About coherent structures in random shell models for passive scalar advection

A study of anomalous scaling in models of passive scalar advection in terms of singular coherent structures is proposed. The stochastic dynamical system considered is a shell model reformulation of Kraichnan model. We extend the method introduced in \cite{DDG99} to the calculation of self-similar instantons and we show how such objects, being the most singular events, are appropriate to capture asymptotic scaling properties of the scalar field. Preliminary results concerning the statistical weight of fluctuations around these optimal configurations are also presented.Comment: 4 pages, 2 postscript figures, submitted to PR

Surmounting collectively oscillating bottlenecks

We study the collective escape dynamics of a chain of coupled, weakly damped nonlinear oscillators from a metastable state over a barrier when driven by a thermal heat bath in combination with a weak, globally acting periodic perturbation. Optimal parameter choices are identified that lead to a drastic enhancement of escape rates as compared to a pure noise-assisted situation. We elucidate the speed-up of escape in the driven Langevin dynamics by showing that the time-periodic external field in combination with the thermal fluctuations triggers an instability mechanism of the stationary homogeneous lattice state of the system. Perturbations of the latter provided by incoherent thermal fluctuations grow because of a parametric resonance, leading to the formation of spatially localized modes (LMs). Remarkably, the LMs persist in spite of continuously impacting thermal noise. The average escape time assumes a distinct minimum by either tuning the coupling strength and/or the driving frequency. This weak ac-driven assisted escape in turn implies a giant speed of the activation rate of such thermally driven coupled nonlinear oscillator chains

Fluctuation-response relation in turbulent systems

We address the problem of measuring time-properties of Response Functions (Green functions) in Gaussian models (Orszag-McLaughin) and strongly non-Gaussian models (shell models for turbulence). We introduce the concept of {\it halving time statistics} to have a statistically stable tool to quantify the time decay of Response Functions and Generalized Response Functions of high order. We show numerically that in shell models for three dimensional turbulence Response Functions are inertial range quantities. This is a strong indication that the invariant measure describing the shell-velocity fluctuations is characterized by short range interactions between neighboring shells

Anomalous and dimensional scaling in anisotropic turbulence

We present a numerical study of anisotropic statistical fluctuations in homogeneous turbulent flows. We give an argument to predict the dimensional scaling exponents, (p+j)/3, for the projections of p-th order structure function in the j-th sector of the rotational group. We show that measured exponents are anomalous, showing a clear deviation from the dimensional prediction. Dimensional scaling is subleading and it is recovered only after a random reshuffling of all velocity phases, in the stationary ensemble. This supports the idea that anomalous scaling is the result of a genuine inertial evolution, independent of large-scale behavior.Comment: 4 pages, 3 figure

IUPAC Critical Evaluation of the Rotational-Vibrational Spectra of Water Vapor, Part III: Energy Levels and Transition Wavenumbers for H216O

This is the third of a series of articles reporting critically evaluated rotational-vibrational line positions, transition intensities, and energy levels, with associated critically reviewed labels and uncertainties, for all the main isotopologues of water. This paper presents experimental line positions, experimental-quality energy levels, and validated labels for rotational-vibrational transitions of the most abundant isotopologue of water, H216O. The latest version of the MARVEL (Measured Active Rotational-Vibrational Energy Levels) line-inversion procedure is used to determine the rovibrational energy levels of the electronic ground state of H216O from experimentally measured lines, together with their self-consistent uncertainties, for the spectral region up to the first dissociation limit. The spectroscopic network of H216O contains two components, an ortho (o) and a para (p) one. For o-H216O and p-H216O, experimentally measured, assigned, and labeled transitions were analyzed from more than 100 sources. The measured lines come from one-photon spectra recorded at room temperature in absorption, from hot samples with temperatures up to 3000K recorded in emission, and from multiresonance excitation spectra which sample levels up to dissociation. The total number of transitions considered is 184667 of which 182156 are validated: 68027 between para states and 114129 ortho ones. These transitions give rise to 18486 validated energy levels, of which 10446 and 8040 belong to o-H216O and p-H216O, respectively. The energy levels, including their labeling with approximate normal-mode and rigid-rotor quantum numbers, have been checked against ones determined from accurate variational nuclear motion computations employing exact kinetic energy operators as well as against previous compilations of energy levels. The extensive list of MARVEL lines and levels obtained are deposited in the supplementary data of this paper, as well as in a distributed information system applied to water, W@DIS, where they can easily be retrieved

