10Be and barium concentrations of sediment core GeoB1008-3

Particle reactive elements are scavenged to a higher degree at ocean margins than in the open ocean due to higher fluxes of biogenic and terrigenous particles. In order to determine the influence of these processes on the depositional fluxes of 10Be and barium we have performed high-resolution measurements on sediment core GeoB1008-3 from the Congo Fan. Because the core is dominated by terrigenous matter supplied by the Congo River, it has a high average mass accumulation rate of 6.5 cm/kyr. Biogenic 10Be and Ba concentrations were calculated from total concentrations by subtracting the terrigenous components of10Be and Ba, which are assumed to be proportional to the flux of Al2O3. The mean Ba/Al weight ratio of the terrigenous component was determined to be 0.0045. The unusualy high terrigenous 10Be concentrations of 9.1 * 10**9 atoms/g Al2O3 are either due to input of particles with high10Be content by the Congo River or due to scavenging of oceanic 10Be by riverine particles. The maxima of biogenic 10Be and Ba concentrations coincide with maxima of the paleoproductivity rates. Time series analysis of the 10Be and of Ba concentration profiles reveals a strong dominance of the precessional period of 24 kyr, which also controls the rates of paleoproductivity in this core. During the maxima of productivity the flux of biogenic Ba is enhanced to a larger extent than that of biogenic 10Be. Applying a model for coastal scavenging, we ascribe the observed higher sensitivity of Ba to biogenic particle fluxes to the fact that the ocean residence time of Ba is approximately 10 times longer than that of 10Be.

Discontinuous Galerkin Methods for Advection-Diffusion-Reaction Problems on Anisotropically Refined Meshes

In this paper we consider the a posteriori and a priori error analysis of discontinuous Galerkin interior penalty methods for second-order partial differential equations with nonnegative characteristic form on anisotropically refined computational meshes. In particular, we discuss the question of error estimation for linear target functionals, such as the outflow flux and the local average of the solution. Based on our a posteriori error bound we design and implement the corresponding adaptive algorithm to ensure reliable and efficient control of the error in the prescribed functional to within a given tolerance. This involves exploiting both local isotropic and anisotropic mesh refinement. The theoretical results are illustrated by a series of numerical experiments.

Discontinuous Galerkin Methods on hp-Anisotropic Meshes I: A Priori Error Analysis

We consider the a priori error analysis of hp-version interior penalty discontinuous Galerkin methods for second-order partial differential equations with nonnegative characteristic form under weak assumptions on the mesh design and the local finite element spaces employed. In particular, we prove a priori hp-error bounds for linear target functionals of the solution, on (possibly) anisotropic computational meshes with anisotropic tensor-product polynomial basis functions. The theoretical results are illustrated by a numerical experiment.

Receção estética do texto e promoção da educação literária : trabalho colaborativo interdisciplinar

Dissertação apresentada à Escola Superior de Educação do Instituto Politécnico de Castelo Branco para cumprimento dos requisitos necessários à obtenção do grau de Mestre em Supervisão e Avaliação Escolar.

Discontinuous Galerkin Methods on hp-Anisotropic Meshes II: A Posteriori Error Analysis and Adaptivity

We consider the a posteriori error analysis and hp-adaptation strategies for hp-version interior penalty discontinuous Galerkin methods for second-order partial differential equations with nonnegative characteristic form on anisotropically refined computational meshes with anisotropically enriched elemental polynomial degrees. In particular, we exploit duality based hp-error estimates for linear target functionals of the solution and design and implement the corresponding adaptive algorithms to ensure reliable and efficient control of the error in the prescribed functional to within a given tolerance. This involves exploiting both local isotropic and anisotropic mesh refinement and isotropic and anisotropic polynomial degree enrichment. The superiority of the proposed algorithm in comparison with standard hp-isotropic mesh refinement algorithms and an h-anisotropic/p-isotropic adaptive procedure is illustrated by a series of numerical experiments.

