Gauge Fields in General Parametrical Approach and Their Finslerian Reduction

The covariance principle of general relativity is extended to internal space. Associated gauge fields and tensors are systematically described, whereupon the variational principle is set up for all gauge fields by applying a Palatini-type method, thereby giving rise to an attractive self-contained theory in which the Einstein equations are intrinsically synthesized with the generalized Yang-Mills equations. General gauge-covariant physical field equations are formulated, showing that currents, external + internal spin tensors, and energy-momentum tensors can be introduced unambiguously under these general conditions and that the associated conservation laws can be derived. The electromagnetic field finds its gauge-geometric origin as the gauge field related to internal densities. To be operative with the tensor indices of external and internal types, this general theory must be bimetric. The assumptions that the gauge-covariant derivatives of metric tensors should vanish simplify the theory to the level of a Finslerian gauge approach.     

A structure refinement strategy for NMR crystallography: an improved crystal structure of silica-ZSM-12 zeolite from 29Si chemical shift tensors

A strategy for performing crystal structure refinements with NMR chemical shift tensors is described in detail and implemented for the zeolite silica-ZSM-12 (framework type code MTW). The 29Si chemical shift tensors were determined from a slow magic-angle spinning spectrum obtained at an ultrahigh magnetic field of 21.1T. The Si and O atomic coordinate parameters were optimized to give the best agreement between experimentally measured and ab initio calculated principal components of the 29Si chemical shift tensors, with the closest Si-O, O-O, and Si-Si distances restrained to correspond with the distributions of the distances found in a set of single-crystal X-ray diffraction (XRD) structures of high-silica zeolites. An improved structure for the silica-ZSM-12 zeolite, compared to a prior structure derived from powder XRD data, is obtained in which the agreement between the experimental and calculated 29Si chemical shift tensors is dramatically improved, the Si-O, O-O, and Si-Si distances correspond to the expected distributions, while the calculated powder XRD pattern remains in good agreement with the experimental powder XRD data. It is anticipated that this "NMR crystallography" structure refinement strategy will be an important tool for the accurate structure determination of materials that are difficult to fully characterize by traditional diffraction methods.     

On the incorporation of cubic and hexagonal interfacial energy anisotropy in phase field models using higher order tensor terms

In this paper, we show how to incorporate cubic and hexagonal anisotropies in interfacial energies in phase field models; this incorporation is achieved by including up to sixth rank tensor terms in the free energy expansion, assuming that the free energy is only a function of coarse-grained composition, its gradient, curvature and aberration. We derive the number of non-zero and independent components of these tensors. Further, by demanding that the resultant interfacial energy is positive definite for inclusion of each of the tensor terms individually, we identify the constraints imposed on the independent components of these tensors. The existing results in the invariant group theory literature can be used to simplify the process of construction of some (but not all) of the higher order tensors. Finally, we derive the relevant phase field evolution equations and describe some preliminary results from our 1D simulations.     

The analysis of high field magnetoresistance data

In magnetoresistance measurements on compensated metals, both maxima and minima have been observed as the magnetic field B becomes perpendicular to the open orbit direction. In this paper we show that this is a natural consequence of the transformation of well known magnetoresistance tensors to the appropriate set of axes. The condition for observing a maximum or minimum is derived. A similar analysis applied to uncompensated metals indicates that there will always be a maximum in the magnetoresistance for B in an open orbit direction, unless B approaches the longitudinal situation, when the presence of open orbits can not be observed in either compensated or uncompensated metals.     

On a Relation Between the Bach Equation and the Equation of Geometrodynamics

The Bach equation and the equation of geometrodynamics are based on two quite different physical motivations, but in both approaches, the conformal properties of gravitation play the key role. In this paper we present an analysis of the relation between these two equations and show that the solutions of the equation of geometrodynamics are of a more general nature. We show the following non-trivial result: there exists a conformally invariant Lagrangian, whose field equation generalizes the Bach equation and has as solutions those Ricci tensors which are solutions to the equation of break geometrodynamics.     

Classification of the space-time curvature tensor,restricted case

Einstein field equations will be assumed in a certain restricted form. The problem to be solved consists, roughly, of the enumeration of all curvature tensors which satisfy these equations. Presented at the International Conference on Gravitation and Relativity, Copenhagen, July 1971.     

