Change, stability and prediction of gross motor co-ordination in portuguese children

The knowledge about intra- and inter-individual variation can stimulate attempts at description, interpretation and prediction of motor co-ordination (MC). Aim: To analyse change, stability and prediction of motor co-ordination (MC) in children. Subjects and methods: A total of 158 children, 83 boys and 75 girls, aged 6, 7 and 8 years, were evaluated in 2006 and re-evaluated in 2012 at 12, 13 and 14 years of age. MC was assessed through the Kiphard-Schilling’s body co-ordination test and growth, skeletal maturity, physical fitness, fundamental motor skills (FMS), physical activity and socioeconomic status (SES) were measured and/or estimated. Results: Repeated-measures MANOVA indicated that there was a significant effect of group, sex and time on a linear combination of the MC tests. Univariate tests revealed that group 3 (8–14 years) scored significantly better than group 1 (6–12 years) in all MC tests and boys performed better than girls in hopping for height and moving sideways. Scores in MC were also higher at follow-up than at baseline. Inter-age correlations for MC were between 0.15–0.74. Childhood predictors of MC were growth, physical fitness, FMS, physical activity and SES. Biological maturation did not contribute to prediction of MC. Conclusion: MC seemed moderately stable from childhood through adolescence and, additionally, inter-individual predictors at adolescence were growth, FMS, physical fitness, physical activity and SES.

Improvement of termite resistance, dimensional stability and mechanical properties of pine wood by paraffin impregnation

Paraffin has been used as surface protection of wood throughout the ages but its use for impregnation to improve wood resistance to biodegradation is recent. This study determined the main improvements on wood properties with paraffin impregnation. Healthy Pinus pinaster Ait. wood was impregnated with paraffin at different levels using a hot–cold process. Weight gain, equilibrium moisture content and dimensional stability (ASE) at 35 and 65 % relative humidity, termite durability against Reticulitermes grassei (Clément), bending strength, bending stiffness (MOE) and Janka hardness were determined. Density increased from 0.57 to 0.99, ASE ranged between 38–96 % and 16–71 % for 35 and 65 % relative humidity, respectively. Equilibrium moisture content decreased from 9.9 and 12.0 % to 0.8 and 3.6 % for 35 and 65 % relative humidity. Termite durability improved from level 4 to level 3 of attack, and higher termite mortality was found in treated wood (52 % against 17 %). Bending strength (MOR) increased with paraffin weight gain, reaching a 39 % increase. MOE also increased by about 13 % for wood with a weight gain around 80 %. Janka hardness increased significantly reaching about 40 % for wood with 80 % weight gain. Paraffin impregnated wood has improved properties with regard to equilibrium moisture content, dimensional stability and density, bending strength and Janka hardness, and resistance against termites.

Regulation, stability and change: Reflections on the UK and Sweden

Despite the impact of neo-liberal agendas, the issue of regulation remains central to our understanding of economic processes, and particularly employment. The concept of regulation is often reduced to a narrowly defined set of functions performed by the state. However, processes of regulation involve a much wider range of sites and actors, within and beyond the boundaries of the state. This paper presents a framework for the analysis of the panoply of regulatory actors and the complex relations between them, including the shifting boundaries between regulatory spaces. The paper concludes with some illustrative examples of shifting regulatory structures within Sweden.

Stability and smoothness improvements for an underactuated biped with a tail

In this work we present an important improvement in our model of biped mechanism that allows the elevation in a stable form of the system's feet during the execution of trajectories. This improvement allows for simpler trajectory planning and also facilitates the reduction of losses in the collision between the feet and the ground. On the other hand, we add to the design phase the study of the displacement of the Zero Moment Point, as well as the variation of the normal component of the ground reaction force during the motion of the system. Consideration of the above mentioned magnitudes in the design phase allows us to design the necessary support area of the system. These magnitudes will be used as a smoothness criterion of the ground contact to facilitate the selection of robot parameters and trajectories.

Change, stability and prediction of gross motor co-ordination in portuguese children

The knowledge about intra- and inter-individual variation can stimulate attempts at description, interpretation and prediction of motor co-ordination (MC). Aim: To analyse change, stability and prediction of motor co-ordination (MC) in children. Subjects and methods: A total of 158 children, 83 boys and 75 girls, aged 6, 7 and 8 years, were evaluated in 2006 and re-evaluated in 2012 at 12, 13 and 14 years of age. MC was assessed through the Kiphard-Schilling’s body co-ordination test and growth, skeletal maturity, physical fitness, fundamental motor skills (FMS), physical activity and socioeconomic status (SES) were measured and/or estimated. Results: Repeated-measures MANOVA indicated that there was a significant effect of group, sex and time on a linear combination of the MC tests. Univariate tests revealed that group 3 (8–14 years) scored significantly better than group 1 (6–12 years) in all MC tests and boys performed better than girls in hopping for height and moving sideways. Scores in MC were also higher at follow-up than at baseline. Inter-age correlations for MC were between 0.15–0.74. Childhood predictors of MC were growth, physical fitness, FMS, physical activity and SES. Biological maturation did not contribute to prediction of MC. Conclusion: MC seemed moderately stable from childhood through adolescence and, additionally, inter-individual predictors at adolescence were growth, FMS, physical fitness, physical activity and SES.

