Identifying with an avatar : a multidisciplinary perspective

Avatars perform a complex range of inter-related functions. They not only allow us to express a digital identity, they facilitate the expression of physical motility and, through non-verbal expression, help to mediate social interaction in networked environments. When well designed, they can contribute to a sense of “presence” (a sense of being there) and a sense of “co-presence” (a sense of being there with others) in digital space. Because of this complexity, the study of avatars can be enriched by theoretical insights from a range of disciplines. This paper considers avatars from the perspectives of critical theory, visual communication, and art theory (on portraiture) to help elucidate the role of avatars as an expression of identity. It goes on to argue that identification with an avatar is also produced through their expression of motility and discusses the benefits of film theory for explaining this process. Conceding the limits of this approach, the paper draws on philosophies of body image, Human Computer Interaction (HCI) theory on embodied interaction, and fields as diverse as dance to explain the sense of identification, immersion, presence and co-presence that avatars can produce.

Numerical method and analytical technique of the modified anomalous subdiffusion equation with a nonlinear source term

In this paper, we consider a modified anomalous subdiffusion equation with a nonlinear source term for describing processes that become less anomalous as time progresses by the inclusion of a second fractional time derivative acting on the diffusion term. A new implicit difference method is constructed. The stability and convergence are discussed using a new energy method. Finally, some numerical examples are given. The numerical results demonstrate the effectiveness of theoretical analysis

Numerical methods for the variable-order fractional advection-diffusion equation with a nonlinear source term

In this paper, we consider a variable-order fractional advection-diffusion equation with a nonlinear source term on a finite domain. Explicit and implicit Euler approximations for the equation are proposed. Stability and convergence of the methods are discussed. Moreover, we also present a fractional method of lines, a matrix transfer technique, and an extrapolation method for the equation. Some numerical examples are given, and the results demonstrate the effectiveness of theoretical analysis.

Numerical simulation for the 3D seepage flow with fractional derivatives in porous media

In this paper, the numerical simulation of the 3D seepage flow with fractional derivatives in porous media is considered under two special cases: non-continued seepage flow in uniform media (NCSFUM) and continued seepage flow in non-uniform media (CSF-NUM). A fractional alternating direction implicit scheme (FADIS) for the NCSF-UM and a modified Douglas scheme (MDS) for the CSF-NUM are proposed. The stability, consistency and convergence of both FADIS and MDS in a bounded domain are discussed. A method for improving the speed of convergence by Richardson extrapolation for the MDS is also presented. Finally, numerical results are presented to support our theoretical analysis.

Stability and convergence of a new explicit finite-difference approximation for the variable-order nonlinear fractional diffusion equation

In this paper, we consider the variable-order nonlinear fractional diffusion equation View the MathML source where xRα(x,t) is a generalized Riesz fractional derivative of variable order View the MathML source and the nonlinear reaction term f(u,x,t) satisfies the Lipschitz condition |f(u1,x,t)-f(u2,x,t)|less-than-or-equals, slantL|u1-u2|. A new explicit finite-difference approximation is introduced. The convergence and stability of this approximation are proved. Finally, some numerical examples are provided to show that this method is computationally efficient. The proposed method and techniques are applicable to other variable-order nonlinear fractional differential equations.

Stability and convergence of an implicit numerical method for the non-linear fractional reaction-subdiffusion process

In this paper, we consider the following non-linear fractional reaction–subdiffusion process (NFR-SubDP): Formula where f(u, x, t) is a linear function of u, the function g(u, x, t) satisfies the Lipschitz condition and 0Dt1–{gamma} is the Riemann–Liouville time fractional partial derivative of order 1 – {gamma}. We propose a new computationally efficient numerical technique to simulate the process. Firstly, the NFR-SubDP is decoupled, which is equivalent to solving a non-linear fractional reaction–subdiffusion equation (NFR-SubDE). Secondly, we propose an implicit numerical method to approximate the NFR-SubDE. Thirdly, the stability and convergence of the method are discussed using a new energy method. Finally, some numerical examples are presented to show the application of the present technique. This method and supporting theoretical results can also be applied to fractional integrodifferential equations.

