Composition operators on Hardy spaces of Riemann surfaces

Our purpose is to define composition operators acting upon Hardy spaces of Riemann surfaces. In terms of counting functions related to analytic self-map on Riemann surfaces, the boundedness and compactness are characterized.     

On(e)-reducible 3-manifolds Which Admit Complete Surface Systems

In the present paper, we consider a class of compact orientable 3-manifolds with one boundary component, and suppose that the manifolds are ?-reducible and admit complete surface systems. One of our main results says that for a compact orientable, irreducible and ?-reducible 3-manifold M with one boundary component F of genus n > 0 which admits a complete surface system S′, if D is a collection of pairwise disjoint compression disks for ?M , then there exists a complete surface system S for M , which is equivalent to S′, such that D is disjoint from S . We also obtain some properties of such 3-manifolds which can be embedded in S3.     

A computer program for automated step edge motion analysis from scanning probe microscopy images

A computer algorithm was developed to automatically track the displacement of straight step edges between sequential scanning probe microscopy images of single-crystal surfaces. The program utilizes the Canny edge detection algorithm followed by the Hough Transform of the edge map to identify step edges according to their direction, relative to the image axes, and according to their displacement, relative to the image origin. The tracking of individual steps is facilitated by the fact that straight edges in general maintain their direction and therefore, steps of similar displacement but different direction can be sorted. The algorithm is based on the assumption that the rate of image acquisition is much greater than the rate of (mono)layer growth/dissolution, requiring that changes in step displacement are small in successive images. The change in step displacement in sequential images leads directly to the calculation of the step speed. By tabulating all changes in step displacement through a sequence of images, a statistical representation of the step edge data is produced. The program was evaluated using a sequence of 20 atomic force microscopy images from a calcite (104) surface growing from a supersaturated aqueous solution. The program required, in total, 5 CPU-minutes running on a Pentium 4 processor to compute the mean step speed with 60% precision whereas the equivalent number of measurements performed “by hand” required 6 person-hours at 70% precision. For comparable output, the computer program therefore represents a factor of about 100 decrease in required effort.     

Hybrid mesh generation with embedded surfaces using a multiple marching direction approach

This paper proposes a method for the creation of hybrid meshes with embedded surfaces for viscous flow simulations as an extension of the multiple marching direction approach (AIAA J. 2007; 45 (1):162–167). The multiple marching direction approach enables to place semi‐structured elements around singular points, where valid semi‐structured elements cannot be placed using conventional hybrid mesh generation methods. This feature is discussed first with a couple of examples. Elements sometimes need to be clustered inside a computational domain to obtain more accurate results. For example, solution features, such as shocks, vortex cores and wake regions, can be extracted during the process of adaptive mesh generation. These features can be represented as surface meshes embedded in a computational domain. Semi‐structured elements can be placed around the embedded surface meshes using the multiple marching direction approach with a pretreatment method. Tetrahedral elements can be placed easily instead. A couple of results are presented to demonstrate the capability of the mesh generation method. Copyright © 2008 John Wiley & Sons, Ltd.     

Structures of CoAl(1 1 1) surface: A first principles study

The structures of the CoAl(1 1 1) surface are studied by first principles calculations. Our calculations show that the surface layer is always occupied by pure Al for all concentrations studied here, which indicates the dominant role of the Al segregation tendency. This is different from the CoAl(0 0 1) surface, where a number of Co anti-sites are found on the top most layer. The calculated surface phase diagram of ground states shows that there are three stable structures. The diffusion barriers of the metastable structure evolving to the stable structure are also calculated. The high diffusion barrier can explain the appearance of metastable structures at low temperature in experiment.     

Step bunching to step-meandering transition induced by electromigration on Si(1 1 1) vicinal surface

The step configuration of a vicinal Si surface is studied under electromigration and a gradient of temperature. An abrupt transition (ΔT = 4 °C) from step-meandering to step bunching is found at 1225 °C for a step-down direct-current direction. This transition starts by random fluctuations which then extend on the whole surface. The transition is studied in the framework of a linear stability analysis of the usual Burton-Cabrera-Frank model by comparing the amplification factors of step-meandering and step bunching instabilities. Both compete at a given temperature, but since the amplification factors behave differently with temperature, bunching abruptly supersedes meandering above a critical temperature.     

Wrinkles formed on a thin gold film deposited onto stretched elastic substrates

In this article the possibility of using various elastic polymer substrates for preparing wrinkled gold films was studied. The gold film was deposited on the substrate using an ion‐sputtering technique, while the substrate was stretched and fixed on a frame. The obtained gold film had wrinkles with a striped pattern. However, whether the pattern was well regulated or not depended on the substrate material. Polydimethylsiloxane (PDMS) was the preferable material when it did not contain fillers. Materials containing fillers are not suitable for this purpose. However, double layer substrates that consist of the PDMS without fillers (the upper layer) and the material containing fillers (the lower layer) could be used to obtain a relatively well‐ordered pattern. Copyright © 2005 John Wiley & Sons, Ltd.     

Plasma Treatment of Polymers

Abstract

Plasma treatment of polymers encompasses a variety of plasma technologies and polymeric materials for a wide range of applications and dates back to at least the 1960s. In this article we provide a brief review of the United States patent literature on plasma surface modification technologies and a brief review of the scientific literature on investigations of the effects of plasma treatment, the nature of the plasma environment, and the mechanisms that drive the plasma–surface interaction. We then discuss low‐radio‐frequency capacitively coupled nitrogen plasmas and their characteristics, suggesting that they provide significant plasma densities and populations of reactive species for effective plasma treatments on a variety of materials, particularly when placing the sample surface in the cathode sheath region. We further discuss surface chemical characterization of treated polymers, including some results on polyesters treated in capacitively coupled nitrogen plasmas driven at 40 kHz. Finally, we connect plasma characterization with surface chemical analysis by applying a surface sites model to nitrogen uptake of poly(ethylene terephthalate) (PET) and poly(ethylene naphthalate) (PEN) treated in a 40 kHz nitrogen plasma. This example serves to suggest an interesting practical approach to comparisons of plasma treatments. In addition, it suggests an approach to defining the investigations required to conclusively identify the underlying treatment mechanisms.     

Young＇s modulus surface and Poisson＇s ratio curve for tetragonal crystals

This paper gives the general expressions for the compliance s′ijkl, Young＇s modulus E（hkl） and Poisson＇s ratio v（hkl, θ） along arbitrary loading direction [hkl] for tetragonal crystals. The representation surface for which the length of the radius vector in the [hkl] direction equals E（hkl） and representation curve for which the length of the radius vector with angle θ deviated from the reference directions [001^-], [100], [001^-], [101^-] and [112^-] equals v（100, θ）, v（001, θ）, v（110,θ）, v（101,θ） and v（111, θ） respectively, are constructed for nine tetragonal crystals （ammonium dihydrogen arsenate, ammonium dihydrogen phosphate, barium titanate, indium, nickel sulfate, potassium dihydrogen arsenate, potassium dihydrogen phosphate, tin and zircon）. The characteristics of them are analysed in detail.