Growth of non-infinitesimal perturbations in turbulence

We discuss the effects of finite perturbations in fully developed turbulence by introducing a measure of the chaoticity degree associated to a given scale of the velocity field. This allows one to determine the predictability time for non-infinitesimal perturbations, generalizing the usual concept of maximum Lyapunov exponent. We also determine the scaling law for our indicator in the framework of the multifractal approach. We find that the scaling exponent is not sensitive to intermittency corrections, but is an invariant of the multifractal models. A numerical test of the results is performed in the shell model for the turbulent energy cascade.Comment: 4 pages, 2 Postscript figures (included), RevTeX 3.0, files packed with uufile

Predictability in Systems with Many Characteristic Times: The Case of Turbulence

In chaotic dynamical systems, an infinitesimal perturbation is exponentially amplified at a time-rate given by the inverse of the maximum Lyapunov exponent $\lambda$. In fully developed turbulence, $\lambda$ grows as a power of the Reynolds number. This result could seem in contrast with phenomenological arguments suggesting that, as a consequence of `physical' perturbations, the predictability time is roughly given by the characteristic life-time of the large scale structures, and hence independent of the Reynolds number. We show that such a situation is present in generic systems with many degrees of freedom, since the growth of a non-infinitesimal perturbation is determined by cumulative effects of many different characteristic times and is unrelated to the maximum Lyapunov exponent. Our results are illustrated in a chain of coupled maps and in a shell model for the energy cascade in turbulence.Comment: 24 pages, 10 Postscript figures (included), RevTeX 3.0, files packed with uufile

Water soluble aerosols and gases at a UK background site. Part 1: Controls of PM2.5 and PM10 aerosol composition

There is limited availability of long-term, high temporal resolution, chemically speciated aerosol measurements which can provide further insight into the health and environmental impacts of particulate matter. The Monitor for AeRosols and Gases (MARGA, Applikon B.V., NL) allows for the characterisation of the inorganic components of PM10 and PM2.5 (NH4+, NO3-, SO42-, Cl-, Na+, K+, Ca2+, Mg2+) and inorganic reactive gases (NH3, SO2, HCl, HONO and HNO3) at hourly resolution. The following study presents 6.5 years (June 2006 to December 2012) of quasi-continuous observations of PM2.5 and PM10 using the MARGA at the UK EMEP supersite, Auchencorth Moss, SE Scotland. Auchencorth Moss was found to be representative of a remote European site with average total water soluble inorganic mass of PM2.5 of 3.82 μg m−3. Anthropogenically derived secondary inorganic aerosols (sum of NH4+, NO3- and nss-SO42−) were the dominating species (63 %) of PM2.5. In terms of equivalent concentrations, NH4+ provided the single largest contribution to PM2.5 fraction in all seasons. Sea salt was the main component (73 %) of the PMcoarse fraction (PM10-PM2.5), though NO3- was also found to make a relatively large contribution to the measured mass (17 %) providing evidence of considerable processing of sea salt in the coarse mode. There was on occasions evidence of aerosol from combustion events being transported to the site in 2012 as high K+ concentrations (deviating from the known ratio in sea salt) coincided with increases in black carbon at the site. Pollution events in PM10 (defined as concentrations > 12 μg m−3) were on average dominated by NH4+ and NO3-, where smaller loadings at the site tended to be dominated by sea salt. As with other western European sites, the charge balance of the inorganic components resolved were biased towards cations, suggesting the aerosol was basic or more likely that organic acids contributed to the charge balance. This study demonstrates the UK background atmospheric composition is primarily driven by meteorology with sea salt dominating air masses from the Atlantic Ocean and the Arctic, whereas secondary inorganic aerosols tended to dominate air masses from continental Europe

Many pion decays of rho(770) and omega(782) mesons in chiral theory

The decays rho(770) to 4 pi and omega(782) to 5pi are considered in detail in the approach based on the Weinberg Lagrangian obtained upon the nonlinear realization of chiral symmetry, added with the term induced by the anomalous Lagrangian of Wess and Zumino. The partial widths and excitation curves of the decays rho^0 to 2 pi^+ 2 pi^-, pi^+ pi^- 2 pi^0, rho^{+-} to 2 pi^{+-} pi^{-+} pi^0, rho^(+-} to pi^(+-} 3 pi^0 are evaluated for e^+e^- annihilation, photoproduction and tau lepton decays. The results of calculations are compared with the recent CMD-2 data on the decay rho^0 to 2 pi^+ 2 pi^- observed in e^+e^- annihilation. The omega to 5 pi decay widths and excitation curves in e^+e^- annihilation are obtained. The angular distributions for various combinations of the final pions in the decays rho to 4 pi and omega to 5 pi are written. The perspectives of the experimental study of the above decays in e^+e^- annihilation, tau lepton decays and photoproduction are discussed.Comment: Revtex, 32 pages including 11 ps figures. Replaced to fit the version published in Phys. Rev. D. Material rearranged, clarifying remarks and references added, typos fixe

TECHNIQUES IN OPTICAL DATA PROCESSING AND COHERENT OPTICS

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73477/1/j.1749-6632.1969.tb12651.x.pd

Attributing scientific and technical progress: the case of holography

Holography, the three-dimensional imaging technology, was portrayed widely as a paradigm of progress during its decade of explosive expansion 1964–73, and during its subsequent consolidation for commercial and artistic uses up to the mid 1980s. An unusually seductive and prolific subject, holography successively spawned scientific insights, putative applications and new constituencies of practitioners and consumers. Waves of forecasts, associated with different sponsors and user communities, cast holography as a field on the verge of success—but with the dimensions of success repeatedly refashioned. This retargeting of the subject represented a degree of cynical marketeering, but was underpinned by implicit confidence in philosophical positivism and faith in technological progressivism. Each of its communities defined success in terms of expansion, and anticipated continual progressive increase. This paper discusses the contrasting definitions of progress in holography, and how they were fashioned in changing contexts. Focusing equally on reputed ‘failures’ of some aspects of the subject, it explores the varied attributes by which success and failure were linked with progress by different technical communities. This important case illuminates the peculiar post-World War II environment that melded the military, commercial and popular engagement with scientific and technological subjects, and the competing criteria by which they assessed the products of science

