Determining Class Maintainability in California

In City of San Jose v. Superior Court, the California Supreme Court incorporated the class certification provision of Rule 23(c)(1) of the Federal Rules of Civil Procedure into California class action practice. The author examines how -the federal courts have construed Rule 23(c) (1), analyzes the practical aspects and underlying policy issues of the class determination, and suggests a method of procedure for California trial courts in light of this recent supreme court directive

Relaxation oscillations and negative strain rate sensitivity in the Portevin - Le Chatelier effect

A characteristic feature of the Portevin - Le Chatelier effect or the jerky flow is the stick-slip nature of stress-strain curves which is believed to result from the negative strain rate dependence of the flow stress. The latter is assumed to result from the competition of a few relevant time scales controlling the dynamics of jerky flow. We address the issue of time scales and its connection to the negative strain rate sensitivity of the flow stress within the framework of a model for the jerky flow which is known to reproduce several experimentally observed features including the negative strain rate sensitivity of the flow stress. We attempt to understand the above issues by analyzing the geometry of the slow manifold underlying the relaxational oscillations in the model. We show that the nature of the relaxational oscillations is a result of the atypical bent geometry of the slow manifold. The analysis of the slow manifold structure helps us to understand the time scales operating in different regions of the slow manifold. Using this information we are able to establish connection with the strain rate sensitivity of the flow stress. The analysis also helps us to provide a proper dynamical interpretation for the negative branch of the strain rate sensitivity.Comment: 7 figures, To appear in Phys. Rev.

Missing physics in stick-slip dynamics of a model for peeling of an adhesive tape

It is now known that the equations of motion for the contact point during peeling of an adhesive tape mounted on a roll introduced earlier are singular and do not support dynamical jumps across the two stable branches of the peel force function. By including the kinetic energy of the tape in the Lagrangian, we derive equations of motion that support stick-slip jumps as a natural consequence of the inherent dynamics. In the low mass limit, these equations reproduce solutions obtained using a differential-algebraic algorithm introduced for the earlier equations. Our analysis also shows that mass of the ribbon has a strong influence on the nature of the dynamics.Comment: Accepted for publication in Phys. Rev. E (Rapid Communication

Testing the assumptions of linear prediction analysis in normal vowels

This paper develops an improved surrogate data test to show experimental evidence, for all the simple vowels of US English, for both male and female speakers, that Gaussian linear prediction analysis, a ubiquitous technique in current speech technologies, cannot be used to extract all the dynamical structure of real speech time series. The test provides robust evidence undermining the validity of these linear techniques, supporting the assumptions of either dynamical nonlinearity and/or non-Gaussianity common to more recent, complex, efforts at dynamical modelling speech time series. However, an additional finding is that the classical assumptions cannot be ruled out entirely, and plausible evidence is given to explain the success of the linear Gaussian theory as a weak approximation to the true, nonlinear/non-Gaussian dynamics. This supports the use of appropriate hybrid linear/nonlinear/non-Gaussian modelling. With a calibrated calculation of statistic and particular choice of experimental protocol, some of the known systematic problems of the method of surrogate data testing are circumvented to obtain results to support the conclusions to a high level of significance

Intracycle interference in ionization of Ar by a laser assisted XUV pulse

Synopsis We present a theoretical and experimental study of the subcycle interference in laser assisted XUV ionization of Ar atoms. Averaging over the focal volume happens to blur the intracycle interference, which thus cannot be measured directly. We show that even at these conditions, the intracycle interference can be obtained through the subtraction of two different angle and energy-resolved distributions at slightly different laser intensities