Tailored nearfield Green's functions for arbitrary geometries

An iterative technique, taken from the field of optics, is used to obtain tailored Green's functions suitable for the evaluation, in the nearfield, of pressure fluctuations generated by turbulent flow in the vicinity of solid boundaries. Comparisons are made with the analytical solution for the solid sphere, and with results obtained using conventional boundary element method (BEM) for the case of a thick semi-infinite plate. A divergence issue in the case of the solid sphere is resolved by the introduction of a relaxation factor. The performance of the iterative approach is found to be comparable to that of conventional BEM, except at irregular frequencies, where the bandwidth of the error is slightly larger than that of the conventional BEM. The main advantage of the iterative approach is a significantly reduced computational cost, which allows for higher surface mesh densities and a broader useful frequency range.     

Fixed points of continuous DCPOs

In this article we show that for a continuous DCPO D, the set of fixed points of every self-map is a continuous DCPO if and only if x<y implies x is way below y. We also prove that some classes of continuous functions have the property that if a self-map on a DCPO is in the class then the set of fixed points is a continuous DCPO. We also investigate when the set of fixed points is a retract.     

Surface-initiated group transfer polymerization mediated by rare earth metal catalysts

We present the first example of a surface-initiated group transfer polymerization (SI-GTP) mediated by rare earth metal catalysts for polymer brush synthesis. The experimentally facile method allows rapid grafting of polymer brushes with a thickness of >150 nm in <5 min at room temperature. We show the preparation of common poly(methacrylate) brushes and demonstrate that SI-GTP is a versatile route for the preparation of novel polymer brushes. The method gives access to both thermoresponsive and proton-conducting brush layers.     

A superdirective array of phase shift sources

A superdirective array of audio drivers is described, which is compact compared with the acoustic wavelength over some of its frequency range. In order to minimize the overall sound power output, and hence reduce the excitation of the reverberant field when used in an enclosed space, the individual drivers are made directional by using phase shift enclosures. The motivating application for the array is the enhancement of sound from a television, in a particular region of space, to aid hearing impaired listeners. The design is initially investigated, using free-field simulations, by comparing the performance of 8 monopoles, 8 phase shift loudspeakers, and a double array of 16 monopoles, with a contrast maximization formulation. The construction and testing of an array of 8 drivers is then discussed, together with its measured response in an anechoic environment. The result of using acoustic contrast maximization is then compared with a least squares formulation, which demonstrates that the performance of the least squares solution can be made similar to that given by acoustic contrast maximization in this application, with a suitable choice of the target field.     

Vibration interaction in a multiple flywheel system

This paper investigates vibration interaction in a multiple flywheel system. Flywheels can be used for kinetic energy storage in a satellite Integrated Power and Attitude Control System (IPACS). One hitherto unstudied problem with IPACS is vibration interaction between multiple unbalanced wheels. This paper uses a linear state-space dynamics model to study the impact of vibration interaction. Specifically, imbalance-induced vibration inputs in one flywheel rotor are used to cause a resonant whirling vibration in another rotor. Extra-synchronous resonant vibrations are shown to exist, but with damping modeled the effect is minimal. Vibration is most severe when both rotors are spinning in the same direction.     

On the degeneracy of <Emphasis Type="Italic">SU</Emphasis>(3)<Subscript><Emphasis Type="Italic">k</Emphasis></Subscript> topological phases

The ground state degeneracy of an SU(N) _k topological phase with n quasiparticle excitations is a relevant quantity for quantum computation, condensed matter physics, and knot theory. It is an open question to find a closed formula for this degeneracy for any N >2. Here we present the problem in an explicit combinatorial way and analyze the case N = 3. While not finding a complete closed-form solution, we obtain generating functions and solve some special cases.     

Atlas-based automatic mouse brain image segmentation revisited: model complexity vs. image registration

Although many atlas-based segmentation methods have been developed and validated for the human brain, limited work has been done for the mouse brain. This paper investigated roles of image registration and segmentation model complexity in the mouse brain segmentation. We employed four segmentation models [single atlas, multiatlas, simultaneous truth and performance level estimation (STAPLE) and Markov random field (MRF) via four different image registration algorithms (affine, B-spline free-form deformation (FFD), Demons and large deformation diffeomorphic metric mapping (LDDMM)] for delineating 19 structures from in vivo magnetic resonance microscopy images. We validated their accuracies against manual segmentation. Our results revealed that LDDMM outperformed Demons, FFD and affine in any of the segmentation models. Under the same registration, increasing segmentation model complexity from single atlas to multiatlas, STAPLE or MRF significantly improved the segmentation accuracy. Interestingly, the multiatlas-based segmentation using nonlinear registrations (FFD, Demons and LDDMM) had similar performance to their STAPLE counterparts, while they both outperformed their MRF counterparts. Furthermore, when the single-atlas affine segmentation was used as reference, the improvement due to nonlinear registrations (FFD, Demons and LDDMM) in the single-atlas segmentation model was greater than that due to increasing model complexity (multiatlas, STAPLE and MRF affine segmentation). Hence, we concluded that image registration plays a more crucial role in the atlas-based automatic mouse brain segmentation as compared to model complexity. Multiple atlases with LDDMM can best improve the segmentation accuracy in the mouse brain among all segmentation models tested in this study.     

Imaging skins: an imaging modality with ultra-thin form factor

Reduction of the volume and mass of an imaging system would be advantageous in a variety of applications. However, the far-field resolution of any such system is fundamentally limited by aperture size. We present a new imaging modality based on waveguide coupling that is completely confined to a two-dimensional surface. One such imaging skin was shown to have the same resolution as a 0.5 cm diameter lens while maintaining an imaging system depth of a few micrometers.     

New results on the lower central series quotients of a free associative algebra

We continue the study of the lower central series and its associated graded components for a free associative algebra with n generators, as initiated in Feigin and Shoikhet (2007) [FS]. We establish a linear bound on the degree of tensor field modules appearing in the Jordan–Hölder series of each graded component. We also bound the leading coefficient of the Hilbert polynomial of each graded component. As applications, we confirm conjectures of P. Etingof and B. Shoikhet concerning the structure of the third graded component.