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Spatial Averaging (spatial + averaging)
Selected AbstractsSpatial averaging of ensemble-based background-error variancesTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 633 2008Laure Raynaud Abstract It is common to compute background-error variances from an ensemble of forecasts, in order to calculate either climatological or flow-dependent estimates. However, the finite size of the ensemble induces a sampling noise, which degrades the accuracy of the variance estimation. An idealized 1D framework is firstly considered, to show that the spatial structure of sampling noise is relatively small-scale, and is closely related to the background-error correlations. This motivates investigations on local spatial averaging, which is here applied to ensemble-based variance fields in this 1D context. It is shown that a spatial averaging, manually optimized, helps to significantly reduce the sampling noise. This provides estimates which are as accurate as those derived from a much bigger ensemble. The dependencies of this optimization on the error correlation length-scale and on the heterogeneity of the variance and length-scale fields are also illustrated. These results are next confirmed in a more realistic 2D problem, by considering the current operational version of the Arpège background-error covariance matrix. Finally, the possibility to objectively and automatically optimize the filtering is explored. The idea is to apply the usual linear estimation theory and to use signal/noise ratios in order to calculate an optimal filter. The efficiency of this objective filtering is illustrated in the idealized 1D framework. Copyright © 2008 Royal Meteorological Society [source] Optimal separation times for electrical field flow fractionation with Couette flowsELECTROPHORESIS, Issue 20 2008Jennifer Pascal Abstract The prediction of optimal times of separation as a function of the applied electrical field and cation valence have been studied for the case of field flow fractionation [Martin M., Giddings J. C., J. Phys. Chem. 1981, 85, 727] with charged solutes. These predictions can be very useful to a priori design or identify optimal operating conditions for a Couette-based device for field flow fractionation when the orthogonal field is an electrical field. Mathematically friendly relationships are obtained by applying the method of spatial averaging to the solute species continuity equation; this is accomplished after the role of the capillary geometrical dimensions on the applied electrical field equations has been assessed [Oyanader M. A., Arce P., Electrophoresis 2005; 26, 2857]. Moreover, explicit analytical expressions are derived for the effective parameters, i.e. diffusivity and convective velocity as functions of the applied (orthogonal) electrical field. These effective transport parameters are used to study the effect of the cation valence of the solutes and of the magnitude of the applied orthogonal electrical field on the values of the optimal time of separation. These parameters play a significant role in controlling the optimal separation time, leading to a family of minimum values, for particular magnitudes of the applied orthogonal electrical field. [source] Role of geometrical dimensions in electrophoresis applications with orthogonal fieldsELECTROPHORESIS, Issue 15 2005Mario A. Oyanader Abstract The role of geometrical dimensions in electrophoresis applications with axial and orthogonal (secondary) electric fields is investigated using a rectangular capillary channel. In particular, the role of the applied orthogonal electrical field in controlling key parameters involved in the effective diffusivity and effective (axial) velocity of the solute is identified. Such mathematically friendly relationships are obtained by applying the method of spatial averaging to the solute species continuity equation; this is accomplished after the role of the capillary geometrical dimensions on the applied electrical field equations has been studied. Moreover, explicit analytical expressions are derived for the effective parameters, i.e., diffusivity and convective velocity as functions of the applied (orthogonal) electric field. Previous attempts (see Sauer et al., 1995) have only led to equations for these parameters that require numerical solution and, therefore, limited the use of such results to practical applications. These may include, for example, the design of separation processes as well as environmental applications such as soil reclamation and wastewater treatment. An illustration of how a secondary electrical field can aid in reducing the optimal separation time is included. [source] How well are velocity effects on ,13C signatures transmitted up the food web from algae to fish?FRESHWATER BIOLOGY, Issue 6 2010JOSEPH B. RASMUSSEN Summary 1. Benthic algae fractionate carbon isotopes less at low water velocities because of reduced boundary layer exchange, and this effect on ,13C is passed on to consumers via trophic transfer. This study examines the relationships between ,13C signatures of consumers (invertebrates and salmonid fishes) and water velocity in the Sainte Marguerite River, QC, Canada, and compares them to patterns for periphyton, both along the river main-stem and in a small tributary. 2. Relationships of ,13C signatures of herbivore/grazers and collector/gatherers with water velocity were strong and similar to those of periphyton, but relationships for filter-feeders were weak, probably reflecting the effect of spatial averaging of their food supply as a result of downstream transport. 