Mathematical modelling for the digital society

We argue the case for a new branch of mathematics and its applications: Mathematics for the Digital Society. There is a challenge for mathematics, a strong “pull” from new and emerging commercial and public activities; and a need to train and inspire a generation of quantitative scientists who will seek careers within the associated sectors. Although now going through an early phase of boiling up, prior to scholarly distillation, we discuss how data rich activities and applications may benefit from a wide range of continuous and discrete models, methods, analysis and inference. In ten years time such applications will be common place and associated courses may be embedded within the undergraduate curriculum.

Fast and accurate SCFT calculations for periodic block-copolymer morphologies using the spectral method with Anderson mixing

We study the numerical efficiency of solving the self-consistent field theory (SCFT) for periodic block-copolymer morphologies by combining the spectral method with Anderson mixing. Using AB diblock-copolymer melts as an example, we demonstrate that this approach can be orders of magnitude faster than competing methods, permitting precise calculations with relatively little computational cost. Moreover, our results raise significant doubts that the gyroid (G) phase extends to infinite $\chi N$. With the increased precision, we are also able to resolve subtle free-energy differences, allowing us to investigate the layer stacking in the perforated-lamellar (PL) phase and the lattice arrangement of the close-packed spherical (S$_{cp}$) phase. Furthermore, our study sheds light on the existence of the newly discovered Fddd (O$^{70}$) morphology, showing that conformational asymmetry has a significant effect on its stability.

Observed adaptation to climate change: UK evidence of transition to a well-adapting society

This paper investigates whether and to what extent a wide range of actors in the UK are adapting to climate change, and whether this is evidence of a social transition. We document evidence of over 300 examples of early adopters of adaptation practice to climate change in the UK. These examples span a range of activities from small adjustments (or coping) to building adaptive capacity, implementing actions and creating deeper systemic change in public and private organisations in a range of sectors. We find that adaptation in the UK has been dominated by government initiatives and has principally occurred in the form of research into climate change impacts. These actions within government stimulate a further set of actions at other scales in public agencies, regulatory agencies and regional government (or in the devolved administrations), though with little real evidence of climate change adaptation initiatives trickling down to local government level. The water supply and flood defence sectors, requiring significant investment in large scale infrastructure such as reservoirs and coastal defences, have invested more heavily in identifying potential impacts and adaptations. Economic sectors that are not dependent on large scale infrastructure appear to be investing far less effort and resources in preparing for climate change. We conclude that while the government-driven top-down targeted adaptation approach has generated anticipatory action at low cost, it may also have created enough niche activities to allow for diffusion of new adaptation practices in response to real or perceived climate change. These results have significant implications for how climate policy can be developed to support autonomous adaptors in the UK and other countries.

The strategy makers: thoughts on war and society from Machiavelli and Clausewitz

Introductory chapter. Introduction and excerpts from works of Seigneur de Fourquevaux (1548); Francois Loque – Saillans (1589); Matthew Sutcliffe (1593); Don Bernardino de Mendoza (1595); Paul Hay du Chastelet (1668); Marquis Santa Cruz de Marcenado & Zanthier (1724-30/1775); Guibert (1772); Rühle von Lilienstern (1816/1817).

Representing geometrical knowledge

This paper introduces perspex algebra which is being developed as a common representation of geometrical knowledge. A perspex can currently be interpreted in one of four ways. First, the algebraic perspex is a generalization of matrices, it provides the most general representation for all of the interpretations of a perspex. The algebraic perspex can be used to describe arbitrary sets of coordinates. The remaining three interpretations of the perspex are all related to square matrices and operate in a Euclidean model of projective space-time, called perspex space. Perspex space differs from the usual Euclidean model of projective space in that it contains the point at nullity. It is argued that the point at nullity is necessary for a consistent account of perspective in top-down vision. Second, the geometric perspex is a simplex in perspex space. It can be used as a primitive building block for shapes, or as a way of recording landmarks on shapes. Third, the transformational perspex describes linear transformations in perspex space that provide the affine and perspective transformations in space-time. It can be used to match a prototype shape to an image, even in so called 'accidental' views where the depth of an object disappears from view, or an object stays in the same place across time. Fourth, the parametric perspex describes the geometric and transformational perspexes in terms of parameters that are related to everyday English descriptions. The parametric perspex can be used to obtain both continuous and categorical perception of objects. The paper ends with a discussion of issues related to using a perspex to describe logic.

Self-consistent field theory for diblock copolymers grafted to a sphere

An efficient numerical self-consistent field theory (SCFT) algorithm is developed for treating structured polymers on spherical surfaces. The method solves the diffusion equations of SCFT with a pseudospectral approach that combines a spherical-harmonics expansion for the angular coordinates with a modified real-space Crank–Nicolson method for the radial direction. The self-consistent field equations are solved with Anderson-mixing iterations using dynamical parameters and an alignment procedure to prevent angular drift of the solution. A demonstration of the algorithm is provided for thin films of diblock copolymer grafted to the surface of a spherical core, in which the sequence of equilibrium morphologies is predicted as a function of diblock composition. The study reveals an array of interesting behaviors as the block copolymer pattern is forced to adapt to the finite surface area of the sphere.

State and society in the English countryside: the rural community movement 1918-1939

This paper assesses the relationship between state and society in interwar rural England, focusing on the hitherto neglected role of the Rural Community Councils (RCCs). The rise of statutory social provision in the early twentieth century created new challenges and opportunities for voluntaryism, and the rural community movement was in part a response. The paper examines the early development of the movement, arguing that a crucial role was played by a close-knit group of academics and local government officials. While largely eschewing party politics, they shared a commitment to citizenship, democracy and the promotion of rural culture; many of them had been close associates of Sir Horace Plunkett. The RCCs engaged in a wide range of activities, including advisory work, adult education, local history, village hall provision, support for rural industries and an ambivalent engagement with parish councils. The paper concludes with an assessment of the achievements of the rural community movement, arguing that it was constrained by its financial dependence on voluntary contributions.