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.

Determination of the effect of lipophilicity on the in vitro permeability and tissue reservoir characteristics of topically applied solutes in human skin layers

In order to establish the relationship between solute lipophilicity and skin penetration (including flux and concentration behavior), we examined the in vitro penetration and membrane concentration of a series of homologous alcohols (C2-C10) applied topically in aqueous solutions to human epidermal, full-thickness, and dermal membranes. The partitioning/distribution of each alcohol between the donor solution, stratum corneum, viable epidermis, dermis, and receptor phase compartments was determined during the penetration process and separately to isolated samples of each tissue type. Maximum flux and permeability coefficients are compared for each membrane and estimates of alcohol diffusivity are made based on flux/concentration data and also the related tissue resistance (the reciprocal of permeability coefficient) for each membrane type. The permeability coefficient increased with increasing lipophilicity to alcohol C8 (octanol) with no further increase for C10 (decanol). Log vehicle:stratum corneum partition coefficients were related to logP , and the concentration of alcohols in each of the tissue layers appeared to increase with lipophilicity. No difference was measured in the diffusivity of smaller more polar alcohols in the three membranes; however, the larger more lipophilic solutes showed slower diffusivity values. The study showed that the dermis may be a much more lipophilic environment than originally believed and that distribution of smaller nonionized solutes into local tissues below a site of topical application may be estimated based on knowledge of their lipophilicity alone.

Large amplitude vibration of thermo-electro-mechanically stressed FGM laminated plates

This paper presents a large amplitude vibration analysis of pre-stressed functionally graded material (FGM) laminated plates that are composed of a shear deformable functionally graded layer and two surface-mounted piezoelectric actuator layers. Nonlinear governing equations of motion are derived within the context of Reddy's higher-order shear deformation plate theory to account for transverse shear strain and rotary inertia. Due to the bending and stretching coupling effect, a nonlinear static problem is solved first to determine the initial stress state and pre-vibration deformations of the plate that is subjected to uniform temperature change, in-plane forces and applied actuator voltage. By adding an incremental dynamic state to the pre-vibration state, the differential equations that govern the nonlinear vibration behavior of pre-stressed FGM laminated plates are derived. A semi-analytical method that is based on one-dimensional differential quadrature and Galerkin technique is proposed to predict the large amplitude vibration behavior of the laminated rectangular plates with two opposite clamped edges. Linear vibration frequencies and nonlinear normalized frequencies are presented in both tabular and graphical forms, showing that the normalized frequency of the FGM laminated plate is very sensitive to vibration amplitude, out-of-plane boundary support, temperature change, in-plane compression and the side-to-thickness ratio. The CSCF and CFCF plates even change the inherent hard-spring characteristic to soft-spring behavior at large vibration amplitudes. (C) 2003 Elsevier B.V. All rights reserved.

Postbuckling of piezoelectric FGM plates subject to thermo-electro-mechanical loading

In this paper, we examine the postbuckling behavior of functionally graded material FGM rectangular plates that are integrated with surface-bonded piezoelectric actuators and are subjected to the combined action of uniform temperature change, in-plane forces, and constant applied actuator voltage. A Galerkin-differential quadrature iteration algorithm is proposed for solution of the non-linear partial differential governing equations. To account for the transverse shear strains, the Reddy higher-order shear deformation plate theory is employed. The bifurcation-type thermo-mechanical buckling of fully clamped plates, and the postbuckling behavior of plates with more general boundary conditions subject to various thermo-electro-mechanical loads, are discussed in detail. Parametric studies are also undertaken, and show the effects of applied actuator voltage, in-plane forces, volume fraction exponents, temperature change, and the character of boundary conditions on the buckling and postbuckling characteristics of the plates. (C) 2003 Elsevier Science Ltd. All rights reserved.

Large sets of large sets of Steiner triple systems of order 9

We describe a direct method of partitioning the 840 Steiner triple systems of order 9 into 120 large sets. The method produces partitions in which all of the large sets are isomorphic and we apply the method to each of the two non-isomorphic large sets of STS(9).

Dynamic stability of laminated FGM plates based on higher-order shear deformation theory

This paper conducts a dynamic stability analysis of symmetrically laminated FGM rectangular plates with general out-of-plane supporting conditions, subjected to a uniaxial periodic in-plane load and undergoing uniform temperature change. Theoretical formulations are based on Reddy's third-order shear deformation plate theory, and account for the temperature dependence of material properties. A semi-analytical Galerkin-differential quadrature approach is employed to convert the governing equations into a linear system of Mathieu-Hill equations from which the boundary points on the unstable regions are determined by Bolotin's method. Free vibration and bifurcation buckling are also discussed as subset problems. Numerical results are presented in both dimensionless tabular and graphical forms for laminated plates with FGM layers made of silicon nitride and stainless steel. The influences of various parameters such as material composition, layer thickness ratio, temperature change, static load level, boundary constraints on the dynamic stability, buckling and vibration frequencies are examined in detail through parametric studies.