The momentum constraints of general relativity and spatial conformal isometries

Transverse-tracefree (TT-) tensors on (R ³,g _ab), withg _ab an asymptotically flat metric of fast decay at infinity, are studied. When the source tensor from which these TT tensors are constructed has fast fall-off at infinity, TT tensors allow a multipole-type expansion. Wheng _ab has no conformal Killing vectors (CKV's) it is proven that any finite but otherwise arbitrary set of moments can be realized by a suitable TT tensor. When CKV's exist there are obstructions — certain (combinations of) moments have to vanish — which we study.Supported by Fonds zur Förderung der wissenschaftlichen Forschung in Österreich, Project No. P9376-PHY.Partially supported by Forbairt Grant SC/94/225.     

Second-order scalar-tensor field equations in a four-dimensional space

Lagrange scalar densities which are concomitants of a pseudo-Riemannian metric-tensor, a scalar field and their derivatives of arbitrary order are considered. The most general second-order Euler-Lagrange tensors derivable from such a Lagrangian in a four-dimensional space are constructed, and it is shown that these Euler-Lagrange tensors may be obtained from a Lagrangian which is at most of second order in the derivatives of the field functions.     

The dual curvature tensors and dynamics of gravitomagnetic matter

Gravitomagnetic charge that can also be referred to as the dual mass or magnetic mass is the topological charge in gravity theory. A gravitomagnetic monopole at rest can produce a stationary gravitomagnetic field. Due to the topological nature of gravitomagnetic charge, the metric of spacetime where the gravitomagnetic matter is present will be nonanalytic. In this paper both the dual curvature tensors (which can characterize the dynamics of gravitational charge/monopoles) and the antisymmetric gravitational field equation of gravitomagnetic matter are presented. We consider and discuss the mathematical formulation and physical properties of the dual curvature tensors and scalar, antisymmetric source tensors, dual spin connection (including the low‐motion weak‐field approximation), dual vierbein field as well as dual current densities of gravitomagnetic charge. It is shown that the dynamics of gravitomagnetic charge can be founded within the framework of the above dual quantities. In addition, the duality relationship in the dynamical theories between the gravitomagnetic charge (dual mass) and the gravitoelectric charge (mass) is also taken into account in the present paper.     

Comments on57Fe Mössbauer spectra for Kramers doublets: A phenomenological interpretation

A static effective spinS=1/2 Hamiltonian is usually specified by a phenomenonological parameter, set, but the typical choice of parameters could be inappropriate. Two main issues are addressed: (i) Which spin Hamiltonian parameters are observable at a given applied field strength, and (ii) how should one deal with skewsymmetric components of the electronic Zeeman and magnetic hyperfine tensors that can be present for spin-coupled multinuclear complexes. Certain Mössbauer experiments were selected, somewhat arbitrarily, as examples; this analysis can be applied to other spectroscopic techniques as well.     

New curvature-torsion relations through decomposition of the Bianchi Identities

The Bianchi Identities relating asymmetric curvature to torsion are obtained as a new set of equations governing second-order curvature tensors. The usual contribution of symmetric curvature to the gravitational field is found to be a subset of these identities though with an added contribution due to torsion gradients. The antisymmetric curvature two-tensor is shown to be related to the divergence of the torsion. Using a model of particle-antiparticle pair production, identification of certain torsion components with electroweak fields is proposed. These components obey equations, similar to Maxwell's, that are subsets of these linear Bianchi identities. These results are shown to be consistent with gauge and other previous analyses.     

Two-dimensional chemical-shift tensor correlation spectroscopy. Analysis of sensitivity and optimal measurement directions

Chemical-shift tensors can be determined from a single crystal placed in six or more orientations in a magnetic field. The sensitivity of this determination as a function of the selected crystal orientations is considered with a statistical figure of merit. A variety of configurations is examined, and it is found that the set of six orientations based on the vertices of an icosahedron optimizes the figure of merit and results in the most sensitive determination of the tensor. The relationship of these optimal orientations to those used previously in two-dimensional chemical-shift tensor correlation spectroscopy is discussed. It is shown that the high symmetry of the icosahedron simplifies the design on which the construction of a new sample orienting mechanism may be based.     

Magnetostatic stresses on a superconductor in a dielectric fluid

Summary The stresses which act on the surface of a superconductor surrounded by an isotropic dielectric fluid at rest are evaluated. Moreover, it is proved that there exists an infinite set of second-order tensors which yield these stresses. The magnetic Helmoltz stress tensor belongs to this set.     

