Preface to the special issue on "recent developments and new directions in thin-film flow"

Thin films of fluids are of central importance in numerous industrial, biomedical, geophysical and domestic applications, and display a rich and varied range of behaviours, including pattern formation, dewetting, rupture and finite-time blow up. As well as being of great interest in their own right, thin-film flows provide a “test bed” for research into a variety of challenging nonlinear problems in engineering, physics, chemistry, biology, and mathematics. As a consequence, research by a wide range of scientists, using a variety of analytical, numerical and experimental techniques on many different aspects of thin-film flow, has grown significantly in recent years, as novel applications have continued to appear and increasingly sophisticated theoretical and experimental techniques have been developed

Compressed materialised views of semi-structured data

Query performance issues over semi-structured data have led to the emergence of materialised XML views as a means of restricting the data structure processed by a query. However preserving the conventional representation of such views remains a significant limiting factor especially in the context of mobile devices where processing power, memory usage and bandwidth are significant factors. To explore the concept of a compressed materialised view, we extend our earlier work on structural XML compression to produce a combination of structural summarisation and data compression techniques. These techniques provide a basis for efficiently dealing with both structural queries and valuebased predicates. We evaluate the effectiveness of such a scheme, presenting results and performance measures that show advantages of using such structures

Pinning, de-pinning and re-pinning of a slowly varying rivulet

The solutions for the unidirectional flow of a thin rivulet with prescribed volume flux down an inclined planar substrate are used to describe the locally unidirectional flow of a rivulet with constant width (i.e. pinned contact lines) but slowly varying contact angle as well as the possible pinning and subsequent de-pinning of a rivulet with constant contact angle and the possible depinning and subsequent re-pinning of a rivulet with constant width as they flow in the azimuthal direction from the top to the bottom of a large horizontal cylinder. Despite being the same locally, the global behaviour of a rivulet with constant width can be very different from that of a rivulet with constant contact angle. In particular, while a rivulet with constant non-zero contact angle can always run from the top to the bottom of the cylinder, the behaviour of a rivulet with constant width depends on the value of the width. Specifically, while a narrow rivulet can run all the way from the top to the bottom of the cylinder, a wide rivulet can run from the top of the cylinder only to a critical azimuthal angle. The scenario in which the hitherto pinned contact lines of the rivulet de-pin at the critical azimuthal angle and the rivulet runs from the critical azimuthal angle to the bottom of the cylinder with zero contact angle but slowly varying width is discussed. The pinning and de-pinning of a rivulet with constant contact angle, and the corresponding situation involving the de-pinning and re-pinning of a rivulet with constant width at a non-zero contact angle which generalises the de-pinning at zero contact angle discussed earlier, are described. In the latter situation, the mass of fluid on the cylinder is found to be a monotonically increasing function of the constant width

Three-dimensional coating and rimming flow : a ring of fluid on a rotating horizontal cylinder

The steady three-dimensional flow of a thin, slowly varying ring of Newtonian fluid on either the outside or the inside of a uniformly rotating large horizontal cylinder is investigated. Specifically, we study “full-ring” solutions, corresponding to a ring of continuous, finite and non-zero thickness that extends all the way around the cylinder. In particular, it is found that there is a critical solution corresponding to either a critical load above which no full-ring solution exists (if the rotation speed is prescribed) or a critical rotation speed below which no full-ring solution exists (if the load is prescribed). We describe the behaviour of the critical solution and, in particular, show that the critical flux, the critical load, the critical semi-width and the critical ring profile are all increasing functions of the rotation speed. In the limit of small rotation speed, the critical flux is small and the critical ring is narrow and thin, leading to a small critical load. In the limit of large rotation speed, the critical flux is large and the critical ring is wide on the upper half of the cylinder and thick on the lower half of the cylinder, leading to a large critical load. We also describe the behaviour of the non-critical full-ring solution, and, in particular, show that the semi-width and the ring profile are increasing functions of the load but, in general, non-monotonic functions of the rotation speed. In the limit of large rotation speed, the ring approaches a limiting non-uniform shape, whereas in the limit of small load, the ring is narrow and thin with a uniform parabolic profile. Finally, we show that, while for most values of the rotation speed and the load the azimuthal velocity is in the same direction as the rotation of the cylinder, there is a region of parameter space close to the critical solution for sufficiently small rotation speed in which backflow occurs in a small region on the upward-moving side of the cylinder

