K. S. Thomas

The Frederiks effect and related phenomena in ferronematic materials

Using continuum and statistical mechanical theories, we study the switching properties of a ferronematic in a nematic liquid crystal cell subject to homeotropic boundary conditions at the cell and particle walls. An external magnetic field normal to the cell plane is also imposed. At low fields we find thresholdless switching of the nematic director, consistent with experimental data. At higher fields, there are three regimes, depending on the strength of the anchoring interaction between the director and the ferroparticle orientation. For low anchoring strengths, there is an inverse Frederiks effect, and the nematic reorientation reduces and then disappears continuously at a critical magnetic field. At intermediate fields, the degree of reorientation reduces at high fields but remains finite. For high fields, however, the director switching saturates. The dimensionless temperature scale in the problem involves the temperature, the mean nematic elastic constant, the colloidal density, and the cell dimensi...

Galerkin methods for singular integral equations

The approximate solution of a singular integral equation by Galerkins method is studied. We discuss the theoretical aspects of such problems and give error bounds for the approximate solution.

Photonic band gaps in 12-fold symmetric quasicrystals

The 12-fold symmetric quasicrystal shows great potential as a novel photonic band gap (PBG) structure exhibiting a band gap for relatively low filling fractions and dielectric contrasts. The band gaps are highly homogeneous with respect to the angle of incidence of the incoming light due to the crystals high degree of rotational symmetry. These crystals have been analyzed using a finite element method developed specifically for modelling PBG structures. We present and discuss quasicrystal structures and their optical properties.

Inverse Frederiks Effect and Bistability in Ferronematic Cells

In recent work we have examined switching properties of a ferronematic in an external magnetic field in a cell with homeotropic boundary conditions, and subject also to a bias field in the plane of the cell. There are three regimes, depending on the strength of the director-ferroparticle coupling. For low coupling, there is a high field inverse Frederiks transition to an undistorted phase. At low non-dimensional temperatures, high magnetic fields can cause the ferroparticles to segregate. Segregation-director distortion coupling can drive the inverse Frederiks transition first order, causing bistability. This article considers homogeneous planar, rather than homeotropic anchoring at the cell walls and particle surfaces. The bias field is unnecessary, but the basic physical picture is retained, with the same set of regimes. The lack of bias field means that this case is a more suitable model for basic studies.

On the approximate solution of operator equations

Prolongations and restrictions are used to derive error estimates when linear operator equations of the second kind are solved by discretisation methods.

Efficient Methods for Handling Long-Range Forces in Particle—Particle Simulations

A number of problems arise when long-range forces, such as those governed by Bessel functions, are used in particle?particle simulations. If a simple cutoff for the interaction is used, the system may find an equilibrium configuration at zero temperature that is not a regular lattice yet has an energy lower than the theoretically predicted minimum for the physical system. We demonstrate two methods to overcome these problems in Monte Carlo and molecular dynamics simulations. The first uses a smoothed potential to truncate the interaction in a single unit cell: this is appropriate for phenomenological characterisations, but may be applied to any potential. The second is a new method for summing the unmodified potential in an infinitely tiled periodic system, which is in excess of 20,000 times faster than previous naive methods which add periodic images in shells of increasing radius: this is suitable for quantitative studies. Finally, we show that numerical experiments which do not handle the long-range force carefully may give misleading results: both of our proposed methods overcome these problems.

Experience with multi-transputer Ada

The transputer is one of the most cost-effective multicomputer components to buy, but still one of the hardest to program. Even if the parts of a program that are destined for individual transputers are programmed in a familiar high-level language (Ada or Fortran or C), users are forced to be aware of occam when connecting transputers together with harnesses. Moreover, the design of parallel and distributed algorithms is in itself a challenging field. This paper describes experience with using the Alsys Ada compiler on single and multiple transputer configurations, and considers whether Ada makes it any easier to gain access to the power of multi-transputers. Early performance figures indicate that Ada running on transputer arrays compares favourably with the speed of other languages. An assessment of the impact of the proposed Ada 9X support for distribution is made.

Applied grid computing: optimisation of photonic devices

\begin{abstract} In this paper, we present an application of grid computing to solve an important industrial problem: that of optimising the band gap of photonic crystals, which are an important technology in future generation telecomms and sensing. The computational power grid enabled months of experimentation to be performed in a weekend. Of particular interest was the necessity to run jobs on both Linux and Windows resources. \end{abstract}

Eigenvalue Spectrum Estimation and Photonic Crystals

We have developed an algorithm for the estimation of eigenvalue spectra and have applied it to the determination of the density of states in a photonic crystal, which requires the repeated solution of a generalized eigenvalue problem. We demonstrate that the algorithm offers significant advantages in time, memory, and ease of parallelization over conventional subspace iteration algorithms. In particular it is possible to obtain more than two orders of magnitude speedup in time over subspace methods for modestly sized matrices. For larger matrices the savings are even greater, whilst retaining accurate resolution of features of the eigenspectrum.

Design of control functions for an internet-based tele-robotic laboratory

Tele-robotic is one of the most popular remote control applications. It proves very useful to help humans perform various tasks, from standard industrial applications to performing tasks that are too difficult or dangerous to do by a person. Nowadays tele-robotic applications as a tool for training and education have also been increasingly popular. The development of a tele-robotic system requires handling the control design as well as the programming, that it gives an excellent practical training to students. In this paper, the development of a control remote laboratory that applies this tele-robotic technology is reported. The system architecture and the control functions within the facility are discussed. The use of minimum hardware for the servers while keeping the functions modular is proposed, and the advantages of this approach in terms of reliability and accessibility are highlighted. Some experimental results are presented, to show the functionalities of this facility to support control engineering and robotics education for engineering students at both introductory and advanced levels.