Relaxation approximation to bed-load sediment transport

In this work we propose and apply a numerical method based on finite volume relaxation approximation for computing the bed-load sediment transport in shallow water flows, in one and two space dimensions. The water flow is modeled by the well-known nonlinear shallow water equations which are coupled with a bed updating equation. Using a relaxation approximation, the nonlinear set of equations (and for two different formulations) is transformed to a semilinear diagonalizable problem with linear characteristic variables. A second order MUSCL-TVD method is used for the advection stage while an implicit–explicit Runge–Kutta scheme solves the relaxation stage. The main advantages of this approach are that neither Riemann problem solvers nor nonlinear iterations are required during the solution process. For the two different formulations, the applicability and effectiveness of the presented scheme is verified by comparing numerical results obtained for several benchmark test problems.     

Sharp integral inequalities for the dyadic maximal operator and applications

Mathematische Zeitschrift - We prove a sharp integral inequality for the dyadic maximal function of $$\phi \in L^p$$ . This inequality connects certain quantities related to integrals of $$\phi $$...     

Relaxation schemes for the shallow water equations

We present a class of first and second order in space and time relaxation schemes for the shallow water (SW) equations. A new approach of incorporating the geometrical source term in the relaxation model is also presented. The schemes are based on classical relaxation models combined with Runge–Kutta time stepping mechanisms. Numerical results are presented for several benchmark test problems with or without the source term present. Copyright © 2003 John Wiley & Sons, Ltd.     

A novel multidimensional solution reconstruction and edge‐based limiting procedure for unstructured cell‐centered finite volumes with application to shallow water dynamics

On unstructured meshes, the cell‐centered finite volume (CCFV) formulation, where the finite control volumes are the mesh elements themselves, is probably the most used formulation for numerically solving the two‐dimensional nonlinear shallow water equations and hyperbolic conservation laws in general. Within this CCFV framework, second‐order spatial accuracy is achieved with a Monotone Upstream‐centered Schemes for Conservation Laws‐type (MUSCL) linear reconstruction technique, where a novel edge‐based multidimensional limiting procedure is derived for the control of the total variation of the reconstructed field. To this end, a relatively simple, but very effective modification to a reconstruction procedure for CCFV schemes, is introduced, which takes into account geometrical characteristics of computational triangular meshes. The proposed strategy is shown not to suffer from loss of accuracy on grids with poor connectivity. We apply this reconstruction in the development of a second‐order well‐balanced Godunov‐type scheme for the simulation of unsteady two‐dimensional flows over arbitrary topography with wetting and drying on triangular meshes. Although the proposed limited reconstruction is independent from the Riemann solver used, the well‐known approximate Riemann solver of Roe is utilized to compute the numerical fluxes, whereas the Green–Gauss divergence formulation for gradient computations is implemented. Two different stencils for the Green–Gauss gradient computations are implemented and critically tested, in conjunction with the proposed limiting strategy, on various grid types, for smooth and nonsmooth flow conditions. Copyright © 2012 John Wiley & Sons, Ltd.     

Polymerization of methyl acrylate and as comonomer with ethylene using a bis(imino)pyridine iron(II) chloride/methylaluminoxane catalyst

This article describes the homopolymerization of methyl acrylate (MA) and its attempted copolymerization with ethylene using three single‐site catalysts. The primary catalyst under investigation is formed from a bis(imino)pyridine iron(II) chloride with methylaluminoxane ( 1 ), which is compared with bis(4,5,6,7‐tetrahydro‐1‐indenyl)zirconium dimethyl/tris(pentafluorenyl)borane) ( 2 ), and a P,O‐chelated nickel(II) enolate catalyst ( 3 ). Catalyst ( 1 ) leads to the highest activities exceeding those of catalyst ( 2 ) by a magnitude, whereas catalyst ( 3 ) results in formation of no polymer. The kinetics of the polymerizations and the effect of the Al/Fe‐ratio and temperature on the activity and molecular weight of the polymers have been determined. In the ethylene/MA copolymerization trials, catalyst ( 1 ) produces a blend of the two homopolymers, polymethyl acrylate (PMA) and polyethylene. Remarkably, using catalyst ( 1 ) it is possible to produce polymer blends with up to 52% PMA at relatively high activities. The polymerization kinetics has been determined based on the directly measured uptake of ethylene during the runs. NMR spectroscopy, DSC and GPC measurements have been used as efficient methods to prove that polymer blends instead of true copolymers were formed. Finally, some conclusions about the polymerization mechanism will be drawn. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 5542–5558, 2008     

Bank-level estimates of market power

The aim of this study is to provide an empirical methodology for the estimation of market power of individual banks. The new method employs the well-known model of Panzar and Rosse (1987) and proposes its estimation using the local regression technique. Local regression yields coefficient estimates equal to the number of observations and, thus, market power is estimated for each bank at each point in time. In addition, a number of restrictive assumptions regarding the properties of the production function of banks are relaxed. A panel of banks from transition countries that has been recently employed by Delis (2010) to obtain market power estimates using the Panzar and Rosse model at the country level is used for comparative purposes. We find that country averages of the bank-level results exhibit a very close relationship with standard, industry-level Panzar-Rosse estimates. However, the empirical results suggest that many banks in countries with fairly competitive banking systems deviate significantly from the country averages and that market power varies substantially across banks in each country.     

3D Morphology and Permeability of Highly Porous Cellulosic Fibrous Material

Fibrous materials are structures whose complexity depends on the size and geometry of the fibres and on their arrangement induced by the manufacturing process. We interest here in the permeability for air of wood-based fibrous materials with high porosity on which experimental measurements are difficult to be implemented without structural modifications. In this study, we show the usefulness of 3D X-ray tomography imaging in both experimental and numerical permeability measurements. Image analysis tools derived from mathematical morphology are used to access quantitative structural parameters of the interconnected pores (porosities, pore size distributions and correlation lengths), as well as needed information on the experimental samples (cross-section area and length). A specific experimental setup and methodology is proposed to assess the permeability derived from Darcy’s law. Results are then compared to direct numerical simulation of Stokes flow carried out on 3D representative volumes of the fibrous materials.     

Technical and allocative efficiency in European banking

This paper specifies an empirical framework for estimating both technical and allocative efficiency using the translog cost-share system, thus providing a solution to the issue known in the literature as the Greene problem. The model is applied to a large panel of European banks and the results are compared with those of a model that does not include an allocative inefficiency term and also with those obtained by using a consistent Bayesian technique. Our results suggest that models which include only technical efficiency, significantly overestimate it, while parameter estimates from the model that includes both technical and allocative efficiency are very close to the ones obtained from the Bayesian approach, thus enhancing our confidence in the proposed methodology. Finally, the fact that allocative efficiency of banks in our sample improves more than technical efficiency underlines the importance of including an allocative inefficiency component in parametric efficiency models.