Diffusion of particles moving with constant speed

The propagation of light in a scattering medium is described as the motion of a special kind of a Brownian particle on which the fluctuating forces act only perpendicular to its velocity. This enforces strictly and dynamically the constraint of constant speed of the photon in the medium. A Fokker-Planck equation is derived for the probability distribution in the phase space assuming the transverse fluctuating force to be a white noise. Analytic expressions for the moments of the displacement $$ along with an approximate expression for the marginal probability distribution function $P(x,t)$ are obtained. Exact numerical solutions for the phase space probability distribution for various geometries are presented. The results show that the velocity distribution randomizes in a time of about eight times the mean free time ($8t^*$) only after which the diffusion approximation becomes valid. This factor of eight is a well known experimental fact. A persistence exponent of $0.435 \pm 0.005$ is calculated for this process in two dimensions by studying the survival probability of the particle in a semi-infinite medium. The case of a stochastic amplifying medium is also discussed.Comment: 9 pages, 9 figures(Submitted to Phys. Rev. E

School-Based Physical Activity Interventions in Prevocational Adolescents: A Systematic Review and Meta-Analyses

Purpose: Literature detailing the effectiveness of school-based physical activity promotion in- terventions in prevocational adolescents was reviewed to identify effective intervention characteristics. Methods: The search strategy assessed studies against inclusion criteria study design, study population, school setting, language, and construct. The risk of bias of the included studies was assessed, and extractions were made of the physical activity (PA) level outcome measures and intervention characteristics regarding organizational, social, and content features. A meta-analysis was conducted to determine the overall effect of the interventions on the PA level. Identification of effective intervention characteristics was done by subgroup analyses. Meta-regression analysis was performed with PA level as dependent variable and intervention characteristics as covariates.  Results: A total of 40 eligible studies was included for meta-analyses. Among the included studies, the overall intervention effect on increasing the PA level of prevocational adolescents was weak (standardized mean difference [SMD] .19, 95% confidence interval [CI] .12e.27). Intervention characteristics that improve the effect size to a moderate level were intracurricular PA (SMD .43, 95% CI .19e.68), involving school staff in an intracurricular intervention (SMD .37, 95% CI .16e.58) and a tailored intracurricular intervention (SMD .35, 95% CI .13e.58). Meta-regression analysis confirmed PA as a positive predictor. Conclusions: The effect of a school-based PA intervention was small to moderate. A sensible choice in the assembly of a multicomponent school-based PA intervention increases the effectiveness considerably. Physical education teachers, school administrators, and policy makers should consider organizational (intracurriculum, short and medium duration), personal (tailoring, participation), social (school staff) and content (PA) determinants

Persistent random walk model for transport trough thin slabs

We present a model for transport in multiply scattering media based on a three-dimensional generalization of the persistent random walk. The model assumes that photons move along directions that are parallel to the axes. Although this hypothesis is not realistic, it allows us to solve exactly the problem of multiple scattering propagation in a thin slab. Among other quantities, the transmission probability and the mean transmission time can be calculated exactly. Besides being completely solvable, the model could be used as a benchmark for approximation schemes to multiple light scattering