Showing papers on "Symmetry (physics) published in 1984"
TL;DR: In this paper, the authors derived similarity solutions which describe the collapse of cold, collisionless matter in a perturbed Einstein-de Sitter universe, and they obtained three classes of solutions, one each with planar, cylindrical, and spherical symmetry.
Abstract: We derive similarity solutions which describe the collapse of cold, collisionless matter in a perturbed Einstein-de Sitter universe. We obtain three classes of solutions, one each with planar, cylindrical, and spherical symmetry. Our solutions can be computed to arbitrary accuracy, and they follow the development of structure in both the linear and nonlinear regimes.
528 citations
TL;DR: In this paper, a system of gravity plus free massless matter fields in 4 + N dimensions is considered, and solutions in which N dimensions form a compact curved manifold, with the energy-momentum tensor responsible for the curvature produced by quantum fluctuations in the matter fields.
314 citations
TL;DR: In this paper, the authors derived explicit expressions for the terms up to and including R -5 in the R -1 expansion of the electrostatic energy of two molecules of arbitrary symmetry, in a simple form which is suitable for use in model potentials.
Abstract: The spherical multipole expansion has been used to derive explicit expressions for the terms up to and including R -5 in the R -1 expansion of the electrostatic energy of two molecules of arbitrary symmetry, in a simple form which is suitable for use in model potentials. We show also how the corresponding forces and torques can be readily derived from these energy expressions, and give explicitly the forces and torques which would be required for a molecular dynamics simulation of a fluid of linear molecules.
195 citations
TL;DR: In this paper, a pedagogical introduction to relaxation methods for the numerical solution of elliptic partial differential equations is given, with particular emphasis on treating nonlinear problems with delta-function source terms and axial symmetry, which arise in the context of Lagrangian approximations to the dynamics of quantized gauge fields.
Abstract: This article gives a pedagogical introduction to relaxation methods for the numerical solution of elliptic partial differential equations, with particular emphasis on treating nonlinear problems with delta-function source terms and axial symmetry, which arise in the context of effective Lagrangian approximations to the dynamics of quantized gauge fields. The authors present a detailed theoretical analysis of three models which are used as numerical examples: the classical Abelian Higgs model (illustrating charge screening), the semiclassical leading logarithm model (illustrating flux confinement within a free boundary or ''bag''), and the axially symmetric Bogomol'nyi-Prasad-Sommerfield monopoles (illustrating the occurrence of p topological quantum numbers in non-Abelian gauge fields). They then proceed to a self-contained introduction to the theory of relaxation methods and allied iterative numerical methods and to the practical aspects of their implementation, with attention to general issues which arise in the three examples. The authors conclude with a brief discussion of details of the numerical solution of the models, presenting sample numerical results.
190 citations
TL;DR: In this article, the authors proposed a scheme to construct a structure composed of anisotropic strata from reflection and transmission properties of individual interfaces using a slightly modified version of the recursion scheme of Kennett.
Abstract: Summary. The response of a structure composed of anisotropic strata can be built up from the reflection and transmission properties of individual interfaces using a slightly modified version of the recursion scheme of Kennett. This scheme is conveniently described in terms of scatterer operators and scatterer products. The effects of a free surface and the introduction of a simple point source at any depth can be accommodated in a manner directly analogous to the treatment for isotropic structures. As in the isotropic case the results so obtained are stable to arbitrary wavenumbers. For isotropic media, synthetic seismograms can be constructed by computing the structure response as a function of frequency and radial wavenumber, then performing the appropriate Fourier and Hankel transforms to obtain the wavefield in time-distance space. Such a scheme is convenient for any system with cylindrical symmetry (including transverse isotropy). Azimuthally anisotropic structures, however, do not display cylindrical symmetry; for these the transverse component of the wavenumber vector will, in general, be non-zero, with the result that phase, group, and energy velocities may all diverge. The problem is then much more conveniently addressed in Cartesian coordinates, with the frequency-wavenumber to time-distance transformation accomplished by 3-D Fourier transform.
186 citations
TL;DR: The role of symmetry in systems displaying period-doubling instabilities was examined in this article, where it was found that symmetric orbits will not undergo period doubling except in extraordinary cases.
