Coerced Mechanical Coarsening of Nanoparticle Assemblies

Coarsening is a ubiquitous phenomenon [1-3] that underpins countless processes in nature, including epitaxial growth [1,3,4], the phase separation of alloys, polymers and binary fluids [2], the growth of bubbles in foams5, and pattern formation in biomembranes6. Here we show, in the first real-time experimental study of the evolution of an adsorbed colloidal nanoparticle array, that tapping-mode atomic force microscopy (TM-AFM) can drive the coarsening of Au nanoparticle assemblies on silicon surfaces. Although the growth exponent has a strong dependence on the initial sample morphology, our observations are largely consistent with modified Ostwald ripening processes [7-9]. To date, ripening processes have been exclusively considered to be thermally activated, but we show that nanoparticle assemblies can be mechanically coerced towards equilibrium, representing a new approach to directed coarsening. This strategy enables precise control over the evolution of micro- and nanostructures.

A Mixed Discontinuous Galerkin Method for Incompressible Magnetohydrodynamics

We introduce and analyze a discontinuous Galerkin method for the numerical discretization of a stationary incompressible magnetohydrodynamics model problem. The fluid unknowns are discretized with inf-sup stable discontinuous P^3_{k}-P_{k-1} elements whereas the magnetic part of the equations is approximated by discontinuous P^3_{k}-P_{k+1} elements. We carry out a complete a-priori error analysis and prove that the energy norm error is convergent of order O(h^k) in the mesh size h. We also show that the method is able to correctly capture and resolve the strongest magnetic singularities in non-convex polyhedral domains. These results are verified in a series of numerical experiments.

An A Posteriori Error Indicator for Discontinuous Galerkin Approximations of Fourth Order Elliptic Problems

We introduce a residual-based a posteriori error indicator for discontinuous Galerkin discretizations of the biharmonic equation with essential boundary conditions. We show that the indicator is both reliable and efficient with respect to the approximation error measured in terms of a natural energy norm, under minimal regularity assumptions. We validate the performance of the indicator within an adaptive mesh refinement procedure and show its asymptotic exactness for a range of test problems.

Rail passenger crowding, stress, health and safety in Britain

There has long been a question as to whether crowding in rail passenger transport poses a threat to passenger health related to the experience of stress. A review of the scientific literature was conducted. Little rail-specific empirical research was identified. The more general research that does exist suggests that high-density environments are not necessarily perceived as crowded and that stress-related physiological, psychological and behavioural reactions do not necessarily follow from exposure to such environments. Several factors are identified that may moderate the impact of a high-density environment on perceptions of crowding and the subsequent experience and effects of stress. These include, inter alia, perceptions of control and predictability of events. However, if caused, the experience and effects of stress may be made worse by inadequate coach design that gives rise to discomfort. The model that emerges from these findings offers a suitable framework for the development of research questions that should help translate emerging knowledge into practical interventions, for the reduction of any adverse health outcomes associated with crowding.

Organizational, systems and human issues in production planning, scheduling and control

With global markets and global competition, pressures are placed on manufacturing organizations to compress order fulfillment times, meet delivery commitments consistently and also maintain efficiency in operations to address cost issues. This chapter argues for a process perspective on planning, scheduling and control that integrates organizational planning structures, information systems as well as human decision makers. The chapter begins with a reconsideration of the gap between theory and practice, in particular for classical scheduling theory and hierarchical production planning and control. A number of the key studies of industrial practice are then described and their implications noted. A recent model of scheduling practice derived from a detailed study of real businesses is described. Socio-technical concepts are then introduced and their implications for the design and management of planning, scheduling and control systems are discussed. The implications of adopting a process perspective are noted along with insights from knowledge management. An overview is presented of a methodology for the (re-)design of planning, scheduling and control systems that integrates organizational, system and human perspectives. The most important messages from the chapter are then summarized.