Modeling height-diameter relationship in pinus pinaster ait. in the forest intervention zone of Lomba, NE-Portugal

In this work, the relationship between diameter at breast height (d) and total height (h) of individual-tree was modeled with the aim to establish provisory height-diameter (h-d) equations for maritime pine (Pinus pinaster Ait.) stands in the Lomba ZIF, Northeast Portugal. Using data collected locally, several local and generalized h-d equations from the literature were tested and adaptations were also considered. Model fitting was conducted by using usual nonlinear least squares (nls) methods. The best local and generalized models selected, were also tested as mixed models applying a first-order conditional expectation (FOCE) approximation procedure and maximum likelihood methods to estimate fixed and random effects. For the calibration of the mixed models and in order to be consistent with the fitting procedure, the FOCE method was also used to test different sampling designs. The results showed that the local h-d equations with two parameters performed better than the analogous models with three parameters. However a unique set of parameter values for the local model can not be used to all maritime pine stands in Lomba ZIF and thus, a generalized model including covariates from the stand, in addition to d, was necessary to obtain an adequate predictive performance. No evident superiority of the generalized mixed model in comparison to the generalized model with nonlinear least squares parameters estimates was observed. On the other hand, in the case of the local model, the predictive performance greatly improved when random effects were included. The results showed that the mixed model based in the local h-d equation selected is a viable alternative for estimating h if variables from the stand are not available. Moreover, it was observed that it is possible to obtain an adequate calibrated response using only 2 to 5 additional h-d measurements in quantile (or random) trees from the distribution of d in the plot (stand). Balancing sampling effort, accuracy and straightforwardness in practical applications, the generalized model from nls fit is recommended. Examples of applications of the selected generalized equation to the forest management are presented, namely how to use it to complete missing information from forest inventory and also showing how such an equation can be incorporated in a stand-level decision support system that aims to optimize the forest management for the maximization of wood volume production in Lomba ZIF maritime pine stands.

Asymptotic stability of a coupled Advection-Diffusion-Reaction system arising in bioreactor processes.

In this work, we perform an asymptotic analysis of a coupled system of two Advection-Diffusion-Reaction equations with Danckwerts boundary conditions, which models the interaction between a microbial population (e.g., bacterias), called biomass, and a diluted organic contaminant (e.g., nitrates), called substrate, in a continuous flow bioreactor. This system exhibits, under suitable conditions, two stable equilibrium states: one steady state in which the biomass becomes extinct and no reaction is produced, called washout, and another steady state, which corresponds to the partial elimination of the substrate. We use the method of linearization to give sufficient conditions for the asymptotic stability of the two stable equilibrium configurations. Finally, we compare our asymptotic analysis with the usual asymptotic analysis associated to the continuous bioreactor when it is modeled with ordinary differential equations.

