On the phenomenology of tachyon radiation

We present a brief overview of the different kinds of electromagnetic radiations expected to come from (or to be induced by) space-like sources (tachyons). New domains of radiation are here considered, and the possibility of experimental observation of tachyons via electromagnetic radiation is discussed.     

A modified large number theory withconstant G

The inspiring “numerology” uncovered by Dirac, Eddington, Weyl,et al. can be explained and derived when it is slightly modified so to connect the “gravitational world” (cosmos) with the “strong world” (hadron), rather than with the electromagnetic one. The aim of this note is to show the following. In the present approach to the “Large Number Theory,” cosmos and hadrons are considered to be (finite)similar systems, so that the ratio \({{\bar R} \mathord{\left/ {\vphantom {{\bar R} {\bar r}}} \right. \kern-0em} {\bar r}}\) of the cosmos typical length \(\bar R\) to the hadron typical length \(\bar r\) is constant in time (for instance, if both cosmos and hadrons undergo an expansion/contraction cycle—according to the “cyclical bigbang” hypothesis—then \(\bar R\) and \(\bar r\) can be chosen to be the maximum radii, or the average radii). As a consequence, then gravitational constantG results to be independent of time. The present note is based on work done in collaboration with P. Caldirola, G. D. Maccarrone, and M. Pav?i?.     

Antiparticles from special Relativity with ortho-chronous and antichronous Lorentz transformations

Special Relativity can be based on the whole proper group of both ortho- and antichronous Lorentz transformations, and a clear physical meaning can be given also to antichronous (i.e., nonorthochronous) Lorentz transformations. From the active point of view, the latter requires existence, for any particle, of its antiparticle within a purely relativistic, classical context. From the passive point of view, they give rise to frames dual to the ordinary ones, whose properties—here briefly discussed—are linked with the fact that in relativity it is impossible to teach another, far observer (by transmitting only instructions, and no physical objects) our own conventions about the choices right/left, matter/antimatter, and positive/negative time direction. Interesting considerations follow, in particular, by considering—as it is the case—theCPT operation as an actual (even if antichronous) Lorentz transformation.Work partially supported by FAPESP and CNPq (Brazil).     

A generalization of Dirac nonlinear electrodynamics,and spinning charged particles

In this paper—dedicated to Prof. Asim O. Barut—we generalize the Diracnon-linear electrodynamics by introducing two potentials(namely, the vector potential A and the pseudo-vector potential ⁵B of the electromagnetic theorywith charges and magnetic monopoles) and by imposing the pseudoscalar part of the product * to be zero, with A+⁵B. We show that the field equations of such a theory possess a soliton-like solution which can representa priori a charged particle, since it is endowed with a Coulomb field plus the field of a magneticdipole. The rest energy of the soliton is finite, and the angular momentum stored in its electromagnetic field can be identified—for suitable choices of the parameters—with the spin of the charged particle. Thus, this approach seems to yield a classical model for the charged (spinning) particle which does not encounter the problems met by earlier attempts in the same direction.Work partially supported by INFN, CNR, MURST and by FUNREI and CNPq.     

A Velocity Field and Operator for Spinning Particles in (Nonrelativistic) Quantum Mechanics

Starting from the formal expressions of the hydrodynamical (or local) quantities employed in the applications of Clifford algebras to quantum mechanics, we introduce—in terms of the ordinary tensorial language—a new definition for the field of a generic quantity. By translating from Clifford into tensor algebra, we also propose a new (nonrelativistic) velocity operator for a spin-1/2 particle. This operator appears as the sum of the ordinary part p/m describing the mean motion (the motion of the center-of-mass), and of a second part associated with the socalled Zitterbewegung, which is the spin internal motion observed in the center-of-mass from (CMF). This spin component of the velocity operator is nonzero not only in the Pauli theoretical framework, i.e., in the presence of external electromagnetic fields with a nonconstant spin function, but also in the Schrödinger case, when the wavefunction is a spin eigenstate. Thus, one gets even in the latter case a decomposition of the velocity field for the Madelung fluid into two distinct parts, which constitutes the nonrelativistic analogue of the Gordon decomposition for the Dirac current. Explicit calculations are presented for the velocity field in the particular cases of the hydrogen atom, of a spherical well potential, and of an electron in a uniform magnetic field. We find, furthermore, that the Zitterbewegung motion involves a velocity field which is solenoidal, and that the local angular velocity is parallel to the spin vector. In the presence of a nonuniform spinvector (Pauli case) we have, besides the component of the local velocity normal to the spin (present even in the Schrödinger theory), also a component which is parallel to the curl of the spin vector.     

