Formal Higher-Spin Theories and Kontsevich-Shoikhet-Tsygan Formality

The formal algebraic structures that govern higher-spin theories within the unfolded approach turn out to be related to an extension of the Kontsevich Formality, namely, the Shoikhet-Tsygan Formality. Effectively, this allows one to construct the Hochschild cocycles of higher-spin algebras that make the interaction vertices. As an application of these results we construct a family of Vasiliev-like equations that generate the Hochschild cocycles with $sp(2n)$ symmetry from the corresponding cycles. A particular case of $sp(4)$ may be relevant for the on-shell action of the $4d$ theory. We also give the exact equations that describe propagation of higher-spin fields on a background of their own. The consistency of formal higher-spin theories turns out to have a purely geometric interpretation: there exists a certain symplectic invariant associated to cutting a polytope into simplices, namely, the Alexander-Spanier cocycle.Comment: typos fixed, many comments added, 36 pages + 20 pages of Appendices, 3 figure

Combustion instability sustained by unsteady vortex combustion

The determination of an internal feedback mechanism which leads to combustion instability inside a small scale laboratory combustor is presented in this paper. During combustion instability, the experimental findings show that a large vortical structure is formed at an acoustic resonant mode of the system. The subsequent unsteady burning, within the vortex as it is convected downstream, feeds energy into the acoustic field and sustains the large resonant oscillations. These vortices are formed when the acoustic velocity fluctuation at the flameholder is a large fraction of the mean flow velocity. The propagation of these vortices is not a strong function of the mean flow speed and appears to be dependent upon the frequency of the instability. Continued existence of large vortical structures which characterize unstable operation depends upon the fuel-air ratio, system acoustics, and fuel type

Influence of phase space localization on the energy diffusion in a quantum chaotic billiard

The quantum dynamics of a chaotic billiard with moving boundary is considered in this work. We found a shape parameter Hamiltonian expansion which enables us to obtain the spectrum of the deformed billiard for deformations so large as the characteristic wave length. Then, for a specified time dependent shape variation, the quantum dynamics of a particle inside the billiard is integrated directly. In particular, the dispersion of the energy is studied in the Bunimovich stadium billiard with oscillating boundary. The results showed that the distribution of energy spreads diffusively for the first oscillations of the boundary ({ =2 D t). We studied the diffusion contant $D$ as a function of the boundary velocity and found differences with theoretical predictions based on random matrix theory. By extracting highly phase space localized structures from the spectrum, previous differences were reduced significantly. This fact provides the first numerical evidence of the influence of phase space localization on the quantum diffusion of a chaotic system.Comment: 5 pages, 5 figure

The Afterglows of Swift-era Gamma-ray Bursts. I. Comparing pre-Swift and Swift-era Long/Soft (Type II) GRB Optical Afterglows

We have gathered optical photometry data from the literature on a large sample of Swift-era gamma-ray burst (GRB) afterglows including GRBs up to 2009 September, for a total of 76 GRBs, and present an additional three pre-Swift GRBs not included in an earlier sample. Furthermore, we publish 840 additional new photometry data points on a total of 42 GRB afterglows, including large data sets for GRBs 050319, 050408, 050802, 050820A, 050922C, 060418, 080413A, and 080810. We analyzed the light curves of all GRBs in the sample and derived spectral energy distributions for the sample with the best data quality, allowing us to estimate the host-galaxy extinction. We transformed the afterglow light curves into an extinction-corrected z = 1 system and compared their luminosities with a sample of pre-Swift afterglows. The results of a former study, which showed that GRB afterglows clustered and exhibited a bimodal distribution in luminosity space, are weakened by the larger sample. We found that the luminosity distribution of the two afterglow samples (Swift-era and pre-Swift) is very similar, and that a subsample for which we were not able to estimate the extinction, which is fainter than the main sample, can be explained by assuming a moderate amount of line-of-sight host extinction. We derived bolometric isotropic energies for all GRBs in our sample, and found only a tentative correlation between the prompt energy release and the optical afterglow luminosity at 1 day after the GRB in the z = 1 system. A comparative study of the optical luminosities of GRB afterglows with echelle spectra (which show a high number of foreground absorbing systems) and those without, reveals no indication that the former are statistically significantly more luminous. Furthermore, we propose the existence of an upper ceiling on afterglow luminosities and study the luminosity distribution at early times, which was not accessible before the advent of the Swift satellite. Most GRBs feature afterglows that are dominated by the forward shock from early times on. Finally, we present the first indications of a class of long GRBs, which form a bridge between the typical high-luminosity, high-redshift events and nearby low-luminosity events (which are also associated with spectroscopic supernovae) in terms of energetics and observed redshift distribution, indicating a continuous distribution overal

Nanocrystalline TiO2 and halloysite clay mineral composite films prepared by sol-gel method:Synergistic effect and the case of silver modification to the photocatalytic degradation of basic blue- 41 azo dye in water

