Advances in the study of boundary value problems for nonlinear integrable PDEs

In this review I summarise some of the most significant advances of the last decade in the analysis and solution of boundary value problems for integrable partial differential equations in two independent variables. These equations arise widely in mathematical physics, and in order to model realistic applications, it is essential to consider bounded domain and inhomogeneous boundary conditions. I focus specifically on a general and widely applicable approach, usually referred to as the Unified Transform or Fokas Transform, that provides a substantial generalisation of the classical Inverse Scattering Transform. This approach preserves the conceptual efficiency and aesthetic appeal of the more classical transform approaches, but presents a distinctive and important difference. While the Inverse Scattering Transform follows the "separation of variables" philosophy, albeit in a nonlinear setting, the Unified Transform is a based on the idea of synthesis, rather than separation, of variables. I will outline the main ideas in the case of linear evolution equations, and then illustrate their generalisation to certain nonlinear cases of particular significance.

Advances in the stochastic modelling of satellite-derived rainfall estimates using a sparse calibration dataset

As satellite technology develops, satellite rainfall estimates are likely to become ever more important in the world of food security. It is therefore vital to be able to identify the uncertainty of such estimates and for end users to be able to use this information in a meaningful way. This paper presents new developments in the methodology of simulating satellite rainfall ensembles from thermal infrared satellite data. Although the basic sequential simulation methodology has been developed in previous studies, it was not suitable for use in regions with more complex terrain and limited calibration data. Developments in this work include the creation of a multithreshold, multizone calibration procedure, plus investigations into the causes of an overestimation of low rainfall amounts and the best way to take into account clustered calibration data. A case study of the Ethiopian highlands has been used as an illustration.

Advances in understanding mineral dust and boundary layer processes over the Sahara from Fennec aircraft observations

The Fennec climate program aims to improve understanding of the Saharan climate system through a synergy of observations and modelling. We present a description of the Fennec airborne observations during 2011 and 2012 over the remote Sahara (Mauritania and Mali) and the advances in the understanding of mineral dust and boundary layer processes they have provided. Aircraft instrumentation aboard the UK FAAM BAe146 and French SAFIRE Falcon 20 is described, with specific focus on instrumentation specially developed and relevant to Saharan meteorology and dust. Flight locations, aims and associated meteorology are described. Examples and applications of aircraft measurements from the Fennec flights are presented, highlighting new scientific results delivered using a synergy of different instruments and aircraft. These include: (1) the first airborne measurement of dust particles sized up to 300 microns and associated dust fluxes in the Saharan atmospheric boundary layer (SABL), (2) dust uplift from the breakdown of the nocturnal low-level jet before becoming visible in SEVIRI satellite imagery, (3) vertical profiles of the unique vertical structure of turbulent fluxes in the SABL, (4) in-situ observations of processes in SABL clouds showing dust acting as CCN and IN at −15 °C, (5) dual-aircraft observations of the SABL dynamics, thermodynamics and composition in the Saharan heat low region (SHL), (6) airborne observations of a dust storm associated with a cold-pool (haboob) issued from deep convection over the Atlas, (7) the first airborne chemical composition measurements of dust in the SHL region with differing composition, sources (determined using Lagrangian backward trajectory calculations) and absorption properties between 2011 and 2012, (8) coincident ozone and dust surface area measurements suggest coarser particles provide a route for ozone depletion, (9) discrepancies between airborne coarse mode size distributions and AERONET sunphotometer retrievals under light dust loadings. These results provide insights into boundary layer and dust processes in the SHL region – a region of substantial global climatic importance.

Understanding advances in the simulation of the Madden-Julian Oscillation in a numerical weather prediction model.

The Madden-Julian Oscillation (MJO) is the dominant mode of intraseasonal variability in the Trop- ics. It can be characterised as a planetary-scale coupling between the atmospheric circulation and organised deep convection that propagates east through the equatorial Indo-Pacific region. The MJO interacts with weather and climate systems on a near-global scale and is a crucial source of predictability for weather forecasts on medium to seasonal timescales. Despite its global signifi- cance, accurately representing the MJO in numerical weather prediction (NWP) and climate models remains a challenge. This thesis focuses on the representation of the MJO in the Integrated Forecasting System (IFS) at the European Centre for Medium-Range Weather Forecasting (ECMWF), a state-of-the-art NWP model. Recent modifications to the model physics in Cycle 32r3 (Cy32r3) of the IFS led to ad- vances in the simulation of the MJO; for the first time the observed amplitude of the MJO was maintained throughout the integration period. A set of hindcast experiments, which differ only in their formulation of convection, have been performed between May 2008 and April 2009 to asses the sensitivity of MJO simulation in the IFS to the Cy32r3 convective parameterization. Unique to this thesis is the attribution of the advances in MJO simulation in Cy32r3 to the mod- ified convective parameterization, specifically, the relative-humidity-dependent formulation for or- ganised deep entrainment. Increasing the sensitivity of the deep convection scheme to environmen- tal moisture is shown to modify the relationship between precipitation and moisture in the model. Through dry-air entrainment, convective plumes ascending in low-humidity environments terminate lower in the atmosphere. As a result, there is an increase in the occurrence of cumulus congestus, which acts to moisten the mid-troposphere. Due to the modified precipitation-moisture relationship more moisture is able to build up which effectively preconditions the tropical atmosphere for the transition to deep convection. Results from this thesis suggest that a tropospheric moisture control on convection is key to simulating the interaction between the physics and large-scale circulation associated with the MJO.

