Global behavior of positive solutions of nonlinear three-point boundary value problems

We investigate the structure of the positive solution set for nonlinear three-point boundary value problems of the form u('') + h(t) f(u) = 0, u(0) = 0, u(1) = lambdau(eta), where eta epsilon (0, 1) is given lambda epsilon (0, 1/n) is a parameter, f epsilon C ([0, infinity), [0, infinity)) satisfies f (s) > 0 for s > 0, and h epsilon C([0, 1], [0, infinity)) is not identically zero on any subinterval of [0, 1]. Our main results demonstrate the existence of continua of positive solutions of the above problem. (C) 2004 Elsevier Ltd. All rights reserved.

Computationally efficient solution techniques for adsorption problems involving steep gradients in bidisperse particles

A piecewise uniform fitted mesh method turns out to be sufficient for the solution of a surprisingly wide variety of singularly perturbed problems involving steep gradients. The technique is applied to a model of adsorption in bidisperse solids for which two fitted mesh techniques, a fitted-mesh finite difference method (FMFDM) and fitted mesh collocation method (FMCM) are presented. A combination (FMCMD) of FMCM and the DASSL integration package is found to be most effective in solving the problems. Numerical solutions (FMFDM and FMCMD) were found to match the analytical solution when the adsorption isotherm is linear, even under conditions involving steep gradients for which global collocation fails. In particular, FMCMD is highly efficient for macropore diffusion control or micropore diffusion control. These techniques are simple and there is no limit on the range of the parameters. The techniques can be applied to a variety of adsorption and desorption problems in bidisperse solids with non-linear isotherm and for arbitrary particle geometry.

Solution of adsorption problems involving steep moving profiles

The moving finite element collocation method proposed by Kill et al. (1995) Chem. Engng Sci. 51 (4), 2793-2799 for solution of problems with steep gradients is further developed to solve transient problems arising in the field of adsorption. The technique is applied to a model of adsorption in solids with bidisperse pore structures. Numerical solutions were found to match the analytical solution when it exists (i.e. when the adsorption isotherm is linear). The method is simple yet sufficiently accurate for use in adsorption problems, where global collocation methods fail. (C) 1998 Elsevier Science Ltd. All rights reserved.

Genetic algorithms for continuous optimization problems - a concept of parameter-space size adjustment

The concept of parameter-space size adjustment is pn,posed in order to enable successful application of genetic algorithms to continuous optimization problems. Performance of genetic algorithms with six different combinations of selection and reproduction mechanisms, with and without parameter-space size adjustment, were severely tested on eleven multiminima test functions. An algorithm with the best performance was employed for the determination of the model parameters of the optical constants of Pt, Ni and Cr.

Prioritizing global conservation efforts

One of the most pressing issues facing the global conservation community is how to distribute limited resources between regions identified as priorities for biodiversity conservation(1-3). Approaches such as biodiversity hotspots(4), endemic bird areas(5) and ecoregions(6) are used by international organizations to prioritize conservation efforts globally(7). Although identifying priority regions is an important first step in solving this problem, it does not indicate how limited resources should be allocated between regions. Here we formulate how to allocate optimally conservation resources between regions identified as priorities for conservation - the 'conservation resource allocation problem'. Stochastic dynamic programming is used to find the optimal schedule of resource allocation for small problems but is intractable for large problems owing to the curse of dimensionality(8). We identify two easy- to- use and easy- to- interpret heuristics that closely approximate the optimal solution. We also show the importance of both correctly formulating the problem and using information on how investment returns change through time. Our conservation resource allocation approach can be applied at any spatial scale. We demonstrate the approach with an example of optimal resource allocation among five priority regions in Wallacea and Sundaland, the transition zone between Asia and Australasia.

Comparative cost-effectiveness of policy instruments for reducing the global burden of alcohol, tobacco and illicit drug use

Alcohol, tobacco and illicit drug use together pose a formidable challenge to international public health. Building on earlier estimates of the demonstrated burden of alcohol, tobacco and illicit drug use at the global level, this review aims to consider the comparative cost-effectiveness of evidence-based interventions for reducing the global burden of disease from these three risk factors. Although the number of published cost-effectiveness studies in the addictions field is now extensive ( reviewed briefly here) there are a series of practical problems in using them for sector-wide decision making, including methodological heterogeneity, differences in analytical reference point and the specificity of findings to a particular context. In response to these limitations, a more generalised form of cost-effectiveness analysis (CEA) is proposed, which enables like-with-like comparisons of the relative efficiency of preventive or individual-based strategies to be made, not only within but also across diseases or their risk factors. The application of generalised CEA to a range of personal and non-personal interventions for reducing the burden of addictive substances is described. While such a development avoids many of the obstacles that have plagued earlier attempts and in so doing opens up new opportunities to address important policy questions, there remain a number of caveats to population-level analysis of this kind, particularly when conducted at the global level. These issues are the subject of the final section of this review.

