Iterated Differential Forms II: Riemannian Geometry Revisited

A natural extension of Riemannian geometry to a much wider context is presented on the basis of the iterated differential form formalism developed in math.DG/0605113 and an application to general relativity is given.Comment: 12 pages, extended version of the published note Dokl. Math. 73, n. 2 (2006) 18

Low-temperature specific heat of real crystals: Possibility of leading contribution of optical and short-wavelength acoustical vibrations

We point out that the repeatedly reported glass-like properties of crystalline materials are not necessarily associated with localized (or quasilocalized) excitations. In real crystals, optical and short-wavelength acoustical vibrations remain damped due to defects down to zero temperature. If such a damping is frequency-independent, e.g. due to planar defects or charged defects, these optical and short-wavelength acoustical vibrations yield a linear-in-$T$ contribution to the low-temperature specific heat of the crystal lattices. At low enough temperatures such a contribution will prevail over that of the long-wavelength acoustical vibrations (Debye contribution). The crossover between the linear and the Debye regime takes place at $T^* \propto \sqrt N$, where $N$ is the concentration of the defects responsible for the damping. Estimates show that this crossover could be observable.Comment: 5 pages. v4: Error in Appendix corrected, which does not change the main results of the pape

Sub-wavelength imaging: Resolution enhancement using metal wire gratings

An experimental evidence of subwavelength imaging with a "lens", which is a uniaxial negative permittivity wire medium slab, is reported. The slab is formed by gratings of long thin parallel conducting cylinders. Taking into account the anisotropy and spatial dispersion in the wire medium we theoretically show that there are no usual plasmons that could be exited on surfaces of such a slab, and there is no resonant enhancement of evanescent fields in the slab. The experimentally observed clear improvement of the resolution in the presence of the slab is explained as filtering out the harmonics with small wavenumbers. In other words, the wire gratings (the wire medium) suppress strong traveling-mode components increasing the role of evanescent waves in the image formation. This effect can be used in near-field imaging and detection applications.Comment: 12 pages, 6 figure

Magnetostrictive Transducers (MsT) Utilizing Reversed Wiedemann Effect

Magnetostrictive transduction has been widely utilized in NDE applications and, specifically, for generation and reception of guided waves for long-range inspection of components such as pipes, vessels, and small tubes. Transverse-motion guided wave modes (e.g., torsional vibrations in pipes) are the most typical choice for long-range inspection applications because the wave motion is in the plane of the structure. Magnetostrictive-based sensors have been available for the last several years for these wave modes based on the Wiedemann effect. For these sensors, a permanent magnetic bias is applied that is perpendicular to the direction of the propagated guided wave. This bias field strains the material preferentially in the desired particle motion direction. A time-varying magnetic field that is much smaller than the bias field is induced in the material and is oriented parallel to the direction of guided wave propagation. This time-varying field is induced using an electric coil located near the surface. The interaction of these two fields produces the guided waves and an inverse effect is present for the receive process. An alternative configuration of a sensor for generating and receiving these traverse-motion guided waves is to reverse the biasing and time-varying magnetic fields directions. Since transverse-motion guided wave sensors are typically much wider in the particle motion direction, the net effect is the magnetic biasing length is shorter and different coil designs can be used. Because of this, the alternative design known as a magnetostrictive transducer (MsT), exhibits a number of unique features compared to the Wiedemann sensor described above, such as: 1) the ability to use smaller rare earth permanent magnets and achieve uniform and self-sustained bias field strengths, 2) the choice of more efficient electric coil arrangements to induce a stronger time-varying magnetic field for a given coil impedance, 3) more easily exhibit nonlinear operating characteristics given the efficiency improvements in both magnetic fields, and 4) the ability to generate unidirectional guided waves when the field arrangement is combined with a magnetostrictive patch. MsT designs will be presented that are suitable for different inspection applications, one using electromagnetic generation and reception directly in a ferromagnetic material and another design that integrates a magnetostrictive patch to improve the efficiency and allow special operating characteristics