Numerical methods for fractional partial differential equations with Riesz space fractional derivatives

In this paper, we consider the numerical solution of a fractional partial differential equation with Riesz space fractional derivatives (FPDE-RSFD) on a finite domain. Two types of FPDE-RSFD are considered: the Riesz fractional diffusion equation (RFDE) and the Riesz fractional advection–dispersion equation (RFADE). The RFDE is obtained from the standard diffusion equation by replacing the second-order space derivative with the Riesz fractional derivative of order αset membership, variant(1,2]. The RFADE is obtained from the standard advection–dispersion equation by replacing the first-order and second-order space derivatives with the Riesz fractional derivatives of order βset membership, variant(0,1) and of order αset membership, variant(1,2], respectively. Firstly, analytic solutions of both the RFDE and RFADE are derived. Secondly, three numerical methods are provided to deal with the Riesz space fractional derivatives, namely, the L1/L2-approximation method, the standard/shifted Grünwald method, and the matrix transform method (MTM). Thirdly, the RFDE and RFADE are transformed into a system of ordinary differential equations, which is then solved by the method of lines. Finally, numerical results are given, which demonstrate the effectiveness and convergence of the three numerical methods.

Power sharing and stability enhancement of an autonomous microgrid with inertial and non-inertial DGs with DSTATCOM

This paper proposes a method of enhancing system stability with a distribution static compensator (DSTATCOM) in an autonomous microgrid with multiple distributed generators (DG). It is assumed that there are both inertial and non-inertial DGs connected to the microgrid. The inertial DG can be a synchronous machine of smaller rating while inertia less DGs (solar) are assumed as DC sources. The inertia less DGs are connected through Voltage Source Converter (VSC) to the microgrid. The VSCs are controlled by either state feedback or current feedback mode to achieve desired voltage-current or power outputs respectively. The power sharing among the DGs is achieved by drooping voltage angle. Once the reference for the output voltage magnitude and angle is calculated from the droop, state feedback controllers are used to track the reference. The angle reference for the synchronous machine is compared with the output voltage angle of the machine and the error is fed to a PI controller. The controller output is used to set the power reference of the synchronous machine. The rate of change in the angle in a synchronous machine is restricted by the machine inertia and to mimic this nature, the rate of change in the VSCs angles are restricted by a derivative feedback in the droop control. The connected distribution static compensator (DSTATCOM) provides ride through capability during power imbalance in the microgrid, especially when the stored energy of the inertial DG is not sufficient to maintain stability. The inclusion of the DSATCOM in such cases ensures the system stability. The efficacies of the controllers are established through extensive simulation studies using PSCAD.

The neuro-muscular and musculo-skeletal characterization of children with joint hypermobility

