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.

Efficiency of pseudo-spectral algorithms with Anderson mixing for the SCFT of periodic block-copolymer phases

This study examines the numerical accuracy, computational cost, and memory requirements of self-consistent field theory (SCFT) calculations when the diffusion equations are solved with various pseudo-spectral methods and the mean field equations are iterated with Anderson mixing. The different methods are tested on the triply-periodic gyroid and spherical phases of a diblock-copolymer melt over a range of intermediate segregations. Anderson mixing is found to be somewhat less effective than when combined with the full-spectral method, but it nevertheless functions admirably well provided that a large number of histories is used. Of the different pseudo-spectral algorithms, the 4th-order one of Ranjan, Qin and Morse performs best, although not quite as efficiently as the full-spectral method.

Chaotic destruction of Anderson localization in a nonlinear lattice

We consider a scattering problem for a nonlinear disordered lattice layer governed by the discrete nonlinear Schrodinger equation. The linear state with exponentially small transparency, due to the Anderson localization, is followed for an increasing nonlinearity, until it is destroyed via a bifurcation. The critical nonlinearity is shown to decay with the lattice length as a power law. We demonstrate that in the chaotic regimes beyond the bifurcation the field is delocalized and this leads to a drastic increase of transparency. Copyright (C) EPLA, 2008

Categories, concepts and units: representing energy demand in and through time

Methods of data collection are unavoidably rooted in some sort of theoretical paradigm, and are inextricably tied to an implicit agenda or broad problem framing. These prior orientations are not always explicit, but they matter for what data is collected and how it is used. They also structure opportunities for asking new questions, for linking or bridging between existing data sets and they matter even more when data is re-purposed for uses not initially anticipated. In this paper we provide an historical and comparative review of the changing categories used in organising and collecting data on mobility/travel and time use as part of ongoing work to understand, conceptualise and describe the changing patterns of domestic and mobility related energy demand within UK society. This exercise reveals systematic differences of method and approach, for instance in units of measurement, in how issues of time/duration and periodicity are handled, and how these strategies relate to the questions such data is routinely used to address. It also points to more fundamental differences in how traditions of research into mobility, domestic energy and time use have developed. We end with a discussion of the practical implications of these diverse histories for understanding and analysing changing patterns of energy/mobility demand at different scales.

Anna In-Between: Caribbean and not Caribbean: attachment, loss and strange Longing: a conversation with Elizabeth Nunez

Presents an interview with Elizabeth Nunez, author and professor. Nunez discusses the issues on migration, family, and intimacy which are the topics of her novel "Anna In-Between." She explains the demands of the publishing industry that cast a shadow in the world of the novel and the real world of Caribbean writers. This interview was translated by Maria Lusia Ruiz.