3. Velocity effects on salmonid signatures were much weaker than those of lower trophic levels, being barely significant except in the small tributary where the fish were resident and isolated from the main river. In the river main-stem, even when reach standardised (reach mean subtracted from each data point), fish signatures were only weakly related to water velocity. 4. The fidelity with which velocity effects are transmitted to consumers from benthic algae is highly variable, and depends on a combination of consumer and resource movements, in addition to the trophic position of the consumer. [source] On the spatial scaling of seismicity rateGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 3 2005G. Molchan SUMMARY Scaling analysis of seismicity in the space,time,magnitude domain very often starts from the relation ,(m, L) =aL 10,bmLc for the rate of seismic events of magnitude M >m in an area of size L. There is some evidence in favour of multifractality being present in seismicity. In this case, the optimal choice of the scale exponent c is not unique. It is shown how different values of c are related to different types of spatial averaging applied to ,(m, L) and what are the values of c for which the distributions of aL best agree for small L. Theoretical analysis is tested using the California data. [source] Homogenization technique for transient heat transfer in unidirectional compositesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 7 2003Marcin Kami Abstract The article presented is devoted to the homogenization of transient heat transfer problems in unidirectional composites. Mathematical model is based on the effective modules method applied to unidirectional periodic composites,the effective heat conductivity is calculated in the closed form; the effective volumetric heat capacity for the entire composite is obtained by simple spatial averaging. Such a homogenization scheme makes it possible to significantly simplify numerical analysis of transient heat phenomena in various types of unidirectional composites with complicated microgeometry. The comparison of transient heat transfer problem for the composite in real and homogenized configuration is carried out using a specially adopted finite element method computer program. Copyright © 2003 John Wiley & Sons, Ltd. [source] Non-local damage model based on displacement averagingINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2005M. Jirásek Abstract Continuum damage models describe the changes of material stiffness and strength, caused by the evolution of defects, in the framework of continuum mechanics. In many materials, a fast evolution of defects leads to stress,strain laws with softening, which creates serious mathematical and numerical problems. To regularize the model behaviour, various generalized continuum theories have been proposed. Integral-type non-local damage models are often based on weighted spatial averaging of a strain-like quantity. This paper explores an alternative formulation with averaging of the displacement field. Damage is assumed to be driven by the symmetric gradient of the non-local displacements. It is demonstrated that an exact equivalence between strain and displacement averaging can be achieved only in an unbounded medium. Around physical boundaries of the analysed body, both formulations differ and the non-local displacement model generates spurious damage in the boundary layers. The paper shows that this undesirable effect can be suppressed by an appropriate adjustment of the non-local weight function. Alternatively, an implicit gradient formulation could be used. Issues of algorithmic implementation, computational efficiency and smoothness of the resolved stress fields are discussed. Copyright © 2005 John Wiley & Sons, Ltd. [source] Spatial averaging of ensemble-based background-error variancesTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 633 2008Laure Raynaud Abstract It is common to compute background-error variances from an ensemble of forecasts, in order to calculate either climatological or flow-dependent estimates. However, the finite size of the ensemble induces a sampling noise, which degrades the accuracy of the variance estimation. An idealized 1D framework is firstly considered, to show that the spatial structure of sampling noise is relatively small-scale, and is closely related to the background-error correlations. This motivates investigations on local spatial averaging, which is here applied to ensemble-based variance fields in this 1D context. It is shown that a spatial averaging, manually optimized, helps to significantly reduce the sampling noise. This provides estimates which are as accurate as those derived from a much bigger ensemble. The dependencies of this optimization on the error correlation length-scale and on the heterogeneity of the variance and length-scale fields are also illustrated. These results are next confirmed in a more realistic 2D problem, by considering the current operational version of the Arpège background-error covariance matrix. Finally, the possibility to objectively and automatically optimize the filtering is explored. The idea is to apply the usual linear estimation theory and to use signal/noise ratios in order to calculate an optimal filter. The efficiency of this objective filtering is illustrated in the idealized 1D framework. Copyright © 2008 Royal Meteorological Society [source] | ||||||||||||||||