A stochastic differential equation SIS epidemic model

In this paper we extend the classical susceptible-infected-susceptible epidemic model from a deterministic framework to a stochastic one and formulate it as a stochastic differential equation (SDE) for the number of infectious individuals $I(t)$. We then prove that this SDE has a unique global positive solution $I(t)$ and establish conditions for extinction and persistence of $I(t)$. We discuss perturbation by stochastic noise. In the case of persistence we show the existence of a stationary distribution and derive expressions for its mean and variance. The results are illustrated by computer simulations, including two examples based on real-life diseases

Entangled granular media

We study the geometrically induced cohesion of ensembles of granular "u-particles" which mechanically entangle through particle interpenetration. We vary the length-to-width ratio $l/w$ of the u-particles and form them into free-standing vertical columns. In laboratory experiment we monitor the response of the columns to sinusoidal vibration (frequency $f$, peak acceleration $\Gamma$). Column collapse occurs in a characteristic time, $\tau$, which follows the relation $\tau = f^{-1} \exp(\Delta / \Gamma)$. $\Delta$ resembles an activation energy and is maximal at intermediate $l/w$. Simulation reveals that optimal strength results from competition between packing and entanglement.Comment: 4 pages, 5 figure

Frequency-dependent attenuation and elasticity in unconsolidated earth materials: effect of damping

We use the Discrete Element Method (DEM) to understand the underlying attenuation mechanism in granular media, with special applicability to the measurements of the so-called effective mass developed earlier. We consider that the particles interact via Hertz-Mindlin elastic contact forces and that the damping is describable as a force proportional to the velocity difference of contacting grains. We determine the behavior of the complex-valued normal mode frequencies using 1) DEM, 2) direct diagonalization of the relevant matrix, and 3) a numerical search for the zeros of the relevant determinant. All three methods are in strong agreement with each other. The real and the imaginary parts of each normal mode frequency characterize the elastic and the dissipative properties, respectively, of the granular medium. We demonstrate that, as the interparticle damping, $\xi$, increases, the normal modes exhibit nearly circular trajectories in the complex frequency plane and that for a given value of $\xi$ they all lie on or near a circle of radius $R$ centered on the point $-iR$ in the complex plane, where $R\propto 1/\xi$. We show that each normal mode becomes critically damped at a value of the damping parameter $\xi \approx 1/\omega_n^0$, where $\omega_n^0$ is the (real-valued) frequency when there is no damping. The strong indication is that these conclusions carry over to the properties of real granular media whose dissipation is dominated by the relative motion of contacting grains. For example, compressional or shear waves in unconsolidated dry sediments can be expected to become overdamped beyond a critical frequency, depending upon the strength of the intergranular damping constant.Comment: 28 pages, 7 figure

Motion of the Zinc Ions in Catalysis by a Dizinc Metallo-β-Lactamase

We report rapid-freeze-quench X-ray absorption spectroscopy of a dizinc metallo-β-lactamase (MβL) reaction intermediate. The Zn(II) ions in the dinuclear active site of the S. maltophilia Class B3 MβL move away from each other, by ∼0.3 Å after 10 ms of reaction with nitrocefin, from 3.4 to 3.7 Å. Together with our previous characterization of the resting enzyme and its nitrocefin product complex, where the Zn(II) ion separation relaxes to 3.6 Å, these data indicate a scissoring motion of the active site that accompanies the ring-opening step. The average Zn(II) coordination number of 4.5 in the resting enzyme appears to be maintained throughout the reaction with nitrocefin. This is the first direct structural information available on early stage dizinc metallo-β-lactamase catalysis

Decoherence and entropy of primordial fluctuations II. The entropy budget

We calculate the entropy of adiabatic perturbations associated with a truncation of the hierarchy of Green functions at the first non trivial level, i.e. in a self-consistent Gaussian approximation. We give the equation governing the entropy growth and discuss its phenomenology. It is parameterized by two model-dependent kernels. We then examine two particular inflationary models, one with isocurvature perturbations, the other with corrections due to loops of matter fields. In the first model the entropy grows rapidely, while in the second the state remains pure (at one loop).Comment: 28 page

The Multiphase Intracluster Medium in Galaxy Groups Probed by the Lyman Alpha Forest

The case is made that the intracluster medium (ICM) in spiral-rich galaxy groups today probably has undergone much slower evolution than that in elliptical-rich groups and clusters. The environments of proto-clusters and proto-groups at z > 2 are likely similar to spiral-rich group environments at lower redshift. Therefore, like the ICM in spiral-rich groups today, the ICM in proto-groups and proto-clusters at z > 2 is predicted to be significantly multiphased. The QSO Lyman alpha forest in the vicinity of galaxies is an effective probe of the ICM at a wide range of redshift. Two recent observations of Lyman alpha absorption around galaxies by Adelberger et al. and by Pascarelle et al are reconciled, and it is shown that observations support the multiphase ICM scenario. Galaxy redshifts must be very accurate for such studies to succeed. This scenario can also explain the lower metallicity and lower hot gas fraction in groups.Comment: 4 pages, 1 figure, replaced with the version after proo

The Scientist–Reporter Collaboration: A Guide to Working with the Press

Science, technology, engineering, and mathematics (STEM) to the public can be challenging. Often, the language that researchers use among themselves is technical and difficult for non-experts to decipher. But as you probably know, communicating your research to non-experts is becoming mandatory. In a direct sense, funding agencies often require outreach for grant fulfillment. There are indirect benefits as well: Conveying the joy of discovery and the relevance of scientific results builds scientific literacy among the public---which of course includes both students who will eventually do research of their own and people who elect the policy makers who allocate funding. How many people know that what scientists do can be fun and interesting