Abstract: The role of symmetry is examined in systems displaying period-doubling instabilities. It is found that symmetric orbits will not undergo period doubling except in extraordinary cases. Such exceptional cases cannot occur in a large class of systems, including the sinusoidally driven damped pendulum and the Lorenz equations.
166 citations
CERN1
TL;DR: In this article, the authors investigated the possibility of spontaneous T violation arising from complex vacuum expectation values with calculable phases, assuming geometrical values, entirely determined by the symmetry of the scalar potential.
135 citations
TL;DR: In this paper, a reaction integral formula is derived from which an anisotropic reaction theorem (modified reciprocity theorem) is developed, and a reduction of the \hat{C} medium into a reciprocal medium is discussed including tensor symmetry attributes and limiting cases.
Abstract: Complex anisotropic media can generally be described by a 6 \times 6 macroscopic constitutive tensor \hat{C} Using \hat{C} properties, a reaction integral formula is derived from which an anisotropic reaction theorem (modified reciprocity theorem) is developed Reduction of the \hat{C} medium into a reciprocal medium is discussed including tensor symmetry attributes and limiting cases The anisotropic reaction theorem is utilized to derive a zero reaction theorem, and then treated in relation to the moment method Mutual and self-impedance elements of a network are also derived in terms of reaction integrals, symmetry covered using the anisotropic reaction theorem, and impedance elements related to moment calculations Use of spectral domain analysis is also covered
126 citations
TL;DR: The decay from the 23+ state at about 2-MeV excitation in the nuclei Ba140, Ce142, and Nd144, with 84 neutrons, was shown to be consistent with its identification as the lowest state of mixed symmetry in the U(5) limit of the neutron-proton version of the interacting-boson model as mentioned in this paper.
Abstract: The decay from the 23+ state at about 2-MeV excitation in the nuclei Ba140, Ce142, and Nd144, with 84 neutrons, is shown to be consistent with its identification as the lowest state of mixed symmetry in the U(5) limit of the neutron-proton version of the interacting-boson model.
121 citations
TL;DR: In this article, the ground reaction force symmetry during walking and running was investigated and the results showed that ground reaction forces varied with walking speed and stride length during running and walking, respectively.
Abstract: (1984). Ground Reaction Force Symmetry during Walking and Running. Research Quarterly for Exercise and Sport: Vol. 55, No. 3, pp. 289-293.
TL;DR: In this paper, translations of the scales of the Lu-Fano plots are introduced phenomenologically to bring out the symmetry of two-channel coupling, which leads to a phase renormalisation of the Coulomb basis wavefunctions of QDT, which eliminates the diagonal elements of Seaton's reactance matrix.
Abstract: Translations of the scales of the Lu-Fano plots are introduced phenomenologically to bring out the symmetry of two-channel coupling. These shifts in the ( nu i) space amount to a phase renormalisation of the Coulomb basis wavefunctions of QDT, which eliminates the diagonal elements of Seaton's reactance matrix. The off-diagonal element of the resulting matrix measures the effective coupling strength and the new origins of the Lu-Fano plot axes mark the extrema of channel admixture. In the continuous energy range, the parameters ( mu i, xi ) provide a compact expression of the cross section for any two-channel (one open and one closed) process, including the whole series of resonances due to the discrete states in the closed channel. A similar generalisation of the Beutler-Fano resonance formula has been previously achieved by Dubau and Seaton (1984).
TL;DR: In this paper, a generalization of Bloch's theorem for electronic states in flat space solids allows explicit diagonalization of tight binding models defined on the curved-space icosahedral crystal.
TL;DR: In this article, the elastic energy expression of de Gennes for non-chiral and chiral smectic-C phases is reformulated, and it is shown that the maximum size of a uniformly oriented sample is limited, not only by the chiral helix but also by a spontaneous bend of the layers.
Abstract: The elastic energy expression of de Gennes for the non-chiral and chiral smectic-C phases is reformulated, and it is shown that the maximum size of a uniformly oriented sample is limited, not only by the chiral helix but also by a spontaneous bend of the smectic layers. A description of the flexoelectric effects is given: 9 different vector fields are involved, and they all remain in non-chiral smectic-C phase. These vector fields are connected to the divergence terms in the elastic free energy. The complexity of the boundary conditions for ferroelectric liquid crystals is discussed, and the concepts ‘bookshelf geometry’ and ‘φ-can’ are introduced. It is shown how the φ-can may be used to describe various monostable and bistable configurations of smectic-C cells. The symmetry of the cell can determine the configuration. Some general rules concerning the optical behaviour of smectic-C cells are given.