Effect of pre-treatments and post-treatments on drying products

Freeze drying technology can give good quality attributes of vegetables and fruits in terms of color, nutrition, volume, rehydration kinetics, stability during storage, among others, when compared with solely air dried ones. However, published scientific works showed that treatments applied before and after air dehydration are effective in food attributes, improving its quality. Therefore, the hypothesis of the present thesis was focus in a vast research of scientific work that showed the possibility to apply a pre-treatment and a post-treatment to food products combined with conventional air drying aiming being close, or even better, to the quality that a freeze dried product can give. Such attributes are the enzymatic inactivation, stability during storage, drying and rehydration kinetics, color, nutrition, volume and texture/structure. With regard to pre-treatments, the ones studied along the present work were: water blanching, steam blanching, ultrasound, freezing, high pressure and osmotic dehydration. High electric pulsed field was also studied but the food attributes were not explained on detailed. Basically, water and steam blanching showed to be adequate to inactivate enzymes in order to prevent enzymatic browning and preserve the product quality during long storage periods. With regard to ultrasound pre-treatment the published results pointed that ultrasound is an effective pre-treatment to reduce further drying times, improve rehydration kinetics and color retention. On the other hand, studies showed that ultrasound allow sugars losses and, in some cases, can lead to cell disruption. For freezing pre-treatment an overall conclusion was difficult to draw for some food attributes, since, each fruit or vegetable is unique and freezing comprises a lot of variables. However, for the studied cases, freezing showed to be a pre-treatment able to enhance rehydration kinetics and color attributes. High pressure pre-treatment showed to inactivate enzymes improving storage stability of food and showed to have a positive performance in terms of rehydration. For other attributes, when high pressure technology was applied, the literature showed divergent results according with the crops used. Finally, osmotic dehydration has been widely used in food processing to incorporate a desired salt or sugar present in aqueous solution into the cellular structure of food matrix (improvement of nutrition attribute). Moreover, osmotic dehydration lead to shorter drying times and the impregnation of solutes during osmose allow cellular strengthens of food. In case of post-treatments, puffing and a new technology denominated as instant controlled pressure drop (DIC) were reported in the literature as treatments able to improve diverse Abstract Effect of Pre-treatments and Post-treatments on Drying Products x food attributes. Basically, both technologies are similar where the product is submitted to a high pressure step and the process can make use of different heating mediums such as CO2, steam, air and N2. However, there exist a significant difference related with the final stage of both which can comprise the quality of the final product. On the other hand, puffing and DIC are used to expand cellular tissues improving the volume of food samples, helping in rehydration kinetics as posterior procedure, among others. The effectiveness of such pre and/or post-treatments is dependent on the state of the vegetables and fruits used which are also dependent of its cellular structure, variety, origin, state (fresh, ripe, raw), harvesting conditions, etc. In conclusion, as it was seen in the open literature, the application of pre-treatments and post-treatments coupled with a conventional air dehydration aim to give dehydrated food products with similar quality of freeze dried ones. Along the present Master thesis the experimental data was removed due to confidential reasons of the company Unilever R&D Vlaardingen

A comparison of finite difference and finite volume methods for solving the space-fractional advection-dispersion equation with variable coefficients

Transport processes within heterogeneous media may exhibit non- classical diffusion or dispersion which is not adequately described by the classical theory of Brownian motion and Fick’s law. We consider a space-fractional advection-dispersion equation based on a fractional Fick’s law. Zhang et al. [Water Resources Research, 43(5)(2007)] considered such an equation with variable coefficients, which they dis- cretised using the finite difference method proposed by Meerschaert and Tadjeran [Journal of Computational and Applied Mathematics, 172(1):65-77 (2004)]. For this method the presence of variable coef- ficients necessitates applying the product rule before discretising the Riemann–Liouville fractional derivatives using standard and shifted Gru ̈nwald formulas, depending on the fractional order. As an alternative, we propose using a finite volume method that deals directly with the equation in conservative form. Fractionally-shifted Gru ̈nwald formulas are used to discretise the Riemann–Liouville fractional derivatives at control volume faces, eliminating the need for product rule expansions. We compare the two methods for several case studies, highlighting the convenience of the finite volume approach.

Ability of commonly used prediction equations to predict resting energy expenditure in children with inflammatory bowel disease

Background: Paediatric onset inflammatory bowel disease (IBD) may cause alterations in energy requirements and invalidate the use of standard prediction equations. Our aim was to evaluate four commonly used prediction equations for resting energy expenditure (REE) in children with IBD. Methods: Sixty-three children had repeated measurements of REE as part of a longitudinal research study yielding a total of 243 measurements. These were compared with predicted REE from Schofield, Oxford, FAO/WHO/UNU, and Harris-Benedict equations using the Bland-Altman method. Results: Mean (±SD) age of the patients was 14.2 (2.4) years. Mean measured REE was 1566 (336) kcal per day compared with 1491 (236), 1441 (255), 1481 (232), and 1435 (212) kcal per day calculated from Schofield, Oxford, FAO/WHO/UNU, and Harris-Benedict, respectively. While the Schofield equation demonstrated the least difference between measured and predicted REE, it, along with the other equations tested, did not perform uniformly across all subjects, indicating greater errors at either end of the spectrum of energy expenditure. Smaller differences were found for all prediction equations for Crohn's disease compared with ulcerative colitis. Conclusions: Of the commonly used equations, the equation of Schofield should be used in pediatric patients with IBD when measured values are not able to be obtained. (Inflamm Bowel Dis 2010;) Copyright © 2010 Crohn's & Colitis Foundation of America, Inc.

