Critical fluctuations and slowing down of chaos

Fluids cooled to the liquid-vapor critical point develop system-spanning fluctuations in density that transform their visual appearance. Despite a rich phenomenology, however, there is not currently an explanation of the mechanical instability in the molecular motion at this critical point. Here, we couple techniques from nonlinear dynamics and statistical physics to analyze the emergence of this singular state. Numerical simulations and analytical models show how the ordering mechanisms of critical dynamics are measurable through the hierarchy of spatiotemporal Lyapunov vectors. A subset of unstable vectors soften near the critical point, with a marked suppression in their characteristic exponents that reflects a weakened sensitivity to initial conditions. Finite-time fluctuations in these exponents exhibit sharply peaked dynamical timescales and power law signatures of the critical dynamics. Collectively, these results are symptomatic of a critical slowing down of chaos that sits at the root of our statistical understanding of the liquid-vapor critical point

The low energy expansion of the one-loop type II superstring amplitude

The one-loop four-graviton amplitude in either of the type II superstring theories is expanded in powers of the external momenta up to and including terms of order s^4 log s R^4, where R^4 denotes a specific contraction of four linearized Weyl tensors and s is a Mandelstam invariant. Terms in this series are obtained by integrating powers of the two-dimensional scalar field theory propagator over the toroidal world-sheet as well as the moduli of the torus. The values of these coefficients match expectations based on duality relations between string theory and eleven-dimensional supergravity.Comment: harvmac (b), 25 pages, 3 eps figures. v2: Factors of 2 corrected. Conclusion unchange

Three-dimensional cometary dust coma modelling in the collisionless regime: strengths and weaknesses

Inverse coma and tail modelling of comets based on the method developed by Finson & Probstein is commonly used to analyse cometary coma images. Models of this type often contain a large number of assumptions that may not be constrained unless wide temporal or spectral coverage is available and the comets are bright and at relatively small geocentric distance. They are used to predict physical parameters, such as the mass distribution of the dust, but rarely give assessments of the accuracy of the estimate. A three-dimensional cometary dust coma model in the collisionless regime has been developed to allow the effectiveness of such models to constrain dust coma properties to be tested. The model is capable of simulating the coma morphology for the following input parameters: the comet nucleus shape, size, rotation, emission function (including active fraction and jets), grain velocity distribution (and dispersion), size distribution, dust production rate, grain material and light scattering from the cometary dust. Characterization of the model demonstrates that the mass distribution cannot be well constrained as is often assumed; the cumulative mass distribution index ? can only be constrained to within ±0.15. The model is highly sensitive to the input grain terminal velocity distribution so model input can be tested with a large degree of confidence. Complex secondary parameters such as jets, rotation and grain composition all have an effect on the structure of the coma in similar ways, so unique solutions for these parameters cannot be derived from a single optical image alone. Multiple images at a variety of geometries close in time can help constrain these effects. The model has been applied to photometric observations of comets 126P/IRAS and 46P/Wirtanen to constrain a number of physical properties including the dust production rate and mass distribution index. The derived dust production rate (Qdust) for 46P/Wirtanen was 3+7/1.5 kg s1 at a pre-perihelion heliocentric distance of 1.8 au, and for P/IRAS was 50+100/20 kg s1 at a pre-perihelion heliocentric distance of 1.7 au; both comets exhibited a mass distribution index ? = 0.8 ± 0.15