On the solution of bivariate population balance equations for aggregation: X-discretization of space for expansion and contraction of computational domain

A new structured discretization of 2D space, named X-discretization, is proposed to solve bivariate population balance equations using the framework of minimal internal consistency of discretization of Chakraborty and Kumar [2007, A new framework for solution of multidimensional population balance equations. Chem. Eng. Sci. 62, 4112-4125] for breakup and aggregation of particles. The 2D space of particle constituents (internal attributes) is discretized into bins by using arbitrarily spaced constant composition radial lines and constant mass lines of slope -1. The quadrilaterals are triangulated by using straight lines pointing towards the mean composition line. The monotonicity of the new discretization makes is quite easy to implement, like a rectangular grid but with significantly reduced numerical dispersion. We use the new discretization of space to automate the expansion and contraction of the computational domain for the aggregation process, corresponding to the formation of larger particles and the disappearance of smaller particles by adding and removing the constant mass lines at the boundaries. The results show that the predictions of particle size distribution on fixed X-grid are in better agreement with the analytical solution than those obtained with the earlier techniques. The simulations carried out with expansion and/or contraction of the computational domain as population evolves show that the proposed strategy of evolving the computational domain with the aggregation process brings down the computational effort quite substantially; larger the extent of evolution, greater is the reduction in computational effort. (C) 2011 Elsevier Ltd. All rights reserved.

On the solution of bivariate population balance equations for aggregation: Pivotwise expansion of solution domain

The solution of a bivariate population balance equation (PBE) for aggregation of particles necessitates a large 2-d domain to be covered. A correspondingly large number of discretized equations for particle populations on pivots (representative sizes for bins) are solved, although at the end only a relatively small number of pivots are found to participate in the evolution process. In the present work, we initiate solution of the governing PBE on a small set of pivots that can represent the initial size distribution. New pivots are added to expand the computational domain in directions in which the evolving size distribution advances. A self-sufficient set of rules is developed to automate the addition of pivots, taken from an underlying X-grid formed by intersection of the lines of constant composition and constant particle mass. In order to test the robustness of the rule-set, simulations carried out with pivotwise expansion of X-grid are compared with those obtained using sufficiently large fixed X-grids for a number of composition independent and composition dependent aggregation kernels and initial conditions. The two techniques lead to identical predictions, with the former requiring only a fraction of the computational effort. The rule-set automatically reduces aggregation of particles of same composition to a 1-d problem. A midway change in the direction of expansion of domain, effected by the addition of particles of different mean composition, is captured correctly by the rule-set. The evolving shape of a computational domain carries with it the signature of the aggregation process, which can be insightful in complex and time dependent aggregation conditions. (c) 2012 Elsevier Ltd. All rights reserved.

Bivariate frequency analysis of floods using a diffusion based kernel density estimator

Recent focus of flood frequency analysis (FFA) studies has been on development of methods to model joint distributions of variables such as peak flow, volume, and duration that characterize a flood event, as comprehensive knowledge of flood event is often necessary in hydrological applications. Diffusion process based adaptive kernel (D-kernel) is suggested in this paper for this purpose. It is data driven, flexible and unlike most kernel density estimators, always yields a bona fide probability density function. It overcomes shortcomings associated with the use of conventional kernel density estimators in FFA, such as boundary leakage problem and normal reference rule. The potential of the D-kernel is demonstrated by application to synthetic samples of various sizes drawn from known unimodal and bimodal populations, and five typical peak flow records from different parts of the world. It is shown to be effective when compared to conventional Gaussian kernel and the best of seven commonly used copulas (Gumbel-Hougaard, Frank, Clayton, Joe, Normal, Plackett, and Student's T) in estimating joint distribution of peak flow characteristics and extrapolating beyond historical maxima. Selection of optimum number of bins is found to be critical in modeling with D-kernel.

Testing the Forecasting Performance of Ibex 35 Option-implied Risk-neutral Densities

Published also as: Documento de Trabajo Banco de España 0504/2005.

Option-Implied Preferences Adjustments and Risk-Neutral Density Forecasts

The main objective of this paper is to analyse the value of information contained in prices of options on the IBEX 35 index at the Spanish Stock Exchange Market. The forward looking information is extracted using implied risk-neutral density functions estimated by a mixture of two-lognormals and three alternative risk-adjustments: the classic power and exponential utility functions and a habit-based specification that allows for a counter-cyclical variation of risk aversion. Our results show that at four-week horizon we can reject the hypothesis that between October 1996 and March 2000 the risk-neutral densities provide accurate predictions of the distributions of future realisations of the IBEX 35 index at a four-week horizon. When forecasting through risk-adjusted densities the performance of this period is statistically improved and we no longer reject that hypothesis. All risk-adjusted densities generate similar forecasting statistics. Then, at least for a horizon of four-weeks, the actual risk adjustment does not seem to be the issue. By contrast, at the one-week horizon risk-adjusted densities do not improve the forecasting ability of the risk-neutral counterparts.

An empirical comparison of the performance of alternative option pricing models

Published as an article in: Investigaciones Economicas, 2005, vol. 29, issue 3, pages 483-523.

Which policy option can be more cost-effective in promoting the use of energy efficient appliances in Europe? A comparison of energy taxes, subsidies, tax credits and bans.

4 p.

