Synthesis and characterization of thermally stable second-order nonlinear optical side-chain polyimides containing thiazole and benzothiazole push-pull chromophores

Push-pull nonlinear optical (NLO) chromophores containing thiazole and benzothiazole acceptors were synthesized and characterized. Using these chromophores a series of second-order NLO polyimides were Successfully prepared from 4,4'-(hexafluoroisopropylidene) diphthalic anhydride (6FDA), pyromellitic dianhydride (PMDA) and 3,3'4,4'-benzophenone tetracarboxylic dianhydride (BTDA) by a standard condensation polymerization technique. These polyimides exhibit high glass transition temperatures ranging from 160 to 188 degrees C. UV-vis spectrum of polyimide exhibited a slight blue shift and decreases in absorption due to birefringence. From the order parameters, it was found that chromophores were aligned effectively. Using in situ poling and temperature ramping technique, the optical temperatures for corona poling were obtained. It was found that the optimal temperatures of polyimides approach their glass transition temperatures. These polyimides demonstrate relatively large d(33) values range between 35.15 and 45.20 pm/V at 532 nm. (C) 2008 Elsevier B.V. All rights reserved.

Stochastic resonance in a nonlinear model of a rotating, stratified shear flow, with a simple stochastic inertia-gravity wave parameterization

We report on a numerical study of the impact of short, fast inertia-gravity waves on the large-scale, slowly-evolving flow with which they co-exist. A nonlinear quasi-geostrophic numerical model of a stratified shear flow is used to simulate, at reasonably high resolution, the evolution of a large-scale mode which grows due to baroclinic instability and equilibrates at finite amplitude. Ageostrophic inertia-gravity modes are filtered out of the model by construction, but their effects on the balanced flow are incorporated using a simple stochastic parameterization of the potential vorticity anomalies which they induce. The model simulates a rotating, two-layer annulus laboratory experiment, in which we recently observed systematic inertia-gravity wave generation by an evolving, large-scale flow. We find that the impact of the small-amplitude stochastic contribution to the potential vorticity tendency, on the model balanced flow, is generally small, as expected. In certain circumstances, however, the parameterized fast waves can exert a dominant influence. In a flow which is baroclinically-unstable to a range of zonal wavenumbers, and in which there is a close match between the growth rates of the multiple modes, the stochastic waves can strongly affect wavenumber selection. This is illustrated by a flow in which the parameterized fast modes dramatically re-partition the probability-density function for equilibrated large-scale zonal wavenumber. In a second case study, the stochastic perturbations are shown to force spontaneous wavenumber transitions in the large-scale flow, which do not occur in their absence. These phenomena are due to a stochastic resonance effect. They add to the evidence that deterministic parameterizations in general circulation models, of subgrid-scale processes such as gravity wave drag, cannot always adequately capture the full details of the nonlinear interaction.

Seeing things: perception, experience and the constraints of excavation

Recent attempts to problematize archaeological fieldwork concerned with excavation at the expense of surface survey, and with questions of procedure more than interpretations of the past. In fact these two kinds of fieldwork offer quite different possibilities and suffer from different constraints. Thought must be given to ways in which they can be combined if they are to make a real contribution to social archaeology. The argument is illustrated by a project carried out at a megalithic cemetery in Scotland.

The sea level conundrum: insights from paleo studies

Empirical Constraints on Future Sea Level Rise; Bern, Switzerland, 25–29 August 2008; Eustatic sea level (ESL) rise during the 21st century is perhaps the greatest threat from climate change, but its magnitude is contested. Geological records identify examples of nonlinear ice sheet response to climate forcing, suggesting a strategy for refining estimates of 21st-century sea level change. In August 2008, Past Global Changes (PAGES), International Marine Past Global Change Study (IMAGES), and the University of Bern cosponsored a workshop to address this possibility. The workshop highlighted several ways that paleoceanography studies can place limits on future sea level rise, and these are enlarged upon here.

Linear and nonlinear generalized Fourier transforms

This article presents an overview of a transform method for solving linear and integrable nonlinear partial differential equations. This new transform method, proposed by Fokas, yields a generalization and unification of various fundamental mathematical techniques and, in particular, it yields an extension of the Fourier transform method.