Refined beam elements with only displacement variables and plate/shell capabilities

This paper proposes a refined beam formulation with displacement variables only. Lagrange-type polynomials, in fact, are used to interpolate the displacement field over the beam cross-section. Three- (L3), four- (L4), and nine-point (L9) polynomials are considered which lead to linear, quasi-linear (bilinear), and quadratic displacement field approximations over the beam cross-section. Finite elements are obtained by employing the principle of virtual displacements in conjunction with the Unified Formulation (UF). With UF application the finite element matrices and vectors are expressed in terms of fundamental nuclei whose forms do not depend on the assumptions made (L3, L4, or L9). Additional refined beam models are implemented by introducing further discretizations over the beam cross-section in terms of the implemented L3, L4, and L9 elements. A number of numerical problems have been solved and compared with results given by classical beam theories (Euler-Bernoulli and Timoshenko), refined beam theories based on the use of Taylor-type expansions in the neighborhood of the beam axis, and solid element models from commercial codes. Poisson locking correction is analyzed. Applications to compact, thin-walled open/closed sections are discussed. The investigation conducted shows that: (1) the proposed formulation is very suitable to increase accuracy when localized effects have to be detected; (2) it leads to shell-like results in case of thin-walled closed cross-section analysis as well as in open cross-section analysis; (3) it allows us to modify the boundary conditions over the cross-section easily by introducing localized constraints; (4) it allows us to introduce geometrical boundary conditions along the beam axis which lead to plate/shell-like cases.     

Maslov index and Morse theory for the relativistic Lorentz force equation

We study the Jacobi equation for fixed endpoints solutions of the Lorentz force equation on a Lorentzian manifold. The flow of the Jacobi equation along each solution preserves the so-called twisted symplectic form, and the corresponding curve in the symplectic group determines an integer valued homology class called the Maslov index of the solution. We introduce the notion of F-conjugate plane for each conjugate instant; the restriction of the spacetime metric to the F-conjugate plane is used to compute the Maslov index, which is given by a sort of algebraic count of the conjugate instants. For a stationary Lorentzian manifold and an exact electromagnetic field admitting a potential vector field preserving the flow of the Killing vector field, we introduce a constrained action functional having finite Morse index and whose critical points are fixed endpoints solution of the Lorentz force equation. We prove that the value of this Morse index equals the Maslov index and we prove the Morse relations for the solutions of the Lorentz force equation in a static spacetime.Mathematics Subject Classification (2002): Primary: 58E10, 83C10; Secondary: 53D12     

Design of a pulse generator and shock tube for measuring hearing protector attenuation of high-amplitude impulsive noise

The effectiveness of hearing protectors against high amplitude impulse noise levels remains the subject of research with objective testing techniques using acoustic test fixtures offering the only realistic method of providing rapid performance data for protector design and qualification. The work presented in this paper examines a prototype test method based on a shock tube and acoustic test fixture for the evaluation of protectors against high-level impulsive noise where established real ear attenuation at threshold methods would be impractical to apply. The results show that the system is capable of producing controlled repeatable high amplitude pressure pulses of variable duration for testing hearing protection devices in a grazing wave type test. A series of pilot tests illustrate how the system can have a sufficient self-insertion loss to reject flanking noise and allow the measurement of protector attenuations of up to 45 dB with little corruption from flanking noise.     

Experimental evaluation of X‐ray optics applied for microanalysis

The performance of x‐ray capillary lenses has been evaluated. The tests were carried out using an x‐ray tube set‐up. A single glass capillary with tapered inner channel, a monolithic glass polycapillary, and an in‐house manufactured single metallic capillary with parabolic inner channel were characterized in terms of gain, spatial resolution, and element detection limits. The spatial resolution of a confocal set‐up utilizing a monolithic glass polycapillary and a polycapillary conical collimator has also been measured. The highest gain of about 2500 was observed for the glass polycapillary. The maximum gain achieved with the single glass capillary was equal to about 25, and the gain of the metallic capillary was only slightly greater than 1. For the glass capillary and polycapillary lenses, significant filtering of the higher‐energy photons (energy > 8 keV) was observed. The lowest relative detection limits were obtained with an ordinary cylindrical collimator and the polycapillary lens. Similar absolute detection limits were achieved with the use of the polycapillary and single capillary lenses. A relation between the ratios of the detection limits of elements achieved with different x‐ray lenses and the lens parameters (spatial resolution and gain) has been proposed and was verified experimentally. The monolithic polycapillary lens was found to be an optimum focusing device for an x‐ray tube‐based scanning spectrometer. This type of x‐ray lens can be coupled with a polycapillary conical collimator or a polycapillary half‐lens to make a confocal x‐ray microscope capable of depth profiling with a spatial resolution equal to about 30 micrometers. Copyright © 2008 John Wiley & Sons, Ltd.