Optical imaging of pattern formation: reflection anisotropy microscopy applied to globally coupled oscillatory CO-oxidation

A reflection anisotropy microscope (RAM) creates the contrast in its images from a change in the polarization orientation of reflected light from a surface. This may stem from local variations of the reconstruction of a surface, being initiated by changes in an adsorption layer. The advantages and disadvantages of a recently improved RAM versus other optical imaging techniques are discussed. We demonstrate the unique features of RAM and present the first experimental findings of so called 2pi phase kinks in the globally coupled CO-oxidation on Pt(110).     

The Potential of Ultrasonic Non-Destructive Measurement of Residual Stresses by Modal Frequency Spacing using Leaky Lamb Waves

This paper investigates the potential of ultrasonic non-destructive measurements of residual stresses using the modal frequency spacing method based on the interference spectrum of leaky Lamb waves as an alternative to the commonly used flight-time approach in ultrasonic methods. Extensive experiments were carried out to verify the viability and robustness of the technique using an instrumented leaky Lamb wave setup with uniaxial stressed samples and welded steel samples. To improve the signal-to-noise ratio, multiple sets of raw signals of specularly reflected and leaky Lamb waves were acquired and then averaged in the time domain. The acquired data in the time domain were then transformed into the frequency domain to form the interference spectrum of leaky Lamb waves with a good repeatability. The acoustoelastic coefficient of carbon steel is then derived from the measured relationship of wave velocity and applied stress. Finally, a welded steel plate was examined and residual stress was evaluated. The current work demonstrates the feasibility and the potential of the proposed method in measuring residual stresses in welded plates and thin-walled structures.     

Consistency of the preoperative and intraoperative diagnosis of benign vocal fold lesions

The purpose of this retrospective study was to compare the preoperative and intraoperative diagnosis of benign vocal fold lesions for consistency. The diagnosis was made in 221 consecutive patients with benign vocal fold lesions for which a microlaryngoscopy was carried out in a general ENT-clinic. The preoperative diagnosis was obtained by both white halogen and stroboscopic light. The intraoperative diagnosis was obtained by direct microscopic visualization and palpation of the vocal folds. In 36% of the patients, the preoperative diagnosis was changed intraoperatively. In 31% of the patients, a lesion was missed at the preoperative examination and a lesion was diagnosed only during microlaryngoscopy. Bilateral lesions were found in 53% of the patients preoperatively, and in 82% of the patients intraoperatively. Specially intracordal lesions constituted a diagnostic pitfall. Because the preoperative and intraoperative diagnosis often differed, both the patients and the ENT-surgeon must keep an open mind about what may need to be done at surgery.     

The Order Completion Method for Systems of Nonlinear PDEs Revisited

In this paper we presents further developments regarding the enrichment of the basic Theory of Order Completion as presented in Oberguggenberger and Rosinger (Solution of continuous nonlinear PDEs through order completion, North-Holland, Amsterdam, 1994). In particular, spaces of generalized functions are constructed that contain generalized solutions to a large class of systems of continuous, nonlinear PDEs. In terms of the existence and uniqueness results previously obtained for such systems of equations (van der Walt, Acta Appl. Math. 103:1–17, 2008), one may interpret the existence of generalized solutions presented here as a regularity result. Furthermore, it is indicated how the methods developed in this paper may be adapted to solve initial and/or boundary value problems. In particular, we consider the Navier-Stokes equations in three spacial dimensions, subject to an initial condition on the velocity. In this regard, we obtain the existence of a generalized solution to a large class of such initial value problems.      

Castelnuovo-Mumford regularity by approximation

The Castelnuovo-Mumford regularity of a module gives a rough measure of its complexity. We bound the regularity of a module given a system of approximating modules whose regularities are known. Such approximations can arise naturally for modules constructed by inductive combinatorial means. We apply these methods to bound the regularity of ideals constructed as combinations of linear ideals and the module of derivations of a hyperplane arrangement as well as to give degree bounds for invariants of finite groups.     

Hilbert series of subspace arrangements

The vanishing ideal I of a subspace arrangement V₁∪V₂∪?∪V_m⊆V is an intersection I₁∩I₂∩?∩I_m of linear ideals. We give a formula for the Hilbert polynomial of I if the subspaces meet transversally. We also give a formula for the Hilbert series of the product ideal J=I₁I₂?I_m without any assumptions about the subspace arrangement. It turns out that the Hilbert series of J is a combinatorial invariant of the subspace arrangement: it only depends on the intersection lattice and the dimension function. The graded Betti numbers of J are determined by the Hilbert series, so they are combinatorial invariants as well. We will also apply our results to generalized principal component analysis (GPCA), a tool that is useful for computer vision and image processing.     

Quadratic data envelopment analysis

Data Envelopment Analysis (DEA) offers a piece-wise linear approximation of the production frontier. The approximation tends to be poor if the true frontier is not concave, eg in case of economies of scale or of specialisation. To improve the flexibility of the DEA frontier and to gain in empirical fit, we propose to extend DEA towards a more general piece-wise quadratic approximation, called Quadratic Data Envelopment Analysis (QDEA). We show that QDEA gives statistically consistent estimates for all production frontiers with bounded Hessian eigenvalues. Our Monte-Carlo simulations suggest that QDEA can substantially improve efficiency estimation in finite samples relative to standard DEA models.     

Imaging of dynamic processes on surfaces by light

This work focuses on imaging of dynamic processes on surfaces, using light to illuminate the area of interest. The methods discussed here are those in which the photoelectrons emitted from or the light reflected off the surface are measured. While the first approach is well-known since electron microscopy was invented and has been used in surface science applications for a decade, genuine optical microscope methods using polarized light were first developed in 1995 for imaging surface reactions.

The results discussed here are from different fields of surface research. These include the imaging of adsorption phenomena, surface diffusion and growth processes. The main emphasis will be on pattern formation of surface reactions under strictly controlled parameters. The most recent techniques expand the range of observable pressure conditions by many orders of magnitude, thus bridging the pressure gap in imaging surface reactions.     

The tilted-plate method for introducing carrier fringes of extension in Moiré interferometry

Experimental Techniques -