Very large inverse problems in atmosphere and ocean modelling

For the very large nonlinear dynamical systems that arise in a wide range of physical, biological and environmental problems, the data needed to initialize a numerical forecasting model are seldom available. To generate accurate estimates of the expected states of the system, both current and future, the technique of ‘data assimilation’ is used to combine the numerical model predictions with observations of the system measured over time. Assimilation of data is an inverse problem that for very large-scale systems is generally ill-posed. In four-dimensional variational assimilation schemes, the dynamical model equations provide constraints that act to spread information into data sparse regions, enabling the state of the system to be reconstructed accurately. The mechanism for this is not well understood. Singular value decomposition techniques are applied here to the observability matrix of the system in order to analyse the critical features in this process. Simplified models are used to demonstrate how information is propagated from observed regions into unobserved areas. The impact of the size of the observational noise and the temporal position of the observations is examined. The best signal-to-noise ratio needed to extract the most information from the observations is estimated using Tikhonov regularization theory. Copyright © 2005 John Wiley & Sons, Ltd.

Finite element approximation of a sixth order nonlinear degenerate parabolic equation

We consider a finite element approximation of the sixth order nonlinear degenerate parabolic equation ut = ?.( b(u)? 2u), where generically b(u) := |u|? for any given ? ? (0,?). In addition to showing well-posedness of our approximation, we prove convergence in space dimensions d ? 3. Furthermore an iterative scheme for solving the resulting nonlinear discrete system is analysed. Finally some numerical experiments in one and two space dimensions are presented.

Scale-invariant moving finite elements for nonlinear partial differential equations in two dimensions

A scale-invariant moving finite element method is proposed for the adaptive solution of nonlinear partial differential equations. The mesh movement is based on a finite element discretisation of a scale-invariant conservation principle incorporating a monitor function, while the time discretisation of the resulting system of ordinary differential equations is carried out using a scale-invariant time-stepping which yields uniform local accuracy in time. The accuracy and reliability of the algorithm are successfully tested against exact self-similar solutions where available, and otherwise against a state-of-the-art h-refinement scheme for solutions of a two-dimensional porous medium equation problem with a moving boundary. The monitor functions used are the dependent variable and a monitor related to the surface area of the solution manifold. (c) 2005 IMACS. Published by Elsevier B.V. All rights reserved.

Observational constraints on past attributable warming and predictions of future global warming

This paper investigates the impact of aerosol forcing uncertainty on the robustness of estimates of the twentieth-century warming attributable to anthropogenic greenhouse gas emissions. Attribution analyses on three coupled climate models with very different sensitivities and aerosol forcing are carried out. The Third Hadley Centre Coupled Ocean - Atmosphere GCM (HadCM3), Parallel Climate Model (PCM), and GFDL R30 models all provide good simulations of twentieth-century global mean temperature changes when they include both anthropogenic and natural forcings. Such good agreement could result from a fortuitous cancellation of errors, for example, by balancing too much ( or too little) greenhouse warming by too much ( or too little) aerosol cooling. Despite a very large uncertainty for estimates of the possible range of sulfate aerosol forcing obtained from measurement campaigns, results show that the spatial and temporal nature of observed twentieth-century temperature change constrains the component of past warming attributable to anthropogenic greenhouse gases to be significantly greater ( at the 5% level) than the observed warming over the twentieth century. The cooling effects of aerosols are detected in all three models. Both spatial and temporal aspects of observed temperature change are responsible for constraining the relative roles of greenhouse warming and sulfate cooling over the twentieth century. This is because there are distinctive temporal structures in differential warming rates between the hemispheres, between land and ocean, and between mid- and low latitudes. As a result, consistent estimates of warming attributable to greenhouse gas emissions are obtained from all three models, and predictions are relatively robust to the use of more or less sensitive models. The transient climate response following a 1% yr(-1) increase in CO2 is estimated to lie between 2.2 and 4 K century(-1) (5-95 percentiles).