Classification of Petrov Type D Generalized Kerr-Schild Transformations

We study the Petrov type D Generalized Kerr-Schild vacuum space-times. If the background is a Minkowski space-time the resulting Kerr-Schild metrics are classified, while if we start from a Petrov type D background we first put restrictions on the possible perturbation null directions. It is then shown that the GKS metrics are different from the background if the null direction has nonvanishing expansion or twist, otherwise the transformation is merely a change of coordinates.     

Aubry-Mather sets and Birkhoff's theorem for geodesic flows on the two-dimensional torus

In this paper we state the graph property for incompressible continuouse tori invariant under goedesic flows of Riemannian metrics on the two-dimensional torus. Also our method gives a new proof of Birkhoff's theorem for twist maps of the cylinder. We prove that if there exist an invariant incompressible torus of geodesic flow with irrational rotation number then it necessarily contains the Aubry-Mather set with this rotation number.     

Single kerr-schild metrics: A double view

Real-vacuum single Kerr-Schild (ISKS) metrics are discussed and new results proved. It is shown that if the Weyl tensor of such a metric has a twist-free expanding principal null direction, then it belongs to the Schwarzschild family of metrics — there are no Petrov type-II Robinson-Trautman metrics of Kerr-Schild type. If such a metric has twist then it belongs either to the Kerr family or else its Weyl tensor is of Petrov type II. The main part of the paper is concerned with complexified versions of Kerr-Schild metrics. The general real ISKS metric is written in double Kerr-Schild (IDKS) form. TheH andl potentials which generate IDKS metrics are determined for the general vacuum ISKS metric and given explicitly for the Schwarzschild and Kerr families of metrics.     

Kerr metric in the deSitter background

In addition to the Kerr metric with cosmological constant Λ several other metrics are presented giving a Kerr-like solution of Einstein’s equations in the background of deSitter universe. A new metric of what may be termed as rotating deSitter space-time—a space-time devoid of matter but containing null fluid with twisting null rays, has been presented. This metric reduces to the standard deSitter metric when the twist in the rays vanishes. Kerr metric in this background is the immediate generalization of Schwarzschild’s exterior metric with cosmological constant.     

TypeN twisting vacuum gravitational fields

For vacuum, typeN, twisting gravitational fields the Einstein field equations reduce to partial differential equations for two functions, one real, the other complex, which may be regarded as initial data on a localJ ⁺. If it is assumed that in some frame these initial data take on a certain product form, one factor involving only a spatial variable, the other only a retarded time variable, then these equations become relatively tractable and reduce further to two ordinary differential equations. Rejecting all solutions which lead to Minkowski space or to zero twist leaves just two possibilities. One corresponds to the only explicitly known spacetime of the kind, namely that of Hauser. The other leads to new typeN twisting metrics. However, these metrics can be constructed explicitly only once a single nonlinear third-order ordinary differential equation has been solved.     

Stability of minimal periodic orbits

Symplectic twist maps are obtained from a Lagrangian variational principle. It is well known that nondegenerate minima of the action correspond to hyperbolic orbits of the map when the twist is negative definite and the map is two-dimensional. We show that for more than two dimensions, periodic orbits with minimal action in symplectic twist maps with negative definite twist are not necessarily hyperbolic. In the proof we show that in the neighborhood of a minimal periodic orbit of period n, the nth iterate of the map is again a twist map. This is true even though in general the composition of twist maps is not a twist map.     

An estimate of higher twist at small x_{\mathrmB} and low Q^2 based upon a Saturation Model

We investigate the influence of higher twist corrections to deep inelastic structure functions in the low- and small-x HERA region. We review the general features of the lowest-order QCD diagrams which contribute to twist-4 at small-x, in particular the sign structure of longitudinal and transverse structure functions which offers the possibility of strong cancellations in . For a numerical analysis we perform a twist analysis of the saturation model which has been very successful both in describing the structure function and the DIS diffractive cross section at HERA. As the main conclusion, twist 4 corrections are not small in or but in they almost cancel. This indicates the limitation on the use of the DGLAP formalism at small x and . We point out that analysis needs a large twist-4 correction. We also indicate the region of validity of the twist expansion. Received: 20 March 2000 / Published online: 9 August 2000     

Radiometry and Radiation Efficiency of Twisted Gaussian Schell-Model Sources

Wavefields endowed with the coherence-induced property of optical twist have recently attracted a good deal of theoretical and experimental attention. We present the generalized radiometric theory of fields generated by twisted Gaussian Schell-model sources. The effects introduced by the novel, rotationally symmetric, twist phenomenon in the radiant intensity, generalized radiance, radiant emittance (irradiance), and the radiation efficiency are assessed. The radiance becomes directionally skewed as a result of the twist, whereas the radiant intensity remains axially symmetric. The twist reduces the radiation efficiency and broadens the radiation distribution, in agreement with the notion that the twist decreases the effective coherence. Several special cases, such as quasihomogeneous sources, are analyzed in detail. The radiometric results, which are physically consistent with the superposition models of twisted sources, are demonstrated by illustrative examples.     

