Instantons and Fluctuations in a Lagrangian Model of Turbulence

We perform a detailed analytical study of the Recent Fluid Deformation (RFD) model for the onset of Lagrangian intermittency, within the context of the Martin-Siggia-Rose-Janssen-de Dominicis (MSRJD) path integral formalism. The model is based, as a key point, upon local closures for the pressure Hessian and the viscous dissipation terms in the stochastic dynamical equations for the velocity gradient tensor. We carry out a power counting hierarchical classification of the several perturbative contributions associated to fluctuations around the instanton-evaluated MSRJD action, along the lines of the cumulant expansion. The most relevant Feynman diagrams are then integrated out into the renormalized effective action, for the computation of velocity gradient probability distribution functions (vgPDFs). While the subleading perturbative corrections do not affect the global shape of the vgPDFs in an appreciable qualitative way, it turns out that they have a significant role in the accurate description of their non-Gaussian cores.Comment: 32 pages, 9 figure

Significance of log-periodic precursors to financial crashes

We clarify the status of log-periodicity associated with speculative bubbles preceding financial crashes. In particular, we address Feigenbaum's [2001] criticism and show how it can be rebuked. Feigenbaum's main result is as follows: ``the hypothesis that the log-periodic component is present in the data cannot be rejected at the 95% confidence level when using all the data prior to the 1987 crash; however, it can be rejected by removing the last year of data.'' (e.g., by removing 15% of the data closest to the critical point). We stress that it is naive to analyze a critical point phenomenon, i.e., a power law divergence, reliably by removing the most important part of the data closest to the critical point. We also present the history of log-periodicity in the present context explaining its essential features and why it may be important. We offer an extension of the rational expectation bubble model for general and arbitrary risk-aversion within the general stochastic discount factor theory. We suggest guidelines for using log-periodicity and explain how to develop and interpret statistical tests of log-periodicity. We discuss the issue of prediction based on our results and the evidence of outliers in the distribution of drawdowns. New statistical tests demonstrate that the 1% to 10% quantile of the largest events of the population of drawdowns of the Nasdaq composite index and of the Dow Jones Industrial Average index belong to a distribution significantly different from the rest of the population. This suggests that very large drawdowns result from an amplification mechanism that may make them more predictable than smaller market moves.Comment: Latex document of 38 pages including 16 eps figures and 3 tables, in press in Quantitative Financ

Controls on spatial and temporal variations in sand delivery to salmonid spawning riffles

Fine sediment infiltration into gravel interstices is known to be detrimental to incubating salmonid embryos. Infiltration into spawning riffles can show large spatial variations at the scale of a morphological unit and over time, with significant implications for embryo survival. Furthermore, some process-based infiltration studies, and incubation-to-emergence models assume that fines are delivered to redds via suspension rather than bedload. This process-based 12-month study examined spatial patterns of predominantly sand infiltration into gravels in an upland trout stream, using infiltration baskets. An assessment of Rouse numbers for infiltrated sand indicated that it was transported predominantly as bedload at flow peaks. Clear temporal and spatial patterns existed, with highest rates of infiltration strongly associated with higher discharges (r2 = 0.7, p < .05). Seasonal variations in the delivery of different grain sizes were also a feature, with enhanced contributions of 0.5–2 mm sediment during elevated winter flows and 0.125–0.5 mm sediment during spring and summer; the latter is potentially harmful to the later stages of embryo incubation. Clear spatial patterns were also evident across riffles, with highest rates of infiltration tending to occur in areas of lower relative roughness—the areas competent to transport sand for longer periods. Incubation-to-emergence models should take into consideration spatial patterns of fine sediment dynamics at the pool–riffle scale, to improve prediction