Marital loss, mental health and the role of perceived social support : findings from six waves of an Australian population based panel study

Objectives: To investigate the impact of transitions out of marriage (separation, widowhood) on the self reported mental health of men and women, and examine whether perceptions of social support play an intervening role. ---------- Methods: The analysis used six waves (2001–06) of an Australian population based panel study, with an analytical sample of 3017 men and 3225 women. Mental health was measured using the MHI-5 scale scored 0–100 (α=0.97), with a higher score indicating better mental health. Perceptions of social support were measured using a 10-item scale ranging from 10 to 70 (α=0.79), with a higher score indicating higher perceived social support. A linear mixed model for longitudinal data was used, with lags for marital status, mental health and social support. ---------- Results: After adjustment for social characteristics there was a decline in mental health for men who separated (−5.79 points) or widowed (−7.63 points), compared to men who remained married. Similar declines in mental health were found for women who separated (−6.65 points) or became widowed (−9.28 points). The inclusion of perceived social support in the models suggested a small mediation effect of social support for mental health with marital loss. Interactions between perceived social support and marital transitions showed a strong moderating effect for men who became widowed. No significant interactions were found for women. ---------- Conclusion: Marital loss significantly decreased mental health. Increasing, or maintaining, high levels of social support has the potential to improve widowed men's mental health immediately after the death of their spouse.

Linear stern waves in finite depth channels

This paper formulates an analytically tractable problem for the wake generated by a long flat bottom ship by considering the steady free surface flow of an inviscid, incompressible fluid emerging from beneath a semi-infinite rigid plate. The flow is considered to be irrotational and two-dimensional so that classical potential flow methods can be exploited. In addition, it is assumed that the draft of the plate is small compared to the depth of the channel. The linearised problem is solved exactly using a Fourier transform and the Wiener-Hopf technique, and it is shown that there is a family of subcritical solutions characterised by a train of sinusoidal waves on the downstream free surface. The amplitude of these waves decreases as the Froude number increases. Supercritical solutions are also obtained, but, in general, these have infinite vertical velocities at the trailing edge of the plate. Consideration of further terms in the expansions suggests a way of canceling the singularity for certain values of the Froude number.

New stress and velocity fields for highly frictional granular materials

The idealised theory for the quasi-static flow of granular materials which satisfy the Coulomb-Mohr hypothesis is considered. This theory arises in the limit that the angle of internal friction approaches $\pi/2$, and accordingly these materials may be referred to as being `highly frictional'. In this limit, the stress field for both two-dimensional and axially symmetric flows may be formulated in terms of a single nonlinear second order partial differential equation for the stress angle. To obtain an accompanying velocity field, a flow rule must be employed. Assuming the non-dilatant double-shearing flow rule, a further partial differential equation may be derived in each case, this time for the streamfunction. Using Lie symmetry methods, a complete set of group-invariant solutions is derived for both systems, and through this process new exact solutions are constructed. Only a limited number of exact solutions for gravity driven granular flows are known, so these results are potentially important in many practical applications. The problem of mass flow through a two-dimensional wedge hopper is examined as an illustration.

Lie group symmetry analysis for granular media stress equations

The Airy stress function, although frequently employed in classical linear elasticity, does not receive similar usage for granular media problems. For plane strain quasi-static deformations of a cohesionless Coulomb–Mohr granular solid, a single nonlinear partial differential equation is formulated for the Airy stress function by combining the equilibrium equations with the yield condition. This has certain advantages from the usual approach, in which two stress invariants and a stress angle are introduced, and a system of two partial differential equations is needed to describe the flow. In the present study, the symmetry analysis of differential equations is utilised for our single partial differential equation, and by computing an optimal system of one-dimensional Lie algebras, a complete set of group-invariant solutions is derived. By this it is meant that any group-invariant solution of the governing partial differential equation (provided it can be derived via the classical symmetries method) may be obtained as a member of this set by a suitable group transformation. For general values of the parameters (angle of internal friction and gravity g) it is found there are three distinct classes of solutions which correspond to granular flows considered previously in the literature. For the two limiting cases of high angle of internal friction and zero gravity, the governing partial differential equation admit larger families of Lie point symmetries, and from these symmetries, further solutions are derived, many of which are new. Furthermore, the majority of these solutions are exact, which is rare for granular flow, especially in the case of gravity driven flows.

