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.

Clinical performance of a new silicone hydrogel contact lens over 6 months of extended wear

Purpose: Silicone hydrogel contact lenses (CLs) are becoming increasingly popular for daily wear (DW), extended wear (EW) and continuous wear (CW), due to their higher oxygen transmissibility compared to hydrogel CLs. The aim of this study was to investigate the clinical and subjective performance of asmofilcon A (Menicon Co., Ltd), a new surface treated silicone hydrogel CL, during 6-night EW over 6 months (M). Methods: A prospective, randomised, single-masked, monadic study was conducted. N=60 experienced DW soft CL wearers were randomly assigned to wear either asmofilcon A (test: Dk=129, water content (WC)=40%, Nanogloss surface treatment) or senofilcon A (control: Dk=103, WC=38%, PVP internal wetting agent, Vistakon, Johnson & Johnson Vision Care) CLs bilaterally for 6 M on an EW basis. A PHMB-preserved solution (Menicon Co., Ltd) was dispensed for CL care. Evaluations were conducted at CL delivery and after 1 week (W), 4 W, 3 M and 6 M of EW. At each visit, a range of objective and subjective clinical performance measures were assessed. Results: N=50 subjects (83%) successfully completed the study, with the majority of discontinuations due to loss to follow-up (n=3) or moving away/travel (n=5). N=2 subjects experienced adverse events; n=1 unilateral red eye with asmofilcon A and n=1 asymptomatic infiltrate with senofilcon A. There were no significant differences in high or low contrast distance visual acuity (HCDVA or LCDVA) between asmofilcon A and senofilcon A; however, LCDVA decreased significantly over time with both CL types (p<0.05). The two CL types did not vary significantly with respect to any of the objective and subjective measures assessed (p>0.05); CL fitting characteristics and CL surface measurements were very similar and mean bulbar and limbal redness measures were always less than grade 1.0. Superior palpebral conjunctival injection showed a statistically, but not clinically, significant increase over time with both CL types (p<0.05). Corneal staining did not vary significantly between asmofilcon A and senofilcon A (p>0.05), with low median gradings of less than 0.5 observed for all areas assessed. There were no solution-related staining reactions observed with either CL type. The asmofilcon A and senofilcon A CLs were both rated highly with respect to overall comfort, with medians of 14 or 15 hours of comfortable lens wearing time per day reported at each of the study visits (p>0.05). Conclusions: Over 6 months of EW, the asmofilcon A and senofilcon A CLs performed in a similar manner with respect to visual acuity, ocular health and CL performance measures. Some changes over time were observed with both CL types, including reduced LCDVA and increased superior palpebral injection, which warrant further investigation in longer-term EW studies. Asmofilcon A appeared to be equivalent in performance to senofilcon A.

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.

Food and interaction design [Extended Abstract]

Food and interaction design presents an interesting challenge to the HCI community in attending to the pervasive nature of food, the socio-cultural differences in food practices and a changing global foodscape. To design for meaningful and positive interactions it is essential to identify daily food practices and the opportunities for the design of technology to support such practices. This workshop brings together a community of researchers and practitioners in human-food interaction to attend to the practical and theoretical difficulties in designing for human-food interactions in everyday life. Through a practical field study and workshop we explore themes of food experiences, health and wellbeing, sustainability and alternative food cultures.

Assessment of flood-related recharge to alluvial aquifers of an irrigated catchment following extended drought conditions using 3D visualisation and environmental tracers, Lockyer Valley, southeast Queensland, Australia.

The Lockyer Valley in southeast Queensland, Australia, hosts an economically significant alluvial aquifer system which has been impacted by prolonged drought conditions (~1997 to ~ 2009). Throughout this time, the system was under continued groundwater extraction, resulting in severe aquifer depletion. By 2008, much of the aquifer was at <30% of storage but some relief occurred with rains in early 2009. However, between December 2010 and January 2011, most of southeast Queensland experienced unprecedented flooding, which generated significant aquifer recharge. In order to understand the spatial and temporal controls of groundwater recharge in the alluvium, a detailed 3D lithological property model of gravels, sands and clays was developed using GOCAD software. The spatial distribution of recharge throughout the catchment was assessed using hydrograph data from about 400 groundwater observation wells screened at the base of the alluvium. Water levels from these bores were integrated into a catchment-wide 3D geological model using the 3D geological modelling software GOCAD; the model highlights the complexity of recharge mechanisms. To support this analysis, groundwater tracers (e.g. major and minor ions, stable isotopes, 3H and 14C) were used as independent verification. The use of these complementary methods has allowed the identification of zones where alluvial recharge primarily occurs from stream water during episodic flood events. However, the study also demonstrates that in some sections of the alluvium, rainfall recharge and discharge from the underlying basement into the alluvium are the primary recharge mechanisms of the alluvium. This is indicated by the absence of any response to the flood, as well as the observed old radiocarbon ages and distinct basement water chemistry signatures at these locations. Within the 3D geological model, integration of water chemistry and time-series displays of water level surfaces before and after the flood suggests that the spatial variations of the flood response in the alluvium are primarily controlled by the valley morphology and lithological variations within the alluvium. The integration of time-series of groundwater level surfaces in the 3D geological model also enables the quantification of the volumetric change of groundwater stored in the unconfined sections of this alluvial aquifer during drought and following flood events. The 3D representation and analysis of hydraulic and recharge information has considerable advantages over the traditional 2D approach. For example, while many studies focus on singular aspects of catchment dynamics and groundwater-surface water interactions, the 3D approach is capable of integrating multiple types of information (topography, geological, hydraulic, water chemistry and spatial) into a single representation which provides valuable insights into the major factors controlling aquifer processes.

