Towards Synthesis of Solar Wind and Geomagnetic Scaling Exponents: A Fractional Lévy Motion Model

Mandelbrot introduced the concept of fractals to describe the non-Euclidean shape of many aspects of the natural world. In the time series context, he proposed the use of fractional Brownian motion (fBm) to model non-negligible temporal persistence, the ‘Joseph Effect’; and Lévy flights to quantify large discontinuities, the ‘Noah Effect’. In space physics, both effects are manifested in the intermittency and long-range correlation which are by now well-established features of geomagnetic indices and their solar wind drivers. In order to capture and quantify the Noah and Joseph effects in one compact model, we propose the application of the ‘bridging’ fractional Lévy motion (fLm) to space physics. We perform an initial evaluation of some previous scaling results in this paradigm, and show how fLm can model the previously observed exponents. We suggest some new directions for the future.     

Perpendicular Shock Reformation and Ion Acceleration

Kinetic simulations of supercritical, quasi-perpendicular shocks yield time-varying solutions that cyclically reform on proton spatio-temporal scales. Whether a shock solution is stationary or reforming depends upon the plasma parameters which, for SNR shocks and the heliospheric termination shock, are ill defined but believed to be within this time-dependent regime. We first review the time-dependent solutions and the acceleration processes of the ions for a proton–electron plasma. We then present recent results for a three-component plasma: background protons, electrons and a second ion population appropriate for SNR (heavy ions) or the termination shock (pickup protons). This ion acceleration generates a suprathermal “injection” population – a seed population for subsequent acceleration at the shock, which may in turn generate ions at cosmic ray energies.     

A study of detonation in methane/air clouds

In the present paper, we study the problem of detonation in unconfined, gaseous mixtures of methane/oxygen/nitrogen. A numerical simulation approach is employed in which we use a one-dimensional (spherical symmetry), time-dependent computer model to simulate the coupled compressible fluid dynamics-chemical kinetics processes which occur upon direct initiation of detonation. We establish the magnitude of explosive yield of tetryl required to initiate detonation in mixtures of CH₄ + 2O₂ with varying degrees of nitrogen dilution, up to and including stoichiometric . The numerical simulations illustrate the features of direct initiation observed in many experimental investigations, e.g. shock-wave breakaway followed by detonation reestablishment via a quasi-steady, oscillatory flow regime which occurs before the establishment of a steadily propagating spherical detonation. Our results compare well with recent experimental data obtained by Bull et al. (1976) over the range of tetryl masses studied by them. We find that tetryl explosive masses in excess of 10⁷ grams would be required to initiate detonation in an unconfined, stoichiometric mixture.     

Circumnutation augmented in clinostatted plants by a tactile stimulus

Dark-grown, 4-day old, $\text{Helianthus annuus}$ seedlings were rotated for 20 hr on horizontal clinostats to minimize the amplitude of circumnutation. Then a Plexiglas sheet was placed gently against the tip of the cotyledons. By time-lapse video imaging (using intermittent IR illumination to which the plants were insensitive) movements of the clinostatted plants were observed before, during, and after the period of mechanical contact. Immediately after the Plexiglas sheet was removed residual nutation increased in amplitude almost three-fold, then declined over the next 7 hr to the prestimulation level. This demonstration of enhancement of circumnutation by mechanical contact is consistent with the model of an endogenous oscillator that can be stimulated by factors other than gravity.