Physically nonlinear and related approximate theories of elasticity,and their invariance properties

The existing developments of physically nonlinear elasticity have several shortcomings. With the aim of remedying these deficiencies, a number of approximate theories of elasticity are discussed in the present paper and, in particular, a theory of physically nonlinear elasticity is systematically developed. More specifically, stress-strain relations for anisotropic physically nonlinear materials are derived. The method of Casey & Naghdi [1] is then applied to obtain properly invariant results. This method involves the use of auxiliary motions obtained by removing from any given motion the translation and rotation at any one particle, called a pivot. The auxiliary motions represent the original motions in the approximate theory. The connection between the transformation of fields under a change of pivot and invariance requirements associated with the auxiliary motions is investigated.     

Twistor Geometry of a Pair of Second Order ODEs

We discuss the twistor correspondence between path geometries in three dimensions with vanishing Wilczynski invariants and anti-self-dual conformal structures of signature (2, 2). We show how to reconstruct a system of ODEs with vanishing invariants for a given conformal structure, highlighting the Ricci-flat case in particular. Using this framework, we give a new derivation of the Wilczynski invariants for a system of ODEs whose solution space is endowed with a conformal structure. We explain how to reconstruct the conformal structure directly from the integral curves, and present new examples of systems of ODEs with point symmetry algebra of dimension four and greater which give rise to anti–self–dual structures with conformal symmetry algebra of the same dimension. Some of these examples are (2, 2) analogues of plane wave space–times in General Relativity. Finally we discuss a variational principle for twistor curves arising from the Finsler structures with scalar flag curvature.     

Study of a vibrating plate: comparison between experimental (ESPI) and analytical results

Real-time electronic speckle pattern interferometry (ESPI) was used for tuning and visualization of natural frequencies of a trapezoidal plate. The plate was excited to resonant vibration by a sinusoidal acoustical source, which provided a continuous range of audio frequencies. Fringe patterns produced during the time-average recording of the vibrating plate—corresponding to several resonant frequencies—were registered. From these interferograms, calculations of vibrational amplitudes by means of zero-order Bessel functions were performed in some particular cases. The system was also studied analytically. The analytical approach developed is based on the Rayleigh–Ritz method and on the use of non-orthogonal right triangular co-ordinates. The deflection of the plate is approximated by a set of beam characteristic orthogonal polynomials generated by using the Gram–Schmidt procedure. A high degree of correlation between computational analysis and experimental results was observed.     

Field expulsion and reconfiguration in polaritonic photonic crystals

We uncover a rich set of optical phenomena stemming from the incorporation of polar materials exhibiting transverse phonon polariton excitations into a photonic crystal structure. We identify in the frequency spectrum two regimes in which the dielectric response of the polaritonic medium can induce extreme localization of the electromagnetic energy. Our analysis of the effect of polarization and the interaction between the polariton and photonic band gaps on the Bloch states leads to a pair of mechanisms for sensitive frequency-controlled relocation and/or reconfiguration of the fields.     

Measurement of branching fractions for B-->eta(c)K(*) decays

We report measurements of branching fractions for charged and neutral B-->eta(c)K decays where the eta(c) meson is reconstructed in the K(0)(S)K+/-pi(-/+), K+K-pi(0), K(*0)K-pi(+), and pp; decay channels. The neutral B0 channel is a CP eigenstate and can be used to measure the CP violation parameter sin(2phi(1). We also report the first observation of the B0-->eta(c)K(*0) mode. The results are based on an analysis of 29.1 fb(-1) of data collected by the Belle detector at KEKB.     

Breather trapping and breather transmission in a DNA model with an interface

We study the dynamics of moving discrete breathers in an interfaced piecewise DNA molecule. This is a DNA chain in which all the base pairs are identical and there exists an interface such that the base pairs dipole moments at each side are oriented in opposite directions. The Hamiltonian of the Peyrard-Bishop model is augmented with a term that includes the dipole-dipole coupling between base pairs. Numerical simulations show the existence of two dynamical regimes. If the translational kinetic energy of a moving breather launched towards the interface is below a critical value, it is trapped in a region around the interface collecting vibrational energy. For an energy larger than the critical value, the breather is transmitted and continues travelling along the double strand with lower velocity. Reflection phenomena never occur. The same study has been carried out when a single dipole is oriented in opposite direction to the other ones. When moving breathers collide with the single inverted dipole, the same effects appear. These results emphasize the importance of this simple type of local inhomogeneity as it creates a mechanism for the trapping of energy. Finally, the simulations show that, under favorable conditions, several launched moving breathers can be trapped successively at the interface region producing an accumulation of vibrational energy. Moreover, an additional colliding moving breather can produce a saturation of energy and a moving breather with all the accumulated energy is transmitted to the chain.     

Annealing effects on the magnetization of Co–Ni–B amorphous nanoparticles

Chemically prepared (Co_xNi_1−x)_1−yB_y (x=0.5, 0.75, 1; y≈0.4) amorphous fine particles were characterized by X-ray diffraction, DTA and TGA, and in situ magnetic measurement as a function of annealing temperature in an inert atmosphere. Magnetic measurement performed in as-prepared and 150°C annealed samples shows an increase of the saturation magnetization and magnetic moment after thermal treatment. Room temperature magnetization increases by factors of 3.5, 1.8, and 1.5, for x=0.5, 0.75, and 1, respectively. These measurements may indicate a local re-ordering of the amorphous phase at temperatures much lower than the full crystallization temperature.     

Synthesis of MFI zeolite films on optical fibers for detection of chemical vapors

We report the development of a novel zeolite-incorporated optical fiber sensor and demonstrate its capability for in situ detection of chemical vapors. The sensor comprises a polycrystalline silicalite thin film grown upon the cleaved end face of a standard single-mode optical fiber. The sensor device operates by measuring the optical reflectivity of the zeolite crystals, which changes reversibly in response to the amount of chemical vapor adsorbed in its crystalline microporous structure. The sensor has been successfully demonstrated for measuring the concentration of isopropanol vapor in mixtures with nitrogen gas.     

The embedding of General Relativity in five dimensions

We argue that General Relativistic solutions can always be locally embedded in Ricci-flat 5-dimensional spaces. This is a direct consequence of a theorem of Campbell (given here for both a timelike and spacelike extra dimension, together with a special case of this theorem) which guarantees that anyn-dimensional Riemannian manifold can be locally embedded in an (n+1)-dimensional Ricci-flat Riemannian manifold. This is of great importance in establishing local generality for a proposal recently put forward and developed by Wesson and others, whereby vacuum (4+1)-dimensional field equations give rise to (3+1)-dimensional equations with sources. An important feature of Campbell's procedure is that it automatically guarantees the compatibility of Gauss-Codazzi equations and therefore allows the construction of embeddings to be in principle always possible. We employ this procedure to construct such embeddings in a number of simple cases.