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Physical Considerations (physical + consideration)
Selected AbstractsReconsideration of the physical and empirical origins of Z,R relations in radar meteorologyTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 572 2001A. R. Jameson Abstract The rainfall rate, R, and the radar reflectivity factor, Z, are represented by a sum over a finite number of raindrops. It is shown here and in past work that these variables should be linearly related. Yet observations show that correlations between R and Z are often more appropriately described by nonlinear power laws. In the absence of measurement effects, why should this be so? In order to justify this observation, there have been many attempts to create physical ,explanations' for power laws. However, the present work argues that, because correlations do not prove causation (an accepted fact in the statistical sciences), such explanations are suspect, particularly since the parametric fits are not unique and because they exhibit fundamental physical inconsistencies. So why, then, do so many correlations fit power laws when physical arguments show that Z and R should be related linearly? It is shown in the present work that physically based, linear, relations between Z and R apply in statistically homogeneous rain. (Note that statistical homogeneity does not mean that the rain is spatially uniform.) In contrast, nonlinear power laws are empirical fits to correlated, but statistically inhomogeneous data. This conclusion is proven theoretically after developing a ,generalized' Z,R relation based upon physical consideration of R and Z as random variables. This relation explicitly incorporates details of the drop microphysics as well as the variability in measurements of Z and R. In statistically homogeneous rain, this generalized expression shows that the coefficient relating Z and R is a constant resulting in a linear Z,R relation. In statistically inhomogeneous rain, however, the coefficient varies in an unknown fashion so that one must resort to statistical fits, often power laws, in order to relate the two quantities empirically over widely varying conditions. This conclusion is independently verified using Monte Carlo simulations of rain from earlier work and is also corroborated using disdrometer observations. Thus, the justification for nonlinear power-law Z,R relations is not physical, but rather statistical, in that they provide convenient parametric fits for estimating mean R from measured mean Z in statistically inhomogeneous rain. Finally, examples based upon disdrometer data suggest that such generalized relations between two variables defined by such sums are potentially useful over a wide range of remote-sensing problems and over a wide range of scales. The examples also offer hope that data collected over disparate sampling-volumes and sampling-frequencies can still be combined to yield meaningful estimates. Although additional testing is required, this allows us to write programs which combine estimates of R using remote-sensing techniques with sparse but direct rainfall observations. [source] Magnetic and viscous coupling at the core,mantle boundary: inferences from observations of the Earth's nutationsGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 1 2007B. A. Buffett SUMMARY Dissipative core,mantle coupling is evident in observations of the Earth's nutations, although the source of this coupling is uncertain. Magnetic coupling occurs when conducting materials on either side of the boundary move through a magnetic field. In order to explain the nutation observations with magnetic coupling, we must assume a high (metallic) conductivity on the mantle side of the boundary and a rms radial field of 0.69 mT. Much of this field occurs at short wavelengths, which cannot be observed directly at the surface. High levels of short-wavelength field impose demands on the power needed to regenerate the field through dynamo action in the core. We use a numerical dynamo model from the study of Christensen & Aubert (2006) to assess whether the required short-wavelength field is physically plausible. By scaling the numerical solution to a model with sufficient short-wavelength field, we obtain a total ohmic dissipation of 0.7,1 TW, which is within current uncertainties. Viscous coupling is another possible explanation for the nutation observations, although the effective viscosity required for this is 0.03 m2 s,1 or higher. Such high viscosities are commonly interpreted as an eddy viscosity. However, physical considerations and laboratory experiments limit the eddy viscosity to 10,4 m2 s,1, which suggests that viscous coupling can only explain a few percent of the dissipative torque between the core and the mantle. [source] Interface Engineering of Inorganic Thin-Film Solar Cells , Materials-Science Challenges for Advanced Physical ConceptsADVANCED MATERIALS, Issue 42 2009Wolfram Jaegermann Abstract The challenges and research needs for the interface engineering of thin-film solar cells using inorganic-compound semiconductors are discussed from a materials-science point of