Numerical methods for solving the multi-term time-fractional wave-diffusion equations

In this paper, the multi-term time-fractional wave diffusion equations are considered. The multiterm time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian.

Analytical solutions for the two- and three-dimensional time-fractional telegraph equations by the method of separating variables

In this paper, a method of separating variables is effectively implemented for solving a time-fractional telegraph equation (TFTE) in two and three dimensions. We discuss and derive the analytical solution of the TFTE in two and three dimensions with nonhomogeneous Dirichlet boundary condition. This method can be extended to other kinds of the boundary conditions.

Analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations on a finite domain

Generalized fractional partial differential equations have now found wide application for describing important physical phenomena, such as subdiffusive and superdiffusive processes. However, studies of generalized multi-term time and space fractional partial differential equations are still under development. In this paper, the multi-term time-space Caputo-Riesz fractional advection diffusion equations (MT-TSCR-FADE) with Dirichlet nonhomogeneous boundary conditions are considered. The multi-term time-fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0, 1], [1, 2] and [0, 2], respectively. These are called respectively the multi-term time-fractional diffusion terms, the multi-term time-fractional wave terms and the multi-term time-fractional mixed diffusion-wave terms. The space fractional derivatives are defined as Riesz fractional derivatives. Analytical solutions of three types of the MT-TSCR-FADE are derived with Dirichlet boundary conditions. By using Luchko's Theorem (Acta Math. Vietnam., 1999), we proposed some new techniques, such as a spectral representation of the fractional Laplacian operator and the equivalent relationship between fractional Laplacian operator and Riesz fractional derivative, that enabled the derivation of the analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations. © 2012.

Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion equations in a finite domain

Multi-term time-fractional differential equations have been used for describing important physical phenomena. However, studies of the multi-term time-fractional partial differential equations with three kinds of nonhomogeneous boundary conditions are still limited. In this paper, a method of separating variables is used to solve the multi-term time-fractional diffusion-wave equation and the multi-term time-fractional diffusion equation in a finite domain. In the two equations, the time-fractional derivative is defined in the Caputo sense. We discuss and derive the analytical solutions of the two equations with three kinds of nonhomogeneous boundary conditions, namely, Dirichlet, Neumann and Robin conditions, respectively.

A randomised controlled trial to prevent hospital readmissions and loss of functional ability in high risk older adults: a study protocol

Background Older people have higher rates of hospital admission than the general population and higher rates of readmission due to complications and falls. During hospitalisation, older people experience significant functional decline which impairs their future independence and quality of life. Acute hospital services comprise the largest section of health expenditure in Australia and prevention or delay of disease is known to produce more effective use of services. Current models of discharge planning and follow-up care, however, do not address the need to prevent deconditioning or functional decline. This paper describes the protocol of a randomised controlled trial which aims to evaluate innovative transitional care strategies to reduce unplanned readmissions and improve functional status, independence, and psycho-social well-being of community-based older people at risk of readmission. Methods/Design The study is a randomised controlled trial. Within 72 hours of hospital admission, a sample of older adults fitting the inclusion/exclusion criteria (aged 65 years and over, admitted with a medical diagnosis, able to walk independently for 3 meters, and at least one risk factor for readmission) are randomised into one of four groups: 1) the usual care control group, 2) the exercise and in-home/telephone follow-up intervention group, 3) the exercise only intervention group, or 4) the in-home/telephone follow-up only intervention group. The usual care control group receive usual discharge planning provided by the health service. In addition to usual care, the exercise and in-home/telephone follow-up intervention group receive an intervention consisting of a tailored exercise program, in-home visit and 24 week telephone follow-up by a gerontic nurse. The exercise only and in-home/telephone follow-up only intervention groups, in addition to usual care receive only the exercise or gerontic nurse components of the intervention respectively. Data collection is undertaken at baseline within 72 hours of hospital admission, 4 weeks following hospital discharge, 12 weeks following hospital discharge, and 24 weeks following hospital discharge. Outcome assessors are blinded to group allocation. Primary outcomes are emergency hospital readmissions and health service use, functional status, psychosocial well-being and cost effectiveness. Discussion The acute hospital sector comprises the largest component of health care system expenditure in developed countries, and older adults are the most frequent consumers. There are few trials to demonstrate effective models of transitional care to prevent emergency readmissions, loss of functional ability and independence in this population following an acute hospital admission. This study aims to address that gap and provide information for future health service planning which meets client needs and lowers the use of acute care services.

