Methods of studying the planar distribution of objects in histological sections of brain tissue

This article reviews the statistical methods that have been used to study the planar distribution, and especially clustering, of objects in histological sections of brain tissue. The objective of these studies is usually quantitative description, comparison between patients or correlation between histological features. Objects of interest such as neurones, glial cells, blood vessels or pathological features such as protein deposits appear as sectional profiles in a two-dimensional section. These objects may not be randomly distributed within the section but exhibit a spatial pattern, a departure from randomness either towards regularity or clustering. The methods described include simple tests of whether the planar distribution of a histological feature departs significantly from randomness using randomized points, lines or sample fields and more complex methods that employ grids or transects of contiguous fields, and which can detect the intensity of aggregation and the sizes, distribution and spacing of clusters. The usefulness of these methods in understanding the pathogenesis of neurodegenerative diseases such as Alzheimer's disease and Creutzfeldt-Jakob disease is discussed. © 2006 The Royal Microscopical Society.

Hairpin vortex solution in planar Couette flow: a tapestry of knotted vortices

A numerical continuation method has been carried out seeking solutions for two distinct flow configurations, planar Couette flow (PCF) and laterally heated flow in a vertical slot (LHF). We found that the spanwise vortex solution in LHF identifies a new solution in PCF. The vortical structure of our new solution has the shape of a hairpin observed ubiquitously in high-Reynolds-number turbulent flow, and we believe this discovery may provide the paradigm for a hierarchical organization of coherent structures in turbulent shear layers.

The application of fibre Bragg grating networks as strain sensors and as phased array antenna true time delay elements

The fabrication of in-fibre Bragg gratings, and the application of arrays of such gratings as strain sensors and as true time delay elements for the control of phased array antennas is reported. Chirped period Bragg gratings were produced using the fibre deformation fabrication technique, with chirps of between 2.9nm and 17.3nm achieved. Arrays of 5mm and 2mm long uniform period Bragg gratings were fabricated using the inscription method, for use as true time delay elements,dissimilar wavefronts and their spectral characteristics recorded. The uniform period grating arrays were used to create minimum time delays of 9.09ps, 19.02ps and 31ps; making them suitable for controlling phased array antennas operating at RF frequencies of up to 3GHz, with 10° phase resolution. Four 4mm long chirped gratings were produced using the dissimilar wavefronts fabrication method, having chirps of 7nm, 12nm, 20nm and 30nm, and were used to create time delays of between 0.3ps and 59ps. Hence they are suitable for controlling phased array antennas at RF frequencies of up to 48GHz. The application of in fibre Bragg gratings as strain sensors within smart structure materials was investigated, with their sensitivity to applied strain and compression measured for both embedded and surface mounted uniform period and fibre Fabry-Perot filter gratings. A fibre Bragg grating sensor demultiplexing scheme based on a liquid crystal filled Fabry-Perot etalon tuneable transmission filter was proposed, successfully constructed and fully characterised. Three characteristics of the LCFP etalon were found to pose operational limitations to its application in a Bragg grating sensor system; most significantly, the resonance peak wavelength was highly (-2,77nm/°C) temperature dependent. Several methods for minimising this temperature sensitivity were investigated, but enjoyed only limited success. It was therefore concluded that this type (E7 filled) of LCFP etalon is unsuitable for use as a Bragg grating sensor demultiplexing element.

Effect of the base station antenna beam tilting on energy consumption in cellular networks

The objective of this paper is to combine the antenna downtilt selection with the cell size selection in order to reduce the overall radio frequency (RF) transmission power in the homogeneous High-Speed Packet Downlink (HSDPA) cellular radio access network (RAN). The analysis is based on the concept of small cells deployment. The energy consumption ratio (ECR) and the energy reduction gain (ERG) of the cellular RAN are calculated for different antenna tilts when the cell size is being reduced for a given user density and service area. The results have shown that a suitable antenna tilt and the RF power setting can achieve an overall energy reduction of up to 82.56%. Equally, our results demonstrate that a small cell deployment can considerably reduce the overall energy consumption of a cellular network.

Determining planar multiple sound-soft obstacles from scattered acoustic fields

An inverse problem is considered where the structure of multiple sound-soft planar obstacles is to be determined given the direction of the incoming acoustic field and knowledge of the corresponding total field on a curve located outside the obstacles. A local uniqueness result is given for this inverse problem suggesting that the reconstruction can be achieved by a single incident wave. A numerical procedure based on the concept of the topological derivative of an associated cost functional is used to produce images of the obstacles. No a priori assumption about the number of obstacles present is needed. Numerical results are included showing that accurate reconstructions can be obtained and that the proposed method is capable of finding both the shapes and the number of obstacles with one or a few incident waves.