A least squares based finite volume method for the Cahn-Hilliard and Cahn-Hilliard-reaction equations

A vertex-centred finite volume method (FVM) for the Cahn-Hilliard (CH) and recently proposed Cahn-Hilliard-reaction (CHR) equations is presented. Information at control volume faces is computed using a high-order least-squares approach based on Taylor series approximations. This least-squares problem explicitly includes the variational boundary condition (VBC) that ensures that the discrete equations satisfy all of the boundary conditions. We use this approach to solve the CH and CHR equations in one and two dimensions and show that our scheme satisfies the VBC to at least second order. For the CH equation we show evidence of conservative, gradient stable solutions, however for the CHR equation, strict gradient-stability is more challenging to achieve.

Solution methods for advection-diffusion-reaction equations on growing domains and subdomains, with application to modelling skin substitutes

Problems involving the solution of advection-diffusion-reaction equations on domains and subdomains whose growth affects and is affected by these equations, commonly arise in developmental biology. Here, a mathematical framework for these situations, together with methods for obtaining spatio-temporal solutions and steady states of models built from this framework, is presented. The framework and methods are applied to a recently published model of epidermal skin substitutes. Despite the use of Eulerian schemes, excellent agreement is obtained between the numerical spatio-temporal, numerical steady state, and analytical solutions of the model.

Bending and blurring blended learning boundaries [Extended Abstract]

This presentation presents a blended learning model that provides greater opportunity for learning to be self-managed and personalized.

Numerical solution of stress intensity factors of multiple cracks in great number with eigen COD boundary integral equations

Based on the eigen crack opening displacement (COD) boundary integral equations, a newly developed computational approach is proposed for the analysis of multiple crack problems. The eigen COD particularly refers to a crack in an infinite domain under fictitious traction acting on the crack surface. With the concept of eigen COD, the multiple cracks in great number can be solved by using the conventional displacement discontinuity boundary integral equations in an iterative fashion with a small size of system matrix. The interactions among cracks are dealt with by two parts according to the distances of cracks to the current crack. The strong effects of cracks in adjacent group are treated with the aid of the local Eshelby matrix derived from the traction BIEs in discrete form. While the relatively week effects of cracks in far-field group are treated in the iteration procedures. Numerical examples are provided for the stress intensity factors of multiple cracks, up to several thousands in number, with the proposed approach. By comparing with the analytical solutions in the literature as well as solutions of the dual boundary integral equations, the effectiveness and the efficiencies of the proposed approach are verified.

Stable strong order 1.0 schemes for solving stochastic ordinary differential equations

The Balanced method was introduced as a class of quasi-implicit methods, based upon the Euler-Maruyama scheme, for solving stiff stochastic differential equations. We extend the Balanced method to introduce a class of stable strong order 1. 0 numerical schemes for solving stochastic ordinary differential equations. We derive convergence results for this class of numerical schemes. We illustrate the asymptotic stability of this class of schemes is illustrated and is compared with contemporary schemes of strong order 1. 0. We present some evidence on parametric selection with respect to minimising the error convergence terms. Furthermore we provide a convergence result for general Balanced style schemes of higher orders.

Comparing measures of fat-free mass in overweight older adults using three different bioelectrical impedance devices and three prediction equations

Objectives: To compare measures of fat-free mass (FFM) by three different bioelectrical impedance analysis (BIA) devices and to assess the agreement between three different equations validated in older adult and/or overweight populations. Design: Cross-sectional study. Setting: Orthopaedics ward of Brisbane public hospital, Australia. Participants: Twenty-two overweight, older Australians (72 yr ± 6.4, BMI 34 kg/m2 ± 5.5) with knee osteoarthritis. Measurements: Body composition was measured using three BIA devices: Tanita 300-GS (foot-to-foot), Impedimed DF50 (hand-to-foot) and Impedimed SFB7 (bioelectrical impedance spectroscopy (BIS)). Three equations for predicting FFM were selected based on their ability to be applied to an older adult and/ or overweight population. Impedance values were extracted from the hand-to-foot BIA device and included in the equations to estimate FFM. Results: The mean FFM measured by BIS (57.6 kg ± 9.1) differed significantly from those measured by foot-to-foot (54.6 kg ± 8.7) and hand-to-foot BIA (53.2 kg ± 10.5) (P < 0.001). The mean ± SD FFM predicted by three equations using raw data from hand-to-foot BIA were 54.7 kg ± 8.9, 54.7 kg ± 7.9 and 52.9 kg ± 11.05 respectively. These results did not differ from the FFM predicted by the hand-to-foot device (F = 2.66, P = 0.118). Conclusions: Our results suggest that foot-to-foot and hand-to-foot BIA may be used interchangeably in overweight older adults at the group level but due to the large limits of agreement may lead to unacceptable error in individuals. There was no difference between the three prediction equations however these results should be confirmed within a larger sample and against a reference standard.

An extended theory of planned behavior intervention for older adults With Type 2 diabetes and cardiovascular disease

A randomized controlled trial evaluated the effectiveness of a 4-wk extended theory of planned behavior (TPB) intervention to promote regular physical activity and healthy eating among older adults diagnosed with Type 2 diabetes or cardiovascular disease (N = 183). Participants completed TPB measures of attitude, subjective norm, perceived behavioral control, and intention, as well as planning and behavior, at preintervention and 1 wk and 6 wk postintervention for each behavior. No significant time-by-condition effects emerged for healthy eating. For physical activity, significant time-by-condition effects were found for behavior, intention, planning, perceived behavioral control, and subjective norm. In particular, compared with control participants, the intervention group showed short-term improvements in physical activity and planning, with further analyses indicating that the effect of the intervention on behavior was mediated by planning. The results indicate that TPB-based interventions including planning strategies may encourage physical activity among older people with diabetes and cardiovascular disease.