TL;DR: In this paper, an optimization procedure for the design of laminated fiber-reinforced plates having midplane symmetry and subject to flexure is proposed, where strain energy is taken as the objective function.
Abstract: An optimization procedure is proposed for the design of laminated fiber-reinforced plates having midplane symmetry and subject to flexure. Strain energy is taken as the objective function, while th...
TL;DR: In this article, a new kind of Lagrangian symmetry is defined in such a way that the resulting set of symmetries coincides with the set of symmetry of its equations of motion.
Abstract: A new kind of Lagrangian symmetry is defined in such a way that the resulting set of Lagrangian symmetries coincides with the set of symmetries of its equations of motion. Several constants of motion may be associated to each of the new symmetry transformations. One example is presented.
TL;DR: In this article, the Boussinesq radiation stress is defined and found to depend directly on an acoustic nonlinearity parameter which characterizes the radiation-induced static strain, a stress-generalized non-linearity, and the energy density of the propagating wave.
Abstract: The general case of acoustic-radiation stress associated with quasi-compressional and quasi-shear waves propagating in infinite and semiinfinite lossless solids of arbitrary crystalline symmetry is studied. The Boussinesq radiation stress is defined and found to depend directly on an acoustic nonlinearity parameter which characterizes the radiation-induced static strain, a stress-generalized nonlinearity parameter which characterizes the stress nonlinearity, and the energy density of the propagating wave. Application of the Boltzmann-Ehrenfest principle of adiabatic invariance to a self-constrained system described by the nonlinear equations of motion allows the acoustic-radiation-induced static strain to be identified with a self-constrained variation in the time-averaged product of the internal energy density and displacement gradient. The time-averaged product is scaled by the acoustic nonlinearity parameter and represents the first-order nonlinearity in the virial theorem. Finally, the relationship between the Boussinesq and the Cauchy radiation stress is obtained in a closed three-dimensional form.
TL;DR: In this article, a self-consistent mean field (SCMF) theory is proposed to decompose the Lagrangian into semiclassical and residual interaction parts by imposing a condition that the dangerous term in Bogoliubov's sense should vanish.
Abstract: The dynamical symmetry breaking phenomena in the Nambu and Jona·Lasinio model are reexamined in the framework of a self· consistent mean·field (SCMF) theory. First, we formulate the SCMF theory in a lucid manner based on a successful decomposition of the Lagrangian into semiclassical and residual interaction parts by imposing a condition that "the dangerous term" in Bogoliubov's sense should vanish. Then, we show that the difference of the energy density between the super and normal phases, the correct expression of which the original authors failed to give, can be readily obtained by applying the SCMF theory. Furthermore, it is shown that the expression thus obtained is identical to that of the effective potential (E. P.) given by the path· integral method with an auxiliary field up to the one loop order in the loop expansion, then one finds a new and simple way to get the E. P. Some numerical results of the E. P. and the dynamically generated mass of fermion are also shown. As another demonstration of the powerfulness of the SCMF theory, we derive, in the Appendix, the energy density of the D(N ).¢4 model including the higher order corrections in the sense of large N expansion.
TL;DR: In this article, an extension of the field emission fluctuation method for studying the diffusion of adsorbates on metal surfaces to the measurement of anisotropic diffusion is described, which consists of using a long, narrow rectangular slit as probed region.
TL;DR: In this paper, the authors show how spontaneous breaking of a global U(1) symmetry, present, for instance, in the minimal SU(5) model, can lead to an inflationary phase.
Abstract: Phase transitions associated with spontaneously broken global symmetries, in case these occur in nature, can have important cosmological implications. This is illustrated through two examples. The first one shows how the spontaneous breaking of a global U(1) symmetry, present, for instance, in the minimal SU(5) model, can lead to an inflationary phase. The second example illustrates how topologically stable strings associated with the breaking of a U(1) symmetry make an appearance at (or near) the end of the inflationary era.
TL;DR: It is shown that a symmetry in an optimization problem induces a decomposition of the optimal feedback control law into factors, which gives a priori information about the structure of that law and indicates a possibly more efficient method for optimizing such systems.