Multiple-Pomeron splitting in QCD—A novel antishadowing effect in coherent dijet production on nuclei

We discuss the salient features of the Pomeron splitting mechanism for coherent diffraction of pions into hard dijets on nuclei. Our findings include antishadowing multiple-Pomeron splitting expansion for diffractive amplitudes, exact cancellation of nuclear attenuation, and broadening/antishadowing effects to leading twist and parameter-free perturbative calculation of nuclear-rescattering-driven higher twist correction. We comment on the pQCD interpretation of the E791 results on diffractive dijets.     

Normal forms for pseudo-Riemannian 2-dimensional metrics whose geodesic flows admit integrals quadratic in momenta

We discuss pseudo-Riemannian metrics on 2-dimensional manifolds such that the geodesic flow admits a nontrivial integral quadratic in velocities. We construct local normal forms of such metrics. We show that these metrics have certain useful properties similar to those of Riemannian Liouville metrics, namely:

•

they admit geodesically equivalent metrics;     

Extracting DNA twist rigidity from experimental supercoiling data

We use an elastic rod model with contact to study the extension versus rotation diagrams of single supercoiled DNA molecules. We reproduce quantitatively the supercoiling response of overtwisted DNA and, using experimental data, we obtain an estimate of the effective supercoiling radius and of the twist rigidity of B-DNA. We find that the twist rigidity of DNA seems to vary widely with the nature and concentration of the salt buffer in which it is immersed.     

Nuclear effects and higher twists in F3 structure function

We analyze the CCFR collaboration iron target data on the xF₃ structure function making particular emphasis on the extraction of the higher twist contributions from the data. Corrections for nuclear effects are applied in order to extract data on the structure function of the isoscalar nucleon. Our analysis confirms the observation made earlier, that the higher twist terms depend strongly on the level to which QCD perturbation theory analysis is applied. We discuss the impact of nuclear effects on the higher twist term as well as on the QCD scale parameter extracted from the fit to data. Received: 4 August 2000 / Accepted: 17 September 2000     

Naturally reductive homogeneous Randers spaces

In this paper, we study naturally reductive Randers metrics on homogeneous manifolds. We first prove that naturally reductive Randers metrics are of Berwald type. We then give an explicit formula for the flag curvature of naturally reductive Randers metrics. Finally a necessary and sufficient condition for invariant Randers metrics on homogeneous manifolds being naturally reductive is given.     

Twist phase-induced polarization changes in electromagnetic Gaussian Schell-model beams

Electromagnetic Gaussian Schell-model (EGSM) beam with twist phase (i.e., twisted EGSM beam) is introduced as an extension of its scalar version based on the unified theory of coherence and polarization. We show how analytical paraxial propagation formulae of isotropic and anisotropic EGSM beams passing through a general astigmatic ABCD optical system can be modified in the presence of the twist phase. Numerical examples demonstrate that the twist phase affects the spectral density, the state of coherence, and the degree of polarization of EGSM beams on propagation.     

Spectral flow of non-hermitian Heisenberg spin chain with complex twist

We investigate the spectral flow of the integrable non-hermitian Heisenberg spin chain under boundary conditions with complex twist angle. It is shown that the period of the spectral flow is 4π up to a certain critical imaginary twist, beyond which the period jumps successively to higher values. We argue that this phenomenon caused by non-hermitian properties of the system is closely related to the metal-insulator transition caused by non-hermitian hoppings for the one-dimensional insulator.     

Geometrically-controlled twist transitions in nematic cells

We study geometrically controlled twist transitions of a nematic confined between a sinusoidal grating and a flat substrate. In these cells, the transition to the twisted state is driven by surface effects. We have identified the mechanisms responsible for the transition analytically and used exact numerical calculations to study the range of surface parameters where the twist instability occurs. Close to these values, the cell operates under minimal external fields or temperature variations.     

Laplacian eigenvalue functionals and metric deformations on compact manifolds

In this paper, we investigate critical points of the eigenvalues of the Laplace operator considered as functionals on the space of Riemannian metrics or a conformal class of metrics on a compact manifold. We introduce a natural notion of the critical metric of such a functional and obtain necessary and sufficient conditions for a metric to be critical. We derive specific consequences concerning possible locally maximizing metrics. We also characterize critical metrics of the ratio of two consecutive eigenvalues.     

Symmetries of Taub-NUT Dual Metrics

In this paper we study the symmetries of thedual Taub-nut metrics. Generic and non-genericsymmetries of dual Taub-nut metrics are investigated.The existence of the Runge-Lenz type symmetry isanalyzed for dual Taub-nut metrics. We find that in somecases the symmetries of the dual metrics are the samewith the symmetries of Taub-nut metric.     

Twisting carbon nanotubes: A molecular dynamics study

We simulate the twist of carbon nanotubes using atomic molecular dynamic simulations. The ultimate twist angle per unit length and the deformation energy are calculated for nanotubes of different geometries. It is found that the thick tube is harder to be twisted while the thin tube exhibits higher ultimate twisting ratio. For multi-walled nanotubes, the zigzag tube is found to be able to stand more deformation than the armchair one. We observed the surface transformation during twisting. Formation of structural defects is observed prior to fracture.