Survival probability and order statistics of diffusion on disordered media

We investigate the first passage time t_{j,N} to a given chemical or Euclidean distance of the first j of a set of N>>1 independent random walkers all initially placed on a site of a disordered medium. To solve this order-statistics problem we assume that, for short times, the survival probability (the probability that a single random walker is not absorbed by a hyperspherical surface during some time interval) decays for disordered media in the same way as for Euclidean and some class of deterministic fractal lattices. This conjecture is checked by simulation on the incipient percolation aggregate embedded in two dimensions. Arbitrary moments of t_{j,N} are expressed in terms of an asymptotic series in powers of 1/ln N which is formally identical to those found for Euclidean and (some class of) deterministic fractal lattices. The agreement of the asymptotic expressions with simulation results for the two-dimensional percolation aggregate is good when the boundary is defined in terms of the chemical distance. The agreement worsens slightly when the Euclidean distance is used.Comment: 8 pages including 9 figure

Order statistics for d-dimensional diffusion processes

We present results for the ordered sequence of first passage times of arrival of N random walkers at a boundary in Euclidean spaces of d dimensions

Order statistics of the trapping problem

When a large number N of independent diffusing particles are placed upon a site of a d-dimensional Euclidean lattice randomly occupied by a concentration c of traps, what is the m-th moment of the time t_{j,N} elapsed until the first j are trapped? An exact answer is given in terms of the probability Phi_M(t) that no particle of an initial set of M=N, N-1,..., N-j particles is trapped by time t. The Rosenstock approximation is used to evaluate Phi_M(t), and it is found that for a large range of trap concentracions the m-th moment of t_{j,N} goes as x^{-m} and its variance as x^{-2}, x being ln^{2/d} (1-c) ln N. A rigorous asymptotic expression (dominant and two corrective terms) is given for for the one-dimensional lattice.Comment: 11 pages, 7 figures, to be published in Phys. Rev.

Intensity of physical education classes in adolescents

Se registró la frecuencia cardiaca de 182 estudiantes (97 chicos y 85 chicas) de entre 12 y 18 años durante sus clases de Educación Física. Los resultados muestran una media del 21,62±14,33% del tiempo de clase en valores MVPA (moderate to vigorous physical activity). Respecto al género, pese a no ser significativo, los mayores valores corresponden a la chicas (23,47±14,45% vs 19,99±14,10%; p=0,106). No se ha observado efecto del tipo de sesión (deportes colectivos, deportes individuales, juegos tradicionales o bailes) sobre el tiempo en valores MVPA (p>0,05; TE0.05; ES<0.020), obtaining the highest values in team sports sessions. Results show that intensity and duration of analyzed classes do not comply with recommendations to become an adequate cardiovascular exercis

Physical Education in English. A proposal for working postural hygiene in Primary Education

In recent years, European Union has increased the demand for bilingual education as a tool to prepare young people in school and at work. This need has been reflected in the educational legislation of its member countries In Spain, since 2006 there is a basic competency related to foreign language learning. The Physical Education area has become an ideal means to facilitate the learning of English through play and movement. In order to facilitate the work of future teachers in the area, this article examines the teaching of Physical Education in the bilingual English. The current legislation that governs the implementation of bilingualism in schools will be presented, along with the most important methodological considerations for teaching our subject in English. Finally, in the section about practical applications, we present a circuit of activities to work postural hygiene in Primary Education. Each activity has its description in Spanish and English, along with the «teacher speech», with specific instructions to carry out in each of the exercise

Simulations for trapping reactions with subdiffusive traps and subdiffusive particles

While there are many well-known and extensively tested results involving diffusion-limited binary reactions, reactions involving subdiffusive reactant species are far less understood. Subdiffusive motion is characterized by a mean square displacement $\sim t^\gamma$ with $0<\gamma<1$. Recently we calculated the asymptotic survival probability $P(t)$ of a (sub)diffusive particle ($\gamma^\prime$) surrounded by (sub)diffusive traps ($\gamma$) in one dimension. These are among the few known results for reactions involving species characterized by different anomalous exponents. Our results were obtained by bounding, above and below, the exact survival probability by two other probabilities that are asymptotically identical (except when $\gamma^\prime=1$ and $0<\gamma<2/3$). Using this approach, we were not able to estimate the time of validity of the asymptotic result, nor the way in which the survival probability approaches this regime. Toward this goal, here we present a detailed comparison of the asymptotic results with numerical simulations. In some parameter ranges the asymptotic theory describes the simulation results very well even for relatively short times. However, in other regimes more time is required for the simulation results to approach asymptotic behavior, and we arrive at situations where we are not able to reach asymptotia within our computational means. This is regrettably the case for $\gamma^\prime=1$ and $0<\gamma<2/3$, where we are therefore not able to prove or disprove even conjectures about the asymptotic survival probability of the particle.Comment: 15 pages, 10 figures, submitted to Journal of Physics: Condensed Matter; special issue on Chemical Kinetics Beyond the Textbook: Fluctuations, Many-Particle Effects and Anomalous Dynamics, eds. K.Lindenberg, G.Oshanin and M.Tachiy

A model for the atomic-scale structure of a dense, nonequilibrium fluid: the homogeneous cooling state of granular fluids

It is shown that the equilibrium Generalized Mean Spherical Model of fluid structure may be extended to nonequilibrium states with equation of state information used in equilibrium replaced by an exact condition on the two-body distribution function. The model is applied to the homogeneous cooling state of granular fluids and upon comparison to molecular dynamics simulations is found to provide an accurate picture of the pair distribution function.Comment: 29 pages, 11 figures Revision corrects formatting of the figure

Spatial fluctuations of a surviving particle in the trapping reaction

We consider the trapping reaction, $A+B\to B$, where $A$ and $B$ particles have a diffusive dynamics characterized by diffusion constants $D_A$ and $D_B$. The interaction with $B$ particles can be formally incorporated in an effective dynamics for one $A$ particle as was recently shown by Bray {\it et al}. [Phys. Rev. E {\bf 67}, 060102 (2003)]. We use this method to compute, in space dimension $d=1$, the asymptotic behaviour of the spatial fluctuation, $^{1/2}$, for a surviving $A$ particle in the perturbative regime, $D_A/D_B\ll 1$, for the case of an initially uniform distribution of $B$ particles. We show that, for $t\gg 1$, $^{1/2} \propto t^{\phi}$ with $\phi=1/4$. By contrast, the fluctuations of paths constrained to return to their starting point at time $t$ grow with the larger exponent 1/3. Numerical tests are consistent with these predictions.Comment: 10 pages, 5 figure

The Whole Brain Activity Map: Merging Nanoscience and Neuroscience for Technology and Health

The ultimate goal of this project is to construct the functional connectome map of the human brain, by assembling a coordinated network of researchers deploying next—generation nanotechnological tools with unprecedented capabilities. Mapping the functional connectome will unravel the fundamental, long-sought paradigms of how the brain computes. Together with these new technologies, this will enable accurate diagnosing, and restoring, of normal patterns of activity to injured or diseased brains; will foster the development of broader biomedical and environmental applications; and will produce a host of associated economic benefits

The Brain Activity Map Project and the Challenge of Functional Connectomics

The function of neural circuits is an emergent property that arises from the coordinated activity of large numbers of neurons. To capture this, we propose launching a large-scale, international public effort, the Brain Activity Map Project, aimed at reconstructing the full record of neural activity across complete neural circuits. This technological challenge could prove to be an invaluable step toward understanding fundamental and pathological brain processes