Velocity spectrum for non-Markovian Brownian motion in a periodic potential

Non-Markovian Brownian motion in a periodic potential is studied by means of an electronic analogue simulator. Velocity spectra, the Fourier transforms of velocity autocorrelation functions, are obtained for three types of random force, that is, a white noise, an Ornstein—Uhlenbeck process, and a quasimonochromatic noise. The analogue results are in good agreement both with theoretical ones calculated with the use of a matrix-continued-fraction method, and with the results of digital simulations. An unexpected extra peak in the velocity spectrum is observed for Ornstein-Uhlenbeck noise with large correlation time. The peak is attributed to a slow oscillatory motion of the Brownian particle as it moves back and forth over several lattice spaces. Its relationship to an approximate Langevin equation is discussed.     

Stochastic resonance in perspective

Summary We outline the historical development of stochastic resonance (SR), a phenomenon in which the signal and/or the signal-to-noise ratio in a nonlinear system increase with increasing intensity of noise. We discuss basic theoretical ideas explaining and describing SR, and we review some revealing experimental data that place SR within the wider context of statistical physics. We emphasize the close relationship of SR to some effects that are well known in condensed-matter physics. Paper presented at the International Workshop ?Fluctuations in Physics and Biology: Stochastic Resonance, Signal Processing and Related Phenomena?, Elba, 5–10 June 1994.     

Rail web fracture in the presence of residual stresses

A recent accident involving roller-straighened alloy rail has raised the question of the safety of such rails. This work shows that the residual stresses in roller-straightened rail can indeed self-drive a long web crack. Specifically, the stress intensity K_I due to release of the key component, longitudinal stress, if of the order of the critical stress intensity for initiation K_Ic for both plain carbon and alloy rail. At cut ends, the resulting vertical residual stresses can give rise to K_Ic if there are 0.1–1 in (3–25 mm) cracks. In this work, checks of the existing residual stress data for self-consistency suggest that the data are only accurate within a factor of two. Therefore, a more direct method is proposed for measuring K_I on a web crack by saw-cutting the web.