Detailed analysis of a conservative difference approximation for the time fractional diffusion equation

Diffusion equations that use time fractional derivatives are attractive because they describe a wealth of problems involving non-Markovian Random walks. The time fractional diffusion equation (TFDE) is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α ∈ (0, 1). Developing numerical methods for solving fractional partial differential equations is a new research field and the theoretical analysis of the numerical methods associated with them is not fully developed. In this paper an explicit conservative difference approximation (ECDA) for TFDE is proposed. We give a detailed analysis for this ECDA and generate discrete models of random walk suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation. The stability and convergence of the ECDA for TFDE in a bounded domain are discussed. Finally, some numerical examples are presented to show the application of the present technique.

Implicit difference approximation for the time fractional diffusion equation

In this paper, we consider a time fractional diffusion equation on a finite domain. The equation is obtained from the standard diffusion equation by replacing the first-order time derivative by a fractional derivative (of order $0<\alpha<1$ ). We propose a computationally effective implicit difference approximation to solve the time fractional diffusion equation. Stability and convergence of the method are discussed. We prove that the implicit difference approximation (IDA) is unconditionally stable, and the IDA is convergent with $O(\tau+h^2)$, where $\tau$ and $h$ are time and space steps, respectively. Some numerical examples are presented to show the application of the present technique.

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.

An advanced implicit meshless approach for the non-linear anomalous subdiffusion equation

Recently, the numerical modelling and simulation for anomalous subdiffusion equation (ASDE), which is a type of fractional partial differential equation( FPDE) and has been found with widely applications in modern engineering and sciences, are attracting more and more attentions. The current dominant numerical method for modelling ASDE is Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings. This paper aims to develop an implicit meshless approach based on the radial basis functions (RBF) for numerical simulation of the non-linear ASDE. The discrete system of equations is obtained by using the meshless shape functions and the strong-forms. The stability and convergence of this meshless approach are then discussed and theoretically proven. Several numerical examples with different problem domains are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. The results obtained by the meshless formulations are also compared with those obtained by FDM in terms of their accuracy and efficiency. It is concluded that the present meshless formulation is very effective for the modeling and simulation of the ASDE. Therefore, the meshless technique should have good potential in development of a robust simulation tool for problems in engineering and science which are governed by the various types of fractional differential equations.

An advanced implicit meshless approach for fractional partial differential equation in computational mechanics

Recently, the numerical modelling and simulation for fractional partial differential equations (FPDE), which have been found with widely applications in modern engineering and sciences, are attracting increased attentions. The current dominant numerical method for modelling of FPDE is the explicit Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings. This paper aims to develop an implicit meshless approach based on the radial basis functions (RBF) for numerical simulation of time fractional diffusion equations. The discrete system of equations is obtained by using the RBF meshless shape functions and the strong-forms. The stability and convergence of this meshless approach are then discussed and theoretically proven. Several numerical examples with different problem domains are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. The results obtained by the meshless formations are also compared with those obtained by FDM in terms of their accuracy and efficiency. It is concluded that the present meshless formulation is very effective for the modelling and simulation for FPDE.

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

Time-dependent fractional advection–diffusion equations by an implicit MLS meshless method

Recently, many new applications in engineering and science are governed by a series of fractional partial differential equations (FPDEs). Unlike the normal partial differential equations (PDEs), the differential order in a FPDE is with a fractional order, which will lead to new challenges for numerical simulation, because most existing numerical simulation techniques are developed for the PDE with an integer differential order. The current dominant numerical method for FPDEs is Finite Difference Method (FDM), which is usually difficult to handle a complex problem domain, and also hard to use irregular nodal distribution. This paper aims to develop an implicit meshless approach based on the moving least squares (MLS) approximation for numerical simulation of fractional advection-diffusion equations (FADE), which is a typical FPDE. The discrete system of equations is obtained by using the MLS meshless shape functions and the meshless strong-forms. The stability and convergence related to the time discretization of this approach are then discussed and theoretically proven. Several numerical examples with different problem domains and different nodal distributions are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. It is concluded that the present meshless formulation is very effective for the modeling and simulation of the FADE.

An implicit RBF meshless approach for time fractional diffusion equations

This paper aims to develop an implicit meshless approach based on the radial basis function (RBF) for numerical simulation of time fractional diffusion equations. The meshless RBF interpolation is firstly briefed. The discrete equations for two-dimensional time fractional diffusion equation (FDE) are obtained by using the meshless RBF shape functions and the strong-forms of the time FDE. The stability and convergence of this meshless approach are discussed and theoretically proven. Numerical examples with different problem domains and different nodal distributions are studied to validate and investigate accuracy and efficiency of the newly developed meshless approach. It has proven that the present meshless formulation is very effective for modeling and simulation of fractional differential equations.

An advanced meshless method for time fractional diffusion equation

Recently, because of the new developments in sustainable engineering and renewable energy, which are usually governed by a series of fractional partial differential equations (FPDEs), the numerical modelling and simulation for fractional calculus are attracting more and more attention from researchers. The current dominant numerical method for modeling FPDE is Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings including difficulty in simulation of problems with the complex problem domain and in using irregularly distributed nodes. Because of its distinguished advantages, the meshless method has good potential in simulation of FPDEs. This paper aims to develop an implicit meshless collocation technique for FPDE. The discrete system of FPDEs is obtained by using the meshless shape functions and the meshless collocation formulation. The stability and convergence of this meshless approach are investigated theoretically and numerically. The numerical examples with regular and irregular nodal distributions are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. It is concluded that the present meshless formulation is very effective for the modeling and simulation of fractional partial differential equations.