Geometric integration applied to moving mesh methods and degenerate Lagrangians

Moving mesh methods (also called r-adaptive methods) are space-adaptive strategies used for the numerical simulation of time-dependent partial differential equations. These methods keep the total number of mesh points fixed during the simulation, but redistribute them over time to follow the areas where a higher mesh point density is required. There are a very limited number of moving mesh methods designed for solving field-theoretic partial differential equations, and the numerical analysis of the resulting schemes is challenging. In this thesis we present two ways to construct r-adaptive variational and multisymplectic integrators for (1+1)-dimensional Lagrangian field theories. The first method uses a variational discretization of the physical equations and the mesh equations are then coupled in a way typical of the existing r-adaptive schemes. The second method treats the mesh points as pseudo-particles and incorporates their dynamics directly into the variational principle. A user-specified adaptation strategy is then enforced through Lagrange multipliers as a constraint on the dynamics of both the physical field and the mesh points. We discuss the advantages and limitations of our methods. The proposed methods are readily applicable to (weakly) non-degenerate field theories---numerical results for the Sine-Gordon equation are presented.

In an attempt to extend our approach to degenerate field theories, in the last part of this thesis we construct higher-order variational integrators for a class of degenerate systems described by Lagrangians that are linear in velocities. We analyze the geometry underlying such systems and develop the appropriate theory for variational integration. Our main observation is that the evolution takes place on the primary constraint and the 'Hamiltonian' equations of motion can be formulated as an index 1 differential-algebraic system. We then proceed to construct variational Runge-Kutta methods and analyze their properties. The general properties of Runge-Kutta methods depend on the 'velocity' part of the Lagrangian. If the 'velocity' part is also linear in the position coordinate, then we show that non-partitioned variational Runge-Kutta methods are equivalent to integration of the corresponding first-order Euler-Lagrange equations, which have the form of a Poisson system with a constant structure matrix, and the classical properties of the Runge-Kutta method are retained. If the 'velocity' part is nonlinear in the position coordinate, we observe a reduction of the order of convergence, which is typical of numerical integration of DAEs. We also apply our methods to several models and present the results of our numerical experiments.

Evaluating the role of energy efficiency labels in the prices of household appliances: the case of refrigerators

4 p.

The use of “Bonus-Malus” schemes for promoting energy-efficient household appliances: a case study for Spain

32 p.

Design and implementation of fishery modules in integrated household surveys in developing countries

Fish and other aquatic animals contribute to the food security of citizens of developing countries, both as a source of income and as a component of healthy diets, yet fishing is not currently captured in most integrated household surveys. This sourcebook provides essential technical guidance on the design of statistical modules and questionnaires aimed at collecting fishery data at the household level. Background on the main policies important to the fishery sector, information on the data needed to analyze issues of policy relevance, and methodology on the construction of survey questions to collect necessary data are also provided. The document is organized to provide essential technical guidance on how to design statistical modules and questionnaires aimed at collecting fishery data at the household level. It includes an overview of the main technical and statistical challenges related to sampling fishery-dependent households. The document starts with an introductory section identifying the potential reasons why fisheries and in particular small-scale fisheries have not been adequately included in national statistical systems in a large number of countries. The report then proposes a succinct review of what is known (and what remains unknown) about small-scale fisheries and their contribution to the livelihoods of households in sub-Saharan Africa. It also provides readers with background on the main policies that are important to the fishery sector, information on the data needed to analyze issues of policy relevance, and methodology on the construction of survey questions to collect necessary data.