Advancing Shannon entropy for measuring diversity in systems

From economic inequality and species diversity to power laws and the analysis of multiple trends and trajectories, diversity within systems is a major issue for science. Part of the challenge is measuring it. Shannon entropy H has been used to re-think diversity within probability distributions, based on the notion of information. However, there are two major limitations to Shannon's approach. First, it cannot be used to compare diversity distributions that have different levels of scale. Second, it cannot be used to compare parts of diversity distributions to the whole. To address these limitations, we introduce a re-normalization of probability distributions based on the notion of case-based entropy Cc as a function of the cumulative probability c. Given a probability density p(x), Cc measures the diversity of the distribution up to a cumulative probability of c, by computing the length or support of an equivalent uniform distribution that has the same Shannon information as the conditional distribution of ^pc(x) up to cumulative probability c. We illustrate the utility of our approach by re-normalizing and comparing three well-known energy distributions in physics, namely, the Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac distributions for energy of sub-atomic particles. The comparison shows that Cc is a vast improvement over H as it provides a scale-free comparison of these diversity distributions and also allows for a comparison between parts of these diversity distributions

Travelling-wave similarity solution for unsteady flow around a dry patch driven by gravity and constant surface shear stress

In this paper we use the lubrication approximation to analyse three-dimensional unsteady flow of a thin film of Newtonian fluid around a symmetric slender moving dry patch on an inclined planar substrate. The flow being driven by gravity and a prescribed constant shear stress at the free surface. We obtain a novel unsteady travelling-wave similarity solution for the dry patch of uniform thickness, in which the dry patch travels at constant speed. This solution predicts that the dry patch has a parabolic shape which may be concave up or concave down the substrate. In all cases investigated numerically the film thickness is found to increase monotonically away from the contact line

How Not to Run An Energy Policy : The Lessons from Three Decades

I stand here as a layman in a room full of experts; as someone who, for a few years, tried to steer the United Kingdom’s energy policy in a safe and sustainable direction and now retains involvement as occasional participant and commentator. But none of that – or even the title of Visiting Professor at the University of Strathclyde - makes me an expert. The only defence I can plead is that, sometimes, you need non-experts making decisions because the one certainty about experts is that their expertise will not all point in the same direction. That is where politicians have come in; balancing the arguments – against cost, against benefits, against ideological objectives, against common sense. Not always successfully. If that process is to succeed, the most desirable ingredient is continuity. The same minister, the same advisers, the same intellectual challenges, the same objectives. On that basis, it just might be possible to steer a path that follows a consistent route, albeit with twists and turns along the way. Unfortunately, these conditions bear little relationship to the realities of how energy policy has evolved. In the absence of continuity, we have lived with a procession of compromises, delays and short-term fixes. At the end of the day, it has not been a disaster because the lights are still on and the wheels of industry – or what is left of it – continue to turn. But that is setting the bar rather low and also begs the question of what we are handing on to the next generation, a quarter of a century after the state-owned industries passed such a handsome legacy to those who succeeded them

Batson v. Kentucky: Can The \u27New\u27 Peremptory Challenge Survive the Resurrection of Strauder v. West Virginia?

It cannot be denied that our jury selection process has lent itself to invidious racial discrimination in the selection of jurors who ultimately decide the black defendant\u27s guilt or innocence. This practice manifested itself in a line of decisions, beginning with Strauder v. West Virginia. The Strauder Court held that excluding qualified venirepersons on the basis of race violated the fourteenth amendment. However, the Supreme Court\u27s refusal in Swain v. Alabama to subject petit jury peremptory challenges to constitutional scrutiny spawned much criticism from courts and commentators. As a result, the Court in Batson v. Kentucky decided to re-examine the role the peremptory challenge plays in exacting justice between the State and the accused