A comparison of finite difference and finite volume methods for solving the space-fractional advection-dispersion equation with variable coefficients

Transport processes within heterogeneous media may exhibit non- classical diffusion or dispersion which is not adequately described by the classical theory of Brownian motion and Fick’s law. We consider a space-fractional advection-dispersion equation based on a fractional Fick’s law. Zhang et al. [Water Resources Research, 43(5)(2007)] considered such an equation with variable coefficients, which they dis- cretised using the finite difference method proposed by Meerschaert and Tadjeran [Journal of Computational and Applied Mathematics, 172(1):65-77 (2004)]. For this method the presence of variable coef- ficients necessitates applying the product rule before discretising the Riemann–Liouville fractional derivatives using standard and shifted Gru ̈nwald formulas, depending on the fractional order. As an alternative, we propose using a finite volume method that deals directly with the equation in conservative form. Fractionally-shifted Gru ̈nwald formulas are used to discretise the Riemann–Liouville fractional derivatives at control volume faces, eliminating the need for product rule expansions. We compare the two methods for several case studies, highlighting the convenience of the finite volume approach.

A derivation of high-frequency asymptotic values of 3D added mass and damping based on properties of the Cummins' equation

This brief paper provides a novel derivation of the known asymptotic values of three-dimensional (3D) added mass and damping of marine structures in waves. The derivation is based on the properties of the convolution terms in the Cummins's Equation as derived by Ogilvie. The new derivation is simple and no approximations or series expansions are made. The results follow directly from the relative degree and low-frequency asymptotic properties of the rational representation of the convolution terms in the frequency domain. As an application, the extrapolation of damping values at high frequencies for the computation of retardation functions is also discussed.

Multi-shot person re-identification via relational stein divergence

Person re-identification is particularly challenging due to significant appearance changes across separate camera views. In order to re-identify people, a representative human signature should effectively handle differences in illumination, pose and camera parameters. While general appearance-based methods are modelled in Euclidean spaces, it has been argued that some applications in image and video analysis are better modelled via non-Euclidean manifold geometry. To this end, recent approaches represent images as covariance matrices, and interpret such matrices as points on Riemannian manifolds. As direct classification on such manifolds can be difficult, in this paper we propose to represent each manifold point as a vector of similarities to class representers, via a recently introduced form of Bregman matrix divergence known as the Stein divergence. This is followed by using a discriminative mapping of similarity vectors for final classification. The use of similarity vectors is in contrast to the traditional approach of embedding manifolds into tangent spaces, which can suffer from representing the manifold structure inaccurately. Comparative evaluations on benchmark ETHZ and iLIDS datasets for the person re-identification task show that the proposed approach obtains better performance than recent techniques such as Histogram Plus Epitome, Partial Least Squares, and Symmetry-Driven Accumulation of Local Features.

Predicting emotional exhaustion among haemodialysis nurses : a structural equation model using Kanter’s structural empowerment theory

Aim To test an explanatory model of the relationships between the nursing work environment, job satisfaction, job stress and emotional exhaustion for haemodialysis nurses, drawing on Kanter's theory of organizational empowerment. Background Understanding the organizational predictors of burnout (emotional exhaustion) in haemodialysis nurses is critical for staff retention and improving nurse and patient outcomes. Previous research has demonstrated high levels of emotional exhaustion among haemodialysis nurses, yet the relationships between nurses' work environment, job satisfaction, stress and emotional exhaustion in this population are poorly understood. Design A cross-sectional online survey. Methods 417 nurses working in haemodialysis units completed an online survey between October 2011–April 2012 using validated measures of the work environment, job satisfaction, job stress and emotional exhaustion. Results Overall, the structural equation model demonstrated adequate fit and we found partial support for the hypothesized relationships. Nurses' work environment had a direct positive effect on job satisfaction, explaining 88% of the variance. Greater job satisfaction, in turn, predicted lower job stress, explaining 82% of the variance. Job satisfaction also had an indirect effect on emotional exhaustion by mitigating job stress. However, job satisfaction did not have a direct effect on emotional exhaustion. Conclusion The work environment of haemodialysis nurses is pivotal to the development of job satisfaction. Nurses' job satisfaction also predicts their level of job stress and emotional exhaustion. Our findings suggest staff retention can be improved by creating empowering work environments that promote job satisfaction among haemodialysis nurses.

Scaling laws for localised states in a nonlocal amplitude equation

It is well known that, although a uniform magnetic field inhibits the onset of small amplitude thermal convection in a layer of fluid heated from below, isolated convection cells may persist if the fluid motion within them is sufficiently vigorous to expel magnetic flux. Such fully nonlinear(‘‘convecton’’) solutions for magnetoconvection have been investigated by several authors. Here we explore a model amplitude equation describing this separation of a fluid layer into a vigorously convecting part and a magnetically-dominated part at rest. Our analysis elucidates the origin of the scaling laws observed numerically to form the boundaries in parameter space of the region of existence of these localised states, and importantly, for the lowest thermal forcing required to sustain them.