Effects of Leakage Neutral Particles on Shocks

In this paper we investigate effects of neutral particles on shocks propagating into the partially ionized medium. We find that for 120 km/s < u_{sh} < 3000 km/s (u_{sh} is the shock velocity), about ten percent of upstream neutral particles leak into the upstream region from the downstream region. Moreover, we investigate how the leakage neutral particles affect the upstream structure of the shock and particle accelerations. Using four fluid approximations (upstream ions, upstream neutral particles, leakage neutral particles and pickup ions), we provide analytical solutions of the precursor structure due to leakage neutral particles. It is shown that the upstream flow is decelerated in the precursor region and the shock compression ratio becomes smaller than without leakage neutral particles, but the total compression ratio does not change. Even if leakage of neutral particles is small (a few percents of total upstream particles), this smaller compression ratio of the shock can explain steep gamma-ray spectra from young supernova remnants. Furthermore, leakage neutral particles could amplify the magnetic field and heat the upstream region.Comment: 9 pages, 4 figures, accepted for publication in Ap

Predictive dynamical and stochastic systems

We study a system whose dynamics are governed by predictions of its future states. A general formalism and concrete examples are presented. We find that the dynamical characteristics depend on how to shape the predictions as well as on how far ahead in time to make them. We also report that noise can induce oscillatory behavior, which we call "predictive stochastic resonance".Comment: Presented and To appear in the Proc. of 9th Granada Seminar, (Granada, Spain, September 11-15, 2006

Quantum Square Well Bound States Described by Equations with Non-locality

We present here a simple equation explicitly incorporating non-locality, which reproduces quantized energy levels of the bound states for the square well potentials. Introduction of this equation is motivated by studies of differential equation with time delayed feedback, which can be viewed as describing temporal non-locality.Comment: 4 pages, 1 figure, submitted for a publicatio