Helping understand nutritional gaps in the elderly (HUNGER) : a prospective study of patient factors associated with inadequate nutritional intake in older medical inpatients

BACKGROUND: Malnutrition, and poor intake during hospitalisation, are common in older medical patients. Better understanding of patient-specific factors associated with poor intake may inform nutritional interventions. AIMS: To measure the proportion of older medical patients with inadequate nutritional intake, and identify patient-related factors associated with this outcome. METHODS: Prospective cohort study enrolling consecutive consenting medical inpatients aged 65 years or older. Primary outcome was energy intake less than resting energy expenditure estimated using weight-based equations. Energy intake was calculated for a single day using direct observation of plate waste. Explanatory variables included age, gender, number of co-morbidities, number of medications, diagnosis, usual residence, nutritional status, functional and cognitive impairment, depressive symptoms, poor appetite, poor dentition, and dysphagia. RESULTS: Of 134 participants (mean age 80 years, 51% female), only 41% met estimated resting energy requirements. Mean energy intake was 1220 kcal/day (SD 440), or 18.1 kcal/kg/day. Factors associated with inadequate energy intake in multivariate analysis were poor appetite, higher BMI, diagnosis of infection or cancer, delirium and need for assistance with feeding. CONCLUSIONS: Inadequate nutritional intake is common, and patient factors contributing to poor intake need to be considered in nutritional interventions.

Mixed-dimensional consistent coupling by multi-point constraint equations for efficient multi-scale modeling

Finding an appropriate linking method to connect different dimensional element types in a single finite element model is a key issue in the multi-scale modeling. This paper presents a mixed dimensional coupling method using multi-point constraint equations derived by equating the work done on either side of interface connecting beam elements and shell elements for constructing a finite element multiscale model. A typical steel truss frame structure is selected as case example and the reduced scale specimen of this truss section is then studied in the laboratory to measure its dynamic and static behavior in global truss and local welded details while the different analytical models are developed for numerical simulation. Comparison of dynamic and static response of the calculated results among different numerical models as well as the good agreement with those from experimental results indicates that the proposed multi-scale model is efficient and accurate.

Isolation and functional characterisation of banana phytoene synthase genes as potential cisgenes

Carotenoids occur in all photosynthetic organisms where they protect photosystems from auto-oxidation, participate in photosynthetic energy-transfer and are secondary metabolites. Of the more than 600 known plant carotenoids, few can be converted into vitamin A by humans and so these pro-vitamin A carotenoids (pVAC) are important in human nutrition. Phytoene synthase (PSY) is a key enzyme in the biosynthetic pathway of pVACs and plays a central role in regulating pVAC accumulation in the edible portion of crop plants. Bananas are a major commercial crop and serve as a staple crop for more than 30 million people. There is natural variation in fruit pVAC content across different banana cultivars, but this is not well understood. Therefore, we isolated PSY genes from banana cultivars with relatively high (cv. Asupina) and low (cv. Cavendish) pVAC content. We provide evidence that PSY in banana is encoded by two paralogs (PSY1 and PSY2), each with a similar gene structure to homologous genes in other monocots. Further, we demonstrate that PSY2 is more highly expressed in fruit pulp compared to leaf. Functional analysis of PSY1 and PSY2 in rice callus and E. coli demonstrate that both genes encode functional enzymes, and that Asupina PSYs have approximately twice the enzymatic activity of the corresponding Cavendish PSYs. These results suggest that differences in PSY enzyme activity contribute significantly to the differences in Asupina and Cavendish fruit pVAC content. Importantly, Asupina PSY genes could potentially be used to generate new cisgenic or intragenic banana cultivars with enhanced pVAC content.