On Roussel–Rubio-type lemmas and their consequences

Roussel and Rubio proved a lemma which is essential in the proof of the Strong Perfect Graph Theorem. We give a new short proof of the main case of this lemma. In this note, we also give a short proof of Hayward’s decomposition theorem for weakly chordal graphs, relying on a Roussel–Rubio-type lemma. We recall how Roussel–Rubio-type lemmas yield very short proofs of the existence of even pairs in weakly chordal graphs and Meyniel graphs.     

Large displacement analysis of shear deformable composite beams with interlayer slips

This paper presents a novel geometric non-linear finite element formulation for the analysis of shear deformable two-layer beams with interlayer slips. We adopt the co-rotational approach where the motion of the element is decomposed into two parts: a rigid body motion which defines a local coordinate system and a small deformational motion of the element relative to this local coordinate system. The main advantage of this approach is that the transformation matrices relating local and global quantities are independent to the choice of the geometrical linear local element. The effect of transverse shear deformation of the layers is taken into account by assuming that each layer behaves as a Timoshenko beam element. The layers are assumed to be continuously connected and partial interaction is considered by considering a continuous relationship between the interface shear flow and the corresponding slip. In order to avoid curvature and shear locking phenomena, the local linear element is formulated using “exact” displacement shape functions derived from the closed-form solution of the governing equations of a two-layer beam element. Finally, three numerical applications are presented in order to assess the performance of the proposed formulation.     

Inducing anisotropy in bulk Nd-Fe-Co-Al-B nanocrystalline alloys by quenching in magnetic field

We have observed magnetic anisotropy in bulk Nd_55−xCo_xFe₃₀Al₁₀B₅ (x=10, 15 and 20) alloys prepared by copper mold suction casting method with a presence of external magnetic field (quenching field) μ₀H=0.25 T. By changing direction of the measuring field from perpendicular to parallel one in comparison with that of the quenching field, coercive force of the alloys slightly decreases while remanent magnetization and squareness of hysteresis loop increase more clearly. It is also found that the higher Co-concentration in the alloys the larger magnetic anisotropy is induced. The structure analyses manifest nanocrystalline particles embedded in residual amorphous matrix of the alloys. The size of the particles is in range of 10-30 nm and their crystalline phases consist of Nd₂(Fe,Co)₁₄B, Nd₃Co, Nd₃Al, NdAl₂ and Nd.     

Lattice dynamics of Eu<Subscript>1-x</Subscript>Y<Subscript>x</Subscript>MnO<Subscript>3</Subscript> (0 ≤ x ≤ 0.5)

A systematic and detailed study of Raman and infrared active lattice excitations in the orthorhombic multiferroic manganite Eu_1−xY_xMnO₃ (0 ≤ x ≤ 0.5) was carried out at room temperature. For the infrared active phonon modes the eigenfrequencies, damping constants and oscillator strengths were analyzed by Fourier-Transform Infrared Spectroscopy in the far infrared frequency range. For the Raman active phonons the same analysis for eigenfrequencies and damping constants was carried out using Raman spectroscopy in the range from 200 cm⁻¹ to 700 cm⁻¹. Y doping leads to mode-dependent phonon frequency shifts up to 8%. These are interpreted in terms of the interplay between the decrease of the reduced ion masses and the axis-dependent change of bond lengths. The latter leads to a bond softening along the a-axis and a strengthening along the c-axis, for which the highest phonon frequency increase is observed. The application of both Raman and Infrared Spectroscopy gives us sensitivity not only to symmetry properties via the selection rules but also to the involvement of different ion types within the unit cell. It is clearly shown that the disorder induced effects are of minor impact on the lattice properties and solely detected on the rare earth sites. The MnO₆ octahedra remain unaffected and show the same behavior as in the stochiometric RMnO₃ making Eu_1−xY_xMnO₃ an excellent model system for a quasi-continuous fine-tuning of the lattice parameters relevant for the appearance of multiferroicity.     

Inclusion of SWCNTs in Nb/Pt co-doped TiO2 thin-film sensor for ethanol vapor detection

Nb-Pt co-doped TiO₂ and the hybrid SWCNTs/Nb-Pt co-doped TiO₂ thin films have been prepared by the sol–gel spin-coating process for gas-sensor fabrication. Field emission scanning electron microscope (FE-SEM, TEM and X-ray diffraction (XRD) characterizations indicated that the SWCNTs inclusion did not affect the morphology of the TiO₂ thin film and the particle size. Additionally, the SWCNTs were well embedded in the TiO₂ matrix. The gas-sensing properties of Nb–Pt co-doped TiO₂ thin films with and without SWCNTs inclusion were investigated. The hybrid sensors with the inclusion of different SWCNTs contents are examined to elucidate the effect of SWCNTs content on the gas-sensing properties. Experimental results revealed that the responses to ethanol of Nb–Pt co-doped TiO₂ sensors with SWNCTs inclusion increase by factors of 2–5 depending on the operating temperature and the ethanol concentration, compared to that of the sensor without SWCNTs inclusion. Moreover, all hybrid sensors can operate with high sensitivity and stability at a relatively low operating temperature (<335 °C). The responses of the hybrid sensors are greatly affected by SWCNTs content inclusion. The optimized SWCNTs content of 0.01% by weight was obtained for our experiment. The improved gas-sensing performance should be attributed to the additional formation of the p/n junction between SWCNTs (p-type) and TiO₂ (n-type).     

Tuning of nanotube mechanical resonances by electric field pulling

We show here that field emission (FE) can be used to directly observe the vibration resonances nu(R) of carbon nanotubes (CNTs) and that the tension created by the applied field allows the tuning of these resonances by up to a factor of 10. The resonances are observable by the changes they create in the FE pattern or the emitted FE current. The tuning is shown to be linear in voltage and to follow from the basic physics of stretched strings. The method allows one to study the mechanical properties of individual multiwall carbon nanotubes within an ensemble and follow their evolution as the CNTs are modified. The tuning and detection should be useful for nanometric resonant devices.     

Measurement of the spectral distribution of a multi-mode dye laser light by using speckle patterns

A simple method of measuring the wavelength γ₁ and the spectral line spacing Δγ of a multi-mode dye laser light by using the correlated speckle patterns produced at the far-field of a diffuser is proposed. Examples of the obtained values of γ₁ and Δγ are 6.0 × 10³ Å and 3.0 × 10¹ Å, respectively.