Statistics of Pressure Fluctuations in Decaying, Isotropic Turbulence

We present results from a systematic direct-numerical simulation study of pressure fluctuations in an unforced, incompressible, homogeneous, and isotropic, three-dimensional turbulent fluid. At cascade completion, isosurfaces of low pressure are found to be organised as slender filaments, whereas the predominant isostructures appear sheet-like. We exhibit several new results, including plots of probability distributions of the spatial pressure-difference, the pressure-gradient norm, and the eigenvalues of the pressure-hessian tensor. Plots of the temporal evolution of the mean pressure-gradient norm, and the mean eigenvalues of the pressure-hessian tensor are also exhibited. We find the statistically preferred orientations between the eigenvectors of the pressure-hessian tensor, the pressure-gradient, the eigenvectors of the strain-rate tensor, the vorticity, and the velocity. Statistical properties of the non-local part of the pressure-hessian tensor are also exhibited, for the first time. We present numerical tests (in the viscous case) of some conjectures of Ohkitani [Phys. Fluids A {\bf 5}, 2570 (1993)] and Ohkitani and Kishiba [Phys. Fluids {\bf 7}, 411 (1995)] concerning the pressure-hessian and the strain-rate tensors, for the unforced, incompressible, three-dimensional Euler equations.Comment: 10 pages, 29 figures, Accepted for publication in Physical Review

Coupled attribute analysis on numerical data

The usual representation of quantitative data is to formalize it as an information table, which assumes the independence of attributes. In real-world data, attributes are more or less interacted and coupled via explicit or implicit relationships. Limited research has been conducted on analyzing such attribute interactions, which only describe a local picture of attribute couplings in an implicit way. This paper proposes a framework of the coupled attribute analysis to capture the global dependency of continuous attributes. Such global couplings integrate the intra-coupled interaction within an attribute (i.e. The correlations between attributes and their own powers) and inter-coupled interaction among different attributes (i.e. The correlations between attributes and the powers of others) to form a coupled representation for numerical objects by the Taylor-like expansion. This work makes one step forward towards explicitly addressing the global interactions of continuous attributes, verified by the applications in data structure analysis, data clustering, and data classification. Substantial experiments on 13 UCI data sets demonstrate that the coupled representation can effectively capture the global couplings of attributes and outperforms the traditional way, supported by statistical analysis

Terminal Proterozoic cyanobacterial blooms and phosphogenesis documented by the Doushantuo granular phosphorites II: Microbial diversity and C isotopes

An unprecedented period of phosphogenesis, along with massive deposition of black shales, major perturbations in the global carbon cycle and the rise of atmospheric oxygen, occurred in the terminal Proterozoic in the aftermath of the Marinoan glaciation. Although causal links between these processes have been postulated, evidence remains challenging. Correlated in situ micro-analyses of granular phosphorites from the Ediacaran Doushantuo Formation in Yichang, South China, suggested that cyanobacteria and associated extracellular polymeric substances (EPS) might have promoted aggregated granule growth and subsequent phosphatization (She et al., 2013). Here, we present new paleontological data for the Doushantuo phosphorites from Yichang, which, combined with Raman microspectroscopy and carbon isotope data, further document links between the biology of cyanobacteria and phosphogenesis. Mapping of microfossils in thin section shows that most phosphatic granules contain microfossils that are dominated by colonies of Myxococcoides, along with several filamentous genera generally considered to represent cyanobacterial sheaths. In addition, the phosphorites and associated rocks have δ13Corg values in the range of −26.0 to −29.7‰ VPDB, consistent with photoautotrophic carbon fixation with the Rubisco enzyme. Close association of phosphorites with the Marinoan tillites in stratigraphic level supports a genetic link between deglaciation and phosphogenesis, at least for the Doushantuo occurrence. Our new data suggest that major cyanobacterial blooms probably took place in the terminal Proterozoic, which might have resulted in rapid scavenging of bioavailable phosphorus and massive accumulations of organic matter (OM). Within a redox-stratified intra-shelf basin, the OM-bound phosphorus could have liberated by microbial sulfate reduction and other anaerobic metabolisms and subsequently concentrated by Fe-redox pumping below the chemocline. Upwelling of the bottom waters or upward fluctuation of the chemocline might have brought P-enriched waters to the photic zone, where it was again scavenged by cyanobacteria through their EPS to be subsequently precipitated as francolite. The feedbacks between enhanced continental weathering, cyanobacterial blooms, carbon burial, and accelerated phosphorus cycle thus controlled the marine biogeochemical changes, which led to further oxygenation of the atmosphere and oceans, ultimately paving the way for the rise of metazoans