Current exchanges and unconstrained higher spins

The (Fang–) Fronsdal formulation for free fully symmetric (spinor-) tensors rests on (γ  -) trace constraints on gauge fields and parameters. When these are relaxed, glimpses of the underlying geometry emerge: the field equations extend to non-local expressions involving the higher-spin curvatures, and with only a pair of additional fields an equivalent “minimal” local formulation is also possible. In this paper we complete the discussion of the “minimal” formulation for fully symmetric (spinor-) tensors, constructing one-parameter families of Lagrangians and extending them to (A)dS$(A)\mathit{dS}$ backgrounds. We then turn on external currents, that in this setting are subject to conventional conservation laws and, by a close scrutiny of current exchanges in the various formulations, we clarify the precise link between the local and non-local versions of the theory. To this end, we first show the equivalence of the constrained and unconstrained local formulations, and then identify a unique set of non-local Lagrangian equations which behave in the same fashion in current exchanges.     

Symmetric Variations of the Metric and Extrema of the Action for Pure Gravity

Symmetries of generalized gravitational actions, yielding field equations which typically involve at most second-order derivatives of the metric, are considered. The field equations for several different higher-derivative theories in the first-order formalism are derived, and variations of a generic set of higher-order curvature terms appearing in string effective actions are studied. It is shown that there often exists a particular set of solutions to the field equations of pure gravity theories, consisting of different combinations of curvature tensors, which satisfies the vacuum equations with cosmological constant. Implications of generalized symmetries of the field equations derived from the superstring effective action for the cosmological constant problem are discussed.     

Group-theoretical method for physical property tensors of quasicrystals

In addition to the phonon variable there is the phason variable in hydrodynamics for quasicrystals. These two kinds of hydrodynamic variables have different transformation properties. The phonon variable transforms under the vector representation, whereas the phason variable transforms under another related representation. Thus, a basis (or a set of basis functions) in the representation space should include such two kinds of variables. This makes it more difficult to determine the physical property tensors of quasicrystals. In this paper the group-theoretical method is given to determine the physical property tensors of quasicrystals. As an illustration of this method we calculate the third-order elasticity tensors of quasicrystals with five-fold symmetry by means of basis functions. It follows that the linear phonon elasticity is isotropic, but the nonlinear phonon elasticity is anisotropic for pentagonal quasicrystals. Meanwhile, the basis functions are constructed for all noncrystallographic point groups of quasicrystals.     

String Theory and the Velo–Zwanziger problem

We examine the behavior of the leading Regge trajectory of the open bosonic string in a uniform electromagnetic background and present a consistent set of Fierz–Pauli conditions for these symmetric tensors that generalizes the Argyres–Nappi spin-2 result. These equations indicate that String Theory does bypass the Velo–Zwanziger problem, i.e. the loss of causality experienced by a massive high-spin field minimally coupled to electromagnetism. Moreover, we provide some evidence that only the first Regge trajectory can be described in isolation and show that the open-string spectrum is free of ghosts in weak constant backgrounds. Finally, we comment on the roles of the critical dimension and of the gyromagnetic ratio.     

Invariant tensors inSU(3). II

InvariantSU(3) octet tensors are constructed in terms of matrices and applied to the problem of forming tensors from a single octet used repeatedly. Next a similar problem but with two octets is considered which demonstrates that different outer products of invariant tensors may be related. Finally, a theorem is proved which shows that the number of invariant tensors is essentially finite, and that relations of ranks greater than six exist on outer products of these tensors.     

Metric construction by length distribution tensor and edge based error for anisotropic adaptive meshing

Metric tensors play a key role to control the generation of unstructured anisotropic meshes. In practice, the most well established error analysis enables to calculate a metric tensor on an element basis. In this paper, we propose to build a metric field directly at the nodes of the mesh for a direct use in the meshing tools. First, the unit mesh metric is defined and well justified on a node basis, by using the statistical concept of length distribution tensors. Then, the interpolation error analysis is performed on the projected approximate scalar field along the edges. The error estimate is established on each edge whatever the dimension is. It enables to calculate a stretching factor providing a new edge length distribution, its associated tensor and the corresponding metric. The optimal stretching factor field is obtained by solving an optimization problem under the constraint of a fixed number of edges in the mesh. Several examples of interpolation error are proposed as well as preliminary results of anisotropic adaptation for interface and free surface problem using a level set method.     

A new gravitational energy tensor

The Bel-Robinson tensor is the most used gravitational energy tensor; however, it has the dimensions of energy squared. How to construct tensors with the dimensions of energy by using Lancoz tensors is shown here. The resulting tensors have a large number of arbitrary parameters, frequently have spacelike currents, and frequently do not reduce to familiar pseudo-energy tensors in the weak field limit. Two particular examples of interest are one with well-behaved currents and one which reduces to an energy pseudo-tensor in the weak field limit.