Fractional diffusion emulates a human mobility network during a simulated disease outbreak

From footpaths to flight routes, human mobility networks facilitate the spread of communicable diseases. Control and elimination efforts depend on characterizing these networks in terms of connections and flux rates of individuals between contact nodes. In some cases, transport can be parameterized with gravity-type models or approximated by a diffusive random walk. As a alternative, we have isolated intranational commercial air traffic as a case study for the utility of non-diffusive, heavy-tailed transport models. We implemented new stochastic simulations of a prototypical influenza-like infection, focusing on the dense, highly-connected United States air travel network. We show that mobility on this network can be described mainly by a power law, in agreement with previous studies. Remarkably, we find that the global evolution of an outbreak on this network is accurately reproduced by a two-parameter space-fractional diffusion equation, such that those parameters are determined by the air travel network.Comment: 26 pages, 4 figure

Long time motion of NLS solitary waves in a confining potential

We study the motion of solitary-wave solutions of a family of focusing generalized nonlinear Schroedinger equations with a confining, slowly varying external potential, $V(x)$. A Lyapunov-Schmidt decomposition of the solution combined with energy estimates allows us to control the motion of the solitary wave over a long, but finite, time interval. We show that the center of mass of the solitary wave follows a trajectory close to that of a Newtonian point particle in the external potential $V(x)$ over a long time interval.Comment: 42 pages, 2 figure

Scattering by ensembles of small particles experiment, theory and application

A hypothetical self consistent picture of evolution of prestellar intertellar dust through a comet phase leads to predictions about the composition of the circum-solar dust cloud. Scattering properties of thus resulting conglomerates with a bird's-nest type of structure are investigated using a micro-wave analogue technique. Approximate theoretical methods of general interest are developed which compared favorably with the experimental results. The principal features of scattering of visible radiation by zodiacal light particles are reasonably reproduced. A component which is suggestive of (ALPHA)-meteoroids is also predicted

Origin and evolution of the zodiacal dust cloud

The astrophysical importance of the zodiacal cloud became more apparent. The most useful source of information on the structure of the zodiacal cloud is the Infrared Astronomical Satellite (IRAS) observations. A substantial fraction of the extensive IRAS data set was analyzed. Also, a numerical model was developed (SIMUL) that allows to calculate the distribution of night-sky brightness that would be produced by any particular distribution of dust particle orbits. This model includes the effects of orbital perturbations by both the planets and solar radiation, it reproduces the exact viewing geometry of the IRAS telescope, and allows for the eccentricity of the Earth's orbit. SIMUL now is used to model not just the solar system dust bands discovered by IRAS but the whole zodiacal cloud

Spatial and temporal filtering of a 10-W Nd:YAG laser with a Fabry-Perot ring-cavity premode cleaner

We report on the use of a fixed-spacer Fabry–Perot ring cavity to filter spatially and temporally a 10-W laser-diode-pumped Nd:YAG master-oscillator power amplifier. The spatial filtering leads to a 7.6-W TEMinfinity beam with 0.1% higher-order transverse mode content. The temporal filtering reduces the relative power fluctuations at 10 MHz to 2.8 x 10^-/sqrtHz, which is 1 dB above the shot-noise limit for 50 mA of detected photocurrent

Energies and wave functions for a soft-core Coulomb potential

For the family of model soft Coulomb potentials represented by V(r) = -\frac{Z}{(r^q+\beta^q)^{\frac{1}{q}}}, with the parameters Z>0, \beta>0, q \ge 1, it is shown analytically that the potentials and eigenvalues, E_{\nu\ell}, are monotonic in each parameter. The potential envelope method is applied to obtain approximate analytic estimates in terms of the known exact spectra for pure power potentials. For the case q =1, the Asymptotic Iteration Method is used to find exact analytic results for the eigenvalues E_{\nu\ell} and corresponding wave functions, expressed in terms of Z and \beta. A proof is presented establishing the general concavity of the scaled electron density near the nucleus resulting from the truncated potentials for all q. Based on an analysis of extensive numerical calculations, it is conjectured that the crossing between the pair of states [(\nu,\ell),(\nu',\ell')], is given by the condition \nu'\geq (\nu+1) and \ell' \geq (\ell+3). The significance of these results for the interaction of an intense laser field with an atom is pointed out. Differences in the observed level-crossing effects between the soft potentials and the hydrogen atom confined inside an impenetrable sphere are discussed.Comment: 13 pages, 5 figures, title change, minor revision

