Pattern generation by dissipative parametric instability

Nonlinear instabilities are responsible for spontaneous pattern formation in a vast number of natural and engineered systems, ranging from biology to galaxy buildup. We propose a new instability mechanism leading to pattern formation in spatially extended nonlinear systems, which is based on a periodic antiphase modulation of spectrally dependent losses arranged in a zigzag way: an effective filtering is imposed at symmetrically located wave numbers k and -k in alternating order. The properties of the dissipative parametric instability differ from the features of both key classical concepts of modulation instabilities, i.e., the Benjamin-Feir instability and the Faraday instabiltyity. We demonstrate how the dissipative parametric instability can lead to the formation of stable patterns in one- and two-dimensional systems. The proposed instability mechanism is generic and can naturally occur or can be implemented in various physical systems.

Mechanical properties of sheet metal under forming conditions

In the bulge test, a sheet metal specimen is clamped over a circular hole in a die and formed into a bulge by the hydraulic pressure on one side of the specirnen. As the unsupported part of the specimen is deformed in this way, its area is increased, in other words, the material is generally stretched and its thickness generally decreased. The stresses causing this stretching action are the membrane stresses in the shell generated by the hydraulic pressure, in the same way as the rubber in a toy balloon is stretched by the membrane stresses caused by the air inside it. The bulge test is a widely used sheet metal test, to determine the "formability" of sheet materials. Research on this forming process (2)-(15)* has hitherto been almost exclusively confined to predicting the behaviour of the bulged specimen through the constitutive equations (stresses and strains in relation to displacements and shapes) and empirical work hardening characteristics of the material as determined in the tension test. In the present study the approach is reversed; the stresses and strains in the specimen are measured and determined from the geometry of the deformed shell. Thus, the bulge test can be used for determining the stress-strain relationship in the material under actual conditions in sheet metal forming processes. When sheet materials are formed by fluid pressure, the work-piece assumes an approximately spherical shape, The exact nature and magnitude of the deviation from the perfect sphere can be defined and measured by an index called prolateness. The distribution of prolateness throughout the workpiece at any particular stage of the forming process is of fundamental significance, because it determines the variation of the stress ratio on which the mode of deformation depends. It is found. that, before the process becomes unstable in sheet metal, the workpiece is exactly spherical only at the pole and at an annular ring. Between the pole and this annular ring the workpiece is more pointed than a sphere, and outside this ring, it is flatter than a sphere. In the forming of sheet materials, the stresses and hence the incremental strains, are closely related to the curvatures of the workpiece. This relationship between geometry and state of stress can be formulated quantitatively through prolateness. The determination of the magnitudes of prolateness, however, requires special techniques. The success of the experimental work is due to the technique of measuring the profile inclination of the meridional section very accurately. A travelling microscope, workshop protractor and surface plate are used for measurements of circumferential and meridional tangential strains. The curvatures can be calculated from geometry. If, however, the shape of the workpiece is expressed in terms of the current radial (r) and axial ( L) coordinates, it is very difficult to calculate the curvatures within an adequate degree of accuracy, owing to the double differentiation involved. In this project, a first differentiation is, in effect, by-passed by measuring the profile inclination directly and the second differentiation is performed in a round-about way, as explained in later chapters. The variations of the stresses in the workpiece thus observed have not, to the knowledge of the author, been reported experimentally. The static strength of shells to withstand fluid pressure and their buckling strength under concentrated loads, both depend on the distribution of the thickness. Thickness distribution can be controlled to a limited extent by changing the work hardening characteristics of the work material and by imposing constraints. A technique is provided in this thesis for determining accurately the stress distribution, on which the strains associated with thinning depend. Whether a problem of controlled thickness distribution is tackled by theory, or by experiments, or by both combined, the analysis in this thesis supplies the theoretical framework and some useful experimental techniques for the research applied to particular problems. The improvement of formability by allowing draw-in can also be analysed with the same theoretical and experimental techniques. Results on stress-strain relationships are usually represented by single stress-strain curves plotted either between one stress and one strain (as in the tension or compression tests) or between the effective stress and effective strain, as in tests on tubular specimens under combined tension, torsion and internal pressure. In this study, the triaxial stresses and strains are plotted simultaneously in triangular coordinates. Thus, both stress and strain are represented by vectors and the relationship between them by the relationship between two vector functions. From the results so obtained, conclusions are drawn on both the behaviour and the properties of the material in the bulge test. The stress ratios are generally equal to the strain-rate ratios (stress vectors collinear with incremental strain vectors) and the work-hardening characteristics, which apply only to the particular strain paths are deduced. Plastic instability of the material is generally considered to have been reached when the oil pressure has attained its maximum value so that further deformation occurs under a constant or lower pressure. It is found that the instability regime of deformation has already occurred long before the maximum pressure is attained. Thus, a new concept of instability is proposed, and for this criterion, instability can occur for any type of pressure growth curves.

