Numerical simulation of the Riesz fractional diffusion equation with a nonlinear source term

In this paper, A Riesz fractional diffusion equation with a nonlinear source term (RFDE-NST) is considered. This equation is commonly used to model the growth and spreading of biological species. According to the equivalent of the Riemann-Liouville(R-L) and Gr¨unwald-Letnikov(GL) fractional derivative definitions, an implicit difference approximation (IFDA) for the RFDE-NST is derived. We prove the IFDA is unconditionally stable and convergent. In order to evaluate the efficiency of the IFDA, a comparison with a fractional method of lines (FMOL) is used. Finally, two numerical examples are presented to show that the numerical results are in good agreement with our theoretical analysis.

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.

Incidental walking activity is sufficient to induce time-dependent conditioning of the Achilles tendon

The Achilles tendon has been seen to exhibit time-dependent conditioning when isometric muscle actions were of a prolonged duration, compared to those involved in dynamic activities, such as walking. Since, the effect of short duration muscle activation associated with dynamic activities is yet to be established, the present study aimed to investigate the effect of incidental walking activity on Achilles tendon diametral strain. Eleven healthy male participants refrained from physical activity in excess of the walking required to carry out necessary daily tasks and wore an activity monitor during the 24 h study period. Achilles tendon diametral strain, 2 cm proximal to the calcaneal insertion, was determined from sagittal sonograms. Baseline sonographic examinations were conducted at ∼08:00 h followed by replicate examinations at 12 and 24 h. Walking activity was measured as either present (1) or absent (0) and a linear weighting function was applied to account for the proximity of walking activity to tendon examination time. Over the course of the day the median (min, max) Achilles tendon diametral strain was −11.4 (4.5, −25.4)%. A statistically significant relationship was evident between walking activity and diametral strain (P < 0.01) and this relationship improved when walking activity was temporally weighted (AIC 131 to 126). The results demonstrate that the short yet repetitive loads generated during activities of daily living, such as walking, are sufficient to induce appreciable time-dependant conditioning of the Achilles tendon. Implications arise for the in vivo measurement of Achilles tendon properties and the rehabilitation of tendinopathy.

A psychometric comparison of the Toronto Alexithymia Scale (TAS-20) and the Observer Alexithymia Scale (OAS) in an alcohol-dependent sample

Alexithymia is characterised by deficits in emotional insight and self reflection, that impact on the efficacy of psychological treatments. Given the high prevalence of alexithymia in Alcohol Use Disorders, valid assessment tools are critical. The majority of research on the relationship between alexithymia and alcohol-dependence has employed the self-administered Toronto Alexithymia Scale (TAS-20). The Observer Alexithymia Scale (OAS) has also been recommended. The aim of the present study was to assess the validity and reliability of the OAS and the TAS-20 in an alcohol-dependent sample. Two hundred and ten alcohol-dependent participants in an outpatient Cognitive Behavioral Treatment program were administered the TAS-20 at assessment and upon treatment completion at 12 weeks. Clinical psychologists provided observer assessment data for a subsample of 159 patients. The findings confirmed acceptable internal consistency, test-retest reliability and scale homogeneity for both the OAS and TAS-20, except for the low internal consistency of the TAS-20 EOT scale. The TAS-20 was more strongly associated with alcohol problems than the OAS.

The ultra-low friction of the articular surface is pH-dependent and is built on a hydrophobic underlay including a hypothesis on joint lubrication mechanism

In this study, the influence of pH on interfacial energy distributed over the phospholipids-bilayer surface model and the effect of hydrophobicity on coefficient of friction (f) were investigated by using microelectrophoresis. An important clinical implication of deficiency in hydrophobicity is the loss of phospholipids that is readily observed in osteoarthritis joints. This paper establishes the influence of pH on interfacial energy upon an increase f, which might be associated with a decrease of hydrophobicity of the articular surface.

Temperature and electric field dependent mobility in poly„3-hexylthiophene diodes

Current-voltage (I-V) curves of Poly(3-hexyl-thiophene) (P3HT) diodes have been collected to investigate the polymer hole-dominated charge transport. At room temperature and at low electric fields the I-V characteristic is purely Ohmic whereas at medium-high electric fields, experimental data shows that the hole transport is Trap Dominated - Space Charge Limited Current (TD-SCLC). In this regime, it is possible to extract the I-V characteristic of the P3HT/Al junction showing the ideal Schottky diode behaviour over five orders of magnitude. At high-applied electric fields, holes’ transport is found to be in the trap free SCLC regime. We have measured and modelled in this regime the holes’ mobility to evaluate its dependence from the electric field applied and the temperature of the device.

Scale-dependent fracture mode in Cu-Ni laminate composites

Fracture behavior of Cu-Ni laminate composites has been investigated by tensile testing. It was found that as the individual layer thickness decreases from 100 to 20nm, the resultant fracture angle of the Cu-Ni laminate changes from 72 degrees to 50 degrees. Cross-sectional observations reveal that the fracture of the Ni layers transforms from opening to shear mode as the layer thickness decreases while that of the Cu layers keeps shear mode. Competition mechanisms were proposed to understand the variation in fracture mode of the metallic laminate composites associated with length scale.

A confirmatory factor analysis of the Toronto Alexithymia Scale (TAS-20) in an alcohol-dependent sample

Confirmatory factor analyses were conducted to evaluate the factorial validity of the Toronto Alexithymia Scale in an alcohol-dependent sample. Several factor models were examined, but all models were rejected given their poor fit. A revision of the TAS-20 in alcohol-dependent populations may be needed.

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.