Oscillatory Instabilities of Standing Waves in One-Dimensional Nonlinear Lattices

In one-dimensional anharmonic lattices, we construct nonlinear standing waves (SWs) reducing to harmonic SWs at small amplitude. For SWs with spatial periodicity incommensurate with the lattice period, a transition by breaking of analyticity versus wave amplitude is observed. As a consequence of the discreteness, oscillatory linear instabilities, persisting for arbitrarily small amplitude in infinite lattices, appear for all wave numbers Q not equal to zero or \pi. Incommensurate analytic SWs with |Q|>\pi/2 may however appear as 'quasi-stable', as their instability growth rate is of higher order.Comment: 4 pages, 6 figures, to appear in Phys. Rev. Let

Recommended isolated-line profile for representing high-resolution spectroscopic transitions (IUPAC Technical Report)

The report of an IUPAC Task Group, formed in 2011 on "Intensities and line shapes in high-resolution spectra of water isotopologues from experiment and theory" (Project No. 2011-022-2-100), on line profiles of isolated high-resolution rotational-vibrational transitions perturbed by neutral gas-phase molecules is presented. The well-documented inadequacies of the Voigt profile (VP), used almost universally by databases and radiative-transfer codes, to represent pressure effects and Doppler broadening in isolated vibrational-rotational and pure rotational transitions of the water molecule have resulted in the development of a variety of alternative line-profile models. These models capture more of the physics of the influence of pressure on line shapes but, in general, at the price of greater complexity. The Task Group recommends that the partially Correlated quadratic-Speed-Dependent Hard-Collision profile should be adopted as the appropriate model for high-resolution spectroscopy. For simplicity this should be called the Hartmann--Tran profile (HTP). The HTP is sophisticated enough to capture the various collisional contributions to the isolated line shape, can be computed in a straightforward and rapid manner, and reduces to simpler profiles, including the Voigt profile, under certain simplifying assumptions.Comment: Accepted for publication in Pure and Applied Chemistr

IUPAC Critical Evaluation of the Rotational-Vibrational Spectra of Water Vapor, Part III: Energy Levels and Transition Wavenumbers for H216O

This is the third of a series of articles reporting critically evaluated rotational-vibrational line positions, transition intensities, and energy levels, with associated critically reviewed labels and uncertainties, for all the main isotopologues of water. This paper presents experimental line positions, experimental-quality energy levels, and validated labels for rotational-vibrational transitions of the most abundant isotopologue of water, H216O. The latest version of the MARVEL (Measured Active Rotational-Vibrational Energy Levels) line-inversion procedure is used to determine the rovibrational energy levels of the electronic ground state of H216O from experimentally measured lines, together with their self-consistent uncertainties, for the spectral region up to the first dissociation limit. The spectroscopic network of H216O contains two components, an ortho (o) and a para (p) one. For o-H216O and p-H216O, experimentally measured, assigned, and labeled transitions were analyzed from more than 100 sources. The measured lines come from one-photon spectra recorded at room temperature in absorption, from hot samples with temperatures up to 3000K recorded in emission, and from multiresonance excitation spectra which sample levels up to dissociation. The total number of transitions considered is 184667 of which 182156 are validated: 68027 between para states and 114129 ortho ones. These transitions give rise to 18486 validated energy levels, of which 10446 and 8040 belong to o-H216O and p-H216O, respectively. The energy levels, including their labeling with approximate normal-mode and rigid-rotor quantum numbers, have been checked against ones determined from accurate variational nuclear motion computations employing exact kinetic energy operators as well as against previous compilations of energy levels. The extensive list of MARVEL lines and levels obtained are deposited in the supplementary data of this paper, as well as in a distributed information system applied to water, W@DIS, where they can easily be retrieved