Gravity field recovery using two low satellites in different orbital planes

This study is concerned with gravity field recovery from low-low satellite to satellite range rate data. An improvement over a coplanar mission is predicted in the errors associated with certain parts of the geopotential by the separation of the orbital planes of the two satellites. Using Hill's equations an analytical scheme to model the range rate residuals is developed. It is flexible enough to model equally well the residuals between pairs of satellites in the same orbital plane or whose planes are separated in right ascension. The possible benefits of such an orientation to gravity field recovery from range rate data can therefore be analysed, and this is done by means of an extensive error analysis. The results of this analysis show that for an optimal planar mission improvements can be made by separating the satellites in right ascension. Gravity field recoveries are performed in order to verify and gauge the limitations of the analytical model, and to support the results of the error analysis. Finally the possible problem of the differential decay rates of two satellites due to the diurnal bulge are evaluated.

May the contact lens force be with you

FULL TEXT: Like many people one of my favourite pastimes over the holiday season is to watch the great movies that are offered on the television channels and new releases in the movie theatres or catching up on those DVDs that you have been wanting to watch all year. Recently we had the new ‘Star Wars’ movie, ‘The Force Awakens’, which is reckoned to become the highest grossing movie of all time, and the latest offering from James Bond, ‘Spectre’ (which included, for the car aficionados amongst you, the gorgeous new Aston Martin DB10). It is always amusing to see how vision correction or eye injury is dealt with by movie makers. Spy movies and science fiction movies have a freehand to design aliens with multiples eyes on stalks or retina scanning door locks or goggles that can see through walls. Eye surgery is usually shown in some kind of day case simplified laser treatment that gives instant results, apart from the great scene in the original ‘Terminator’ movie where Arnold Schwarzenegger's android character encounters an injury to one eye and then proceeds to remove the humanoid covering to this mechanical eye over a bathroom sink. I suppose it is much more difficult to try and include contact lenses in such movies. Although you may recall the film ‘Charlie's Angels’, which did have a scene where one of the Angels wore a contact lens that had a retinal image imprinted on it so she could by-pass a retinal scan door lock and an Eddy Murphy spy movie ‘I-Spy’, where he wore contact lenses that had electronic gadgetry that allowed whatever he was looking at to be beamed back to someone else, a kind of remote video camera device. Maybe we aren’t quite there in terms of devices available but these things are probably not the behest of science fiction anymore as the technology does exist to put these things together. The technology to incorporate electronics into contact lenses is being developed and I am sure we will be reporting on it in the near future. In the meantime we can continue to enjoy the unrealistic scenes of eye swapping as in the film ‘Minority Report’ (with Tom Cruise). Much more closely to home, than in a galaxy far far away, in this issue you can find articles on topics much nearer to the closer future. More and more optometrists in the UK are becoming registered for therapeutic work as independent prescribers and the number is likely to rise in the near future. These practitioners will be interested in the review paper by Michael Doughty, who is a member of the CLAE editorial panel (soon to be renamed the Jedi Council!), on prescribing drugs as part of the management of chronic meibomian gland dysfunction. Contact lenses play an active role in myopia control and orthokeratology has been used not only to help provide refractive correction but also in the retardation of myopia. In this issue there are three articles related to this topic. Firstly, an excellent paper looking at the link between higher spherical equivalent refractive errors and the association with slower axial elongation. Secondly, a paper that discusses the effectiveness and safety of overnight orthokeratology with high-permeability lens material. Finally, a paper that looks at the stabilisation of early adult-onset myopia. Whilst we are always eager for new and exciting developments in contact lenses and related instrumentation in this issue of CLAE there is a demonstration of a novel and practical use of a smartphone to assisted anterior segment imaging and suggestions of this may be used in telemedicine. It is not hard to imagine someone taking an image remotely and transmitting that back to a central diagnostic centre with the relevant expertise housed in one place where the information can be interpreted and instruction given back to the remote site. Back to ‘Star Wars’ and you will recall in the film ‘The Phantom Menace’ when Qui-Gon Jinn first meets Anakin Skywalker on Tatooine he takes a sample of his blood and sends a scan of it back to Obi-Wan Kenobi to send for analysis and they find that the boy has the highest midichlorian count ever seen. On behalf of the CLAE Editorial board (or Jedi Council) and the BCLA Council (the Senate of the Republic) we wish for you a great 2016 and ‘may the contact lens force be with you’. Or let me put that another way ‘the CLAE Editorial Board and BCLA Council, on behalf of, a great 2016, we wish for you!’