Fractal diffusion coefficient from dynamical zeta functions

Dynamical zeta functions provide a powerful method to analyze low dimensional dynamical systems when the underlying symbolic dynamics is under control. On the other hand even simple one dimensional maps can show an intricate structure of the grammar rules that may lead to a non smooth dependence of global observable on parameters changes. A paradigmatic example is the fractal diffusion coefficient arising in a simple piecewise linear one dimensional map of the real line. Using the Baladi-Ruelle generalization of the Milnor-Thurnston kneading determinant we provide the exact dynamical zeta function for such a map and compute the diffusion coefficient from its smallest zero.Comment: 8 pages, 2 figure

Natural boundary for the susceptibility function of generic piecewise expanding unimodal maps

We consider the susceptibility function Psi(z) of a piecewise expanding unimodal interval map f with unique acim mu, a perturbation X, and an observable phi. Combining previous results (deduced from spectral properties of Ruelle transfer operators) with recent work of Breuer-Simon (based on techniques from the spectral theory of Jacobi matrices and a classical paper of Agmon), we show that density of the postcritical orbit (a generic condition) implies that Psi(z) has a strong natural boundary on the unit circle. The Breuer-Simon method provides uncountably many candidates for the outer functions of Psi(z), associated to precritical orbits. If the perturbation X is horizontal, a generic condition (Birkhoff typicality of the postcritical orbit) implies that the nontangential limit of the Psi(z) as z tends to 1 exists and coincides with the derivative of the acim with respect to the map (linear response formula). Applying the Wiener-Wintner theorem, we study the singularity type of nontangential limits as z tends to e^{i\omega}. An additional LIL typicality assumption on the postcritical orbit gives stronger results.Comment: LaTex, 23 pages, to appear ETD

Dissipation time and decay of correlations

We consider the effect of noise on the dynamics generated by volume-preserving maps on a d-dimensional torus. The quantity we use to measure the irreversibility of the dynamics is the dissipation time. We focus on the asymptotic behaviour of this time in the limit of small noise. We derive universal lower and upper bounds for the dissipation time in terms of various properties of the map and its associated propagators: spectral properties, local expansivity, and global mixing properties. We show that the dissipation is slow for a general class of non-weakly-mixing maps; on the opposite, it is fast for a large class of exponentially mixing systems which include uniformly expanding maps and Anosov diffeomorphisms.Comment: 26 Pages, LaTex. Submitted to Nonlinearit

On the susceptibility function of piecewise expanding interval maps

We study the susceptibility function Psi(z) associated to the perturbation f_t=f+tX of a piecewise expanding interval map f. The analysis is based on a spectral description of transfer operators. It gives in particular sufficient conditions which guarantee that Psi(z) is holomorphic in a disc of larger than one. Although Psi(1) is the formal derivative of the SRB measure of f_t with respect to t, we present examples satisfying our conditions so that the SRB measure is not Lipschitz.*We propose a new version of Ruelle's conjectures.* In v2, we corrected a few minor mistakes and added Conjectures A-B and Remark 4.5. In v3, we corrected the perturbation (X(f(x)) instead of X(x)), in particular in the examples from Section 6. As a consequence, Psi(z) has a pole at z=1 for these examples.Comment: To appear Comm. Math. Phy

Effects of the Bacterial Extract OM-85 on Phagocyte Functions and the Stress Response

The effects of the bacterial extract OM-85 on the respiratory burst, intracellular calcium and the stress response have been investigated in human peripheral blood monocytes from normal donors. Activation of the respiratory burst during bacterial phagocytosis has been previously associated with heat shock/stress proteins synthesis. Whereas OM-85 stimulated superoxide production and increased Ca2+ mobilization, it fared to induce synthesis of classical HSPs. The lack of stress protein induction was observed even in the presence of iron which potentiates both oxidative injury and stress protein induction during bacterial phagocytosis. However OM-85 induced a 75–78 kDa protein, which is likely to be a glucose regulated protein (GRP78), and enhanced intracellular expression of interleukin-lβ precursor

Convergence of invariant densities in the small-noise limit

This paper presents a systematic numerical study of the effects of noise on the invariant probability densities of dynamical systems with varying degrees of hyperbolicity. It is found that the rate of convergence of invariant densities in the small-noise limit is frequently governed by power laws. In addition, a simple heuristic is proposed and found to correctly predict the power law exponent in exponentially mixing systems. In systems which are not exponentially mixing, the heuristic provides only an upper bound on the power law exponent. As this numerical study requires the computation of invariant densities across more than 2 decades of noise amplitudes, it also provides an opportunity to discuss and compare standard numerical methods for computing invariant probability densities.Comment: 27 pages, 19 figures, revised with minor correction

Rare events, escape rates and quasistationarity: some exact formulae

We present a common framework to study decay and exchanges rates in a wide class of dynamical systems. Several applications, ranging form the metric theory of continuons fractions and the Shannon capacity of contrained systems to the decay rate of metastable states, are given

SUPPLEMENTAL PACKAGE FOR THE SCOPING SUMMARY FOR THE P-AREA OPERABLE UNIT

Arsenic and selenium were tentatively identified as ecological RCOCs for the PAOU Ash Basin (PAOU Post-Characterization/Problem Identification Scoping Meeting, March 2007). Core Team agreed to consider eliminating these constituents as RCOCs based on a revised uncertainty discussion. The ecological risk tables and revised text (in its entirety) for the PAOU Ash Basin are provided in the Supplemental Information Package for the FS Scoping Meeting (June 2007). Arsenic and selenium have been traditionally carried through as ecological RCOCs (D-Area Ash Basin, A-Area Ash Pile)

SCOPING SUMMARY FOR THE P-AREA OPERABLE UNIT

This scoping summary supports development of the combined Remedial Investigation (RI)/Baseline Risk Assessment (BRA)/Feasibility Study (FS) for the P-Area Operable Unit (PAOU), or Combined document, which will be submitted on or before 09/28/2007. The objective of this Feasibility Study scoping summary meeting is to agree on the likely response actions to be evaluated and developed as alternatives in the combined document and agree on the uncertainties identified and whether they have been adequately managed

AREA COMPLETION STRATEGIES AT SAVANNAH RIVER SITE: CHARACTERIZATION FOR CLOSURE AND BEYOND

During the first four decades of its 56 year existence, the Savannah River Site (SRS) was a key supplier of nuclear material for national defense. During the 1990s, the site's primary missions became waste site closure, environmental restoration, and deactivation and decommissioning (D&D) of remnant cold war apparatus. Since 1989, with the approval of State and Federal regulatory agencies and with the participation of interested stakeholders, SRS has implemented a final remedy for a majority of the more than 500 individual waste sites at the former nuclear materials complex. These waste sites range from small, inert rubble pits to large, heavy industrial areas and radioactive waste disposal grounds. The closure and final remediation of these waste sites mark significant progress toward achieving SRS's overarching goal of reducing or eliminating future environmental damage and human health threats. However, larger challenges remain. For example, what are appropriate and achievable end-states for decommissioned nuclear facilities? What environmental and human health risks are associated with these end-states? To answer these questions within the strictures of smaller budgets and accelerated schedules, SRS is implementing an ''area completion'' strategy that: (1) unites several discrete waste units into one conceptual model, (2) integrates historically disparate environmental characterization and D&D activities, (3) reduces the number of required regulatory documents, and (4) in some cases, compresses schedules for achieving a stakeholder-approved end-state