"Locally homogeneous turbulence" Is it an inconsistent framework?

In his first 1941 paper Kolmogorov assumed that the velocity has increments which are homogeneous and independent of the velocity at a suitable reference point. This assumption of local homogeneity is consistent with the nonlinear dynamics only in an asymptotic sense when the reference point is far away. The inconsistency is illustrated numerically using the Burgers equation. Kolmogorov's derivation of the four-fifths law for the third-order structure function and its anisotropic generalization are actually valid only for homogeneous turbulence, but a local version due to Duchon and Robert still holds. A Kolomogorov--Landau approach is proposed to handle the effect of fluctuations in the large-scale velocity on small-scale statistical properties; it is is only a mild extension of the 1941 theory and does not incorporate intermittency effects.Comment: 4 pages, 2 figure

Lagrangian Refined Kolmogorov Similarity Hypothesis for Gradient Time-evolution in Turbulent Flows

We study the time evolution of velocity and pressure gradients in isotropic turbulence, by quantifying their decorrelation time scales as one follows fluid particles in the flow. The Lagrangian analysis uses data in a public database generated using direct numerical simulation of the Naiver-Stokes equations, at a Reynolds number 430. It is confirmed that when averaging over the entire domain, correlation functions decay on timescales on the order of the mean Kolmogorov turnover time scale, computed from the globally averaged rate of dissipation and viscosity. However, when performing the analysis in different subregions of the flow, turbulence intermittency leads to large spatial variability in the decay time scales. Remarkably, excellent collapse of the auto-correlation functions is recovered when using the `local Kolmogorov time-scale' defined using the locally averaged, rather than the global, dissipation-rate. This provides new evidence for the validity of Kolmogorov's Refined Similarity Hypothesis, but from a Lagrangian viewpoint that provides a natural frame to describe the dynamical time evolution of turbulence.Comment: 4 Pages, 4 figure

Adsorption of arsenate on Fe-(hydr)oxide

Adsorption using metal oxide materials has been demonstrated to be an effective technique to remove hazardous materials from water, due to its easy operation, low cost, and high efficiency. The high number of oxyanions in aquatic ecosystems causes serious pollution problems. Removal of arsenate (H2AsO4 -), is one of the major concerns, since it is a highly toxic anion for life. Within the metal oxides, the iron oxide is considered as a suitable material for the elimination of oxyanions. The adsorption of H2AsO4 - on Fe-(hydr)oxide is through the formation of inner or outer sphere complexes. In this work, through computational methods, a complete characterization of the adsorbed surface complexes was performed. Three different pH conditions were simulated (acidic, intermediate and basic), and it was found that, the thermodynamic favourability of the different adsorbed complexes was directly related to the pH. Monodentate complex (MM1) was the most thermodynamically favourable complex with an adsorption energy of -96.0kJ/mol under intermediate pH conditions. © Published under licence by IOP Publishing Ltd

Analogy between turbulence and quantum gravity: beyond Kolmogorov's 1941 theory

Simple arguments based on the general properties of quantum fluctuations have been recently shown to imply that quantum fluctuations of spacetime obey the same scaling laws of the velocity fluctuations in a homogeneous incompressible turbulent flow, as described by Kolmogorov 1941 (K41) scaling theory. Less noted, however, is the fact that this analogy rules out the possibility of a fractal quantum spacetime, in contradiction with growing evidence in quantum gravity research. In this Note, we show that the notion of a fractal quantum spacetime can be restored by extending the analogy between turbulence and quantum gravity beyond the realm of K41 theory. In particular, it is shown that compatibility of a fractal quantum-space time with the recent Horava-Lifshitz scenario for quantum gravity, implies singular quantum wavefunctions. Finally, we propose an operational procedure, based on Extended Self-Similarity techniques, to inspect the (multi)-scaling properties of quantum gravitational fluctuations.Comment: Sliglty modified version of the article about to appear in IJMP

Electromagnetic Vacuum of Complex Media: Dipole Emission vs. Light Propagation, Vacuum Energy, and Local Field Factors

We offer a unified approach to several phenomena related to the electromagnetic vacuum of a complex medium made of point electric dipoles. To this aim, we apply the linear response theory to the computation of the polarization field propagator and study the spectrum of vacuum fluctuations. The physical distinction among the local density of states which enter the spectra of light propagation, total dipole emission, coherent emission, total vacuum energy and Schwinger-bulk energy is made clear. Analytical expressions for the spectrum of dipole emission and for the vacuum energy are derived. Their respective relations with the spectrum of external light and with the Schwinger-bulk energy are found. The light spectrum and the Schwinger-bulk energy are determined by the Dyson propagator. The emission spectrum and the total vacuum energy are determined by the polarization propagator. An exact relationship of proportionality between both propagators is found in terms of local field factors. A study of the nature of stimulated emission from a single dipole is carried out. Regarding coherent emission, it contains two components. A direct one which is transferred radiatively and directly from the emitter into the medium and whose spectrum is that of external light. And an indirect one which is radiated by induced dipoles. The induction is mediated by one (and only one) local field factor. Regarding the vacuum energy, we find that in addition to the Schwinger-bulk energy the vacuum energy of an effective medium contains local field contributions proportional to the resonant frequency and to the spectral line-width.Comment: Typos fixed, journal ref. adde

