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Previous Formulations (previous + formulations)

Distribution by Scientific Domains

Earth and Environmental Science	50%
Engineering	33%

Selected Abstracts

A new formulation of garnet,clinopyroxene geothermometer based on accumulation and statistical analysis of a large experimental data set

JOURNAL OF METAMORPHIC GEOLOGY, Issue 7 2009
D. NAKAMURAArticle first published online: 13 JUL 200
Abstract Published experimental data including garnet and clinopyroxene as run products were used to develop a new formulation of the garnet,clinopyroxene geothermometer based on 333 garnet,clinopyroxene pairs. Only experiments with graphite capsules were selected because of difficulty in estimating the Fe3+ content of clinopyroxene. For the calibration, a published subregular-solution model was adopted to express the non-ideality of garnet. The magnitude of the Fe,Mg excess interaction parameter for clinopyroxene (WFeMgCpx), and differences in enthalpy and entropy of the Fe,Mg exchange reaction were regressed from the accumulated experimental data set. As a result, a markedly negative value was obtained for the Fe,Mg excess interaction parameter of clinopyroxene (WFeMgCpx = , 3843 J mol,1). The pressure correction is simply treated as linear, and the difference in volume of the Fe,Mg exchange reaction was calculated from a published thermodynamic data set and fixed to be ,120.72 (J kbar,1 mol,1). The regressed and obtained thermometer formulation is as follows: where T = temperature, P = pressure (kbar), A = 0.5 Xgrs (Xprp , Xalm , Xsps), B = 0.5 Xgrs (Xprp , Xalm + Xsps), C = 0.5 (Xgrs + Xsps) (Xprp , Xalm), Xprp = Mg/(Fe2+ + Mn + Mg + Ca)Grt, Xalm = Fe/(Fe2+ + Mn + Mg + Ca)Grt, Xsps = Mn/(Fe2+ + Mn + Mg + Ca)Grt, Xgrs = Ca/(Fe2+ + Mn + Mg + Ca)Grt, XMgCpx = Mg/(Al + Fetotal + Mg)Cpx, XFeCpx = Fe2+/(Al + Fetotal + Mg)Cpx, KD = (Fe2+/Mg)Grt/(Fe2+/Mg)Cpx, Grt = garnet, Cpx = clinopyroxene. A test of this new formulation to the accumulated data gave results that are concordant with the experimental temperatures over the whole range of the experimental temperatures (800,1820 °C), with a standard deviation (1 sigma) of 74 °C. Previous formulations of the thermometer are inconsistent with the accumulated data set; they underestimate temperatures by about 100 °C at >1300 °C and overestimate by 100,200 °C at <1300 °C. In addition, they tend to overestimate temperatures for high-Ca garnet (Xgrs , 0.30,0.50). This new formulation has been tested against previous formulations of the thermometer by application to natural eclogites. This gave temperatures some 20,100 °C lower than previous formulations. [source]

On the theory of optimal sensor placement

AICHE JOURNAL, Issue 5 2002
Donald J. Chmielewski
On the Theory of Optimal Sensor Placement An optimal sensor placement is defined as a sensor configuration that achieves the minimum capital cost while observing prespecified performance criteria. Previous formulations of this problem have resulted in the definition of a mixed-integer nonlinear program (MINLP) with dimensions dependent on the value of the integer decision variables. The main contribution of this work is an equivalent reformulation of the design problem such that the dimension of the NLP is independent of all decision variables. Additionally, the traditional sensor-placement problem, based on static process conditions, is extended to linear dynamic processes. The final contribution is the exact conversion of the general NLP into a convex program through the use of linear matrix inequalities. The aggregation of these results show that the sensor-placement problem can be solved globally and eficiently using standard interior-point and branch-and-bound search algorithms. [source]

On the differentiation of the Rodrigues formula and its significance for the vector-like parameterization of Reissner,Simo beam theory

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 2002
M. Ritto-Corrêa
Abstract In this paper we present a systematic way of differentiating, up to the second directional derivative, (i) the Rodrigues formula and (ii) the spin-rotation vector variation relationship. To achieve this goal, several trigonometric functions are grouped into a family of scalar quantities, which can be expressed in terms of a single power series. These results are then applied to the vector-like parameterization of Reissner,Simo beam theory, enabling a straightforward derivation and leading to a clearer formulation. In particular, and in contrast with previous formulations, a relatively compact and obviously symmetric form of the tangent operator is obtained. The paper also discusses several relevant issues concerning a beam finite element implementation and concludes with the presentation of a few selected illustrative examples. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Alternative formulation and applications aspects of the generalized projection method for array antenna synthesis

INTERNATIONAL JOURNAL OF RF AND MICROWAVE COMPUTER-AIDED ENGINEERING, Issue 6 2009
E. Botha
Abstract An array synthesis technique is formulated, which implements the method of generalized projections in the array excitation space. This permits the use of relaxation in the overall recursion relation that is not possible with previous formulations, resulting in accelerated convergence for slowly converging problems. Weighted least squares is introduced as a backward operator in an integral way that enhances the method. Means are described for determining starting points that assist the synthesis algorithm in avoiding so-called traps. The results obtained for a diverse selection of applications of the method are discussed. These demonstrate the effects on convergence of the use of relaxation, different pattern sampling angle selection schemes, and different starting point selection schemes. © 2009 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2009. [source]

A new formulation of garnet,clinopyroxene geothermometer based on accumulation and statistical analysis of a large experimental data set

The characteristics of Hessian singular vectors using an advanced data assimilation scheme

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 642 2009
A. R. Lawrence
Abstract Initial condition uncertainty is a significant source of forecast error in numerical weather prediction. Singular vectors of the tangent linear propagator can identify directions in phase-space where initial errors are likely to make the largest contribution to forecast-error variance. The physical characteristics of these singular vectors depend on the choice of initial-time metric used to represent analysis-error covariances: the total-energy norm serves as a proxy to the analysis-error covariance matrix, whereas the Hessian of the cost function of a 4D-Var assimilation scheme represents a more sophisticated estimate of the analysis-error covariances, consistent with observation and background-error covariances used in the 4D-Var scheme. This study examines and compares the structure of singular vectors computed with the European Centre for Medium-Range Weather Forecasts (ECMWF) Integrated Forecasting System using these two types of initial metrics. Unlike earlier studies that use background errors derived from lagged forecast differences (the NMC method), the background-error covariance matrix in the Hessian metric is based on statistics from an ensemble of 4D-Vars using perturbed observations, which produces tighter correlations of background-error statistics than in previous formulations. In light of these new background-error statistics, this article re-examines the properties of Hessian singular vectors (and their relationship to total-energy singular vectors) using cases from different periods between 2003 and 2005. Energy profiles and wavenumber spectra reveal that the total-energy singular vectors are similar to Hessian singular vectors that use all observation types in the operational 4D-Var assimilation. This is in contrast to the structure of Hessian singular vectors without observations. Increasing the observation density tends to reduce the spatial scale of the Hessian singular vectors. Copyright © 2009 Royal Meteorological Society [source]