A benchmark method for global optimization problems in structure determination from powder diffraction data

Quasi-Newton-Raphson minimization and conjugate gradient minimization have been used to solve the crystal structures of famotidine form B and capsaicin from X-ray powder diffraction data and characterize the chi(2) agreement surfaces. One million quasi-Newton-Raphson minimizations found the famotidine global minimum with a frequency of ca 1 in 5000 and the capsaicin global minimum with a frequency of ca 1 in 10 000. These results, which are corroborated by conjugate gradient minimization, demonstrate the existence of numerous pathways from some of the highest points on these chi(2) agreement surfaces to the respective global minima, which are passable using only downhill moves. This important observation has significant ramifications for the development of improved structure determination algorithms.

Boundary value problems for third-order linear PDEs in time-dependent domains

We present the extension of a methodology to solve moving boundary value problems from the second-order case to the case of the third-order linear evolution PDE qt + qxxx = 0. This extension is the crucial step needed to generalize this methodology to PDEs of arbitrary order. The methodology is based on the derivation of inversion formulae for a class of integral transforms that generalize the Fourier transform and on the analysis of the global relation associated with the PDE. The study of this relation and its inversion using the appropriate generalized transform are the main elements of the proof of our results.

Decentralized load balancing for highly irregular search problems

In this paper, we present a distributed computing framework for problems characterized by a highly irregular search tree, whereby no reliable workload prediction is available. The framework is based on a peer-to-peer computing environment and dynamic load balancing. The system allows for dynamic resource aggregation, does not depend on any specific meta-computing middleware and is suitable for large-scale, multi-domain, heterogeneous environments, such as computational Grids. Dynamic load balancing policies based on global statistics are known to provide optimal load balancing performance, while randomized techniques provide high scalability. The proposed method combines both advantages and adopts distributed job-pools and a randomized polling technique. The framework has been successfully adopted in a parallel search algorithm for subgraph mining and evaluated on a molecular compounds dataset. The parallel application has shown good calability and close-to linear speedup in a distributed network of workstations.

Assimilation of stratospheric ozone from MIPAS into a global general-circulation model: The September 2002 vortex split

Ozone and temperature profiles from the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) have been assimilated, using three-dimensional variational assimilation, into a stratosphere troposphere version of the Met Office numerical weather-prediction system. Analyses are made for the month of September 2002, when there was an unprecedented split in the southern hemisphere polar vortex. The analyses are validated against independent ozone observations from sondes, limb-occultation and total column ozone satellite instruments. Through most of the stratosphere, precision varies from 5 to 15%, and biases are 15% or less of the analysed field. Problems remain in the vortex and below the 60 hPa. level, especially at the tropopause where the analyses have too much ozone and poor agreement with independent data. Analysis problems are largely a result of the model rather than the data, giving confidence in the MIPAS ozone retrievals, though there may be a small high bias in MIPAS ozone in the lower stratosphere. Model issues include an excessive Brewer-Dobson circulation, which results both from known problems with the tracer transport scheme and from the data assimilation of dynamical variables. The extreme conditions of the vortex split reveal large differences between existing linear ozone photochemistry schemes. Despite these issues, the ozone analyses are able to successfully describe the ozone hole split and compare well to other studies of this event. Recommendations are made for the further development of the ozone assimilation system.

Improving flood models using LiDAR: progress and problems

Airborne scanning laser altimetry (LiDAR) is an important new data source for river flood modelling. LiDAR can give dense and accurate DTMs of floodplains for use as model bathymetry. Spatial resolutions of 0.5m or less are possible, with a height accuracy of 0.15m. LiDAR gives a Digital Surface Model (DSM), so vegetation removal software (e.g. TERRASCAN) must be used to obtain a DTM. An example used to illustrate the current state of the art will be the LiDAR data provided by the EA, which has been processed by their in-house software to convert the raw data to a ground DTM and separate vegetation height map. Their method distinguishes trees from buildings on the basis of object size. EA data products include the DTM with or without buildings removed, a vegetation height map, a DTM with bridges removed, etc. Most vegetation removal software ignores short vegetation less than say 1m high. We have attempted to extend vegetation height measurement to short vegetation using local height texture. Typically most of a floodplain may be covered in such vegetation. The idea is to assign friction coefficients depending on local vegetation height, so that friction is spatially varying. This obviates the need to calibrate a global floodplain friction coefficient. It’s not clear at present if the method is useful, but it’s worth testing further. The LiDAR DTM is usually determined by looking for local minima in the raw data, then interpolating between these to form a space-filling height surface. This is a low pass filtering operation, in which objects of high spatial frequency such as buildings, river embankments and walls may be incorrectly classed as vegetation. The problem is particularly acute in urban areas. A solution may be to apply pattern recognition techniques to LiDAR height data fused with other data types such as LiDAR intensity or multispectral CASI data. We are attempting to use digital map data (Mastermap structured topography data) to help to distinguish buildings from trees, and roads from areas of short vegetation. The problems involved in doing this will be discussed. A related problem of how best to merge historic river cross-section data with a LiDAR DTM will also be considered. LiDAR data may also be used to help generate a finite element mesh. In rural area we have decomposed a floodplain mesh according to taller vegetation features such as hedges and trees, so that e.g. hedge elements can be assigned higher friction coefficients than those in adjacent fields. We are attempting to extend this approach to urban area, so that the mesh is decomposed in the vicinity of buildings, roads, etc as well as trees and hedges. A dominant points algorithm is used to identify points of high curvature on a building or road, which act as initial nodes in the meshing process. A difficulty is that the resulting mesh may contain a very large number of nodes. However, the mesh generated may be useful to allow a high resolution FE model to act as a benchmark for a more practical lower resolution model. A further problem discussed will be how best to exploit data redundancy due to the high resolution of the LiDAR compared to that of a typical flood model. Problems occur if features have dimensions smaller than the model cell size e.g. for a 5m-wide embankment within a raster grid model with 15m cell size, the maximum height of the embankment locally could be assigned to each cell covering the embankment. But how could a 5m-wide ditch be represented? Again, this redundancy has been exploited to improve wetting/drying algorithms using the sub-grid-scale LiDAR heights within finite elements at the waterline.