Seeing it my way: a case of a selective deficit in inhibiting self-perspective

Little is known about the functional and neural architecture of social reasoning, one major obstacle being that we crucially lack the relevant tools to test potentially different social reasoning components. In the case of belief reasoning, previous studies tried to separate the processes involved in belief reasoning per se from those involved in the processing of the high incidental demands such as the working memory demands of typical belief tasks (e.g., Stone et al., 1998; Samson et al., 2004). In this study, we developed new belief tasks in order to disentangle, for the first time, two perspective taking components involved in belief reasoning: (1) the ability to inhibit one’s own perspective (self-perspective inhibition) and (2) the ability to infer someone else’s perspective as such (other-perspective taking). The two tasks had similar demands in other-perspective taking as they both required the participant to infer that a character has a false belief about an object’s location. However, the tasks varied in the self-perspective inhibition demands. In the task with the lowest self-perspective inhibition demands, at the time the participant had to infer the character’s false belief, he or she had no idea what the new object’s location was. In contrast, in the task with the highest self-perspective inhibition demands, at the time the participant had to infer the character’s false belief, he or she knew where the object was actually located (and this knowledge had thus to be inhibited). The two tasks were presented to a stroke patient, WBA, with right prefrontal and temporal damage. WBA performed well in the low-inhibition false belief task but showed striking difficulty in the task placing high self-perspective inhibition demands, showing a selective deficit in inhibiting self-perspective. WBA also made egocentric errors in other social and visual perspective taking tasks, indicating a difficulty with belief attribution extending to the attribution of emotions, desires and visual experiences to other people. The case of WBA, together with the recent report of three patients impaired in belief reasoning even when self-perspective inhibition demands were reduced (Samson et al., 2004), provide the first neuropsychological evidence that (a) the inhibition of one’s own point of view and (b) the ability to infer someone else’ s point of view, rely on distinct neural and functional processes.

Error analyses reveal contrasting deficits in “theory of mind”: neuropsychological evidence from a 3-option false belief task

Perspective taking is a crucial ability that guides our social interactions. In this study, we show how the specific patterns of errors of brain-damaged patients in perspective taking tasks can help us further understand the factors contributing to perspective taking abilities. Previous work (e.g., Samson, Apperly, Chiavarino, & Humphreys, 2004; Samson, Apperly, Kathirgamanathan, & Humphreys, 2005) distinguished two components of perspective taking: the ability to inhibit our own perspective and the ability to infer someone else’s perspective. We assessed these components using a new nonverbal false belief task which provided different response options to detect three types of response strategies that participants might be using: a complete and spared belief reasoning strategy, a reality-based response selection strategy in which participants respond from their own perspective, and a simplified mentalising strategy in which participants avoid responding from their own perspective but rely on inaccurate cues to infer the other person’s belief. One patient, with a self-perspective inhibition deficit, almost always used the reality-based response strategy; in contrast, the other patient, with a deficit in taking other perspectives, tended to use the simplified mentalising strategy without necessarily transposing her own perspective. We discuss the extent to which the pattern of performance of both patients could relate to their executive function deficit and how it can inform us on the cognitive and neural components involved in belief reasoning.

When “happy” means “sad”: neuropsychological evidence for the right prefrontal cortex contribution to executive semantic processing

The contribution of the left inferior prefrontal cortex in semantic processing has been widely investigated in the last decade. Converging evidence from functional imaging studies shows that this region is involved in the “executive” or “controlled” aspects of semantic processing. In this study, we report a single case study of a patient, PW, with damage to the right prefrontal and temporal cortices following stroke. PW showed a problem in executive control of semantic processing, where he could not easily override automatic but irrelevant semantic processing. This case thus shows the necessary role of the right inferior prefrontal cortex in executive semantic processing. Compared to tasks previously used in the literature, our tasks placed higher demands on executive semantic processing. We suggest that the right inferior prefrontal cortex is recruited when the demands on executive semantic processing are particularly high.

Bayesian alignment of continuous molecular shapes using random fields

Statistical methodology is proposed for comparing molecular shapes. In order to account for the continuous nature of molecules, classical shape analysis methods are combined with techniques used for predicting random fields in spatial statistics. Applying a modification of Procrustes analysis, Bayesian inference is carried out using Markov chain Monte Carlo methods for the pairwise alignment of the resulting molecular fields. Superimposing entire fields rather than the configuration matrices of nuclear positions thereby solves the problem that there is usually no clear one--to--one correspondence between the atoms of the two molecules under consideration. Using a similar concept, we also propose an adaptation of the generalised Procrustes analysis algorithm for the simultaneous alignment of multiple molecular fields. The methodology is applied to a dataset of 31 steroid molecules.

