Fabrication and measurement of low-loss planar optical tapers

Accurate loss-measurements on planar optical tapers are reported and a comparison is made with theoretical results obtained with the Beam Propagation Method.     

Molecular order and disorder of surfactants in clay nanocomposites

Disorder of intercalated surfactant molecules in clay minerals causes gradual swelling, rather than commonly assumed swelling in discrete steps.     

String theory and algebraic geometry of moduli spaces

It is shown how the algebraic geometry of the moduli space of Riemann surfaces entirely determines the partition function of Polyakov's string theory. This is done by using elements of Arakelov's intersection theory applied to determinants of families of differential operators parametrized by moduli space. As a result we write the partition function in terms of exponentials of Arakelov's Green functions and Faltings' invariant on Riemann surfaces. Generalizing to arithmetic surfaces, i.e. surfaces which are associated to an algebraic number fieldK, we establish a connection between string theory and the infinite primes ofK. As a result we conjecture that the usual partition function is a special case of a new partition function on the moduli space defined overK.     

Higher regularity of the free boundary in the parabolic Signorini problem

We show that the quotient of two caloric functions which vanish on a portion of an \(H^{k+ \alpha }\) regular slit is \(H^{k+ \alpha }\) at the slit, for \(k \ge 2\). In the case \(k=1\), we show that the quotient is in \(H^{1+\alpha }\) if the slit is assumed to be space-time \(C^{1, \alpha }\) regular. This can be thought of as a parabolic analogue of a recent important result in De Silva and Savin (Boundary Harnack estimates in slit domains and applications to thin free boundary problems, 2014), whose ideas inspired us. As an application, we show that the free boundary near a regular point of the parabolic thin obstacle problem studied in Danielli et al. (Optimal regularity and the free boundary in the parabolic Signorini problem. Mem. Am. Math. Soc., 2013) with zero obstacle is \(C^{\infty }\) regular in space and time.     

Residual Stress Measurement in Composite Laminates Using Incremental Hole-Drilling with Power Series

Current methods for incremental hole-drilling in composite laminates have not been successfully applied in laminates of arbitrary construction or where significant variation of residual stress exists within a single ply. This work presents a method to overcome these limitations. Series expansion is applied to each ply orientation separately so that the discontinuities in the residual stresses at ply interfaces can be correctly captured. Temperature variations described by power series are used to set up eigenstrains and consequent stresses which vary in the through-thickness direction. The calibration coefficients at each incremental hole depth are calculated through the use of finite element modelling. The inverse solution employs a least-squares approach which makes the resulting solution insensitive to measurement uncertainty. Robust uncertainties in the residual stress distributions are determined using Monte Carlo simulation. The residual stress distribution is found from that combination of series orders in the different ply orientations that has the lowest RMS uncertainty, selected only from those combinations that have converged. The method is demonstrated on a GFRP laminate of [0₂/+45/?45]_s construction where it is found that transverse cracking of the plies at the inner surface of the hole may have impacted on the accuracy of the results.     

Measurements on a molecular beam apparatus for mass spectrometric study of reactions in flames

Summary The formation of a molecular beam in sampling 1 torr to 1 atm. gases (Ar or H₂) is studied for three diameters of the sampling orifice. To modulate the beam, use is made of a mechanical chopper placed very near the sampling orifice. This enables us to measure the scattering of the beam by collisions between beam molecules. From our measurements it follows that these collisions are very important for >0.020 mm at an initial pressure of 1 atm. We discuss the consequences of our results for mass spectrometric studies of flames.     

Pflanzenchemie

Analytical and Bioanalytical Chemistry -