Free surface problems for static Coulomb-Mohr granular solids

This paper is concerned with some plane strain and axially symmetric free surface problems which arise in the study of static granular solids that satisfy the Coulomb-Mohr yield condition. Such problems are inherently nonlinear, and hence difficult to attack analytically. Given a Coulomb friction condition holds on a solid boundary, it is shown that the angle a free surface is allowed to attach to the boundary is dependent only on the angle of wall friction, assuming the stresses are all continuous at the attachment point, and assuming also that the coefficient of cohesion is nonzero. As a model problem, the formation of stable cohesive arches in hoppers is considered. This undesirable phenomena is an obstacle to flow, and occurs when the hopper outlet is too small. Typically, engineers are concerned with predicting the critical outlet size for a given hopper and granular solid, so that for hoppers with outlets larger than this critical value, arching cannot occur. This is a topic of considerable practical interest, with most accepted engineering methods being conservative in nature. Here, the governing equations in two limiting cases (small cohesion and high angle of internal friction) are considered directly. No information on the critical outlet size is found; however solutions for the shape of the free boundary (the arch) are presented, for both plane and axially symmetric geometries.

Sequential nonlinear manifold learning

The computation of compact and meaningful representations of high dimensional sensor data has recently been addressed through the development of Nonlinear Dimensional Reduction (NLDR) algorithms. The numerical implementation of spectral NLDR techniques typically leads to a symmetric eigenvalue problem that is solved by traditional batch eigensolution algorithms. The application of such algorithms in real-time systems necessitates the development of sequential algorithms that perform feature extraction online. This paper presents an efficient online NLDR scheme, Sequential-Isomap, based on incremental singular value decomposition (SVD) and the Isomap method. Example simulations demonstrate the validity and significant potential of this technique in real-time applications such as autonomous systems.

An analytical method to solve a general class of nonlinear reactive transport models

Three recent papers published in Chemical Engineering Journal studied the solution of a model of diffusion and nonlinear reaction using three different methods. Two of these studies obtained series solutions using specialized mathematical methods, known as the Adomian decomposition method and the homotopy analysis method. Subsequently it was shown that the solution of the same particular model could be written in terms of a transcendental function called Gauss’ hypergeometric function. These three previous approaches focused on one particular reactive transport model. This particular model ignored advective transport and considered one specific reaction term only. Here we generalize these previous approaches and develop an exact analytical solution for a general class of steady state reactive transport models that incorporate (i) combined advective and diffusive transport, and (ii) any sufficiently differentiable reaction term R(C). The new solution is a convergent Maclaurin series. The Maclaurin series solution can be derived without any specialized mathematical methods nor does it necessarily involve the computation of any transcendental function. Applying the Maclaurin series solution to certain case studies shows that the previously published solutions are particular cases of the more general solution outlined here. We also demonstrate the accuracy of the Maclaurin series solution by comparing with numerical solutions for particular cases.

Focus of attention and its impact on movement behaviour

Investigations into the relative effectiveness of either focusing on movement form (internal focus) or movement effects (external focus) have tended to dominate research on instructional constraints. However, rather than adopting a comparative approach to determine which focus of attention is more effective, analysis of the relative efficacy of each specific instruction focus during motor learning could be more relevant for both researchers and practitioners. Theoretical advances in the motor learning literature from a nonlinear dynamics perspective might explain the processes that underlie the effect of different attentional focus instructions. Referencing ideas and concepts from a current motor learning model, differential effects of either internal or external focus of instructions are examined. This paper also highlights some deficiencies in extant theory and research design on focus of attention which require further investigations.

