Random walk of magnetic field lines for different values of the energy range spectral index

An analytical nonlinear description of field-line wandering in partially statistically magnetic systems was proposed recently. In this article the influence of the wave spectrum in the energy range onto field-line random walk is investigated by applying this formulation. It is demonstrated that in all considered cases we clearly obtain a superdiffusive behavior of the field-lines. If the energy range spectral index exceeds unity a free-streaming behavior of the field-lines can be found for all relevant length-scales of turbulence. Since the superdiffusive results obtained for the slab model are exact, it seems that superdiffusion is the normal behavior of field-line wandering.

Validity of a 1 minute walk test for children with cerebral palsy.

The concurrent validity of a 1 minute walk test at a child's maximum walking speed was assessed in children with bilateral spastic cerebral palsy (BSCP). The distance covered during the 1 minute walk test was compared with the children's gross motor function as assessed by the Gross Motor Function Measure (GMFM). Twenty-four male and 10 female children with CP (mean age 11y, range 4 to 16y) participated in the study. Gross Motor Function Classification System (GMFCS) levels were; level I (n=3), level II (n=17), level III (n=10), and level IV (n=4). Participants had clinical diagnoses of symmetrical diplegia (n=19), asymmetrical diplegia (n=14), and quadriplegia (n=1). Results showed a significant correlation between GMFM score and the distance covered during the 1 minute walk (r=0.92; p<0.001). There was also a significant decrease in the distance walked with increasing GMFCS level (p<0.001). We concluded that the 1 minute walk test is a valid measure for assessing functional ability in children with ambulatory BSCP. Its cost-effectiveness and user friendliness make it a potentially useful tool in the clinical setting. Further study needs to address its reliability and ability to detect change over time.

Random walk simulations of fossil proxy data

A wealth of palaeoecological studies (e.g. pollen, diatoms, chironomids and macrofossils from deposits such as lakes or bogs) have revealed major as well as more subtle ecosystem changes over decadal to multimillennial timescales. Such ecosystem changes are usually assumed to have been forced by specific environmental changes. Here, we test if the observed changes in palaeoecological records may be reproduced by random simulations, and we find that simple procedures generate abrupt events, long-term trends, quasi-cyclic behaviour, extinctions and immigrations. Our results highlight the importance of replicated and multiproxy data for reliable reconstructions of past climate and environmental changes.

Detailed analytical investigation of magnetic field line random walk in turbulent plasmas: I. Two-component slab/two-dimensional turbulence

The random displacement of magnetic field lines in the presence of magnetic turbulence in plasmas is investigated from first principles. A two-component (slab/two-dimensional composite) model for the turbulence spectrum is employes. An analytical investigation of the asymptotic behavior of the field-line mean square displacement (FL-MSD) is carried out. It is shown that the magnetic field lines behave superdifusively for every large values of the position variable z, since the FL-MSD sigma varies as sigma similar to z(4/3). An intermediate diffusive regime may also possible exist for finite values of z under conditions which are explicitly determined in terms of the intrinsic turbulent plasma parameters. The superdiffusie asymptotic result is confirmed numerically via an iterative algorithm. The relevance to previous resuslts is discussed.

Detailed analytical investigation of magnetic field line random walk in turbulent plasmas: II. Isotropic turbulence

The random walk of magnetic field lines in the presence of magnetic turbulence in plasmas is investigated from first principles. An isotropic model is employed for the magnetic turbulence spectrum. An analytical investigation of the asymptotic behavior of the field-line mean-square displacement is carried out. in terms of the position variable z. It is shown that varies as similar to z ln z for large distance z. This result corresponds to a superdiffusive behavior of field line wandering. This investigation complements previous work, which relied on a two-component model for the turbulence spectrum. Contrary to that model, quasilinear theory appears to provide an adequate description of the field line random walk for isotropic turbulence.