Jamin Fabry-Perot interferometer

A novel type of interferometer was designed and tested experimentally. It combines the advantages of the spatial path separation used in the two-wave polarized Jamin interferometer and the high sensitivity that characterizes the multiwave Fabry-Perot interferometer. Furthermore, when it is sandwiched between crossed polarizers it shows a sensitivity to intracavity anisotropies that is proportional to the square of the Fabry-Perot interferometer's finesse.     

On large half-factorial sets in elementary<Emphasis Type="Italic">p</Emphasis>-groups: Maximal cardinality and structural characterization

Half-factoriality is a central concept in the theory of non-unique factorization, with applications for instance in algebraic number theory. A subsetG ₀ of an abelian group is called half-factorial if the block monoid overG ₀, which is the monoid of all zero-sum sequences of elements ofG ₀, is a half-factorial monoid. In this paper we study half-factorial sets with large cardinality in elementaryp-groups. First, we determine the maximal cardinality of such half-factorial sets, and generalize a result which has been only known for groups of even rank. Second, we characterize the structure of all half-factorial sets with large cardinality (in a sense made precise in the paper). Both results have a direct application in the study of some counting functions related to factorization properties of algebraic integers. This work was supported by the Austrian Science Fund FWF (Project P16770-N12) and by the Austrian-French Program ‘Amadeus 2003–2004’.     

Sound-field reproduction in-room using optimal control techniques: simulations in the frequency domain

This paper describes the simulations and results obtained when applying optimal control to progressive sound-field reproduction (mainly for audio applications) over an area using multiple monopole loudspeakers. The model simulates a reproduction system that operates either in free field or in a closed space approaching a typical listening room, and is based on optimal control in the frequency domain. This rather simple approach is chosen for the purpose of physical investigation, especially in terms of sensing microphones and reproduction loudspeakers configurations. Other issues of interest concern the comparison with wave-field synthesis and the control mechanisms. The results suggest that in-room reproduction of sound field using active control can be achieved with a residual normalized squared error significantly lower than open-loop wave-field synthesis in the same situation. Active reproduction techniques have the advantage of automatically compensating for the room's natural dynamics. For the considered cases, the simulations show that optimal control results are not sensitive (in terms of reproduction error) to wall absorption in the reproduction room. A special surrounding configuration of sensors is introduced for a sensor-free listening area in free field.     

Numerical description of the edge mode at the beveled extremity of a plate

This paper deals with the reflection of a two-dimensional harmonic Lamb wave at the beveled end of a plate. The existence of a resonant edge mode is described by a numerical model. It is proved that the edge mode is the resonance of different complex modes. The behavior of this mode as a function of the bevel angle is studied. Its amplitude decreases and its resonance frequency shifts as the bevel angle decreases from 90 to 85 deg. An unexpected strong variation of the repartition of the reflected energy is linked to this phenomenon.     

Raman modes of index-identified freestanding single-walled carbon nanotubes

Using electron diffraction on freestanding single-walled carbon nanotubes, we have determined the structural indices (n,m) of tubes in the diameter range from 1.4 to 3 nm. On the same freestanding tubes, we have recorded Raman spectra of the tangential modes and the radial breathing mode. For the smaller diameters (1.4-1.7 nm), these measurements confirm previously established radial breathing mode frequency versus diameter relations and would be consistent with the theoretically predicted proportionality to the inverse diameter. However, for extending the relation to larger diameters, either a yet unexplained environmental constant has to be assumed, or the linear relation has to be abandoned.     

Crack path prediction in anisotropic brittle materials

A force balance condition to predict quasistatic crack paths in anisotropic brittle materials is derived from an analysis of diffuse interface continuum models that describe both short-scale failure and macroscopic linear elasticity. The path is uniquely determined by the directional anisotropy of the fracture energy, independent of details of the failure process. The derivation exploits the gradient dynamics and translation symmetry properties of this class of models to define a generalized energy-momentum tensor whose integral around an arbitrary closed path enclosing the crack tip yields all forces acting on this tip, including Eshelby's configurational forces, cohesive forces, and dissipative forces. Numerical simulations are in very good agreement with analytic predictions.     

A model-based inverse method for positioning scatterers in a cladded component inspected by ultrasonic waves

Nondestructive methods aim at detecting, locating and identifying defects. Inversion of ultrasonic measurements obtained by inspecting a steel component of regular geometry with an immersed transducer leads to accurate location of defects. When the component is cladded, the irregular geometry of the surface and the anisotropic nature of the cladding material lead to aberrations of the radiated field (e.g., beam distortions, splitting and defocusing, these varying with the transducer scanning position). As a consequence, defect location may be inaccurate and defects (e.g., cracks) sizing impossible. In the present paper, a model-based inverse method is developed to solve this problem. It relies on the time-dependent simulation of ultrasonic propagation in this material of complex geometry and structure, in order to determine a set of probable positions for the defect at the origin of the measured ultrasonic echo-structure. The most probable position is determined by minimizing a cost-function of likeness between the simulated and measured ultrasonic images. The overall scheme shall generally apply to inverse measured ultrasonic echo-structures as soon as the simulation of the forward problem is tractable. To validate the method, examples of application are given dealing with actual measurements obtained in the real configuration of pressure vessel inspection.     

Fractional Moment Estimates for Random Unitary Operators

We consider unitary analogs of d-dimensional Anderson models on l²( $$\mathbb(z)$$^d) defined by the product U=D S where S is a deterministic unitary and D is a diagonal matrix of i.i.d. random phases. The operator S is an absolutely continuous band matrix which depends on parameters controlling the size of its off-diagonal elements. We adapt the method of Aizenman–Molchanov to get exponential estimates on fractional moments of the matrix elements of U(U –z)^–1, provided the distribution of phases is absolutely continuous and the parameters correspond to small off-diagonal elements of S. Such estimates imply almost sure localization for U.     

Solvent-free condensation of phenylacetonitrile and nonanenitrile with 4-methoxybenzaldehyde: optimization and mechanistic studies

The condensation of phenylacetonitrile with 4-methoxybenzaldehyde can be carried out by two solvent-free methods: i) using neat powdered KOH at room temperature with equivalent amounts of aldehyde, nitrile and base for 3 min, and ii) using K2CO3 in the presence of a phase transfer agent for 3 min under microwave activation or conventional heating. By extending the reaction time up to 10 min, four different products were obtained from phenyl or nitrile group migration. With nonanenitrile, only the second method could be applied to give two kinds of condensed compounds with or without phenyl (or nitrile) group migration. The intervention of non-thermal MW-specific effects was proved in some cases and interpreted.     

Synthesis and triplex forming properties of pyrrolidino pseudoisocytidine containing oligodeoxynucleotides

Pyrrolidino pseudo-C-nucleosides are isosteres of natural deoxynucleosides which are protonated at the pyrrolidino ring nitrogen under physiological conditions. As constituents of a triplex forming oligodeoxynucleotide (TFO), the positive charge is expected to stabilise DNA triple helices via electrostatic interactions with the phosphodiester backbone of the target DNA. We describe the synthesis of the pyrrolidino isocytidine pseudonucleoside and the corresponding phosphoramidite building block and its incorporation into TFOs. Such TFOs show substantially increased DNA affinity compared to unmodified oligodeoxynucleotides. The increase in affinity is shown to be due to the positive charge at the pyrrolidino subunit.