Nucleated polymerization with secondary pathways. I. Time evolution of the principal moments.

Self-assembly processes resulting in linear structures are often observed in molecular biology, and include the formation of functional filaments such as actin and tubulin, as well as generally dysfunctional ones such as amyloid aggregates. Although the basic kinetic equations describing these phenomena are well-established, it has proved to be challenging, due to their non-linear nature, to derive solutions to these equations except for special cases. The availability of general analytical solutions provides a route for determining the rates of molecular level processes from the analysis of macroscopic experimental measurements of the growth kinetics, in addition to the phenomenological parameters, such as lag times and maximal growth rates that are already obtainable from standard fitting procedures. We describe here an analytical approach based on fixed-point analysis, which provides self-consistent solutions for the growth of filamentous structures that can, in addition to elongation, undergo internal fracturing and monomer-dependent nucleation as mechanisms for generating new free ends acting as growth sites. Our results generalise the analytical expression for sigmoidal growth kinetics from the Oosawa theory for nucleated polymerisation to the case of fragmenting filaments. We determine the corresponding growth laws in closed form and derive from first principles a number of relationships which have been empirically established for the kinetics of the self-assembly of amyloid fibrils.

MEAN FLOW EFFECTS OF THE LOW-WAVENUMBER PRESSURE SPECTRUM ON A FLEXIBLE SURFACE.

The Lighthill theory is extended so that it may be used to determine the flow noise induced by a turbulent boundary layer over a plane homogeneous flexible surface. The influence of the surface properties and the mean flow on the sound generation is brought out explicitly through the use of a Green function. The form of the low-wavenumber wall-pressure spectrum on a rigid surface with an arbitrary mean flow profile is determined. The effect of a coating layer is investigated.

How to avoid the problems of target-setting

Purpose: Advocates and critics of target-setting in the workplace seem unable to reach beyond their own well-entrenched battle lines. While the advocates of goal-directed behaviour point to what they see as demonstrable advantages, the critics of target-setting highlight equally demonstrable disadvantages. Indeed, the academic literature on this topic is currently mired in controversy, with neither side seemingly capable of envisaging a better way forward. This paper seeks to break the current deadlock and move thinking forward in this important aspect of performance measurement and management by outlining a new, more fruitful approach, based on both theory and practical experience. Design/methodology/approach: The topic was approached in three phases: assembling and reading key academic and other literature on the subject of target-setting and goal-directed behaviour, with a view to understanding, in depth, the arguments advanced by the advocates and critics of target-setting; comparing these published arguments with one's own experiential findings, in order to bring the essence of disagreement into much sharper focus; and then bringing to bear the academic and practical experience to identify the essential elements of a new, more fruitful approach offering all the benefits of goal-directed behaviour with none of the typical disadvantages of target-setting. Findings: The research led to three key findings: the advocates of goal-directed behaviour and critics of target-setting each make valid points, as seen from their own current perspectives; the likelihood of these two communities, left to themselves, ever reaching a new synthesis, seems vanishingly small (with leading thinkers in the goal-directed behaviour community already acknowledging this); and, between the three authors, it was discovered that their unusual combination of academic study and practical experience enabled them to see things differently. Hence, they would like to share their new thinking more widely. Research limitations/implications: The authors fully accept that their paper is informed by extensive practical experience and, as yet, there have been no opportunities to test their findings, conclusions and recommendations through rigorous academic research. However, they hope that the paper will move thinking forward in this arena, thereby informing future academic research. Practical implications: The authors hope that the practical implications of the paper will be significant, as it outlines a novel way for organisations to capture the benefits of goal-directed behaviour with none of the disadvantages typically associated with target-setting. Social implications: Given that increased efficiency and effectiveness in the management of organisations would be good for society, the authors think the paper has interesting social implications. Originality/value: Leading thinkers in the field of goal-directed behaviour, such as Locke and Latham, and leading critics of target-setting, such as Ordóñez et al. continue to argue with one another - much like, at the turn of the nineteenth century, proponents of the "wave theory of light" and proponents of the "particle theory of light" were similarly at loggerheads. Just as this furious scientific debate was ultimately resolved by Taylor's experiment, showing that light could behave both as a particle and wave at the same time, the authors believe that the paper demonstrates that goal-directed behaviour and target-setting can successfully co-exist. © Emerald Group Publishing Limited.

Precise description of the different far fields encountered in the problem of diffraction of acoustic waves by a quarter-plane

This paper provides a review of important results concerning the Geometrical Theory of Diffraction and Geometrical Optics. It also reviews the properties of the existing solution for the problem of diffraction of a time harmonic plane wave by a half-plane. New mathematical expressions are derived for the wave fields involved in the problem of diffraction of a time harmonic plane wave by a quarter-plane, including the secondary radiated waves. This leads to a precise representation of the diffraction coefficient describing the diffraction occurring at the corner of the quarter-plane. Our results for the secondary radiated waves are an important step towards finding a formula giving the corner diffraction coefficient everywhere. © 2012 The authors.

Classical plume theory: 1937-2010 and beyond

Developing a theoretical description of turbulent plumes, the likes of which may be seen rising above industrial chimneys, is a daunting thought. Plumes are ubiquitous on a wide range of scales in both the natural and the man-made environments. Examples that immediately come to mind are the vapour plumes above industrial smoke stacks or the ash plumes forming particle-laden clouds above an erupting volcano. However, plumes also occur where they are less visually apparent, such as the rising stream of warmair above a domestic radiator, of oil from a subsea blowout or, at a larger scale, of air above the so-called urban heat island. In many instances, not only the plume itself is of interest but also its influence on the environment as a whole through the process of entrainment. Zeldovich (1937, The asymptotic laws of freely-ascending convective flows. Zh. Eksp. Teor. Fiz., 7, 1463-1465 (in Russian)), Batchelor (1954, Heat convection and buoyancy effects in fluids. Q. J. R. Meteor. Soc., 80, 339-358) and Morton et al. (1956, Turbulent gravitational convection from maintained and instantaneous sources. Proc. R. Soc. Lond. A, 234, 1-23) laid the foundations for classical plume theory, a theoretical description that is elegant in its simplicity and yet encapsulates the complex turbulent engulfment of ambient fluid into the plume. Testament to the insight and approach developed in these early models of plumes is that the essential theory remains unchanged and is widely applied today. We describe the foundations of plume theory and link the theoretical developments with the measurements made in experiments necessary to close these models before discussing some recent developments in plume theory, including an approach which generalizes results obtained separately for the Boussinesq and the non-Boussinesq plume cases. The theory presented - despite its simplicity - has been very successful at describing and explaining the behaviour of plumes across the wide range of scales they are observed. We present solutions to the coupled set of ordinary differential equations (the plume conservation equations) that Morton et al. (1956) derived from the Navier-Stokes equations which govern fluid motion. In order to describe and contrast the bulk behaviour of rising plumes from general area sources, we present closed-form solutions to the plume conservation equations that were achieved by solving for the variation with height of Morton's non-dimensional flux parameter Γ - this single flux parameter gives a unique representation of the behaviour of steady plumes and enables a characterization of the different types of plume. We discuss advantages of solutions in this form before describing extensions to plume theory and suggesting directions for new research. © 2010 The Author. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.