser spectrometer.
TL;DR: The derivatives with respect to hydrostatic pressure of the deep energy levels associated with substitutional point defects in GaAs are evaluated and are found to be considerably smaller than the corresponding derivative of the fundamental band-gap energy as discussed by the authors.
Abstract: The derivatives with respect to hydrostatic pressure of the deep energy levels associated with substitutional point defects in GaAs are evaluated and are found to be considerably smaller than the corresponding derivative of the fundamental band-gap energy A deep level can be driven out of the gap by pressure, depending on its site, symmetry, and nearness to a band edge The pressure dependence can be used to identify the site of a defect and the symmetry of its deep levels A combination of the energy of a deep level, its pressure dependence, a theory of deep-level energies (which need be no more accurate than \ifmmode\pm\else\textpm\fi{}06 eV), and the present theory eliminates all but a few point defects as candidates for producing a given level In GaAs, $E$ 2 is assigned to an As vacancy, $E$ 3 and $E$ 4 are probably associated with defect complexes, and $\mathrm{EL}$ 2 is very likely caused by either substitutional oxygen on an As site or As on a Ga site
TL;DR: An exact analytical solution for the attitude motion of a class of asymmetric dual-spin spacecraft which may be modeled as free systems of two rigid bodies, one asymmetric and one axisymmetric, was obtained in this article.
Abstract: An exact analytical solution is obtained for the attitude motion of a class of asymmetric dual-spin spacecraft which may be modeled as free systems of two rigid bodies, one asymmetric and one axisymmetric. The type system considered constitutes a gyrostat. The symmetry axis of the axisymmetric rigid body and either the axis of the largest, or that of the smallest, moment of inertia of the system are assumed to be parallel. Zero internal torque is assumed also. The integral of rotational angular momentum of the system, an integral of energy of the system and the constancy of the symmetry-axis component of rotational angular momentum of the symmetric body are used to reduce the solution of the problem to quadratures, which are evaluated in terms of Jacobian elliptic functions and elliptic integrals. Internal resonances, which may exist in imperfect spacecraft, are discussed. Resonance curves, constructed using the exact solution, are presented for a typical, asymmetric, dualspin spacecraft.
TL;DR: In this article, the coadjoint orbit method was used to construct a model of elementary particles endowed with internal structure using the co-junctive geometry of minimal coupling and conservation laws were derived for symmetric external Einstein-Yang-Mills fields.
TL;DR: In this paper, the eigenfield perturbation theory of R. L. Belford and co-workers results in a significant reduction on the amount of computer time required for the calculations compared to the full matrix solution to the spin Hamiltonian.
TL;DR: In this paper, the symmetry rules of Buckingham and Love (1970), relating the number of independent components of the indirect spin-spin coupling tensor J to the symmetry of the nuclear sites, are shown to require modification if the two nuclei are exchanged by a symmetry operation.
Abstract: The symmetry rules of Buckingham and Love (1970), relating the number of independent components of the indirect spin-spin coupling tensor J to the symmetry of the nuclear sites, are shown to require modification if the two nuclei are exchanged by a symmetry operation. In that case, the anti-symmetric part of J does not transform as a second-rank polar tensor under symmetry operations that interchange the coupled nuclei and may be called an anti-tensor. New rules are derived and illustrated by simple molecular models.
01 Jan 1982
TL;DR: In this paper, it is shown how the reduced dimensionality and the surface symmetry can produce some original properties in two-dimensional matter, such as order-disorder, solid-solid and gas-liquid transitions.
Abstract: Various two-dimensional phases are stable when adsorbed on crystalline surfaces. It is shown how the reduced dimensionality and the surface symmetry can produce some original properties in two-dimensional matter. The subject is illustrated by a few typical examples taken among the order-disorder, solid-solid and gas-liquid transitions.
TL;DR: In this paper, the behavior of stationary equilibrium solutions to the MHD equations possessing a well-defined symmetry to perturbations lacking that symmetry is explored and the results show that in these cases changes in solution topology are not accessible to small-parameter (epsilon) expansions, so that such expansions do not describe the full range of behavior.
Abstract: The behavior of stationary equilibrium solutions to the MHD equations possessing a well-defined symmetry to perturbations lacking that symmetry is explored. Two distinct situations of astrophysical interest are considered: solutions of the magnetostatic equations and of the magnetoconvection equations. The results show that in these cases changes in solution topology are not accessible to small-parameter (epsilon) expansions, so that such expansions do not describe the full range of behavior. In particular, finite-amplitude perturbations can lead to new stationary solutions possessing different symmetries from the initial solution.