Physical activity and sedentary behavior: A population-based study of barriers, enjoyment, and preference

The associations of physical activity and sedentary behavior with barriers, enjoyment, and preferences were examined in a population-based mail survey of 1,332 adults. Respondents reporting high enjoyment and preference for physical activity were more likely to report high levels of activity. Those reporting cost, the weather, and personal barriers to physical activity were less likely to be physically active. Preference for sedentary behavior was associated with the decreased likelihood of being physically active, and the weather as a barrier to physical activity was associated with the increased likelihood of sedentary behavior. These constructs can be used to examine individual and environmental influences on physical activity and sedentary behavior in specific populations and could inform the development of targeted interventions.

A review of drainage and spontaneous rupture in free standing thin films with tangentially immobile interfaces

A review of spontaneous rupture in thin films with tangentially immobile interfaces is presented that emphasizes the theoretical developments of film drainage and corrugation growth through the linearization of lubrication theory in a cylindrical geometry. Spontaneous rupture occurs when corrugations from adjacent interfaces become unstable and grow to a critical thickness. A corrugated interface is composed of a number of waveforms and each waveform becomes unstable at a unique transition thickness. The onset of instability occurs at the maximum transition thickness, and it is shown that only upper and lower bounds of this thickness can be predicted from linear stability analysis. The upper bound is equivalent to the Freakel criterion and is obtained from the zeroth order approximation of the H-3 term in the evolution equation. This criterion is determined solely by the film radius, interfacial tension and Hamaker constant. The lower bound is obtained from the first order approximation of the H-3 term in the evolution equation and is dependent on the film thinning velocity A semi-empirical equation, referred to as the MTR equation, is obtained by combining the drainage theory of Manev et al. [J. Dispersion Sci. Technol., 18 (1997) 769] and the experimental measurements of Radoev et al. [J. Colloid Interface Sci. 95 (1983) 254] and is shown to provide accurate predictions of film thinning velocity near the critical thickness of rupture. The MTR equation permits the prediction of the lower bound of the maximum transition thickness based entirely on film radius, Plateau border radius, interfacial tension, temperature and Hamaker constant. The MTR equation extrapolates to Reynolds equation under conditions when the Plateau border pressure is small, which provides a lower bound for the maximum transition thickness that is equivalent to the criterion of Gumerman and Homsy [Chem. Eng. Commun. 2 (1975) 27]. The relative accuracy of either bound is thought to be dependent on the amplitude of the hydrodynamic corrugations, and a semiempirical correlation is also obtained that permits the amplitude to be calculated as a function of the upper and lower bound of the maximum transition thickness. The relationship between the evolving theoretical developments is demonstrated by three film thickness master curves, which reduce to simple analytical expressions under limiting conditions when the drainage pressure drop is controlled by either the Plateau border capillary pressure or the van der Waals disjoining pressure. The master curves simplify solution of the various theoretical predictions enormously over the entire range of the linear approximation. Finally, it is shown that when the Frenkel criterion is used to assess film stability, recent studies reach conclusions that are contrary to the relevance of spontaneous rupture as a cell-opening mechanism in foams. (C) 2003 Elsevier Science B.V. All rights reserved.

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.

Injury related risk behavior - a study of Australian skydivers

Risk taking behaviour has been identified as an important host-related determinant of injury in young adults. The aim of this study is to clarify the relationship between the two key elements of risk taking behaviour - ie, risk assessment and risk acceptance - in participants of a high risk sporting activity. Skydivers registered with the Australian Parachute Federation were sampled at several jump meetings held at three 'drop-zones' in North Eastern Australia. A cross sectional survey of 215 skydivers ascertained each subject's risk assessment of each of nine hypothetical sky diving scenes and whether or not they would jump in the described conditions. Variables which independently predicted an individual's risk assessment were age group (p < 0.05), gender (p < 0.05) and scene details (p < 0.001). Risk assessment was found to be a statistically significant predictor of the decision to jump, with a 22% decrease in the odds of jumping with every unit increase in risk assessment (OR = 0.78: 95% Cl; 0.76, 0.80). Gender was also found to be a statistically significant predictor of the decision to jump, with males being 19% more likely to jump than females, after controlling for age, experience, currency and risk assessment (OR = 1.19: 95% CI; 1.04, 1.38). The importance of these results is that, by quantifying the relationship between two key elements of risk taking behaviour and several important host factor determinants, they facilitate more informed discussion about the possible role of risk taking behaviour in the causation of injury.