What is wrong with the global support facility for small-scale mining?

The World Bank, United Nations and UK Department for International Development (DfID) have spearheaded a recent global drive to regularize artisanal and small-scale mining (ASM), and provide assistance to its predominantly impoverished participants. To date, millions of dollars have been pledged toward the design of industry-specific policies and regulations; implementation of mechanized equipment; extension; and the launch of alternative livelihood (AL) programmes aimed at diversifying local economies. Much of this funding, however, has failed to facilitate marked improvements, and in many cases, has exacerbated problems. This paper argues that a poor understanding of artisanal, mine-community dynamics and operators’ needs has, in a number of cases, led to the design and implementation of inappropriate industry support schemes and interventions. The discussion focuses upon experiences from sub-Saharan Africa, where ASM is in the most rudimentary of states.

A moving-mesh finite element method and its application to the numerical solution of phase-change problems

A distributed Lagrangian moving-mesh finite element method is applied to problems involving changes of phase. The algorithm uses a distributed conservation principle to determine nodal mesh velocities, which are then used to move the nodes. The nodal values are obtained from an ALE (Arbitrary Lagrangian-Eulerian) equation, which represents a generalization of the original algorithm presented in Applied Numerical Mathematics, 54:450--469 (2005). Having described the details of the generalized algorithm it is validated on two test cases from the original paper and is then applied to one-phase and, for the first time, two-phase Stefan problems in one and two space dimensions, paying particular attention to the implementation of the interface boundary conditions. Results are presented to demonstrate the accuracy and the effectiveness of the method, including comparisons against analytical solutions where available.

Governing the clean development mechanism: global rhetoric versus local realities in carbon sequestration projects

Global agreements have proliferated in the past ten years. One of these is the Kyoto Protocol, which contains provisions for emissions reductions by trading carbon through the Clean Development Mechanism (CDM). The CDM is a market-based instrument that allows companies in Annex I countries to offset their greenhouse gas emissions through energy and tree offset projects in the global South. I set out to examine the governance challenges posed by the institutional design of carbon sequestration projects under the CDM. I examine three global narratives associated with the design of CDM forest projects, specifically North – South knowledge politics, green developmentalism, and community participation, and subsequently assess how these narratives match with local practices in two projects in Latin America. Findings suggest that governance problems are operating at multiple levels and that the rhetoric of global carbon actors often asserts these schemes in one light, while the rhetoric of those who are immediately involved locally may be different. I also stress the alarmist’s discourse that blames local people for the problems of environmental change. The case studies illustrate the need for vertical communication and interaction and nested governance arrangements as well as horizontal arrangements. I conclude that the global framing of forests as offsets requires better integration of local relationships to forests and their management and more effective institutions at multiple levels to link the very local to the very large scale when dealing with carbon sequestration in the CDM.

Concordance in global office market cycles

A large proportion of international real estate investment is concentrated in the office markets of the world’s largest cities. However, many of these global cities are also key financial services centres, highlighting the possibility of reduced economic diversification from an investor’s perspective. This paper assesses the degree of synchronization in cycles across twenty of the world’s largest office markets, finding evidence of significant concordance across a large number of markets. The results highlight the problems associated with commonalities in the underlying economic bases of the markets. The concentration of investment also raises the possibility of common flow of funds effects that may further reduce diversification opportunities.

Advanced global optimisation for mission analysis and design

This report describes the analysis and development of novel tools for the global optimisation of relevant mission design problems. A taxonomy was created for mission design problems, and an empirical analysis of their optimisational complexity performed - it was demonstrated that the use of global optimisation was necessary on most classes and informed the selection of appropriate global algorithms. The selected algorithms were then applied to the di®erent problem classes: Di®erential Evolution was found to be the most e±cient. Considering the speci¯c problem of multiple gravity assist trajectory design, a search space pruning algorithm was developed that displays both polynomial time and space complexity. Empirically, this was shown to typically achieve search space reductions of greater than six orders of magnitude, thus reducing signi¯cantly the complexity of the subsequent optimisation. The algorithm was fully implemented in a software package that allows simple visualisation of high-dimensional search spaces, and e®ective optimisation over the reduced search bounds.