An alternating potential based approach for a Cauchy problem for the Laplace equation in a planar domain with a cut

We consider a Cauchy problem for the Laplace equation in a bounded region containing a cut, where the region is formed by removing a sufficiently smooth arc (the cut) from a bounded simply connected domain D. The aim is to reconstruct the solution on the cut from the values of the solution and its normal derivative on the boundary of the domain D. We propose an alternating iterative method which involves solving direct mixed problems for the Laplace operator in the same region. These mixed problems have either a Dirichlet or a Neumann boundary condition imposed on the cut and are solved by a potential approach. Each of these mixed problems is reduced to a system of integral equations of the first kind with logarithmic and hypersingular kernels and at most a square root singularity in the densities at the endpoints of the cut. The full discretization of the direct problems is realized by a trigonometric quadrature method which has super-algebraic convergence. The numerical examples presented illustrate the feasibility of the proposed method.

Recovering boundary data in planar heat conduction using boundary integral equation method

We consider a Cauchy problem for the heat equation, where the temperature field is to be reconstructed from the temperature and heat flux given on a part of the boundary of the solution domain. We employ a Landweber type method proposed in [2], where a sequence of mixed well-posed problems are solved at each iteration step to obtain a stable approximation to the original Cauchy problem. We develop an efficient boundary integral equation method for the numerical solution of these mixed problems, based on the method of Rothe. Numerical examples are presented both with exact and noisy data, showing the efficiency and stability of the proposed procedure and approximations.

Transition of planar Couette flow at infinite Reynolds numbers

An outline of the state space of planar Couette flow at high Reynolds numbers (Re<105) is investigated via a variety of efficient numerical techniques. It is verified from nonlinear analysis that the lower branch of the hairpin vortex state (HVS) asymptotically approaches the primary (laminar) state with increasing Re. It is also predicted that the lower branch of the HVS at high Re belongs to the stability boundary that initiates a transition to turbulence, and that one of the unstable manifolds of the lower branch of HVS lies on the boundary. These facts suggest HVS may provide a criterion to estimate a minimum perturbation arising transition to turbulent states at the infinite Re limit. © 2013 American Physical Society.

Planar variations in normal anisotropy in mild steel strip

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Controlled growth of poly(2-(diethylamino)ethyl methacrylate) brushes via atom transfer radical polymerisation on planar silicon surfaces

Progress in making pH-responsive polyelectrolyte brushes with a range of different grafting densities is reported. Polymer brushes of poly(2-(diethylamino)ethyl methacrylate) were synthesised via atom transfer radical polymerisation on silicon wafers using a 'grafted from' approach. The [11-(2-bromo-2-methyl) propionyloxy]undecyl trichlorosilane initiator was covalently attached to the silicon via silylation, from which the brushes were grown using a catalytic system of copper(I) chloride and pentamethyldiethylenetriamine in tetrahydrofuran at 80°C. X-ray reflectivity was used to assess the initiator surfaces and an upper limit on the grafting density of the polymer was determined. The quality of the brushes produced was analysed using ellipsometry and atomic force microscopy, which is also discussed.

High-gain frequency reconfigurable Vivaldi antenna

This article proposes a frequency agile antenna whose operating frequency band can be switched. The design is based on a Vivaldi antenna. High-performance radio-frequency microelectromechanical system (RF-MEMS) switches are used to realize the 2.7 GHz and 3.9 GHz band switching. The low band starts from 2.33 GHz and works until 3.02 GHz and the high band ranges from 3.29 GHz up to 4.58 GHz. The average gains of the antenna at the low and high bands are 10.9 and 12.5 dBi, respectively. This high-gain frequency reconfigurable antenna could replace several narrowband antennas for reducing costs and space to support multiple communication systems, while maintaining good performance.

A flexible approach for the apodization of planar waveguide Bragg gratings

A novel single-step technique for the apodization of planar waveguide Bragg gratings based on the polarization control method is proposed. First results are presented, showing successful side-lobe suppression in the reflection spectrum of the gratings.

Numerical solution of parabolic Cauchy problems in planar corner domains

An iterative method for the parabolic Cauchy problem in planar domains having a finite number of corners is implemented based on boundary integral equations. At each iteration, mixed well-posed problems are solved for the same parabolic operator. The presence of corner points renders singularities of the solutions to these mixed problems, and this is handled with the use of weight functions together with, in the numerical implementation, mesh grading near the corners. The mixed problems are reformulated in terms of boundary integrals obtained via discretization of the time-derivative to obtain an elliptic system of partial differential equations. To numerically solve these integral equations a Nyström method with super-algebraic convergence order is employed. Numerical results are presented showing the feasibility of the proposed approach. © 2014 IMACS.

Evaluation on a 60 GHz radio over fiber system employing photonic up conversion and optically beam formed linear array antenna for broadband indoor access

In this study, two linear coplanar array antennas based on Indium Phosphide (InP) substrate are designed, presented and compared in terms of bandwidth and gain. Slot introduction in combination with coplanar structure is investigated, providing enhanced antenna gain and bandwidth at the 60 GHz frequency band. In addition the proposed array antennas are evaluated in terms of integration with a high-speed photodiode and investigated in terms of matching, providing a bandwidth that reaches 2 GHz. Moreover a potential beam forming scenario combined with photonic up-conversion scheme has been proposed. © 2013 IEEE.