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Field Models (field + models)

Distribution by Scientific Domains

Mathematics and Statistics	37%
Earth and Environmental Science	37%

Selected Abstracts

Equilibrium and growth shapes of crystals: how do they differ and why should we care?

CRYSTAL RESEARCH AND TECHNOLOGY, Issue 4-5 2005
Robert F. SekerkaArticle first published online: 15 MAR 200
Abstract Since the death of Prof. Dr. Jan Czochralski nearly 50 years ago, crystals grown by the Czochralski method have increased remarkably in size and perfection, resulting today in the industrial production of silicon crystals about 30 cm in diameter and two meters in length. The Czochralski method is of great technological and economic importance for semiconductors and optical crystals. Over this same time period, there have been equally dramatic improvements in our theoretical understanding of crystal growth morphology. Today we can compute complex crystal growth shapes from robust models that reproduce most of the features and phenomena observed experimentally. We should care about this because it is likely to result in the development of powerful and economical design tools to enable future progress. Crystal growth morphology results from an interplay of crystallographic anisotropy and growth kinetics by means of interfacial processes and long-range transport. The equilibrium shape of a crystal results from minimizing its anisotropic surface free energy under the constraint of constant volume; it is given by the classical Wulff construction but can also be represented by an analytical formula based on the ,-vector formalism of Hoffman and Cahn. We now have analytic criteria for missing orientations (sharp corners or edges) on the equilibrium shape, both in two (classical) and three (new) dimensions. Crystals that grow under the control of interfacial kinetic processes tend asymptotically toward a "kinetic Wulff shape", the analogue of the Wulff shape, except it is based on the anisotropic interfacial kinetic coefficient. If it were not for long range transport, crystals would presumably nucleate with their equilibrium shape and then evolve toward their "kinetic Wulff shape". Allowing for long range transport leads to morphological instabilities on the scale of the geometric mean of a transport length (typically a diffusivity divided by the growth speed) and a capillary length (of the order of atomic dimensions). Resulting crystal growth shapes can be cellular or dendritic, but can also exhibit corners and facets related to the underlying crystallographic anisotropy. Within the last decade, powerful phase field models, based on a diffuse interface, have been used to treat simultaneously all of the above phenomena. Computed morphologies can exhibit cells, dendrites and facets, and the geometry of isotherms and isoconcentrates can also be determined. Results of such computations are illustrated in both two and three dimensions. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Analysis of particulate matter air pollution using Markov random field models of spatial dependence

ENVIRONMETRICS, Issue 5-6 2002
Mark S. Kaiser
Abstract Researchers are beginning to realize the need to take spatial structure into account when modeling data on air pollutants. We develop several models for particulate matter in an urban region that allow spatial dependence to be represented in different manners over a time period of one year. The models are based on a Markov random field approach, and a conceptualization of observed data as arising from two random processes, a conditionally independent observation process and a spatially dependent latent pollution process. Optimal predictors are developed for both of these processes, and predictions of the observation process are used for model assessment. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Sensitivity of multi-coil frequency domain electromagnetic induction sensors to map soil magnetic susceptibility

EUROPEAN JOURNAL OF SOIL SCIENCE, Issue 4 2010
D. Simpson
Magnetic susceptibility is an important indicator of anthropogenic disturbance in the natural soil. This property is often mapped with magnetic gradiometers in archaeological prospection studies. It is also detected with frequency domain electromagnetic induction (FDEM) sensors, which have the advantage that they can simultaneously measure the electrical conductivity. The detection level of FDEM sensors for magnetic structures is very dependent on the coil configuration. Apart from theoretical modelling studies, a thorough investigation with field models has not been conducted until now. Therefore, the goal of this study was to test multiple coil configurations on a test field with naturally enhanced magnetic susceptibility in the topsoil and with different types of structures mimicking real archaeological features. Two FDEM sensors were used with coil separations between 0.5 and 2 m and with three coil orientations. First, a vertical sounding was conducted over the undisturbed soil to test the validity of a theoretical layered model, which can be used to infer the depth sensitivity of the coil configurations. The modelled sounding values corresponded well with the measured data, which means that the theoretical models are applicable to layered soils. Second, magnetic structures were buried in the site and the resulting anomalies measured to a very high resolution. The results showed remarkable differences in amplitude and complexity between the responses of the coil configurations. The 2-m horizontal coplanar and 1.1-m perpendicular coil configurations produced the clearest anomalies and resembled best a gradiometer measurement. [source]

Predicting toxic gas concentrations resulting from enclosure fires using local equivalence ratio concept linked to fire field models

