The Levi-Civita spacetime

We consider two exact solutions of Einstein's field equations corresponding to a cylinder of dust with net zero angular momentum. In one of the cases, the dust distribution is homogeneous, whereas in the other, the angular velocity of dust particles is constant [1]. For both solutions we studied the junction conditions to the exterior static vacuum Levi-Civita spacetime. From this study we find an upper limit for the energy density per unit length $\sigma$ of the source equal ${1\over 2}$ for the first case and ${1\over 4}$ for the second one. Thus the homogeneous cluster provides another example [2] where the range of $\sigma$ is extended beyond the limit value ${1\over 4}$ previously found in the literature [3,4]. Using the Cartan Scalars technics we show that the Levi-Civita spacetime gets an extra symmetry for $\sigma={1\over 2}$ or ${1\over 4}$. We also find that the cluster of homogeneous dust has a superior limit for its radius, depending on the constant volumetric energy density $\rho_0$

Multiple Photonic Shells Around a Line Singularity

Line singularities including cosmic strings may be screened by photonic shells until they appear as a planar wall.Comment: 6 page

Quasi-BiHamiltonian Systems and Separability

Two quasi--biHamiltonian systems with three and four degrees of freedom are presented. These systems are shown to be separable in terms of Nijenhuis coordinates. Moreover the most general Pfaffian quasi-biHamiltonian system with an arbitrary number of degrees of freedom is constructed (in terms of Nijenhuis coordinates) and its separability is proved.Comment: 10 pages, AMS-LaTeX 1.1, to appear in J. Phys. A: Math. Gen. (May 1997

Levi-Civita cylinders with fractional angular deficit

The angular deficit factor in the Levi-Civita vacuum metric has been parametrized using a Riemann-Liouville fractional integral. This introduces a new parameter into the general relativistic cylinder description, the fractional index {\alpha}. When the fractional index is continued into the negative {\alpha} region, new behavior is found in the Gott-Hiscock cylinder and in an Israel shell.Comment: 5 figure

Revealing the secrets of composite helmets of ancient Japanese tradition

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Evaluation of a sampling method for Xylella fastidiosa detection in olive trees

To assess the presence of the xylem-limited bacterium Xylella fastidiosa subsp. pauca strain CoDiRO in olive trees, a specific sampling method was evaluated. Symptomatic and symptomless plants were randomly selected in four olive orchards located in the province of Lecce (Southern Italy). The crown of each plant was subdivided into a lower and an upper portion; four samples were collected from each layer in the main four cardinal directions. A total of eight samples per plant, composed of one- or two-year-old asymptomatic twigs, were collected next to branches showing leafscorch symptoms. In this preliminary study, the null hypothesis was tested. i.e. there is no difference between the lower and the upper portions of the tree canopy and across the four cardinal directions. Samples (472), collected from 60 plants belonging to 11 different olive cultivars, were tested by qPCR. Out of 236 samples taken from the upper and lower parts of the canopy only 38.1% of lower samples, in contrast to 56.8% taken from the upper crown layer, were positive to the bacterium,. The McNemar test determined that there is a statistically significant difference in the proportion of positive samples between the upper and lower crown (p < 0.001). The Cochran’s Q test was performed to evaluate differences in the four cardinal directions. The null hypothesis suggesting there is no difference across cardinal directions was confirmed (p = 0.097). Based on these preliminary results, it appears that sampling should be directed to the upper part of the canopy. However, further studies are needed to improve the efficiency of the sampling technique

The Geometry of Integrable and Superintegrable Systems

The group of automorphisms of the geometry of an integrable system is considered. The geometrical structure used to obtain it is provided by a normal form representation of integrable systems that do not depend on any additional geometrical structure like symplectic, Poisson, etc. Such geometrical structure provides a generalized toroidal bundle on the carrier space of the system. Non--canonical diffeomorphisms of such structure generate alternative Hamiltonian structures for complete integrable Hamiltonian systems. The energy-period theorem provides the first non--trivial obstruction for the equivalence of integrable systems

Gyroscope precession in cylindrically symmetric spacetimes

We present calculations of gyroscope precession in spacetimes described by Levi-Civita and Lewis metrics, under different circumstances. By doing so we are able to establish a link between the parameters of the metrics and observable quantities, providing thereby a physical interpretation for those parameters, without specifying the source of the field.Comment: 13 pages, Latex. To appear in Class.Q.Gra

Experimental test for extra dimensions in Kaluza-Klein gravity

5D Kaluza-Klein gravity has several nonasymptotically flat solutions which generally, possessed both electric and magnetic charges. In this paper we suggest that these solutions can act as quantum virtual handles (wormholes) in spacetime foam models. By applying a sufficently large, external electric and/or magnetic field it may be possible to ``inflate'' these solutions from a quantum to a classical state. This effect would lead to a possible experimental signal for higher dimensions in multidimensional gravity.Comment: 11 pages, 3 PS.figures, REVTEX, the quality of the figures are improve

On the physical meaning of Fermi coordinates

(Some Latex problems should be removed in this version) Fermi coordinates (FC) are supposed to be the natural extension of Cartesian coordinates for an arbitrary moving observer in curved space-time. Since their construction cannot be done on the whole space and even not in the whole past of the observer we examine which construction principles are responsible for this effect and how they may be modified. One proposal for a modification is made and applied to the observer with constant acceleration in the two and four dimensional Minkowski space. The two dimensional case has some surprising similarities to Kruskal space which generalize those found by Rindler for the outer region of Kruskal space and the Rindler wedge. In perturbational approaches the modification leads also to different predictions for certain physical systems. As an example we consider atomic interferometry and derive the deviation of the acceleration-induced phase shift from the standard result in Fermi coordinates.Comment: 11 pages, KONS-RGKU-94/02 (Latex