Advances in Discourse Studies

Methods of approaching the study of discourse have developed rapidly in the last ten years, influenced by a growing interdisciplinary spirit among linguistics and anthropology, sociology, cognitive and cultural psychology and cultural studies, as well as among established sub-fields within linguistics itself. Among the more recent developments are an increasing ‘critical’ turn in discourse analysis, a growing interest in historical, ethnographic and corpus-based approaches to discourse, more concern with the social contexts in which discourse occurs, the social actions that it is used to take and the identities that are constructed through it, as well as a revaluation of what counts as ‘discourse’ to include multi-modal texts and interaction. Advances in Discourse Studies brings together contributions from leading scholars in the field, investigating the historical and theoretical relationships between new advances in discourse studies and pointing towards new directions for the future of the discipline. Featuring discussion questions, classroom projects and recommended readings at the end of each section, as well as case studies illustrating each approach discussed, this is an invaluable resource for students of interdisciplinary discourse analysis.

Newly Automated System For Integrated Assessment Of The Conditions Of Underwater Gas Pipelines

An underwater gas pipeline is the portion of the pipeline that crosses a river beneath its bottom. Underwater gas pipelines are subject to increasing dangers as time goes by. An accident at an underwater gas pipeline can lead to technological and environmental disaster on the scale of an entire region. Therefore, timely troubleshooting of all underwater gas pipelines in order to prevent any potential accidents will remain a pressing task for the industry. The most important aspect of resolving this challenge is the quality of the automated system in question. Now the industry doesn't have any automated system that fully meets the needs of the experts working in the field maintaining underwater gas pipelines. Principle Aim of this Research: This work aims to develop a new system of automated monitoring which would simplify the process of evaluating the technical condition and decision making on planning and preventive maintenance and repair work on the underwater gas pipeline. Objectives: Creation a shared model for a new, automated system via IDEF3; Development of a new database system which would store all information about underwater gas pipelines; Development a new application that works with database servers, and provides an explanation of the results obtained from the server; Calculation of the values MTBF for specified pipelines based on quantitative data obtained from tests of this system. Conclusion: The new, automated system PodvodGazExpert has been developed for timely and qualitative determination of the physical conditions of underwater gas pipeline; The basis of the mathematical analysis of this new, automated system uses principal component analysis method; The process of determining the physical condition of an underwater gas pipeline with this new, automated system increases the MTBF by a factor of 8.18 above the existing system used today in the industry.

Development, technological change and innovation, Schumpeter and neo-Schumpeterians

This review essay is devoted to a discussion of some central aspects of the Schumpeterian and neo-Schumpeterian approaches to the dynamic processes of development, technological change and innovation. This essay is organised in two parts. In the first, Schumpeter's insightful distinction between circular flow and development is discussed. In the second, some central elements of the neo-Schumpeterian interpretation and extension of Schumpeter's views are critically outlined, special emphasis being placed on some recent attempts to formalize several of his insights on the cyclical dynamics of the processes of technological change and innovation. I should stress that due to space constraints I will focus primarily upon macrotheoretic issues, thus paying only secondary attention to the neo-Schumpeterian literature on the microeconomics of technological change and to the burgeoning empirical developments along those lines.

Endogenous growth with deferred technological change

Lucas (2009) propôs um modelo com dois setores para explicar padrões observados em dados de crescimento. Entretanto, a análise de Lucas não envolve uma decisão intertemporal para o consumidor. O comportamento das variáveis é determinado à priori pela tecnologia escolhida. Rodriguez (2006) propôs um modelo com a tecnologia com dois setores apresentada por Lucas adicionando um processo de decisão intertemporal para o consumidor. Adicionalmente aos resultados obtidos por Rodriguez, nós caracterizamos suficiência e apresentamos exemplos esclarecedores de casos particulares do modelo. Ademais, nós fazemos um esforço para derivar novos insights e esclarecer alguns pontos técnicos. Finalmente, nós obtemos condições sob as quais a economia investe em capital humano mesmo com benefícios diferidos.