Discrete breathers in a two-dimensional hexagonal Fermi-Pasta-Ulam lattice

We consider a two-dimensional Fermi-Pasta-Ulam (FPU) lattice with hexagonal symmetry. Using asymptotic methods based on small amplitude ansatz, at third order we obtain a eduction to a cubic nonlinear Schr{\"o}dinger equation (NLS) for the breather envelope. However, this does not support stable soliton solutions, so we pursue a higher-order analysis yielding a generalised NLS, which includes known stabilising terms. We present numerical results which suggest that long-lived stationary and moving breathers are supported by the lattice. We find breather solutions which move in an arbitrary direction, an ellipticity criterion for the wavenumbers of the carrier wave, symptotic estimates for the breather energy, and a minimum threshold energy below which breathers cannot be found. This energy threshold is maximised for stationary breathers, and becomes vanishingly small near the boundary of the elliptic domain where breathers attain a maximum speed. Several of the results obtained are similar to those obtained for the square FPU lattice (Butt \& Wattis, {\em J Phys A}, {\bf 39}, 4955, (2006)), though we find that the square and hexagonal lattices exhibit different properties in regard to the generation of harmonics, and the isotropy of the generalised NLS equation.

Asymptotic analysis of combined breather-kink modes in a Fermi-Pasta-Ulam chain

We find approximations to travelling breather solutions of the one-dimensional Fermi-Pasta-Ulam (FPU) lattice. Both bright breather and dark breather solutions are found. We find that the existence of localised (bright) solutions depends upon the coefficients of cubic and quartic terms of the potential energy, generalising an earlier inequality derived by James [CR Acad Sci Paris 332, 581, (2001)]. We use the method of multiple scales to reduce the equations of motion for the lattice to a nonlinear Schr{\"o}dinger equation at leading order and hence construct an asymptotic form for the breather. We show that in the absence of a cubic potential energy term, the lattice supports combined breathing-kink waveforms. The amplitude of breathing-kinks can be arbitrarily small, as opposed to traditional monotone kinks, which have a nonzero minimum amplitude in such systems. We also present numerical simulations of the lattice, verifying the shape and velocity of the travelling waveforms, and confirming the long-lived nature of all such modes.

Coarse-graining and renormalisation group methods for the elucidation of the kinetics of complex nucleation and growth processes

We review our work on generalisations of the Becker-Doring model of cluster-formation as applied to nucleation theory, polymer growth kinetics, and the formation of upramolecular structures in colloidal chemistry. One valuable tool in analysing mathematical models of these systems has been the coarse-graining approximation which enables macroscopic models for observable quantities to be derived from microscopic ones. This permits assumptions about the detailed molecular mechanisms to be tested, and their influence on the large-scale kinetics of surfactant self-assembly to be elucidated. We also summarise our more recent results on Becker-Doring systems, notably demonstrating that cross-inhibition and autocatalysis can destabilise a uniform solution and lead to a competitive environment in which some species flourish at the expense of others, phenomena relevant in models of the origins of life.

Symmetry-breaking in chiral polymerisation

We propose a model for chiral polymerisation and investigate its symmetric and asymmetric solutions. The model has a source species which decays into left- and right-handed types of monomer, each of which can polymerise to form homochiral chains; these chains are susceptible to `poisoning' by the opposite handed monomer. Homochiral polymers are assumed to influence the proportion of each type of monomer formed from the precursor. We show that for certain parameter values a positive feedback mechanism makes the symmetric steady-state solution unstable. The kinetics of polymer formation are then analysed in the case where the system starts from zero concentrations of monomers and chains. We show that following a long induction time, extremely large concentrations of polymers are formed for a short time, during this time an asymmetry introduced into the system by a random external perturbation may be massively amplified. The system then approaches one of the steady-state solutions described above.

Chiral polymerisation and the RNA world

The purpose of this paper is to review two mathematical models: one for the formation of homochiral polymers from an originally chirally symmetric system; and the other, to show how, in an RNA-world scenario, RNA can simultaneously act both as information storage and a catalyst for its own production. We note the similarities and differences in chemical mechanisms present in the systems. We review these two systems, analysing steady-states, interesting kinetics and the stability of symmetric solutions. In both systems we show that there are ranges of parameter values where some chains increase their own concentrations faster than others.

Speculative document evaluation

Optimisation of real world Variable Data printing (VDP) documents is a dicult problem because the interdependencies between layout functions may drastically reduce the number of invariant blocks that can be factored out for pre-rasterisation. This paper examines how speculative evaluation at an early stage in a document-preparation pipeline, provides a generic and effective method of optimising VDP documents that contain such interdependencies. Speculative evaluation will be at its most effective in speeding up print runs if sets of layout invariances can either be discovered automatically, or designed into the document at an early stage. In either case the expertise of the layout designer needs to be supplemented by expertise in exploiting potential invariances and also in predicting the effects of speculative evaluation on the caches used at various stages in the print production pipeline.