Optical loss measurements in femtosecond laser written waveguides in glass

The optical loss is an important parameter for waveguides used in integrated optics. We measured the optical loss in waveguides written in silicate glass slides with high repetition-rate (MHz) femtosecond laser pulses. The average transmission loss of straight waveguides is about 0.3 dB/mm at a wavelength of 633 nm and 0.05 dB/mm at a wavelength of 1.55 μm. The loss is not polarization dependent and the waveguides allow a minimum bending radius of 36 mm without additional loss. The average numerical aperture of the waveguides is 0.065 at a wavelength of 633 nm and 0.045 at a wavelength of 1.55 μm. In straight waveguides more than 90% of the transmission loss is due to scattering.     

Prediction of initial motion of a gas bubble in liquids

Numerical predictions are presented for the motion and distortion of a single gas bubble rising through the liquid. The computations were made with an implicit finite-difference procedure which solves the transient equations of motion throughout the bubble and the liquid, such that the free surface between the gas bubble and the liquid is not a boundary of the computational domain.The predictions compare well with the experimental results of others. Computations are presented for bubble sizes from 0.02 to 0.05 m radius and for bubbles of different gas densities rising in liquids of different densities. Surface tension effects are neglected.     

Charge correlations as non-trivial tests of QCD

It is shown that the additive quark model is compatible with the data on double scattering of pions and protons in deuterium. The cross-section for interaction of the hadrons created in the first collision with the second nucleon of the target is determined to be 20–25 mb.     

The Hardy classes for functions in the class MV[α, k]

Suppose that f(z) = z + a₂z² + ··· + a_nz_n + ··· is regular in the unit disc $\text{D}\text{with}\text{[f(z) f′}\text{(z)}\text{z] ≠ 0}\text{in}\text{D}$, and further let α ? 0 and k ? 2. If $\text{∝}{}^{\mathrm{2\pi }}{}_{\mathrm{o}}\text{¦}\text{Re}\text{{(1 ? α)z[}\text{f′(z)}\text{f(z)}\text{] + α(1 + z[}\text{f″(z)}\text{f′(z)}\text{])}¦ dθ ? kπ}\text{for}\text{z ? D}$, then f(z) is said to belong to the class MV[α, k]. This class contains many of the special classes of regular and univalent functions. The authors determine the Hardy classes of which f(z), f′(z) and f″(z) belong and obtain growth estimates of a_n.     

Stress-fit applications to experimental shell analyses

The stress-fit method is a procedure for determining complete stress distribution in shells from experimental data. Displacement, slope and shearing-force distributions may also be calculated. The method is applicable to all shell configurations for which closed-form solutions have been formulated and may be applied to certain asymmetrically loaded shells as well as those loaded axisymmetrically. Application to cylindrical and spherical shells is discussed in detail, and the procedure is shown to be verfied experimentally.     

On the univalence of functions defined by certain integral transforms

The integral transform $\text{F(z) = ∝}{}_0{}^{\mathrm{z}}\text{(f′(t))}{}^{\mathrm{\alpha }}\text{(}\text{g(t)}\text{t}\text{)}{}^{\mathrm{\beta }}\text{dt}$, where α and β are real, of pairs of special analytic functions f(z) = z + ···, g(z) = z + ···, univalent in the open unit disc Δ is studied. The transform and our results extend some recent results due to Shirakova.     

Probing the dimensions of semi-rigid inner functionalised U-shaped bis-porphyrin cavities

The synthesis of a series of open U-shaped bis-porphyrin cavity molecules is described, with bridged bicyclic backbones to confer rigidity, and a pendant substituted aromatic probe unit suspended on the inside of the cavity. The dimensions and flexibility of the bis-zincporphyrin cavity were probed using several different techniques. Initially the molecular ruler concept was employed, using flexible bidentate ligands as guests with a range of possible linear dimensions. Secondly, NMR methods were employed with rigid bidentate ligand guests of fixed lengths, and thirdly diffusion based NMR methods were utilised. The range of inter-porphyrin distances estimated by these methods suggests that these types of open-cavity systems have a surprising degree of flexibility.