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.

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.

Prevention of child behavior problems through universal implementation of a group behavioral family intervention.

The aim of this mental health promotion initiative was to evaluate the effectiveness of a universally delivered group behavioral family intervention (BFI) in preventing behavior problems in children. This study investigates the transferability of an efficacious clinical program to a universal prevention intervention delivered through child and community health services targeting parents of preschoolers within a metropolitan health region. A quasiexperimental two-group (BFI, n=804 vs. Comparison group, n=806) longitudinal design followed preschool aged children and their parents over a 2-year period. BFI was associated with significant reductions in parent-reported levels of dysfunctional parenting and parent-reported levels of child behavior problems. Effect sizes on child behavior problems ranged from large (.83) to moderate (.47). Positive and significant effects were also observed in parent mental health, marital adjustment, and levels of child rearing conflict. Findings are discussed with respect to their implication for significant population reductions in child behavior problems as well as the pragmatic challenges for prevention science in encouraging both the evaluation and uptake of preventive initiatives in real world settings.

How to unravel and solve soil fertility problems

This book provides a way for farmers in developing countries to benefit from scientific knowledge on plant nutrition and soil fertility. Specifically, it will help farmers recognise and deal with shortages or excesses of chemical elements.

Theory manual to OctVCE – a cartesian cell CFD code with special application to blast wave problems, Department of Mechanical Engineering Report 2007/12

OctVCE is a cartesian cell CFD code produced especially for numerical simulations of shock and blast wave interactions with complex geometries, in particular, from explosions. Virtual Cell Embedding (VCE) was chosen as its cartesian cell kernel for its simplicity and sufficiency for practical engineering design problems. The code uses a finite-volume formulation of the unsteady Euler equations with a second order explicit Runge-Kutta Godonov (MUSCL) scheme. Gradients are calculated using a least-squares method with a minmod limiter. Flux solvers used are AUSM, AUSMDV and EFM. No fluid-structure coupling or chemical reactions are allowed, but gas models can be perfect gas and JWL or JWLB for the explosive products. This report also describes the code’s ‘octree’ mesh adaptive capability and point-inclusion query procedures for the VCE geometry engine. Finally, some space will also be devoted to describing code parallelization using the shared-memory OpenMP paradigm. The user manual to the code is to be found in the companion report 2007/13.

Finite element analysis of steady-state natural convection problems in fluid-saturated porous media heated from below

In this paper, a progressive asymptotic approach procedure is presented for solving the steady-state Horton-Rogers-Lapwood problem in a fluid-saturated porous medium. The Horton-Rogers-Lapwood problem possesses a bifurcation and, therefore, makes the direct use of conventional finite element methods difficult. Even if the Rayleigh number is high enough to drive the occurrence of natural convection in a fluid-saturated porous medium, the conventional methods will often produce a trivial non-convective solution. This difficulty can be overcome using the progressive asymptotic approach procedure associated with the finite element method. The method considers a series of modified Horton-Rogers-Lapwood problems in which gravity is assumed to tilt a small angle away from vertical. The main idea behind the progressive asymptotic approach procedure is that through solving a sequence of such modified problems with decreasing tilt, an accurate non-zero velocity solution to the Horton-Rogers-Lapwood problem can be obtained. This solution provides a very good initial prediction for the solution to the original Horton-Rogers-Lapwood problem so that the non-zero velocity solution can be successfully obtained when the tilted angle is set to zero. Comparison of numerical solutions with analytical ones to a benchmark problem of any rectangular geometry has demonstrated the usefulness of the present progressive asymptotic approach procedure. Finally, the procedure has been used to investigate the effect of basin shapes on natural convection of pore-fluid in a porous medium. (C) 1997 by John Wiley & Sons, Ltd.

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.

A state-contingent production approach to principal-agent problems with an application to point-source pollution control

Two basic representations of principal-agent relationships, the 'state-space' and 'parameterized distribution' formulations, have emerged. Although the state-space formulation appears more natural, analytical studies using this formulation have had limited success. This paper develops a state-space formulation of the moral-hazard problem using a general representation of production under uncertainty. A closed-form solution for the agency-cost problem is derived. Comparative-static results are deduced. Next we solve the principal's problem of selecting the optimal output given the agency-cost function. The analysis is applied to the problem of point-source pollution control. (C) 1998 Published by Elsevier Science S.A. All rights reserved.

Injuries and noncommunicable diseases: emerging health problems of children in developing countries

The present article identifies, for children living in developing countries, the major causes of ill-health that are inadequately covered by established health programmes. Injuries and noncommunicable diseases, notably asthma, epilepsy, dental caries, diabetes mellitus and rheumatic heart disease, are growing in significance. In countries where resources are scarce it is to be expected that increasing importance will be attached to the development and implementation of measures against these problems. Their control may benefit from the application of elements of programmes directed against infectious, nutritional and perinatal disorders, which continue to predominate.

Finite element modelling of reactive mass transport problems in fluid-saturated porous media

We use the finite element method to solve reactive mass transport problems in fluid-saturated porous media. In particular, we discuss the mathematical expression of the chemical reaction terms involved in the mass transport equations for an isothermal, non-equilibrium chemical reaction. It has turned out that the Arrhenius law in chemistry is a good mathematical expression for such non-equilibrium chemical reactions especially from the computational point of view. Using the finite element method and the Arrhenius law, we investigate the distributions of PH (i.e. the concentration of H+) and the relevant reactive species in a groundwater system. Although the main focus of this study is on the contaminant transport problems in groundwater systems, the related numerical techniques and principles are equally applicable to the orebody formation problems in the geosciences. Copyright (C) 1999 John Wiley & Sons, Ltd.