High-resolution global climate simulations with the ECMWF model in Project Athena: experimental design, model climate, and seasonal forecast skill

The sensitivity to the horizontal resolution of the climate, anthropogenic climate change, and seasonal predictive skill of the ECMWF model has been studied as part of Project Athena—an international collaboration formed to test the hypothesis that substantial progress in simulating and predicting climate can be achieved if mesoscale and subsynoptic atmospheric phenomena are more realistically represented in climate models. In this study the experiments carried out with the ECMWF model (atmosphere only) are described in detail. Here, the focus is on the tropics and the Northern Hemisphere extratropics during boreal winter. The resolutions considered in Project Athena for the ECMWF model are T159 (126 km), T511 (39 km), T1279 (16 km), and T2047 (10 km). It was found that increasing horizontal resolution improves the tropical precipitation, the tropical atmospheric circulation, the frequency of occurrence of Euro-Atlantic blocking, and the representation of extratropical cyclones in large parts of the Northern Hemisphere extratropics. All of these improvements come from the increase in resolution from T159 to T511 with relatively small changes for further resolution increases to T1279 and T2047, although it should be noted that results from this very highest resolution are from a previously untested model version. Problems in simulating the Madden–Julian oscillation remain unchanged for all resolutions tested. There is some evidence that increasing horizontal resolution to T1279 leads to moderate increases in seasonal forecast skill during boreal winter in the tropics and Northern Hemisphere extratropics. Sensitivity experiments are discussed, which helps to foster a better understanding of some of the resolution dependence found for the ECMWF model in Project Athena

Boundary value problems for the elliptic sine-Gordon equation in a semi-strip

We study boundary value problems posed in a semistrip for the elliptic sine-Gordon equation, which is the paradigm of an elliptic integrable PDE in two variables. We use the method introduced by one of the authors, which provides a substantial generalization of the inverse scattering transform and can be used for the analysis of boundary as opposed to initial-value problems. We first express the solution in terms of a 2 by 2 matrix Riemann-Hilbert problem whose \jump matrix" depends on both the Dirichlet and the Neumann boundary values. For a well posed problem one of these boundary values is an unknown function. This unknown function is characterised in terms of the so-called global relation, but in general this characterisation is nonlinear. We then concentrate on the case that the prescribed boundary conditions are zero along the unbounded sides of a semistrip and constant along the bounded side. This corresponds to a case of the so-called linearisable boundary conditions, however a major difficulty for this problem is the existence of non-integrable singularities of the function q_y at the two corners of the semistrip; these singularities are generated by the discontinuities of the boundary condition at these corners. Motivated by the recent solution of the analogous problem for the modified Helmholtz equation, we introduce an appropriate regularisation which overcomes this difficulty. Furthermore, by mapping the basic Riemann-Hilbert problem to an equivalent modified Riemann-Hilbert problem, we show that the solution can be expressed in terms of a 2 by 2 matrix Riemann-Hilbert problem whose jump matrix depends explicitly on the width of the semistrip L, on the constant value d of the solution along the bounded side, and on the residues at the given poles of a certain spectral function denoted by h. The determination of the function h remains open.

Current problems in four-dimensional data assimilation

The purpose of this lecture is to review recent development in data analysis, initialization and data assimilation. The development of 3-dimensional multivariate schemes has been very timely because of its suitability to handle the many different types of observations during FGGE. Great progress has taken place in the initialization of global models by the aid of non-linear normal mode technique. However, in spite of great progress, several fundamental problems are still unsatisfactorily solved. Of particular importance is the question of the initialization of the divergent wind fields in the Tropics and to find proper ways to initialize weather systems driven by non-adiabatic processes. The unsatisfactory ways in which such processes are being initialized are leading to excessively long spin-up times.

Introduction and the problems of weather interpretation

Numerical forecasts of the atmosphere based on the fundamental dynamical and thermodynamical equations have now been carried for almost 30 years. The very first models which were used were drastic simplifications of the governing equations and permitting only the prediction of the geostrophic wind in the middle of the troposphere based on the conservation of absolute vorticity. Since then we have seen a remarkable development in models predicting the large-scale synoptic flow. Verification carried out at NMC Washington indicates an improvement of about 40% in 24h forecasts for the 500mb geopotential since the end of the 1950’s. The most advanced models of today use the equations of motion in their more original form (i.e. primitive equations) which are better suited to predicting the atmosphere at low latitudes as well as small scale systems. The model which we have developed at the Centre, for instance, will be able to predict weather systems from a scale of 500-1000 km and a vertical extension of a few hundred millibars up to global weather systems extending through the whole depth of the atmosphere. With a grid resolution of 1.5 and 15 vertical levels and covering the whole globe it is possible to describe rather accurately the thermodynamical processes associated with cyclone development. It is further possible to incorporate sub-grid-scale processes such as radiation, exchange of sensible heat, release of latent heat etc. in order to predict the development of new weather systems and the decay of old ones. Later in this introduction I will exemplify this by showing some results of forecasts by the Centre’s model.