An asymptotic theory for the re-equilibration of a micellar surfactant solution

Micellar surfactant solutions are characterized by a distribution of aggregates comprised predominantly of pre-micellar aggregates (monomers, dimers, trimers, etc.) and a region of proper micelles close to the peak aggregation number, connected by an intermediate region containing a very low concentration of aggregates. Such a distribution gives rise to a distinct two-timescale re-equilibration following a system dilution, known as the 1 and 2 processes, whose dynamics may be described by the Becker–Döring equations. We use a continuum version of these equations to develop a reduced asymptotic description that elucidates the behavior during each of these processes

Ultraviolet HST Observations of the Jet in M87

We present new ultraviolet photometry of the jet in M87 obtained from HST WFPC2 imaging. We combine these ultraviolet data with previously published photometry for the knots of the jet in radio, optical, and X-ray, and fit three theoretical synchrotron models to the full data set. The synchrotron models consistently overpredict the flux in the ultraviolet when fit over the entire dataset. We show that if the fit is restricted to the radio through ultraviolet data, the synchrotron models can provide a good match to the data. The break frequencies of these fits are much lower than previous estimates. The implied synchrotron lifetimes for the bulk of the emitting population are longer than earlier work, but still much shorter than the estimated kinematic lifetimes of the knots. The observed X-ray flux cannot be successfully explained by the simple synchrotron models that fit the ultraviolet and optical fluxes. We discuss the possible implications of these results for the physical properties of the M87 jet. We also observe increased flux for the HST-1 knot that is consistent with previous results for flaring. This observation fills in a significant gap in the time coverage early in the history of the flare, and therefore sets constraints on the initial brightening of the flare.Comment: 14 pages, 2 figures, Accepted for publication in ApJ, changed lightcurve and caption in Figure

P5_2 Spaghettification: Surviving a Black Hole Event Horizon

We found that it is possible to stay conscious falling through the event horizon of aBlack Hole if the mass exceeds 19,000M_sol. This assumes the average person is ofgood health and can stay conscious with a relative force less than 5 g acting upon them

On the predictions and limitations of the BeckerDoring model for reaction kinetics in micellar surfactant solutions

We investigate the breakdown of a system of micellar aggregates in a surfactant solution following an order-one dilution. We derive a mathematical model based on the Becker–Döring system of equations, using realistic expressions for the reaction constants fit to Molecular Dynamics simulations. We exploit the largeness of typical aggregation numbers to derive a continuum model, substituting a large system of ordinary differential equations for a partial differential equation in two independent variables: time and aggregate size. Numerical solutions demonstrate that re-equilibration occurs in two distinct stages over well-separated time-scales, in agreement with experiment and with previous theories. We conclude by exposing a limitation in the Becker–Döring theory for re-equilibration and discuss potential resolutions

P5_3 Pigs on the Wing

This article explores the possibility of a pig flying over Battersea Power Station, as shown on the Pink Floyd album ’Animals,’ and the time it would take for the pig’s height to exceed the height of the chimneys. Using the lift force equation, we graphically show the minimum wind velocity required to lift a 70 kg pig 101 m, the height of the Battersea Power Station. We find that for a pig of this mass, a wind velocity of 20.4 ms-1 was required. Furthermore, in order to measure the time for the pig to reach the height of Battersea Power Station, an acceleration of 3.8 ms-2 was calculated; this assumes a severe gale wind velocity of 24 ms-1 as defined by The Met Office. We find that it would take 7.3 s to travel the required height, assuming only vertical movement.

P5_1 ”Everybody knows the Moon is made of cheese...”: Return of the Cheddar

This Letter explores the repercussions of the Moon turning into cheddar, and finds that with the same volume and lighter mass of m = 2.49 × 1022kg, it would escape the Earth’s sphere of influence. We looked at two possible escape trajectories, prograde and retrograde, and found the new orbital distances to be between 0.73AU and 1.00AU, and between 1.00AU and 1.51AU, respectively. Thus potentially carrying the Moon very near to the orbits of Venus or Mars.

EOS MLS observations of dehydration in the 2004-2005 polar winters

We prove various estimates for the first eigenvalue of the magnetic Dirichlet Laplacian on a bounded domain in two dimensions. When the magnetic field is constant, we give lower and upper bounds in terms of geometric quantities of the domain. We furthermore prove a lower bound for the first magnetic Neumann eigenvalue in the case of constant field.Comment: 19 page