River-based artificial propagation of the African catfish Clarias gariepinus: an option for the small fish farmer

A cheap method of propagating the African catfish, Clarias gariepinus, by incubating the fertilized eggs in a cage placed directly in a flowing river is described. Hatching ranged between 39 and 70%. This is not significantly different from the commonly used water recirculating flow through system. The economic advantages of the river hatching method are discussed with special emphasis on the rural fish farmers.

Estradas e conectividade na Mata Atlântica: identificando áreas prioritárias para aplicação de medidas de mitigação

As rodovias podem representar um importante fator na fragmentação de habitat para espécies silvestres adaptadas a habitats de alta complexidade estrutural, como as florestas tropicais. As estradas reduzem a conectividade da paisagem e a capacidade da população regional em habitar todas as áreas adequadas e estes efeitos são mais significativos nas espécies que evitam a estrada, que são, muitas vezes, espécies de interior de florestas. A magnitude dos efeitos de barreira dependerá do comportamento e mobilidade destas espécies. Quando as estradas representam ralos (sink) ou barreiras para as populações, devido, respectivamente, aos atropelamentos ou à repulsa, medidas mitigadoras são indicadas para aumentar a conectividade entre as manchas de habitat separadas por essas estradas. A qualidade do habitat é um fator que deve ser considerado, mesmo com baixas frequências de atropelamentos nesses locais. O objetivo desse estudo foi propor dois métodos de seleção de áreas prioritárias para implantação de medidas mitigadoras dos efeitos das estradas sobre espécies de vertebrados florestais: Seleção Hierárquica Multivariada e Seleção Bivariada. A área de estudo foi o bioma Mata Atlântica, sendo recortado em paisagens hexagonais em três escalas diferentes (10.000, 1.000 e 100 km), usando a extensão Repeating Shapes no programa ArcGIS 9.3. Em cada hexágono foram calculados: área de floresta e de Unidade de Conservação, densidade de estradas e de hidrografia. Apenas os hexágonos cobertos por no mínimo 45% pela Mata Atlântica, com mais de 50% de cobertura florestal e mais de 1% de Unidades de Conservação foram incluídos nas análises. Após esta seleção, no método Seleção Hierárquica Multivariada, foi feita uma análise de componentes principais (PCA) com as quatro variáveis medidas, para cada escala separadamente. Os hexágonos foram então ordenados segundo o posicionamento deles no 1 Eixo da PCA de forma hierárquica e da maior para menor escala de hexágonos. Para área de estudo o método de Seleção Bivariada foi construído um gráfico de pontos, para cada escala de hexágono, com as variáveis cobertura florestal e rios. Foram selecionados os hexágonos que estavam localizados no quadrante do gráfico que representasse maior densidade de rios e maior porcentagem de cobertura florestal. Posteriormente foi feita uma simulação para avaliar se os métodos eram capazes de recuperar escores tão alto quanto a ordenação seguindo apenas o posicionamento dos hexágonos no Eixo 1 da PCA, sem uma análise hierárquica. O método de Seleção Hierárquica Multivariada foi mais eficiente para escolha de áreas prioritárias do que a Seleção Bivariada tanto para a escala intermediária (1.000 km) quanto para a menor escala (100 km). Os cinco hexágonos de 100 km mais prioritários estão localizados em São Paulo e Paraná, abrangendo quatro UCs (PARES de Jacupiranga, APA de Guaraqueçaba, APA Cananéia- Jacuípe e PARES da Ilha do Cardoso). Devido à simplicidade e fácil aplicabilidade do método, acredita-se que este pode ser uma opção interessante para escolha de áreas prioritárias para implantação de medidas mitigadoras dos efeitos de estradas

Analysis of dimensions involved in the option of improved fish curing practices

A statistical analysis was made of the dimensions involved in the adoption of improved fish curing practices.

The water hyacinth problem and the biological control option in the highland lake region of the upper Nile basin: Uganda's experience

The rapid proliferation and extensive spread of water hyacinth Eichhornia crassipes (Mart) Solms in the highland lakes of the Nile Basin within less than 15 years of introduction into the basin in the 1980s pauses potential environmental and social economic menace if the noxious weed is not controlled soon. The water weed has spread all round Lake Victoria and, in Uganda where infes tation is mos t severe, water hyacinth estimated at 1,330,000 ton smothers over 2,000 ha of the lakeshore (August,1994). Lake Kyoga which already constantly supplies River Nile with the weed is infested with over 570 ha, while over 80% of the river course in Uganda is fringed on either side with an average width of about 5m of water hyacinth. As the impact of infestation with water hyacinth on water quality and availability, transportation by water, fishing activities, fisheries ecology, hydro-power generation etc becomes clear in Uganda, serious discussion is under way on how to control and manage the noxious weed. This paper pauses some of the questions being asked regarding the possible application of mechanical and chemical means to control the water weed.Uganda has already initiated the use of biological control of water hyacinth on Lake Kyoga with a strategy to use two weevils namely Neochetinabruchi and Neochetina eichhorniae. The strategy to build capacity and infrastructure for mass multiplication and deployment of biological control of the weevils in the field developed in Uganda by the Fisheries Research Insti tu te (FIRI) and the Namulonge Agricultural and Animal production Research Insti tute (NAARI) is proposed in outline for evaluation. Plans to deploy this strategy on lake Kyoga are under way