Electron diffusion and back reaction in dye-sensitized solar cells : the effect of nonlinear recombination kinetics

The electron collection efficiency in dye-sensitized solar cells (DSCs) is usually related to the electron diffusion length, L = (Dτ)^1/2, where D is the diffusion coefficient of mobile electrons and τ is their lifetime, which is determined by electron transfer to the redox electrolyte. Analysis of incident photon-to-current efficiency (IPCE) spectra for front and rear illumination consistently gives smaller values of L than those derived from small amplitude methods. We show that the IPCE analysis is incorrect if recombination is not first-order in free electron concentration, and we demonstrate that the intensity dependence of the apparent L derived by first-order analysis of IPCE measurements and the voltage dependence of L derived from perturbation experiments can be fitted using the same reaction order, γ ≈ 0.8. The new analysis presented in this letter resolves the controversy over why L values derived from small amplitude methods are larger than those obtained from IPCE data.

Minimising wave drag for free surface flow past a two-dimensional stern

Free surface flow past a two-dimensional semi-infinite curved plate is considered, with emphasis given to solving for the shape of the resulting wave train that appears downstream on the surface of the fluid. This flow configuration can be interpreted as applying near the stern of a wide blunt ship. For steady flow in a fluid of finite depth, we apply the Wiener-Hopf technique to solve a linearised problem, valid for small perturbations of the uniform stream. Weakly nonlinear results found using a forced KdV equation are also presented, as are numerical solutions to the fully nonlinear problem, computed using a conformal mapping and a boundary integral technique. By considering different families of shapes for the semi-infinite plate, it is shown how the amplitude of the waves can be minimised. For plates that increase in height as a function of the direction of flow, reach a local maximum, and then point slightly downwards at the point at which the free surface detaches, it appears the downstream wavetrain can be eliminated entirely.

Application of an optimisation algorithm to configure an internal fixation device

Fractures of long bones are sometimes treated using various types of fracture fixation devices including internal plate fixators. These are specialised plates which are used to bridge the fracture gap(s) whilst anatomically aligning the bone fragments. The plate is secured in position by screws. The aim of such a device is to support and promote the natural healing of the bone. When using an internal fixation device, it is necessary for the clinician to decide upon many parameters, for example, the type of plate and where to position it; how many and where to position the screws. While there have been a number of experimental and computational studies conducted regarding the configuration of screws in the literature, there is still inadequate information available concerning the influence of screw configuration on fracture healing. Because screw configuration influences the amount of flexibility at the area of fracture, it has a direct influence on the fracture healing process. Therefore, it is important that the chosen screw configuration does not inhibit the healing process. In addition to the impact on the fracture healing process, screw configuration plays an important role in the distribution of stresses in the plate due to the applied loads. A plate that experiences high stresses is prone to early failure. Hence, the screw configuration used should not encourage the occurrence of high stresses. This project develops a computational program in Fortran programming language to perform mathematical optimisation to determine the screw configuration of an internal fixation device within constraints of interfragmentary movement by minimising the corresponding stress in the plate. Thus, the optimal solution suggests the positioning and number of screws which satisfies the predefined constraints of interfragmentary movements. For a set of screw configurations the interfragmentary displacement and the stress occurring in the plate were calculated by the Finite Element Method. The screw configurations were iteratively changed and each time the corresponding interfragmentary displacements were compared with predefined constraints. Additionally, the corresponding stress was compared with the previously calculated stress value to determine if there was a reduction. These processes were continued until an optimal solution was achieved. The optimisation program has been shown to successfully predict the optimal screw configuration in two cases. The first case was a simplified bone construct whereby the screw configuration solution was comparable with those recommended in biomechanical literature. The second case was a femoral construct, of which the resultant screw configuration was shown to be similar to those used in clinical cases. The optimisation method and programming developed in this study has shown that it has potential to be used for further investigations with the improvement of optimisation criteria and the efficiency of the program.

Numerical simulation for the variable-order Galilei invariant advection diffusion equation with a nonlinear source term

In this paper, we consider the variable-order Galilei advection diffusion equation with a nonlinear source term. A numerical scheme with first order temporal accuracy and second order spatial accuracy is developed to simulate the equation. The stability and convergence of the numerical scheme are analyzed. Besides, another numerical scheme for improving temporal accuracy is also developed. Finally, some numerical examples are given and the results demonstrate the effectiveness of theoretical analysis. Keywords: The variable-order Galilei invariant advection diffusion equation with a nonlinear source term; The variable-order Riemann–Liouville fractional partial derivative; Stability; Convergence; Numerical scheme improving temporal accuracy