view. It is, in principle, easily possible to define optimized device structures from physical considerations. However, to realize these structures, many materials' limitations must be overcome by complex processing strategies. In this paper, interface properties and growth morphology are discussed using CdTe solar cells as an example. The need for a better fundamental understanding of cause,effect relationships for improving thin-film solar cells is emphasized. [source] Numerical modelling of anisotropy and eddy current effects in ferromagnetic laminations using a co-energy formulationINTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Issue 5 2001L. R. Dupré Abstract The paper deals with a numerical model for the evaluation of electromagnetic fields in one steel lamination under the influence of a rotating magnetic flux, taking into account anisotropy effects. For this purpose a detailed material model, described by a differential permeability tensor, is included in the macroscopic electromagnetic field calculations in one lamination. Here, by geometrical and physical considerations, the governing Maxwell equations are reduced to a system of parabolic PDEs for the components of the magnetic field vector, under appropriate boundary and initial conditions. We present a suitable numerical approximation based upon a finite element,finite difference method, which properly takes into account the material characteristics. The study leads to a more realistic numerical modelling of the electromagnetic phenomena inside electric and magnetic conducting laminations due to anisotropy effects. Numerical results are compared with those from simplified analytical formulae. Copyright © 2001 John Wiley & Sons, Ltd. [source] Eulerian backtracking of atmospheric tracers.THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 615 2006I: Adjoint derivation, parametrization of subgrid-scale transport Abstract The problem of identification of sources of atmospheric tracers is most classically addressed through either Lagrangian backtracking or adjoint integration. On the basis of physical considerations, the retro-transport equation, which is at the basis of Lagrangian backtracking, can be derived in a Eulerian framework as well. Because of a fundamental time symmetry of fluid transport, Lagrangian or Eulerian backtracking can be used for inverting measurements of the concentration of an atmospheric tracer. The retro-transport equation turns out to be the adjoint of the direct transport equation, with respect to the scalar product defined by integration with respect to air mass. In the present paper, the exact equivalence between the physically-derived retro-transport and adjoint equations is proved. The transformation from the direct to the retro-transport equation requires only simple transformations. The sign of terms describing explicit advection is changed. Terms describing linear sources or sinks of tracers are kept unchanged. Terms representing diffusion by unresolved time-symmetric motions of the transporting air are also unchanged. This is rigorously shown for turbulent eddy-diffusion or mixing length theory. The case of subgrid-scale vertical transport by non-time-symmetric motions of air is studied using the example of the Tiedtke mass-flux scheme for cumulus convection. The retro-transport equation is then obtained by simply inverting the roles of updraughts and downdraughts, as well as of entrainment and detrainment. Conservation of mass of the transporting air is critical for all those properties to hold. Copyright © 2006 Royal Meteorological Society [source] ESTIMATING A PARAMETER WHEN IT IS KNOWN THAT THE PARAMETER EXCEEDS A GIVEN VALUEAUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 4 2009Ian R. Gordon Summary In some statistical problems a degree of explicit, prior information is available about the value taken by the parameter of interest, , say, although the information is much less than would be needed to place a prior density on the parameter's distribution. Often the prior information takes the form of a simple bound, ,, > ,1' or ,, < ,1', where ,1 is determined by physical considerations or mathematical theory, such as positivity of a variance. A conventional approach to accommodating the requirement that,, > ,1,is to replace an estimator,,, of , by the maximum of,,and ,1. However, this technique is generally inadequate. For one thing, it does not respect the strictness of the inequality,, > ,1, which can be critical in interpreting results. For another, it produces an estimator that does not respond in a natural way to perturbations of the data. In this paper we suggest an alternative approach, in which bootstrap aggregation, or bagging, is used to overcome these difficulties. Bagging gives estimators that, when subjected to the constraint,, > ,1, strictly exceed ,1 except in extreme settings in which the empirical evidence strongly contradicts the constraint. Bagging also reduces estimator variability in the important case for which,,is close to ,1, and more generally produces estimators that respect the constraint in a smooth, realistic fashion. [source] | ||||||||||