Anomalous diffusion and heat transfer on comb structure with anisotropic relaxation in fractal porous media

A kind of anomalous diffusion and heat transfer on a comb structure with anisotropic relaxation are studied, which can be used to model many problems in Biologic and Nature in fractal porous media. The Hausdorff derivative is introduced and new governing equations is formulated in view of fractal dimension. Numerical solutions are obtained and the Fox H-function analytical solutions is given for special cases. The particles spatial-temporal evolution(STE)and the mean square displacement(MSD)versus time are presented. The effects of back bone and finger relaxation parameters, and the time fractal parameter are discussed. Results show that the MSD decreases with the increase of back bone parameter or the decrease of finger relaxation parameter in a short of time, but they have little effect on MSD in a long period. Particularly, the MSD has time dependence in the form of t?/2 (0 < ? ? 1)when t>?, which indicates that the diffusion is an anomalous sub-diffusion and heat transfer.

Competitive Swimming and Handball Participation Have a Positive Influence on Bone Parameters as Assessed by Phalangeal Quantitative Ultrasound in Female Adolescents

Purpose:To examine the influence of participation in competitive sports on bone parameters, as assessed by quantitative ultrasound (QUS) of the phalanges in female adolescents.Methods:Female adolescents (n = 329, 13.0–16.7 years old) were classified into handball (n = 55), swimming (n = 49) and control (n = 225) groups. QUS was used to evaluate the amplitude-dependent speed of sound (AD-SoS) and bone transmission time (BTT), and their z-scores (zAD-SoS and zBTT) were calculated. Anthropometric measurements and Tanner’s stages were also obtained.Results:Swimmers had higher AD-SoS (2089 ± 43.8 m/s) and zAD-SoS (0.47 ± 0.8) than controls (2060 ± 54.0 m/s; 0.09 ± 1.0; both p ≤ .05) and both groups of athletes had higher BTT (handball: 1.44 ± 0.2 μs; swimming: 1.45 ± 0.2) and zBTT (handball: 0.71 ± 0.8; swimming: 0.72 ± 1.1) than the control group (1.37 ± 0.2 μs; 0.32 ± 0.9; all p ≤ .05). Swimmers had a higher total training time (TTT: 52.5 ± 27.6 months) and frequency of training per week (FT: 5.38 ± 0.1) compared with the handball group (35.9 ± 18.1; 3.32 ±0.8; p ≤ .05). zAD-SoS, BTT and zBTT were positively correlated with FT, while BTT and zBTT showed a positive correlation with TTT.Conclusions:Sports practice influences bone parameters and higher bone parameter values are related to the amount of time and frequency of weekly training. The differences in phalangeal QUS parameters are independent of the impact of weight-bearing exercise.