Composite scheme using localized relaxation with non-standard finite difference method for hyperbolic conservation laws

Non-standard finite difference methods (NSFDM) introduced by Mickens [Non-standard Finite Difference Models of Differential Equations, World Scientific, Singapore, 1994] are interesting alternatives to the traditional finite difference and finite volume methods. When applied to linear hyperbolic conservation laws, these methods reproduce exact solutions. In this paper, the NSFDM is first extended to hyperbolic systems of conservation laws, by a novel utilization of the decoupled equations using characteristic variables. In the second part of this paper, the NSFDM is studied for its efficacy in application to nonlinear scalar hyperbolic conservation laws. The original NSFDMs introduced by Mickens (1994) were not in conservation form, which is an important feature in capturing discontinuities at the right locations. Mickens [Construction and analysis of a non-standard finite difference scheme for the Burgers–Fisher equations, Journal of Sound and Vibration 257 (4) (2002) 791–797] recently introduced a NSFDM in conservative form. This method captures the shock waves exactly, without any numerical dissipation. In this paper, this algorithm is tested for the case of expansion waves with sonic points and is found to generate unphysical expansion shocks. As a remedy to this defect, we use the strategy of composite schemes [R. Liska, B. Wendroff, Composite schemes for conservation laws, SIAM Journal of Numerical Analysis 35 (6) (1998) 2250–2271] in which the accurate NSFDM is used as the basic scheme and localized relaxation NSFDM is used as the supporting scheme which acts like a filter. Relaxation schemes introduced by Jin and Xin [The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Communications in Pure and Applied Mathematics 48 (1995) 235–276] are based on relaxation systems which replace the nonlinear hyperbolic conservation laws by a semi-linear system with a stiff relaxation term. The relaxation parameter (λ) is chosen locally on the three point stencil of grid which makes the proposed method more efficient. This composite scheme overcomes the problem of unphysical expansion shocks and captures the shock waves with an accuracy better than the upwind relaxation scheme, as demonstrated by the test cases, together with comparisons with popular numerical methods like Roe scheme and ENO schemes.

A characteristic based numerical method with tracking for nonlinear wave equations

Many physical problems can be modeled by scalar, first-order, nonlinear, hyperbolic, partial differential equations (PDEs). The solutions to these PDEs often contain shock and rarefaction waves, where the solution becomes discontinuous or has a discontinuous derivative. One can encounter difficulties using traditional finite difference methods to solve these equations. In this paper, we introduce a numerical method for solving first-order scalar wave equations. The method involves solving ordinary differential equations (ODEs) to advance the solution along the characteristics and to propagate the characteristics in time. Shocks are created when characteristics cross, and the shocks are then propagated by applying analytical jump conditions. New characteristics are inserted in spreading rarefaction fans. New characteristics are also inserted when values on adjacent characteristics lie on opposite sides of an inflection point of a nonconvex flux function, Solutions along characteristics are propagated using a standard fourth-order Runge-Kutta ODE solver. Shocks waves are kept perfectly sharp. In addition, shock locations and velocities are determined without analyzing smeared profiles or taking numerical derivatives. In order to test the numerical method, we study analytically a particular class of nonlinear hyperbolic PDEs, deriving closed form solutions for certain special initial data. We also find bounded, smooth, self-similar solutions using group theoretic methods. The numerical method is validated against these analytical results. In addition, we compare the errors in our method with those using the Lax-Wendroff method for both convex and nonconvex flux functions. Finally, we apply the method to solve a PDE with a convex flux function describing the development of a thin liquid film on a horizontally rotating disk and a PDE with a nonconvex flux function, arising in a problem concerning flow in an underground reservoir.