Existence of multiple solutions for finite difference approximations to second-order boundary value problems

Error condition detected We consider discrete two-point boundary value problems of the form D-2 y(k+1) = f (kh, y(k), D y(k)), for k = 1,...,n - 1, (0,0) = G((y(0),y(n));(Dy-1,Dy-n)), where Dy-k = (y(k) - Yk-I)/h and h = 1/n. This arises as a finite difference approximation to y" = f(x,y,y'), x is an element of [0,1], (0,0) = G((y(0),y(1));(y'(0),y'(1))). We assume that f and G = (g(0), g(1)) are continuous and fully nonlinear, that there exist pairs of strict lower and strict upper solutions for the continuous problem, and that f and G satisfy additional assumptions that are known to yield a priori bounds on, and to guarantee the existence of solutions of the continuous problem. Under these assumptions we show that there are at least three distinct solutions of the discrete approximation which approximate solutions to the continuous problem as the grid size, h, goes to 0. (C) 2003 Elsevier Science Ltd. All rights reserved.

A high definition, finite difference time domain method

A high definition, finite difference time domain (HD-FDTD) method is presented in this paper. This new method allows the FDTD method to be efficiently applied over a very large frequency range including low frequencies, which are problematic for conventional FDTD methods. In the method, no alterations to the properties of either the source or the transmission media are required. The method is essentially frequency independent and has been verified against analytical solutions within the frequency range 50 Hz-1 GHz. As an example of the lower frequency range, the method has been applied to the problem of induced eddy currents in the human body resulting from the pulsed magnetic field gradients of an MRI system. The new method only requires approximately 0.3% of the source period to obtain an accurate solution. (C) 2003 Elsevier Science Inc. All rights reserved.

Biaxial failure model for fiber reinforced concrete

Steel fiber reinforced concrete (SFRC) is widely applied in the construction industry. Numerical elastoplastic analysis of the macroscopic behavior is complex. This typically involves a piecewise linear failure curve including corner singularities. This paper presents a single smooth biaxial failure curve for SFRC based on a semianalytical approximation. Convexity of the proposed model is guaranteed so that numerical problems are avoided. The model has sufficient flexibility to closely match experimental results. The failure curve is also suitable for modeling plain concrete under biaxial loading. Since this model is capable of simulating the failure states in all stress regimes with a single envelope, the elastoplastic formulation is very concise and simple. The finite element implementation is developed to demonstrate the conciseness and the effectiveness of the model. The computed results display good agreement with published experimental data.

Multiple ordered phases in Langmuir-Blodgett films of cadmium arachidate at elevated temperatures

Using synchrotron X-ray grazing incidence diffraction, superlattice structures have been observed to develop in Langmuir-Blodgett films of cadmium arachidate as the temperature is raised. The previously reported superstructure in the stacked lamellae at room temperature changes at about 70 degreesC and there are further changes at about 90 and 103 degreesC before the major phase transition from stacked lamellae to hexagonally packed rods occurs at 107 degreesC (Langmuir 1997, 13, 1602). Between 70 and 103 degreesC there is a 1 x 10 one-dimensional in-plane superstructure, which is commensurate with the local structure and has an interlayer shift along [01] by a distance of b (of the local structure) at lower temperatures, and a further shift at about 90 degreesC. At lower (

The application of wave induced forces to a two-dimensional finite element long wave hydrodynamic model

This paper describes the modification of a two-dimensional finite element long wave hydrodynamic model in order to predict the net current and water levels attributable to the influences of waves. Tests examine the effects of the application of wave induced forces, including comparisons to a physical experiment. An example of a real river system is presented with comparisons to measured data, which demonstrate the importance of simulating the combined effects of tides and waves upon hydrodynamic behavior. (C) 2002 Elsevier Science Ltd. All rights reserved.

Low temperature induced spikelet sterility in rice. II. Effects of panicle and root temperatures

Low temperatures impose restrictions on rice (Oryza sativa L.) production at high latitudes. This study is related to low temperature damage that can arise mid-season during the panicle development phase. The objective of this study was to determine whether low temperature experienced by the root, panicle, or foliage is responsible for increased spikelet sterility. In temperature-controlled glasshouse experiments, water depth, and water and air temperatures, were changed independently to investigate the effects of low temperature in the root, panicle, and foliage during microspore development on spikelet sterility. The total number of pollen and number of engorged pollen grains per anther, and the number of intercepted and germinated pollen grains per stigma, were measured. Spikelet sterility was then analysed in relation to the total number of pollen grains per spikelet and the efficiency with which these pollen grains became engorged, were intercepted by the stigma, germinated, and were involved in fertilisation. There was a significant combined effect of average minimum panicle and root temperatures on spikelet sterility that accounted for 86% of the variation in spikelet sterility. Total number of pollen grains per anther was reduced by low panicle temperature, but not by low root temperature. Whereas engorgement efficiency ( the percentage of pollen grains that were engorged) was determined by both root and panicle temperature, germination efficiency (the percentage of germinated pollen grains relative to the number of engorged pollen grains intercepted by the stigma) was determined only by root temperature. Interception efficiency (i.e. percentage of engorged pollen grains intercepted by the stigma), however, was not affected by either root or panicle temperature. Engorgement efficiency was the dominant factor explaining the variation in spikelet sterility. It is concluded that both panicle and root temperature affect spikelet sterility in rice when the plant encounters low temperatures during the microspore development stage.