Universal statistics of non-linear energy transfer in turbulent models

A class of shell models for turbulent energy transfer at varying the inter-shell separation, $\lambda$, is investigated. Intermittent corrections in the continuous limit of infinitely close shells ($\lambda \rightarrow 1$) have been measured. Although the model becomes, in this limit, non-intermittent, we found universal aspects of the velocity statistics which can be interpreted in the framework of log-poisson distributions, as proposed by She and Waymire (1995, Phys. Rev. Lett. 74, 262). We suggest that non-universal aspects of intermittency can be adsorbed in the parameters describing statistics and properties of the most singular structure. On the other hand, universal aspects can be found by looking at corrections to the monofractal scaling of the most singular structure. Connections with similar results reported in other shell models investigations and in real turbulent flows are discussed.Comment: 4 pages, 2 figures available upon request to [email protected]

Volatility modeling and analysis via coupled Wishart process

University of Technology, Sydney. Faculty of Engineering and Information Technology.Volatility refers to the measure for price fluctuation of specific financial instrument over time. It is a very important factor that can greatly influence investor’s decisions and concerns every other participant in the stock market. High volatility implies great insatiability and will definitely increase liquidity whereas low volatility indicates poor activeness. Hence the research on volatility draws great attention and interest of researchers from different backgrounds. Including the methods from data mining and machine learning is essential to improve the quality of volatility analysis. There are two main types of models on volatility analysis: the deterministic models and stochastic models. The deterministic models assume the volatility at particular time is a deterministic function of the past. The generalized autoregressive conditional heteroskedasticity (GARCH) model and its variations are in such category. The stochastic volatility (SV) models take the assumption that the volatility follows certain random process. Recent literature has shows that the stochastic models outperform the deterministic models to some extent. Among them, the Wishart process is a hot tool for modeling multivariate volatility. However, the stock market is closely connected with the society and human behavior, which makes it difficult to model. Almost all the existing models assume independence between our target objects: prices or the hidden covariance matrices behind them. These assumption works well for rough research or when the relationship between objects is weak. For a more solid research, the coupling relationship must be taken into account. In this thesis, we present two kinds of coupled Wishart process to model volatility: the homogenous coupled Wishart process and heterogenous coupled Wishart process. And corresponding algorithms are developed based on the models. The homogenous coupled Wishart process refers to model that our target objects belong to the same category. A two-chain coupled Wishart process is introduced in this thesis. Within such a model, the matrix in one chain is not only related with the past one from its own chain but also from its neighbors. After the derivation of its learning procedures, synthetic data are tested. Then, experiments are implemented with real data from two markets: U.S. and Hong Kong. In the two-chain coupled Wishart process, one chain indicates the volatility from U.S. stock market and the other the volatility indicates Hong Kong stock market. The latter one is the heterogenous coupled Wishart process. Unlike the homogenous one, in such a model, the covariance matrices are coupled with vectors, scalars or even a system. We aim to model how the outside influence from other kinds of data affect the evolving of covariance matrices. For time limitation, we make a simplified setup to illustrate how the heterogeneous coupling works. Then we construct the learning algorithm based on the setups and test it on synthetic data. To conclude, we include the thought of coupling into the analysis of volatility via Wishart process, with machine learning techniques. Sufficient experiments have proved the effectiveness of coupling in volatility analysis

Bifractality of the Devil's staircase appearing in the Burgers equation with Brownian initial velocity

It is shown that the inverse Lagrangian map for the solution of the Burgers equation (in the inviscid limit) with Brownian initial velocity presents a bifractality (phase transition) similar to that of the Devil's staircase for the standard triadic Cantor set. Both heuristic and rigorous derivations are given. It is explained why artifacts can easily mask this phenomenon in numerical simulations.Comment: 12 pages, LaTe

Developed turbulence: From full simulations to full mode reductions

Developed Navier-Stokes turbulence is simulated with varying wavevector mode reductions. The flatness and the skewness of the velocity derivative depend on the degree of mode reduction. They show a crossover towards the value of the full numerical simulation when the viscous subrange starts to be resolved. The intermittency corrections of the scaling exponents of the pth order velocity structure functions seem to depend mainly on the proper resolution of the inertial subrange. Universal scaling properties (i.e., independent of the degree of mode reduction) are found for the relative scaling exponents rho which were recently defined by Benzi et al.Comment: 4 pages, 5 eps-figures, replaces version from August 5th, 199

A new scaling property of turbulent flows

We discuss a possible theoretical interpretation of the self scaling property of turbulent flows (Extended Self Similarity). Our interpretation predicts that, even in cases when ESS is not observed, a generalized self scaling, must be observed. This prediction is checked on a number of laboratory experiments and direct numerical simulations.Comment: Plain Latex, 1 figure available upon request to [email protected]