FIRE AND MATERIALS, Issue 1 2007
Z. Wang
Abstract A practical CFD method is presented in this study to predict the generation of toxic gases in enclosure fires. The model makes use of local combustion conditions to determine the yield of carbon monoxide, carbon dioxide, hydrocarbon, soot and oxygen. The local conditions used in the determination of these species are the local equivalence ratio (LER) and the local temperature. The heat released from combustion is calculated using the volumetric heat source model or the eddy dissipation model (EDM). The model is then used to simulate a range of reduced-scale and full-scale fire experiments. The model predictions for most of the predicted species are then shown to be in good agreement with the test results. Copyright © 2006 John Wiley & Sons, Ltd. [source]

The design of an optimal filter for monthly GRACE gravity models

GEOPHYSICAL JOURNAL INTERNATIONAL, Issue 2 2008
R. Klees
SUMMARY Most applications of the publicly released Gravity Recovery and Climate Experiment monthly gravity field models require the application of a spatial filter to help suppressing noise and other systematic errors present in the data. The most common approach makes use of a simple Gaussian averaging process, which is often combined with a ,destriping' technique in which coefficient correlations within a given degree are removed. As brute force methods, neither of these techniques takes into consideration the statistical information from the gravity solution itself and, while they perform well overall, they can often end up removing more signal than necessary. Other optimal filters have been proposed in the literature; however, none have attempted to make full use of all information available from the monthly solutions. By examining the underlying principles of filter design, a filter has been developed that incorporates the noise and full signal variance,covariance matrix to tailor the filter to the error characteristics of a particular monthly solution. The filter is both anisotropic and non-symmetric, meaning it can accommodate noise of an arbitrary shape, such as the characteristic stripes. The filter minimizes the mean-square error and, in this sense, can be considered as the most optimal filter possible. Through both simulated and real data scenarios, this improved filter will be shown to preserve the highest amount of gravity signal when compared to other standard techniques, while simultaneously minimizing leakage effects and producing smooth solutions in areas of low signal. [source]

A comprehensive model of the quiet-time, near-Earth magnetic field: phase 3

GEOPHYSICAL JOURNAL INTERNATIONAL, Issue 1 2002
Terence J. Sabaka
Summary The near-Earth magnetic field is caused by sources in the Earth's core, ionosphere, magnetosphere, lithosphere and from coupling currents between the ionosphere and the magnetosphere, and between hemispheres. Traditionally, the main field (low degree internal field) and magnetospheric field have been modelled simultaneously, with fields from other sources being modelled separately. Such a scheme, however, can introduce spurious features, especially when the spatial and temporal scales of the fields overlap. A new model, designated CM3 (Comprehensive Model: phase 3), is the third in a series of efforts to coestimate fields from all of these sources. This model has been derived from quiet-time Magsat and POGO satellite and observatory hourly means measurements for the period 1960,1985. It represents a significant advance in the treatment of the aforementioned field sources over previous attempts, and includes an accounting for main field influences on the magnetosphere, main field and solar activity influences on the ionosphere, seasonal influences on the coupling currents, a priori characterization of the influence of the ionosphere and the magnetosphere on Earth-induced fields, and an explicit parametrization and estimation of the lithospheric field. The result is a model that describes well the 591 432 data with 16 594 parameters, implying a data-to-parameter ratio of 36, which is larger than several popular field models. [source]

On a Penrose,Fife type system with Dirichlet boundary conditions for temperature

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 15 2003
Gianni Gilardi
We deal with the Dirichlet problem for a class of Penrose,Fife phase field models for phase transitions. An existence result is obtained by approximating the non-homogeneous Dirichlet condition with classical third type conditions on the heat flux at the boundary of the domain where the model is considered. Moreover, we prove a regularity and uniqueness result under stronger assumptions on the regularity of the data. Suitable assumptions on the behaviour of the heat flux at zero and +,are considered. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Exploring Dependence with Data on Spatial Lattices

BIOMETRICS, Issue 3 2009
Mark S. Kaiser
Summary The application of Markov random field models to problems involving spatial data on lattice systems requires decisions regarding a number of important aspects of model structure. Existing exploratory techniques appropriate for spatial data do not provide direct guidance to an investigator about these decisions. We introduce an exploratory quantity that is directly tied to the structure of Markov random field models based on one-parameter exponential family conditional distributions. This exploratory diagnostic is shown to be a meaningful statistic that can inform decisions involved in modeling spatial structure with statistical dependence terms. In this article, we develop the diagnostic, illustrate its use in guiding modeling decisions with simulated examples, and reexamine a previously published application. [source]