Quasi-analytical solutions for APSIDAL motion in the three-body problem: Sun—minor planet—Jupiter

This paper deals with the effect of a third body on the apsidal motion of two bodies. The specific case involves a third body-planet Jupiter and the apsidal line motion of a minor planet that orbits the Sun and has its apsidal line go through the major axis of an ellipse. The third body (Jupiter) which satisfies the Langrangian solution will affect the apsidal line motion and therefore affects the ascending and descending motions of the minor planet. In this case no analytical solutions can be obtained, and therefore specific assumptions are made along with numerical solutions. For convenience, we adopt the Lagrangian solution in the three-body problem and obtain quasi-analytical results, which are used to evaluate the effect of the planet on the d Omega/dt (Omega ascending node) of each minor planet. This method is beneficial for improving our knowledge of the orbital elements of the asteroids, and perhaps even much smaller effects such as the effects of the planets on the interplanetary dust complex. Information on the latter may be provided by using this method to investigate Jupiter\u27s effect on the inclination of the symmetry surface of the zodiacal dust cloud

String Effects on Fermi--Dirac Correlation Measurements

We investigate some recent measurements of Fermi--Dirac correlations by the LEP collaborations indicating surprisingly small source radii for the production of baryons in $e^+e^-$-annihilation at the $Z^0$ peak. In the hadronization models there are besides the Fermi--Dirac correlation effect also a strong dynamical (anti-)correlation. We demonstrate that the extraction of the pure FD effect is highly dependent on a realistic Monte Carlo event generator, both for separation of those dynamical correlations which are not related to Fermi--Dirac statistics, and for corrections of the data and background subtractions. Although the model can be tuned to well reproduce single particle distributions, there are large model-uncertainties when it comes to correlations between identical baryons. We therefore, unfortunately, have to conclude that it is at present not possible to make any firm conclusion about the source radii relevant for baryon production at LEP

Body mass index, mini nutritional assessment, and their association with five-year mortality in very old people

Objectives: To investigate the prevalence of malnutrition and the association between Body Mass Index (BMI), Mini Nutritional Assessment (MNA) and five-year mortality in a representative population of very old (>85 years) people. Design: A prospective cohort study. Setting: A population-based study of very old people in northern Sweden and western Finland, living in institutional care or in the community. Participants: Out of 1195 potential participants, 832 were included (mean age 90.2[+ or -]4.6 years). Measurements: Nutritional status was assessed using BMI and MNA and the association of those two variables with five-year mortality was analyzed. Results: The mean BMI value for the whole population was 25.1[+ or -]4.5 kg/m2, with no difference between genders (P=0.938). The mean MNA score was 22.5[+ or -]4.6 for the whole sample, and it was lower for women than for men (PA<0.001). Thirteen percent were malnourished (MNA<17) and 40.3% at risk of malnutrition (MNA 17--23.5) according to MNA. Also, 34.8% of those with a MNA score A<17 still had a BMI value a[yen]22.2 kg/m2. A BMI value A<22.2 kg/m2 and a MNA scoreA<17 were associated with lower survival. The association with mortality seemed to be J-shaped for BMI, and linear for MNA. Conclusions: Malnutrition according to MNA was common, but a substantial portion of those with a low MNA score still had a high BMI value, and vice versa. The association with mortality appeared to be J-shaped for BMI, and linear for MNA. The MNA seems to be a good measurement of malnutrition in very old people, and BMI might be misleading and could underestimate the prevalence of malnutrition, especially in women

Quantum Zeno subspaces

The quantum Zeno effect is recast in terms of an adiabatic theorem when the measurement is described as the dynamical coupling to another quantum system that plays the role of apparatus. A few significant examples are proposed and their practical relevance discussed. We also focus on decoherence-free subspaces.Comment: 5 pages, 1 figure, to be published in Phys. Rev. Let