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Finite Domain (finite + domain)
Selected AbstractsApparent/spurious multifractality of data sampled from fractional Brownian/Lévy motionsHYDROLOGICAL PROCESSES, Issue 15 2010Shlomo P. Neuman Abstract Many earth and environmental variables appear to be self-affine (monofractal) or multifractal with spatial (or temporal) increments having exceedance probability tails that decay as powers of , , where 1 < , , 2. The literature considers self-affine and multifractal modes of scaling to be fundamentally different, the first arising from additive and the second from multiplicative random fields or processes. We demonstrate theoretically that data having finite support, sampled across a finite domain from one or several realizations of an additive Gaussian field constituting fractional Brownian motion (fBm) characterized by , = 2, give rise to positive square (or absolute) increments which behave as if the field was multifractal when in fact it is monofractal. Sampling such data from additive fractional Lévy motions (fLm) with 1 < , < 2 causes them to exhibit spurious multifractality. Deviations from apparent multifractal behaviour at small and large lags are due to nonzero data support and finite domain size, unrelated to noise or undersampling (the causes cited for such deviations in the literature). Our analysis is based on a formal decomposition of anisotropic fLm (fBm when , = 2) into a continuous hierarchy of statistically independent and homogeneous random fields, or modes, which captures the above behaviour in terms of only E + 3 parameters where E is Euclidean dimension. Although the decomposition is consistent with a hydrologic rationale proposed by Neuman (2003), its mathematical validity is independent of such a rationale. Our results suggest that it may be worth checking how closely would variables considered in the literature to be multifractal (e.g. experimental and simulated turbulent velocities, some simulated porous flow velocities, landscape elevations, rain intensities, river network area and width functions, river flow series, soil water storage and physical properties) fit the simpler monofractal model considered in this paper (such an effort would require paying close attention to the support and sampling window scales of the data). Parsimony would suggest associating variables found to fit both models equally well with the latter. Copyright © 2010 John Wiley & Sons, Ltd. [source] A partition-of-unity-based finite element method for level setsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2008Stéphane Valance Abstract Level set methods have recently gained much popularity to capture discontinuities, including their possible propagation. Typically, the partial differential equations that arise in level set methods, in particular the Hamilton,Jacobi equation, are solved by finite difference methods. However, finite difference methods are less suited for irregular domains. Moreover, it seems slightly awkward to use finite differences for the capturing of a discontinuity, while in a subsequent stress analysis finite elements are normally used. For this reason, we here present a finite element approach to solving the governing equations of level set methods. After a review of the governing equations, the initialization of the level sets, the discretization on a finite domain, and the stabilization of the resulting finite element method will be discussed. Special attention will be given to the proper treatment of the internal boundary condition, which is achieved by exploiting the partition-of-unity property of finite element shape functions. Finally, a quantitative analysis including accuracy analysis is given for a one-dimensional example and a qualitative example is given for a two-dimensional case with a curved discontinuity. Copyright © 2008 John Wiley & Sons, Ltd. [source] Smart element method II.INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2005An element based on the finite Eshelby tensor Abstract In this study, we apply the newly derived finite Eshelby tensor in a variational multiscale formulation to construct a smart element through a more accurate homogenization procedure. The so-called Neumann,Eshelby tensor for an inclusion in a finite domain is used in the fine scale feedback procedure to take into account the interactions among different scales and elements. Numerical experiments have been conducted to compare the performance and robustness of the new element to earlier formulations. The results showed that the smart element constructed via the Neumann,Eshelby tensor of a finite domain provides better numerical accuracy than that constructed via the Eshelby tensor of an infinite domain. Moreover, it can relieve volumetric locking. Copyright © 2005 John Wiley & Sons, Ltd. [source] Finite element analysis of time-dependent semi-infinite wave-guides with high-order boundary treatmentINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2003Dan Givoli Abstract A new finite element (FE) scheme is proposed for the solution of time-dependent semi-infinite wave-guide problems, in dispersive or non-dispersive media. The semi-infinite domain is truncated via an artificial boundary ,, and a high-order non-reflecting boundary condition (NRBC), based on the Higdon non-reflecting operators, is developed and applied on ,. The new NRBC does not involve any high derivatives beyond second order, but its order of accuracy is as high as one desires. It involves some parameters which are chosen automatically as a pre-process. A C0 semi-discrete FE formulation incorporating this NRBC is constructed for the problem in the finite domain bounded by ,. Augmented and split versions of this FE formulation are proposed. The semi-discrete system of equations is solved by the Newmark time-integration scheme. Numerical examples concerning dispersive waves in a semi-infinite wave guide are used to demonstrate the performance of the new method. Copyright © 2003 John Wiley & Sons, Ltd. [source] Non-reflecting artificial boundaries for transient scalar wave propagation in a two-dimensional infinite homogeneous layerINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2003Chongbin Zhao Abstract This paper presents an exact non-reflecting boundary condition for dealing with transient scalar wave propagation problems in a two-dimensional infinite homogeneous layer. In order to model the complicated geometry and material properties in the near field, two vertical artificial boundaries are considered in the infinite layer so as to truncate the infinite domain into a finite domain. This treatment requires the appropriate boundary conditions, which are often referred to as the artificial boundary conditions, to be applied on the truncated boundaries. Since the infinite extension direction is different for these two truncated vertical boundaries, namely one extends toward x ,, and another extends toward x,- ,, the non-reflecting boundary condition needs to be derived on these two boundaries. Applying the variable separation method to the wave equation results in a reduction in spatial variables by one. The reduced wave