On the decay of Burgers turbulence

This work is devoted to the decay ofrandom solutions of the unforced Burgers equation in one dimension in the limit of vanishing viscosity. The initial velocity is homogeneous and Gaussian with a spectrum proportional to $k^n$ at small wavenumbers $k$ and falling off quickly at large wavenumbers. In physical space, at sufficiently large distances, there is an ``outer region'', where the velocity correlation function preserves exactly its initial form (a power law) when $n$ is not an even integer. When $1<n<2$ the spectrum, at long times, has three scaling regions : first, a $|k|^n$ region at very small $k$\ms1 with a time-independent constant, stemming from this outer region, in which the initial conditions are essentially frozen; second, a $k^2$ region at intermediate wavenumbers, related to a self-similarly evolving ``inner region'' in physical space and, finally, the usual $k^{-2}$ region, associated to the shocks. The switching from the $|k|^n$ to the $k^2$ region occurs around a wave number $k_s(t) \propto t^{-1/[2(2-n)]}$, while the switching from $k^2$ to $k^{-2}$ occurs around $k_L(t)\propto t^{-1/2}$ (ignoring logarithmic corrections in both instances). The key element in the derivation of the results is an extension of the Kida (1979) log-corrected $1/t$ law for the energy decay when $n=2$ to the case of arbitrary integer or non-integer $n>1$. A systematic derivation is given in which both the leading term and estimates of higher order corrections can be obtained. High-resolution numerical simulations are presented which support our findings.Comment: In LaTeX with 11 PostScript figures. 56 pages. One figure contributed by Alain Noullez (Observatoire de Nice, France

On Making Good Games - Using Player Virtue Ethics and Gameplay Design Patterns to Identify Generally Desirable Gameplay Features

This paper uses a framework of player virtues to perform a theoretical exploration of what is required to make a game good. The choice of player virtues is based upon the view that games can be seen as implements, and that these are good if they support an intended use, and the intended use of games is to support people to be good players. A collection of gameplay design patterns, identified through their relation to the virtues, is presented to provide specific starting points for considering design options for this type of good games. 24 patterns are identified supporting the virtues, including RISK/REWARD, DYNAMIC ALLIANCES, GAME MASTERS, and PLAYER DECIDED RESULTS, as are 7 countering three or more virtues, including ANALYSIS PARALYSIS, EARLY ELIMINATION, and GRINDING. The paper concludes by identifying limitations of the approach as well as by showing how it can be applied using other views of what are preferable features in games

On the von Karman-Howarth equations for Hall MHD flows

The von Karman-Howarth equations are derived for three-dimensional (3D) Hall magnetohydrodynamics (MHD) in the case of an homogeneous and isotropic turbulence. From these equations, we derive exact scaling laws for the third-order correlation tensors. We show how these relations are compatible with previous heuristic and numerical results. These multi-scale laws provide a relevant tool to investigate the non-linear nature of the high frequency magnetic field fluctuations in the solar wind or, more generally, in any plasma where the Hall effect is important.Comment: 11 page

Real-space Manifestations of Bottlenecks in Turbulence Spectra

An energy-spectrum bottleneck, a bump in the turbulence spectrum between the inertial and dissipation ranges, is shown to occur in the non-turbulent, one-dimensional, hyperviscous Burgers equation and found to be the Fourier-space signature of oscillations in the real-space velocity, which are explained by boundary-layer-expansion techniques. Pseudospectral simulations are used to show that such oscillations occur in velocity correlation functions in one- and three-dimensional hyperviscous hydrodynamical equations that display genuine turbulence.Comment: 5 pages, 2 figure

Helical rotating turbulence. Part II. Intermittency, scale invariance and structures

We study the intermittency properties of the energy and helicity cascades in two 1536^3 direct numerical simulations of helical rotating turbulence. Symmetric and anti-symmetric velocity increments are examined, as well as probability density functions of the velocity field and of the helicity density. It is found that the direct cascade of energy to small scales is scale invariant and non-intermittent, whereas the direct cascade of helicity is highly intermittent. Furthermore, the study of structure functions of different orders allows us to identify a recovery of isotropy of strong events at very small scales in the flow. Finally, we observe the juxtaposition in space of strong laminar and persistent helical columns next to time-varying vortex tangles, the former being associated with the self-similarity of energy and the latter with the intermittency of helicity.Comment: 11 pages, 10 figure