An hr-adaptive method for the cubic nonlinear Schrödinger equation

The nonlinear Schrödinger equation (NLSE) is one of the most important equations in quantum mechanics, and appears in a wide range of applications including optical fibre communications, plasma physics and biomolecule dynamics. It is a notoriously difficult problem to solve numerically as solutions have very steep temporal and spatial gradients. Adaptive moving mesh methods (r-adaptive) attempt to optimise the accuracy obtained using a fixed number of nodes by moving them to regions of steep solution features. This approach on its own is however limited if the solution becomes more or less difficult to resolve over the period of interest. Adaptive mesh refinement (h-adaptive), where the mesh is locally coarsened or refined, is an alternative adaptive strategy which is popular for time-independent problems. In this paper, we consider the effectiveness of a combined method (hr-adaptive) to solve the NLSE in one space dimension. Simulations are presented indicating excellent solution accuracy compared to other moving mesh approaches. The method is also shown to control the spatial error based on the user's input error tolerance. Evidence is also presented indicating second-order spatial convergence using a novel monitor function to generate the adaptive moving mesh

Law, politics and the governance of English and Scottish joint-stock companies 1600-1850

This article examines the impact of law on corporate governance by means of a case study of joint-stock enterprise in England and Scotland before 1850. Based on a dataset of over 450 company constitutions together with qualitative information on governance practice, it finds little evidence to support the hypothesis that common-law regimes such as England were more supportive of economic growth than civil-law jurisdictions such as Scotland: indeed, levels of shareholder protection were slightly stronger in the civil-law zone. Other factors, such as local political institutions, played a bigger role in shaping organisational forms and business practice

Questions of presence

This article considers some of the ways in which ‘the black woman’ as both representation and embodied, sentient being is rendered visible and invisible and to link these to the multiple and competing ways in which she is ‘present’. The issues are engaged through three distinct but overlapping conceptualisations of ‘presence’. ‘Presence’ as conceived (and highly contested) in performance studies; ‘presence’ as conceived and worked with in psychoanalysis; and ‘presence’ as decolonising political praxis among indigenous communities. I use these conceptualisations of presence to consider the various ways in which the black woman as figure and as embodied/sentient subject has been made present/absent in different discursive registers. I also explore what is foreclosed and how this is itself linked to legacies of colonial ‘worlding’. I end with consideration of alternative modes of black women’s presence and how this offers a resource for new modes of sociality. Keywords Black women; presence; colonial violence; de-gendering; psychosocial; triangular spac

First observation of J/\psi and \psi(2S) decaying to n K^0_S\bar\Lambda +c.c

The decays of \jpsi and \psip to ${n}{K^0_S}\bar{\Lambda}+c.c.$ are observed and measured for the first time, and the perturbative QCD ``12%'' rule is tested, based on $5.8 \times 10^7$ \jpsi and $1.4 \times 10^7$ \psip events collected with BESII detector at the Beijing Electron-Positron Collider. No obvious enhancement near $n\bar{\Lambda}$ threshold in \jpsi \to {n}{K^0_S}\bar{\Lambda}+c.c. is observed, and the upper limit on the branching ratio of \jpsi \to {K^0_S} X, X \to n \bar \Lambda is determined.Comment: 10 pages, 10 figure

Nature’s nations: the shared conservation history of Canada and the USA

Historians often study the history of conservation within the confines of national borders, concentrating on the bureaucratic and political manifestations of policy within individual governments. Even studies of the popular expression of conservationist ideas are generally limited to the national or sub-national (province, state, etc.) scale. This paper suggests that conservationist discourse, policy and practice in Canada and the USA were the products of a significant cross-border movement of ideas and initiatives derived from common European sources. In addition, the historical development of common approaches to conservation in North America suggests, contrary to common assumptions, that Canada did not always lag behind the USA in terms of policy innovation. The basic tenets of conservation (i.e. state control over resource, class-based disdain for subsistence hunters and utilitarian approaches to resource management) have instead developed at similar time periods and along parallel ideological paths in Canada and the USA

On the use of moving mesh methods to solve PDEs

This chapter explores the use of moving mesh methods to solve PDE

An unconditionally stable second-order accurate ALE–FEM scheme for two-dimensional convection–diffusion problems

The aim of this paper is to investigate the stability of time integration schemes for the solution of a finite element semi-discretization of a scalar convection–diffusion equation defined on a moving domain. An arbitrary Lagrangian–Eulerian formulation is used to reformulate the governing equation with respect to a moving reference frame. We devise an adaptive θ-method time integrator that is shown to be unconditionally stable and asymptotically second-order accurate for smoothly evolving meshes. An essential feature of the method is that it satisfies a discrete equivalent of the well-known geometric conservation law. Numerical experiments are presented to confirm the findings of the analysis