Perturbations and moduli space dynamics of tachyon kinks

The dynamic process of unstable D-branes decaying into stable ones with one dimension lower can be described by a tachyon field with a Dirac-Born-Infeld effective action. In this paper we investigate the fluctuation modes of the tachyon field around a two-parameter family of static solutions representing an array of brane-antibrane pairs. Besides a pair of zero modes associated with the parameters of the solution, and instabilities associated with annihilation of the brane-antibrane pairs, we find states corresponding to excitations of the tachyon field around the brane and in the bulk. In the limit that the brane thickness tends to zero, the support of the eigenmodes is limited to the brane, consistent with the idea that propagating tachyon modes drop out of the spectrum as the tachyon field approaches its ground state. The zero modes, and other low-lying excited states, show a fourfold degeneracy in this limit, which can be identified with some of the massless superstring modes in the brane-antibrane system. Finally, we also discuss the slow motion of the solution corresponding to the decay process in the moduli space, finding a trajectory which oscillates periodically between the unstable D-brane and the brane-antibrane pairs of one dimension lower

A generalisation of the nonlinear small-gain theorem for systems with abstract initial conditions

We consider the development of a general nonlinear small-gain theorem for systems with abstract initial conditions. Systems are defined in a set theoretic manner from input-output pairs on a doubly infinite time axis, and a general construction of the initial conditions (i.e. a state at time zero) is given in terms of an equivalence class of trajectories on the negative time axis. By using this formulation, an ISS-type nonlinear small-gain theorem is established with complete disconnection between the stability property and the existence, uniqueness properties. We provide an illustrative example

Qualitative Case Studies in Operations Management: Trends, Research Outcomes, And Future Research Implications

Our study examines the state of qualitative case studies in operations management. Five main operations management journals are included for their impact on the field. They are in alphabetical order: Decision Sciences, International Journal of Operations and Production Management, Journal of Operations Management, Management Science, and Production and Operations Management. The qualitative case studies chosen were published between 1992 and 2007. With an increasing trend toward using more qualitative case studies, there have been meaningful and significant contributions to the field of operations management, especially in the area of theory building. However, in many of the qualitative case studies we reviewed, sufficient details in research design, data collection, and data analysis were missing. For instance, there are studies that do not offer sampling logic or a description of the analysis through which research out-comes are drawn. Further, research protocols for doing inductive case studies are much better developed compared to the research protocols for doing deductive case studies. Consequently, there is a lack of consistency in the way the case method has been applied. As qualitative researchers, we offer suggestions on how we can improve on what we have done and elevate the level of rigor and consistency

Frequency-dependent AVO attribute: theory and example

Fluid-saturated rocks generally have seismic velocities that depend upon frequency. Exploring this property may help us discriminate different fluids from seismic data. In this paper, we introduce a scheme to calculate a frequency-dependent AVO attribute in order to estimate seismic dispersion from pre-stack data, and apply it to North Sea data. The scheme essentially combines the two-term approximation of Smith and Gidlow (1987) with the method of spectral decomposition based on the Wigner-Ville distribution, which is used to achieve high resolution. The result suggests the potential of this method for detection of seismic dispersion due to fluid saturation