Wave-induced perturbations in cylindrically layered smectic A liquid crystals

We consider the stability of a cylindrically layered smectic A liquid crystal sample under a sinusoidal perturbation where we allow for the decoupling between the layer normal and the director. Two forms of general anstazes are proposed: one provides exact solutions for the flow and layer undulations while the other provides series solutions for the hydrodynamic variables. Both cases provide an estimate for a stability parameter. Plots of the flow, layer undulations and pressure are provided.     

Synthesis,characterization, and star polymer assembly of boronic acid end‐functionalized polycaprolactone

Boronic acid end‐functionalized polycaprolactone (PCL) polymers were synthesized by ring‐opening polymerization using a pinacol boronate ester‐containing (Bpin) initiator. The polymerization provides access to boron‐terminated polymers (i.e. Bpin‐PCL‐OH) with narrow molecular weight distributions (PDI = 1.09). Postsynthetic manipulation of the polymer's terminal hydroxyl group by copper‐catalyzed azide‐alkyne cycloaddition chemistry provides a series of bis end‐functionalized polymers with significant structural diversity at the termini. Deprotection of the boronate ester end group was accomplished with an acidic solid phase DOWEX resin. The boronate ester deprotection methodology does not result in hydrolysis of the polymeric backbone. The boronic acid‐tipped polymers were converted into star polymer assemblies using thermal dehydration and ligand‐facilitated trimerization. Thermal dehydration of (HO)₂B‐PCL‐OAc to the corresponding boroxine‐based star polymer assembly was inefficient and lead to degradation products. Ligand‐facilitated trimerization using either pyridine or 7‐azaindole as the Lewis base was efficient and mild. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2010     

Accuracy of a pulse-echo boundary tomogram

An ultrasonic tomogram was developed with a view to providing the outline of a cross section of the ulna in vivo. The construction and design of the instrument was undertaken to obtain a resolution as close as possible to theoretical limits. The apparatus was constructed to be used in conjunction with a system for assessing bone mineral content using a conventional clinical x-ray set. It had been expected that the information from the two instruments would make it possible to obtain a precise spatial plot of bone density. It was thought that the tomograph would respond only to reflections at the bone--soft tissue interface, where there is a large change in acoustic impedance, but in vivo trials have shown that other soft tissue interfaces give rise to reflection, which makes the performance unsatisfactory. However, some interesting results have been obtained from solid objects in water, which have shown that there is a limitation on the accuracy of the plot depending on the angle of incidence of the ultrasonic beam and not dependent on errors of mechanical or electronic origin. Some theory is put forward to account for irregularities in plots for these objects.     

Unsteady Separation Processes at High Reynolds Number and Their Control

Physical situations where a viscous boundary layer breaks down and interacts strongly with an effectively inviscid external flow are common place. For large Reynolds numbers, viscous effects are normally confined to thin boundary layers on all solid surfaces for the majority of any observation time. In most practical situations, exposure of such layers to an adverse pressure gradient is inevitable and in this circumstance, a sequence of events commences near the wall that culminates in an eruption and a strong viscous-inviscid interaction with the external flow. The events leading up to eruption are known as the Van Dommelen–Shen process and the eruption itself is referred to as boundary-layer separation; here the term ‘separation’ denotes the first process of interaction between a hitherto thin boundary layer and the external flow. The event is sufficiently complicated that extraordinary measures are needed to compute its evolution. In most situations, the onset of separation is subtle and hard to detect and thus development of rational control procedures is a challenging task. Here recent calculations of unsteady separation events are discussed for two- and three-dimensional flows. The phenomena involved are generic but leading-edge separation on airfoils and rotorcraft blades is emphasized. Recent studies on various control mechanisms are described, which are found to have the effect of slowing down and/or weakening the separation process. For some control processes, it has proved possible to eliminate separation entirely.     

The diffraction of elastic waves by an imperfect fusion bond

We consider diffraction by a semi-infinite crack located alonga fusion interface between two differing elastic media. Twotypes of crack, namely open and partially closed cracks, areinvestigated. An open crack is modelled by a stress-free contactboundary condition and a partially closed crack is modelledby a spring contact boundary condition. For the latter, thejump in the stress across the crack is assumed to be proportionalto the jump in the displacement across the crack. This situationarises in, for example, a K-weld where the fine grain of theparent material (for example, ferritic or forged austeniticsteel) is in stark contrast with the coarse-grained weld metal(for example, austenitic weld metal). In the metal weld thedirection of the grain axis varies through the metal. However,diffraction is a local phenomenon and so the austenitic steelis assumed to have a zonal axis so that it may be modelled bya transversely isotropic composite. The ferritic or forged austeniticsteel will be modelled as an isotropic material.     

Limit to high-spin isomeric fission

The possibility that high-spin isomers in heavy nuclei might undergo fission has been investigated experimentally. The partial fission lifetime of the 34 μs, I = 34 isomer in ²¹²Fr is found to be at least one hour.     

A simpler GMRES

The generalized minimal residual (GMRES) method is widely used for solving very large, nonsymmetric linear systems, particularly those that arise through discretization of continuous mathematical models in science and engineering. By shifting the Arnoldi process to begin with Ar₀ instead of r₀, we obtain simpler Gram–Schmidt and Householder implementations of the GMRES method that do not require upper Hessenberg factorization. The Gram–Schmidt implementation also maintains the residual vector at each iteration, which allows cheaper restarts of GMRES(m) and may otherwise be useful.