Convergence of nonconforming multigrid methods without full elliptic regularity

We consider nonconforming multigrid methods for symmetric positive definite second and fourth order elliptic boundary value problems which do not have full elliptic regularity. We prove that there is a bound () for the contraction number of the -cycle algorithm which is independent of mesh level, provided that the number of smoothing steps is sufficiently large. We also show that the symmetric variable -cycle algorithm is an optimal preconditioner.

     

Application of field-ion microscopy techniques to metallurgical problems

The invention of field-ion microscopy and related techniques by E.W. Müller has created a new field of high-resolution analyses. While much of its application to metallurgy in the past was oriented towards instrumentation and technique, today there is an increasing trend towards using the techniques for problem-related studies. Some examples of the application of field-ion microscopy in studies of grain boundaries, ordering and clustering, and precipitation will be reviewed.     

Number fluctuation analysis of random locomotion. Statistics of a Smoluchowski process

We analyze a scheme, originally suggested by Smoluchowski, by which a diffusion coefficientD can be estimated by measuring the number of particles occupying a fixed region of a surface at various times. An expression is derived relating the variance of the estimated valueD to several experimental parameters. This expression is evaluated numerically to determine how statistical uncertainty depends on adjustable variables. Particular attention is given to experiments involving locomotion of migrating leukocytes.     

Korn's inequalities for piecewise vector fields

Korn's inequalities for piecewise vector fields are established. They can be applied to classical nonconforming finite element methods, mortar methods and discontinuous Galerkin methods.

     

Slopes of vector bundles on projective curves and applications to tight closure problems

We study different notions of slope of a vector bundle over a smooth projective curve with respect to ampleness and affineness in order to apply this to tight closure problems. This method gives new degree estimates from above and from below for the tight closure of a homogeneous -primary ideal in a two-dimensional normal standard-graded algebra in terms of the minimal and the maximal slope of the sheaf of relations for some ideal generators. If moreover this sheaf of relations is semistable, then both degree estimates coincide and we get a vanishing type theorem.

     

Atomic-level studies of superconducting and nonsuperconducting YBa2Cu3O7−x

Atomic-resolution images from superconducting and nonsuperconducting samples of YBa₂Cu₃O_7–x have been obtained by field ion microscopy. Both phases of the material exhibit a similar layered structure in the field ion images. Transmission electron micrographs of superconducting field ion tips show vividly the twinned structure of the orthorhombic phase. Time-of-flight (atom-probe) mass spectra from the two materials differ primarily in an enhanced molecular oxygen signal from the superconducting samples indicating that oxygen in the O(4) sites (CuO chains) is field desorbed preferentially as molecular oxygen ions.     

The practical synthesis of a novel and highly potent analogue of bryostatin

Macrocycle 1 is a new highly potent analogue of bryostatin 1, a promising anti-cancer agent currently in human clinical trials. In vitro, 1 displays picomolar affinity for PKC and exhibits over 100-fold greater potency than bryostatin 1 when tested against various human cancer cell lines. Macrocycle 1 can be generated in clinically required amounts by chemical synthesis in only 19 steps (LLS) and represents a new clinical lead for the treatment of cancer.     

Numerical approximation of AR‐XPS spectra for rough surfaces considering the effect of electron shadowing

A computational scheme is presented that takes into account the topography, i.e. the shadowing and hence the local emission angle of the electrons when evaluating AR‐XPS data of macroscopic rough surfaces. The topography of the sample surface is supposed to be recorded by atomic force microscopy and/or optical microscopy. The emitted photoelectrons are simulated based on an extension of the Beer–Lambert law that includes the shadowing, the current local emission angle, and the geometrical instrument setup. The obtained angle‐resolved XPS spectra are optimized in accordance with experimental ones via a self‐consistent minimization algorithm that also allows one to determine the layer thicknesses of the corrugated sample. In order to validate the proposed numerical scheme, the simulation program simulation of electron spectra for surface analysis is used. An additional analysis is then performed considering only experimental data. The numerical scheme gives good agreement in simulation–simulation as well as simulation–experiment comparisons and permits a comprehensible interpretation of the measured data. Copyright © 2014 John Wiley & Sons, Ltd.