The opacity coefficient method—nongray determination of inhomogeneous atmospheric extinction

The computation of radiation transmittance in nongray, inhomogeneous atmospheric models is frequently complicated by complex bands of line spectra which range in value over many orders of magnitudes and depend strongly on either or both of pressure and temperature. We present here a new opacity sampling technique which is shown to determine correctly the wavelength-averaged extinction due to path-dependent realizations of banded line spectra. The technique is easy to implement computationally and is applicable to a wide variety of atmospheric problems in which frequent iteration of the radiative transfer model is required. We consider two such instances: modeling of solar flux attenuation for use in a time-dependent planetary ionosphere model and retrieval from nadir measurements of backscattered solar irradiance. The power of the new method lies in its straightforward analytical treatment of both atmospheric inhomogeneity and spectral complexity. It is thus relevant for both retrieval and radiative transfer modeling purposes.     

The modified characteristic finite difference fractional steps method for the coupled system of fluid dynamics in porous media and its analysis

For the coupled system of multilayer fluid dynamics in porous media, the modified characteristic finite difference fractional steps method applicable to parallel arithmetic is put forward and two‐dimensional and three‐dimensional schemes are used to form a complete set. Some techniques, such as calculus of variations, energy method, piecewise biquadratic interpolation, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates are adopted. Optimal order estimates in L² norm are derived to determine the error in the approximate solution. This method has already been applied to the numerical simulation of multilayer fluid dynamics in porous media. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 665–681, 2003.     

Sterically stabilized emulsion polymerization of styrene: Pseudo‐semicontinuous approach

The sterically stabilized emulsion polymerization of styrene initiated by a water‐soluble initiator at different temperatures has been investigated. The rate of polymerization (R_p) versus conversion curve shows the two non‐stationary‐rate intervals typical for the polymerization proceeding under non‐stationary‐state conditions. The shape of the R_p versus conversion curve results from two opposite effects—the increased number of particles and the decreased monomer concentration at reaction loci as the polymerization advances. At elevated temperatures the monomer emulsion equilibrates to a two‐phase or three‐phase system. The upper phase is transparent (monomer), and the lower one is blue colored, typical for microemulsion. After stirring such a multiphase system and initiation of polymerization, the initial coarse polymer emulsion was formed. The average size of monomer/polymer particles strongly decreased up to about 40% conversion and then leveled off. The initial large particles are assumed to be highly monomer‐swollen particles formed by the heteroagglomeration of unstable polymer particles and monomer droplets. The size of the “highly monomer” swollen particles continuously decreases with conversion, and they merge with the growing particles at about 40–50% conversion. The monomer droplets and/or large highly monomer‐swollen polymer particles also serve as a reservoir of monomer and emulsifier. The continuous release of nonionic (hydrophobic) emulsifier from the monomer phase increases the colloidal stability of primary particles and the number of polymer particles, that is, the particle nucleation is shifted to the higher conversion region. Variations of the square and cube of the mean droplet radius with aging time indicate that neither the coalescence nor the Ostwald ripening is the main driving force for the droplet instability. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 804–820, 2003     

A Generalized Markov Sampler

A recent development of the Markov chain Monte Carlo (MCMC) technique is the emergence of MCMC samplers that allow transitions between different models. Such samplers make possible a range of computational tasks involving models, including model selection, model evaluation, model averaging and hypothesis testing. An example of this type of sampler is the reversible jump MCMC sampler, which is a generalization of the Metropolis–Hastings algorithm. Here, we present a new MCMC sampler of this type. The new sampler is a generalization of the Gibbs sampler, but somewhat surprisingly, it also turns out to encompass as particular cases all of the well-known MCMC samplers, including those of Metropolis, Barker, and Hastings. Moreover, the new sampler generalizes the reversible jump MCMC. It therefore appears to be a very general framework for MCMC sampling. This paper describes the new sampler and illustrates its use in three applications in Computational Biology, specifically determination of consensus sequences, phylogenetic inference and delineation of isochores via multiple change-point analysis.     

B-Theory of Runge-Kutta methods for stiff volterra functional differential equations

B-stability andB-convergence theories of Runge-Kutta methods for nonlinear stiff Volterra functional differential equations (VFDEs) are established which provide unified theoretical foundation for the study of Runge-Kutta methods when applied to nonlinear stiff initial value problems (IVPs) in ordinary differential equations (ODEs), delay differential equations (DDEs), integro-differential equations (IDEs) and VFDEs of other type which appear in practice.     

Sensitivity of trust-region algorithms to their parameters

In this paper, we examine the sensitivity of trust-region algorithms on the parameters related to the step acceptance and update of the trust region. We show, in the context of unconstrained programming, that the numerical efficiency of these algorithms can easily be improved by choosing appropriate parameters. Recommended ranges of values for these parameters are exhibited on the basis of extensive numerical tests. MSC classification: 65K05, 90C26, 90C30     

A class of polynomial variable metric algorithms for linear optimization

In the paper, the behaviour of interior point algorithms is analyzed by using a variable metric method approach. A class of polynomial variable metric algorithms is given achieving O ((n/β)L) iterations for solving a canonical form linear optimization problem with respect to a wide class of Riemannian metrics, wheren is the number of dimensions and β a fixed value. It is shown that the vector fields of several interior point algorithms for linear optimization is the negative Riemannian gradient vector field of a linear a potential or a logarithmic barrier function for suitable Riemannian metrics. Research Partially supported by the Hungarian National Research Foundation, Grant Nos. OTKA-T016413 and OTKA-2116.     

Solving Nonlinear Programming Problems with Noisy Function Values and Noisy Gradients

An efficient algorithm for solving nonlinear programs with noisy equality constraints is introduced and analyzed. The unknown exact constraints are replaced by surrogates based on the bundle idea, a well-known strategy from nonsmooth optimization. This concept allows us to perform a fast computation of the surrogates by solving simple quadratic optimization problems, control the memory needed by the algorithm, and prove the differentiability properties of the surrogate functions. The latter aspect allows us to invoke a sequential quadratic programming method. The overall algorithm is of the quasi-Newton type. Besides convergence theorems, qualification results are given and numerical test runs are discussed.     

土壤盐渍化的研究进展

根据近年来国内外土壤学者在土壤盐渍化的研究成果，从土壤盐渍化的基本理论，改良方法以及预测预报方面的研究，综述了土壤盐渍化的研究现状，通过分析土壤盐渍化研究多方面存在的问题，对其发展趋势和今后研究重点进行了展望，望能为进一步的深入研究工作提供帮助．     

Combined X-ray-electron imaging techniques: Limitations on lateral resolution

Capabilities of the imaging techniques, in which X-rays are converted to electrons and then the emitted electrons are registered by means of an electron microscope, are analyzed, the focus being on the factors limiting lateral resolution at the stage of electron emission. Bearing in mind the tendency to use harder synchrotron X-rays for some combined X-ray-electron microscopy methods, calculations were made for two significantly different X-ray energies: E = 1.828 keV (K-edge of Si) and E = 11.923 keV (L₃-edge of Au). By using Monte Carlo simulations of the electron trajectories beneath the surface of the sample we show that the radius of the spot from which photoelectrons are emitted could be as small as 1 nm. However, when proper account is taken of an entire electron cascade associated with the re-building of electron shells after photoelectron emission, spots more than one order of magnitude larger result, limiting the best lateral resolution to 20–30 nm.