TL;DR: In this article, a property of the symmetry axis of the metric describing a superposition of two Kerr·NUT solutions is examined, in order to ensure that the two constituent masses are dynamically balanced by the rotational repulsion against the gravitational attraction, and the total mass becomes positive.
Abstract: A property of the symmetry axis of the metric describing a superposition of two Kerr·NUT solutions is examined. We give some conditions to the parameters included in the metric, in order to assure that the two constituent masses are dynamically balanced by the rotational repulsion against the gravitational attraction, and the total mass becomes positive. It is shown that a suitable choice of the two NUT terms of the constituent solutions is especially important. The space-time structure of single black hole has been extensively studied. However, we have little knowledge about the metric which describes many interacting black holes. Usually, such a metric is dependent on time, and the radiation of gravitational waves cannot be neglected. There exists another possibility that several black holes align along their common rotational axis and take a stationary configuration due to the dynamical balance between the gravi tational attraction and the rotational repulsion. Recent investigationsi),2) of stationary and axi-symmetric solutions of the vacuum Einstein equation have presented an interesting class of metrics which may represent such an equilibrium configuration. It is obvious that these metrics can be interpreted as a nonlinear superposition of several Kerr-NUT solutions. However, on the symmetry (rotational) axis between the horizons of the Kerr-NUT constituents there may exist any weak singularities of violation of local Euclidean behavior. In order to see whether this superposition is physically acceptable or not, it is necessary to examine the space-time properties on the symmetry axis. The line element of stationary and axi-symmetric vacuum space-time can be written in the form
TL;DR: In this article, a common construction of the three-dimensional equivalents of these symmetry relations is presented, which is used to derive, in a geometric way applying simultaneously to different kinds of spin models, the consequent global properties, i.e., the commutativity of the transfer matrices and the inverse functional equations on the transfer matrix and the partition function.
Abstract: Symmetry relations such as the star-triangle or the inverse relation are very useful in determining the partition function of two-dimensional exactly soluble models. A common construction of the three-dimensional equivalents of these symmetry relations is presented. They are used to derive, in a geometric way applying simultaneously to different kinds of spin models, the consequent global properties, i.e. the commutativity of the transfer matrices and the inverse functional equations on the transfer matrix and the partition function. The usefulness of the inverse relation is illustrated by an application to the three-dimensional Ising model.
TL;DR: In this article, the authors examined the anisotropy of the internuclei magnetic interactions in condensed matter, namely the properties and the experimental measurement of the magnetic shielding tensor σ and of the indirect nuclear spin-spin coupling tensor J.
TL;DR: In this paper, the diffusion equations for interstitials and vacancies in the field of an edge dislocation are numerically solved within a theoretical model that takes into account the full lattice and defect symmetry in the migration jump.
Abstract: The diffusion equations for interstitials and vacancies in the field of an edge dislocation are numerically solved within a theoretical model that takes into account the full lattice and defect symmetry in the migration jump The defect concentration is calculated within two different approximations: In one, only the defect drift contribution to the diffusion is considered, while in the other, the drift and gradient terms are included as well as a constant defect generation rate In this second approximation the steady-state concentration is calculated The influence on the solutions of an external uniaxial stress with different orientations with respect to the dislocation is studied Numerical results for the dislocation sink strength are obtained for vacancies and interstitials in Cu These are compared with previous approximations in the literature The relevance of the results to the establishing of a radiation creep mechanism is discussed
TL;DR: In this article, a theoretical analysis of nonferroic phase transitions is presented, based on Landau's symmetry criteria for continuous transitons, of the order-parameter symmetries, space-group changes, and free-energy expansions.
Abstract: Nonferroic phase transitions are defined as the structural transitions occurring with a breaking of translational symmetry within the same crystal class. They involve no new macroscopic tensor components below the transition point, and they are generally identified experimentally through the onset of superlattice reflections denoting the multiplication of the crystal's unit cell. A theoretical analysis of these transitions is presented, based on Landau's symmetry criteria for continuous transitons, of the order-parameter symmetries, space-group changes, and free-energy expansions. We establish that the order parameters of such transitions are necessarily related to one-dimensional (real or complex) small representations of the group of the $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$ vector. Their symmetry characteristics are, in general, simpler than those of other types of structural transitions. Most of them possess a one-component order parameter inducing a doubling of the unit cell. The remaining ones are associated with order-parameter dimensions as high as six, and unit-cell multiplications up to thirty-two. The coupling of the order parameter to macroscopic quantities, illustrated by the example of dielectric ones, is shown to belong to two possible schemes. The relation between nonferroics and antiferroelectrics is discussed. The theoretical results are compared to the available experimental data which pertain mainly to organic compounds and metallic alloys.