Atmospheric predictability revisited

This article examines the potential to improve numerical weather prediction (NWP) by estimating upper and lower bounds on predictability by re-visiting the original study of Lorenz (1982) but applied to the most recent version of the European Centre for Medium Range Weather Forecasts (ECMWF) forecast system, for both the deterministic and ensemble prediction systems (EPS). These bounds are contrasted with an older version of the same NWP system to see how they have changed with improvements to the NWP system. The computations were performed for the earlier seasons of DJF 1985/1986 and JJA 1986 and the later seasons of DJF 2010/2011 and JJA 2011 using the 500-hPa geopotential height field. Results indicate that for this field, we may be approaching the limit of deterministic forecasting so that further improvements might only be obtained by improving the initial state. The results also show that predictability calculations with earlier versions of the model may overestimate potential forecast skill, which may be due to insufficient internal variability in the model and because recent versions of the model are more realistic in representing the true atmospheric evolution. The same methodology is applied to the EPS to calculate upper and lower bounds of predictability of the ensemble mean forecast in order to explore how ensemble forecasting could extend the limits of the deterministic forecast. The results show that there is a large potential to improve the ensemble predictions, but for the increased predictability of the ensemble mean, there will be a trade-off in information as the forecasts will become increasingly smoothed with time. From around the 10-d forecast time, the ensemble mean begins to converge towards climatology. Until this point, the ensemble mean is able to predict the main features of the large-scale flow accurately and with high consistency from one forecast cycle to the next. By the 15-d forecast time, the ensemble mean has lost information with the anomaly of the flow strongly smoothed out. In contrast, the control forecast is much less consistent from run to run, but provides more detailed (unsmoothed) but less useful information

On compatibility of string effective action with an accelerating universe

In this paper, we fully investigate the cosmological effects of the moduli dependent one-loop corrections to the gravitational couplings of the string effective action to explain the cosmic acceleration problem in early (and/or late) universe. These corrections comprise a Gauss-Bonnet (GB) invariant multiplied by universal non-trivial functions of the common modulus $\sigma$ and the dilaton $\phi$. The model exhibits several features of cosmological interest, including the transition between deceleration and acceleration phases. By considering some phenomenologically motivated ansatzs for one of the scalars and/or the scale factor (of the universe), we also construct a number of interesting inflationary potentials. In all examples under consideration, we find that the model leads only to a standard inflation ($w \geq -1$) when the numerical coefficient $\delta$ associated with modulus-GB coupling is positive, while the model can lead also to a non-standard inflation ($w<-1$), if $\delta$ is negative. In the absence of (or trivial) coupling between the GB term and the scalars, there is no crossing between the $w -1$ phases, while this is possible with non-trivial GB couplings, even for constant dilaton phase of the standard picture. Within our model, after a sufficient amount of e-folds of expansion, the rolling of both fields $\phi$ and $\sigma$ can be small. In turn, any possible violation of equivalence principle or deviations from the standard general relativity may be small enough to easily satisfy all astrophysical and cosmological constraints.Comment: 30 pages, 8 figures; v2 significant changes in notations, appendix and refs added; v3 significant revisions, refs added; v4 appendix extended, new refs, published versio

Slow-roll, acceleration, the Big Rip and WKB approximation in NLS-type formulation of scalar field cosmology

Aspects of non-linear Schr\"{o}dinger-type (NLS) formulation of scalar (phantom) field cosmology on slow-roll, acceleration, WKB approximation and Big Rip singularity are presented. Slow-roll parameters for the curvature and barotropic density terms are introduced. We reexpress all slow-roll parameters, slow-roll conditions and acceleration condition in NLS form. WKB approximation in the NLS formulation is also discussed when simplifying to linear case. Most of the Schr\"{o}dinger potentials in NLS formulation are very slowly-varying, hence WKB approximation is valid in the ranges. In the NLS form of Big Rip singularity, two quantities are infinity in stead of three. We also found that approaching the Big Rip, $w_{\rm eff}\to -1 + {2}/{3q}$, $(q<0)$ which is the same as effective phantom equation of state in the flat case.Comment: [7 pages, no figure, more reference added, accepted by JCAP

The role of large-scale spatial patterns in the chaotic amplification of perturbations in a Lorenz’96 model

The preparation of perturbed initial conditions to initialize an ensemble of numerical weather forecasts is a crucial task in current ensemble prediction systems (EPSs). Perturbations are added in the places where they are expected to grow faster, in order to provide an envelope of uncertainty along with the deterministic forecast. This work analyses the influence of large-scale spatial patterns on the growth of small perturbations. Therefore, we compare Lyapunov vector (LV) definitions, used in the initialization of state-of-the-art EPSs, with the so-called characteristic LVs. We test the dynamical behaviour of these LVs in the two-scale Lorenz’96 system. We find that the commonly used definitions of LVs include non-intrinsic and spurious effects due to their mutual orthogonality. We also find that the spatial locations where the small-scale perturbations are growing are ‘quantized’ by the large-scale pattern. This ‘quantization’ enhances the artificial disposition of the LVs, which is only avoided using the characteristic LVs, an unambiguous basis which may also be of great use in realistic models for assessing or initializing EPSs