A new relaxation method for roll forming problems

Finite element analysis (FEA) of nonlinear problems in solid mechanics is a time consuming process, but it can deal rigorously with the problems of both geometric, contact and material nonlinearity that occur in roll forming. The simulation time limits the application of nonlinear FEA to these problems in industrial practice, so that most applications of nonlinear FEA are in theoretical studies and engineering consulting or troubleshooting. Instead, quick methods based on a global assumption of the deformed shape have been used by the roll-forming industry. These approaches are of limited accuracy. This paper proposes a new form-finding method - a relaxation method to solve the nonlinear problem of predicting the deformed shape due to plastic deformation in roll forming. This method involves applying a small perturbation to each discrete node in order to update the local displacement field, while minimizing plastic work. This is iteratively applied to update the positions of all nodes. As the method assumes a local displacement field, the strain and stress components at each node are calculated explicitly. Continued perturbation of nodes leads to optimisation of the displacement field. Another important feature of this paper is a new approach to consideration of strain history. For a stable and continuous process such as rolling and roll forming, the strain history of a point is represented spatially by the states at a row of nodes leading in the direction of rolling to the current one. Therefore the increment of the strain components and the work-increment of a point can be found without moving the object forward. Using this method we can find the solution for rolling or roll forming in just one step. This method is expected to be faster than commercial finite element packages by eliminating repeated solution of large sets of simultaneous equations and the need to update boundary conditions that represent the rolls.

A wavelet-based adaptive technique for adsorption problems involving steep gradients

A general, fast wavelet-based adaptive collocation method is formulated for heat and mass transfer problems involving a steep moving profile of the dependent variable. The technique of grid adaptation is based on sparse point representation (SPR). The method is applied and tested for the case of a gas–solid non-catalytic reaction in a porous solid at high Thiele modulus. Accurate and convergent steep profiles are obtained for Thiele modulus as large as 100 for the case of slab and found to match the analytical solution.

Gauge P-representations for quantum-dynamical problems: Removal of boundary terms

P-representation techniques, which have been very successful in quantum optics and in other fields, are also useful for general bosonic quantum-dynamical many-body calculations such as Bose-Einstein condensation. We introduce a representation called the gauge P representation, which greatly widens the range of tractable problems. Our treatment results in an infinite set of possible time evolution equations, depending on arbitrary gauge functions that can be optimized for a given quantum system. In some cases, previous methods can give erroneous results, due to the usual assumption of vanishing boundary conditions being invalid for those particular systems. Solutions are given to this boundary-term problem for all the cases where it is known to occur: two-photon absorption and the single-mode laser. We also provide some brief guidelines on how to apply the stochastic gauge method to other systems in general, quantify the freedom of choice in the resulting equations, and make a comparison to related recent developments.

Evidence for a global Wolbachia replacement in Drosophila melanogaster

Wolbachia are maternally inherited intracellular α-Proteobacteria found in numerous arthropod and filarial nematode species [1, 2 and 3]. They influence the biology of their hosts in many ways. In some cases, they act as obligate mutualists and are required for the normal development and reproduction of the host [4 and 5]. They are best known, however, for the various reproductive parasitism traits that they can generate in infected hosts. These include cytoplasmic incompatibility (CI) between individuals of different infection status, the parthenogenetic production of females, the selective killing of male embryos, and the feminization of genetic males [1 and 2]. Wolbachia infections of Drosophila melanogaster are extremely common in both wild populations and long-term laboratory stocks [6, 7 and 8]. Utilizing the newly completed genome sequence of Wolbachia pipientis wMel [9], we have identified a number of polymorphic markers that can be used to discriminate among five different Wolbachia variants within what was previously thought to be the single clonal infection of D. melanogaster. Analysis of long-term lab stocks together with wild-caught flies indicates that one of these variants has replaced the others globally within the last century. This is the first report of a global replacement of a Wolbachia strain in an insect host species. The sweep is at odds with current theory that cannot explain how Wolbachia can invade this host species given the observed cytoplasmic incompatibility characteristics of Wolbachia infections in D. melanogaster in the field [6].

Existence of Multiple Solutions for Second Order Boundary Value Problems

We give conditions on f involving pairs of lower and upper solutions which lead to the existence of at least three solutions of the two point boundary value problem y" + f(x, y, y') = 0, x epsilon [0, 1], y(0) = 0 = y(1). In the special case f(x, y, y') = f(y) greater than or equal to 0 we give growth conditions on f and apply our general result to show the existence of three positive solutions. We give an example showing this latter result is sharp. Our results extend those of Avery and of Lakshmikantham et al.

Nodal solutions for nonlinear eigenvalue problems

We are concerned with determining values of, for which there exist nodal solutions of the boundary value problems u" + ra(t) f(u) = 0, 0 < t < 1, u(O) = u(1) = 0. The proof of our main result is based upon bifurcation techniques.

Useful representations of series solutions for transport problems

Simple techniques are presented for rearrangement of an infinite series in a systematic way such that the convergence of the resulting expression is accelerated. These procedures also allow calculation of required boundary derivatives. Several examples of conduction and diffusion-reaction problems illustrate the methods.

An improved novel method for solving nonlinear boundary value problems

A modified formula for the integral transform of a nonlinear function is proposed for a class of nonlinear boundary value problems. The technique presented in this paper results in analytical solutions. Iterations and initial guess, which are needed in other techniques, are not required in this novel technique. The analytical solutions are found to agree surprisingly well with the numerically exact solutions for two examples of power law reaction and Langmuir-Hinshelwood reaction in a catalyst pellet.