equation, which is a time-dependent partial differential equation with only one spatial variable, can be further changed into a linear first-order ordinary differential equation by using both the operator splitting method and the modal radiation function concept simultaneously. As a result, the non-reflecting artificial boundary condition can be obtained by solving the ordinary differential equation whose stability is ensured. Some numerical examples have demonstrated that the non-reflecting boundary condition is of high accuracy in dealing with scalar wave propagation problems in infinite and semi-infinite media. Copyright © 2003 John Wiley & Sons, Ltd. [source] High-order boundary conditions for linearized shallow water equations with stratification, dispersion and advection,INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2004Vince J. van Joolen Abstract The two-dimensional linearized shallow water equations are considered in unbounded domains with density stratification. Wave dispersion and advection effects are also taken into account. The infinite domain is truncated via a rectangular artificial boundary ,, and a high-order open boundary condition (OBC) is imposed on ,. Then the problem is solved numerically in the finite domain bounded by ,. A recently developed boundary scheme is employed, which is based on a reformulation of the sequence of OBCs originally proposed by Higdon. The OBCs can easily be used up to any desired order. They are incorporated here in a finite difference scheme. Numerical examples are used to demonstrate the performance and advantages of the computational method, with an emphasis is on the effect of stratification. Published in 2004 by John Wiley & Sons, Ltd. [source] Non-isothermal multi-phase modeling of PEM fuel cell cathodeINTERNATIONAL JOURNAL OF ENERGY RESEARCH, Issue 7 2010Nada Zamel Abstract In this study, numerical simulation has been carried out for the heat transfer and temperature distribution in the cathode of polymer electrolyte membrane fuel cells along with the multi-phase and multi-species transport under the steady-state condition. The commercial software, COMSOL Multiphysics, is used to solve the conservation equations for momentum, mass, species, charge and energy numerically. The conservation equations are applied to the solid, liquid and vapor phases in the bipolar plate and gas diffusion (GDL) and catalyst layers of a two-dimensional cross section of the cathode. The catalyst layer is assumed to be a finite domain and the water production in the catalyst layer is considered to be in the liquid form. The temperature distribution in the cathode is simulated and then the effects of the relative humidity of the air stream, the permeability of the cathode and the flow channel shoulder to channel width ratio are investigated. It is shown that the highest temperature change, both in the in-plane and across-the-plane directions, occurs in the GDL, while the highest temperature is reached in the catalyst layer. The distribution of temperature in the bipolar plate is shown to be relatively uniform due to the high thermal conductivity of the plate. A decrease in the inlet relative humidity of the air stream results in the decrease of the maximum temperature due to the absorption of heat during the evaporation of liquid water in the GDL and catalyst layer. The non-uniformity of the temperature distribution, especially in the catalyst layer, is observed with the increase of the permeability of the cathode. Similarly, the decrease of the channel shoulder to channel width ratio leads to a non-uniform distribution of temperature especially under the channel areas. Copyright © 2009 John Wiley & Sons, Ltd. [source] A parametric study of multi-phase and multi-species transport in the cathode of PEM fuel cellsINTERNATIONAL JOURNAL OF ENERGY RESEARCH, Issue 8 2008Nada Zamel Abstract In this study, a mathematical model is developed for the cathode of PEM fuel cells, including multi-phase and multi-species transport and electrochemical reaction under the isothermal and steady-state conditions. The conservation equations for mass, momentum, species and charge are solved using the commercial software COMSOL Multiphysics. The catalyst layer is modeled as a finite domain and assumed to be composed of a uniform distribution of supported catalyst, liquid water, electrolyte and void space. The Stefan,Maxwell equation is used to model the multi-species diffusion in the gas diffusion and catalyst layers. Owing to the low relative species' velocity, Darcy's law is used to describe the transport of gas and liquid phases in the gas diffusion and catalyst layers. A serpentine flow field is considered to distribute the oxidant over the active cathode electrode surface, with pressure loss in the flow direction along the channel. The dependency of the capillary pressure on the saturation is modeled using the Leverette function and the Brooks and Corey relation. A parametric study is carried out to investigate the effects of pressure drop in the flow channel, permeability, inlet relative humidity and shoulder/channel width ratio on the performance of the cell and the transport of liquid water. An inlet relative humidity of 90 and 80% leads to the highest performance in the cathode. Owing to liquid water evaporation, the relative humidity in the catalyst layer reaches 100% with an inlet relative humidity of 90 and 80%, resulting in a high electrolyte conductivity. The electrolyte conductivity plays a significant role in determining the overall performance up to a point. Further, the catalyst layer is found to be important in controlling the water concentration in the cell. The cross-flow phenomenon is shown to enhance the removal of liquid water from the cell. Moreover, a shoulder/channel width ratio of 1:2 is found to be an optimal ratio. A decrease in the shoulder/channel ratio results in an increase in performance and an increase in cross flow. Finally, the Leverette function leads to lower liquid water saturations in the backing and catalyst layers than the Brooks and Corey relation. The overall trend, however, is similar for both functions. Copyright © 2007 John Wiley & Sons, Ltd. [source] Organic glasses: cluster structure of the random energy landscapeANNALEN DER PHYSIK, Issue 12 2009S.V. Novikov Abstract An appropriate model for the random energy landscape in organic glasses is a spatially correlated Gaussian field. We calculated the distribution of the average value of a Gaussian random field in a finite domain. The results of the calculation demonstrate a strong dependence of the width of the distribution on the spatial correlations of the field. Comparison with the simulation results for the distribution of the size of the cluster indicates that the distribution of an average field could serve as a useful tool for the estimation of the asymptotic behavior of the distribution of the size of the clusters for "deep" clusters where value of the field on each site is much greater than the rms disorder. We also demonstrate significant modification of the properties of energetic disorder in organic glasses at the vicinity of the electrode. [source] | ||||||||||