Tubular halloysite clay mineral and nanocrystalline TiO2 were incorporated in the preparation of nanocomposite films on glass substrates via sol-gel method at 450 °C. The synthesis involves a simple chemical method employing nonionic surfactant molecule as pore directing agent along with the acetic acid-based sol-gel route without addition of water molecules. Drying and thermal treatment of composite films ensure elimination of organic material and lead to the formation of TiO2 nanoparticles homogeneously distributed on the surface of the halloysite. Nanocomposite films without cracks of active anatase crystal phase and small crystallite size on halloysite nanotubes are characterized by microscopy techniques and porosimetry methods in order to examine their structural properties. The composite halloysite-TiO2 films with variable quantities of halloysite were examined as photocatalysts to the discoloration of Basic Blue 41 azo dye in water. These nanocomposite films proved to be very promising photocatalysts and highly effective to dye's discoloration in spite of small amount of halloysite/TiO2 catalyst immobilized onto glass substrates. It also has been shown that the efficiency of the halloysite/TiO2 films could be further improved when silver particles were deposited on their surface after successful adsorption from an aqueous solution of a silver salt and UV reduction of the adsorbed ions

From the area under the Bessel excursion to anomalous diffusion of cold atoms

Levy flights are random walks in which the probability distribution of the step sizes is fat-tailed. Levy spatial diffusion has been observed for a collection of ultra-cold Rb atoms and single Mg+ ions in an optical lattice. Using the semiclassical theory of Sisyphus cooling, we treat the problem as a coupled Levy walk, with correlations between the length and duration of the excursions. The problem is related to the area under Bessel excursions, overdamped Langevin motions that start and end at the origin, constrained to remain positive, in the presence of an external logarithmic potential. In the limit of a weak potential, the Airy distribution describing the areal distribution of the Brownian excursion is found. Three distinct phases of the dynamics are studied: normal diffusion, Levy diffusion and, below a certain critical depth of the optical potential, x~ t^{3/2} scaling. The focus of the paper is the analytical calculation of the joint probability density function from a newly developed theory of the area under the Bessel excursion. The latter describes the spatiotemporal correlations in the problem and is the microscopic input needed to characterize the spatial diffusion of the atomic cloud. A modified Montroll-Weiss (MW) equation for the density is obtained, which depends on the statistics of velocity excursions and meanders. The meander, a random walk in velocity space which starts at the origin and does not cross it, describes the last jump event in the sequence. In the anomalous phases, the statistics of meanders and excursions are essential for the calculation of the mean square displacement, showing that our correction to the MW equation is crucial, and points to the sensitivity of the transport on a single jump event. Our work provides relations between the statistics of velocity excursions and meanders and that of the diffusivity.Comment: Supersedes arXiv: 1305.008

Scaling Green-Kubo relation and application to three aging systems

The Green-Kubo formula relates the spatial diffusion coefficient to the stationary velocity autocorrelation function. We derive a generalization of the Green-Kubo formula valid for systems with long-range or nonstationary correlations for which the standard approach is no longer valid. For the systems under consideration, the velocity autocorrelation function $\langle v(t+\tau) v(t) \rangle$ asymptotically exhibits a certain scaling behavior and the diffusion is anomalous $\langle x^2(t) \rangle \simeq 2 D_\nu t^{\nu}$. We show how both the anomalous diffusion coefficient $D_\nu$ and exponent $\nu$ can be extracted from this scaling form. Our scaling Green-Kubo relation thus extends an important relation between transport properties and correlation functions to generic systems with scale invariant dynamics. This includes stationary systems with slowly decaying power law correlations as well as aging systems, whose properties depend on the the age of the system. Even for systems that are stationary in the long time limit, we find that the long time diffusive behavior can strongly depend on the initial preparation of the system. In these cases, the diffusivity $D_{\nu}$ is not unique and we determine its values for a stationary respectively nonstationary initial state. We discuss three applications of the scaling Green-Kubo relation: Free diffusion with nonlinear friction corresponding to cold atoms diffusing in optical lattices, the fractional Langevin equation with external noise recently suggested to model active transport in cells and the L\'evy walk with numerous applications, in particular blinking quantum dots. These examples underline the wide applicability of our approach, which is able to treat very different mechanisms of anomalous diffusion.Comment: 16 pages, 6 figures, 1 tabl

Mod-discrete expansions

In this paper, we consider approximating expansions for the distribution of integer valued random variables, in circumstances in which convergence in law cannot be expected. The setting is one in which the simplest approximation to the $n$'th random variable $X_n$ is by a particular member $R_n$ of a given family of distributions, whose variance increases with $n$. The basic assumption is that the ratio of the characteristic function of $X_n$ and that of R_n$ converges to a limit in a prescribed fashion. Our results cover a number of classical examples in probability theory, combinatorics and number theory