Abstract: It is shown that a symmetry in an optimization problem induces a decomposition of the optimal feedback control law into factors. One factor can be calculated algebraically and depends only on the symmetry; the other factor corresponds to a lower dimensional optimization problem. This gives a priori information about the structure of the optimal feedback control law and indicates a possibly more efficient method for optimizing such systems.
TL;DR: In this article, a numerical solution method of Laplace's equation with cylindrical symmetry and mixed boundary conditions along the Z coordinate is presented for the evaluation of current density distribution in the region surrounding electrodes used for intracerebral electrical stimulations.
Abstract: A numerical solution method of Laplace’s equation with cylindrical symmetry and mixed boundary conditions along the Z coordinate is presented. The method is based on an iterative process. It is applied to the evaluation of current density distribution in the region surrounding electrodes used for intracerebral electrical stimulations. The procedure converges quickly and after only twelve iterations the boundary conditions are satisfied within an accuracy of 0.1%. The convergence criterion is discussed and the results obtained on the current density distribution are presented.
TL;DR: In this paper, it was shown that a Killing vector of the kinetic energy metric of a classical mechanical system can generate a symmetry of the system, and thus a constant of the motion.
TL;DR: In this paper, the wave field around each atom is expanded in symmetry-adapted functions where the local point symmetry of the atomic site applies, and for overlayer systems with more than one atom per unit cell symmetry adapted functions can be used when the division of the crystal into monoatomic subplanes is replaced by division into subplanes containing all symmetrically equivalent atomic positions.
Abstract: The calculation of LEED intensities in a spherical-wave representation can be substantially simplified by symmetry relations. The wave field around each atom is expanded in symmetry-adapted functions where the local point symmetry of the atomic site applies. For overlayer systems with more than one atom per unit cell symmetry-adapted functions can be used when the division of the crystal into monoatomic subplanes is replaced by division into subplanes containing all symmetrically equivalent atomic positions.
TL;DR: Magnetic coordinates for hydromagnetic equilibria are defined in this article which treat toroidal and straight helical plasmas equivalently and yet exploit the existence of a continuous symmetry to derive relations between various geometrical and physical qualities.
Abstract: Magnetic coordinates for hydromagnetic equilibria are defined which treat toroidal and ‘‘straight’’ helical plasmas equivalently and yet exploit the existence of a continuous symmetry to derive relations between various geometrical and physical qualities. This allows the number of equilibrium quantities which must be known to be reduced to a minimal, or primitive, set. Practical formulas for various quantities required in hydromagnetic stability calculations (interchange, ballooning, and global) are given in terms of this primitive set.
TL;DR: In this article, a model based on permutation symmetry that predicts 25 GeV ⩽ mt⩽ 35 GeV and mixing angles consistent with τB has been studied.
TL;DR: In this paper, a symmetry classification of the continuous vortices with broken axial symmetry is presented, and it is found that the discrete internal symmetry may in addition be broken in two inequivalent ways, producing two different continuous Vortices.
Abstract: New NMR measurements are reported on continuous $^{3}\mathrm{He}$-$A$ vortices in tilted magnetic fields. We introduce a symmetry classification of the continuous vortices with broken axial symmetry. It is found that the discrete internal symmetry may in addition be broken in two inequivalent ways, producing two different continuous vortices. Although NMR may not distinguish between these two vortices, the observed vortex satellite peak is well accounted for by spin waves localized in the soft core of such vortices.
TL;DR: In this paper, the authors investigated the hypothesis that the observed weak interactions are the residual interactions of quasi Goldstone fermions and showed that left-handed quarks and leptons arise from the spontaneous symmetry breaking U(6) → U(4) × SU(2) in a supersymmetric theory.
TL;DR: In this article, a general study of symmetry and stability of the fixed points of the quartic Hamiltonian of an order parameter field was made, and it was shown that when it exists, the stable fixed point is unique.
Abstract: We make a general study of symmetry and stability of the fixed points of the quartic Hamiltonian of an $n$-component field (or order parameter) for $n\ensuremath{
e}4$. Simple proofs of known results are given. Among new results, we show that when it exists the stable fixed point is unique; we give some precision on its symmetry and on its attractor basin.