In children, joint hypermobility (typified by structural instability of joints) manifests clinically as neuro-muscular and musculo-skeletal conditions and conditions associated with development and organization of control of posture and gait (Finkelstein, 1916; Jahss, 1919; Sobel, 1926; Larsson, Mudholkar, Baum and Srivastava, 1995; Murray and Woo, 2001; Hakim and Grahame, 2003; Adib, Davies, Grahame, Woo and Murray, 2005:). The process of control of the relative proportions of joint mobility and stability, whilst maintaining equilibrium in standing posture and gait, is dependent upon the complex interrelationship between skeletal, muscular and neurological function (Massion, 1998; Gurfinkel, Ivanenko, Levik and Babakova, 1995; Shumway-Cook and Woollacott, 1995). The efficiency of this relies upon the integrity of neuro-muscular and musculo-skeletal components (ligaments, muscles, nerves), and the Central Nervous System’s capacity to interpret, process and integrate sensory information from visual, vestibular and proprioceptive sources (Crotts, Thompson, Nahom, Ryan and Newton, 1996; Riemann, Guskiewicz and Shields, 1999; Schmitz and Arnold, 1998) and development and incorporation of this into a representational scheme (postural reference frame) of body orientation with respect to internal and external environments (Gurfinkel et al., 1995; Roll and Roll, 1988). Sensory information from the base of support (feet) makes significant contribution to the development of reference frameworks (Kavounoudias, Roll and Roll, 1998). Problems with the structure and/ or function of any one, or combination of these components or systems, may result in partial loss of equilibrium and, therefore ineffectiveness or significant reduction in the capacity to interact with the environment, which may result in disability and/ or injury (Crotts et al., 1996; Rozzi, Lephart, Sterner and Kuligowski, 1999b). Whilst literature focusing upon clinical associations between joint hypermobility and conditions requiring therapeutic intervention has been abundant (Crego and Ford, 1952; Powell and Cantab, 1983; Dockery, in Jay, 1999; Grahame, 1971; Childs, 1986; Barton, Bird, Lindsay, Newton and Wright, 1995a; Rozzi, et al., 1999b; Kerr, Macmillan, Uttley and Luqmani, 2000; Grahame, 2001), there has been a deficit in controlled studies in which the neuro-muscular and musculo-skeletal characteristics of children with joint hypermobility have been quantified and considered within the context of organization of postural control in standing balance and gait. This was the aim of this project, undertaken as three studies. The major study (Study One) compared the fundamental neuro-muscular and musculo-skeletal characteristics of 15 children with joint hypermobility, and 15 age (8 and 9 years), gender, height and weight matched non-hypermobile controls. Significant differences were identified between previously undiagnosed hypermobile (n=15) and non-hypermobile children (n=15) in passive joint ranges of motion of the lower limbs and lumbar spine, muscle tone of the lower leg and foot, barefoot CoP displacement and in parameters of barefoot gait. Clinically relevant differences were also noted in barefoot single leg balance time. There were no differences between groups in isometric muscle strength in ankle dorsiflexion, knee flexion or extension. The second comparative study investigated foot morphology in non-weight bearing and weight bearing load conditions of the same children with and without joint hypermobility using three dimensional images (plaster casts) of their feet. The preliminary phase of this study evaluated the casting technique against direct measures of foot length, forefoot width, RCSP and forefoot to rearfoot angle. Results indicated accurate representation of elementary foot morphology within the plaster images. The comparative study examined the between and within group differences in measures of foot length and width, and in measures above the support surface (heel inclination angle, forefoot to rearfoot angle, normalized arch height, height of the widest point of the heel) in the two load conditions. Results of measures from plaster images identified that hypermobile children have different barefoot weight bearing foot morphology above the support surface than non-hypermobile children, despite no differences in measures of foot length or width. Based upon the differences in components of control of posture and gait in the hypermobile group, identified in Study One and Study Two, the final study (Study Three), using the same subjects, tested the immediate effect of specifically designed custom-made foot orthoses upon balance and gait of hypermobile children. The design of the orthoses was evaluated against the direct measures and the measures from plaster images of the feet. This ascertained the differences in morphology of the modified casts used to mould the orthoses and the original image of the foot. The orthoses were fitted into standardized running shoes. The effect of the shoe alone was tested upon the non-hypermobile children as the non-therapeutic equivalent condition. Immediate improvement in balance was noted in single leg stance and CoP displacement in the hypermobile group together with significant immediate improvement in the percentage of gait phases and in the percentage of the gait cycle at which maximum plantar flexion of the ankle occurred in gait. The neuro-muscular and musculo-skeletal characteristics of children with joint hypermobility are different from those of non-hypermobile children. The Beighton, Solomon and Soskolne (1973) screening criteria successfully classified joint hypermobility in children. As a result of this study joint hypermobility has been identified as a variable which must be controlled in studies of foot morphology and function in children. The outcomes of this study provide a basis upon which to further explore the association between joint hypermobility and neuro-muscular and musculo-skeletal conditions, and, have relevance for the physical education of children with joint hypermobility, for footwear and orthotic design processes, and, in particular, for clinical identification and treatment of children with joint hypermobility.

Fundamental solution and discrete random walk model for time-space fractional diffusion equation

In this paper, we consider a time-space fractional diffusion equation of distributed order (TSFDEDO). The TSFDEDO is obtained from the standard advection-dispersion equation by replacing the first-order time derivative by the Caputo fractional derivative of order α∈(0,1], the first-order and second-order space derivatives by the Riesz fractional derivatives of orders β 1∈(0,1) and β 2∈(1,2], respectively. We derive the fundamental solution for the TSFDEDO with an initial condition (TSFDEDO-IC). The fundamental solution can be interpreted as a spatial probability density function evolving in time. We also investigate a discrete random walk model based on an explicit finite difference approximation for the TSFDEDO-IC.