A causal multifractal stochastic equation and its statistical properties

Multiplicative cascades have been introduced in turbulence to generate random or deterministic fields having intermittent values and long-range power-law correlations. Generally this is done using discrete construction rules leading to discrete cascades. Here a causal log-normal stochastic process is introduced; its multifractal properties are demonstrated together with other properties such as the composition rule for scale dependence and stochastic differential equations for time and scale evolutions. This multifractal stochastic process is continuous in scale ratio and in time. It has a simple generating equation and can be used to generate sequentially time series of any length.Comment: Eur. Phys. J. B (in press

Lagrangian Cascade in Three-Dimensional Homogeneous and Isotropic Turbulence

In this work, the scaling statistics of the dissipation along Lagrangian trajectories are investigated by using fluid tracer particles obtained from a high resolution direct numerical simulation with $Re_{\lambda}=400$. Both the energy dissipation rate $\epsilon$ and the local time averaged $\epsilon_{\tau}$ agree rather well with the lognormal distribution hypothesis. Several statistics are then examined. It is found that the autocorrelation function $\rho(\tau)$ of $\ln(\epsilon(t))$ and variance $\sigma^2(\tau)$ of $\ln(\epsilon_{\tau}(t))$ obey a log-law with scaling exponent $\beta'=\beta=0.30$ compatible with the intermittency parameter $\mu=0.30$. The $q$th-order moment of $\epsilon_{\tau}$ has a clear power-law on the inertial range $10<\tau/\tau_{\eta}<100$. The measured scaling exponent $K_L(q)$ agrees remarkably with $q-\zeta_L(2q)$ where $\zeta_L(2q)$ is the scaling exponent estimated using the Hilbert methodology. All these results suggest that the dissipation along Lagrangian trajectories could be modelled by a multiplicative cascade.Comment: 10 pages with 7 figures accepted for Journal of Fluid Mechanics as Rapid

Time dependent intrinsic correlation analysis of temperature and dissolved oxygen time series using empirical mode decomposition

In the marine environment, many fields have fluctuations over a large range of different spatial and temporal scales. These quantities can be nonlinear \red{and} non-stationary, and often interact with each other. A good method to study the multiple scale dynamics of such time series, and their correlations, is needed. In this paper an application of an empirical mode decomposition based time dependent intrinsic correlation, \red{of} two coastal oceanic time series, temperature and dissolved oxygen (saturation percentage) is presented. The two time series are recorded every 20 minutes \red{for} 7 years, from 2004 to 2011. The application of the Empirical Mode Decomposition on such time series is illustrated, and the power spectra of the time series are estimated using the Hilbert transform (Hilbert spectral analysis). Power-law regimes are found with slopes of 1.33 for dissolved oxygen and 1.68 for temperature at high frequencies (between 1.2 and 12 hours) \red{with} both close to 1.9 for lower frequencies (time scales from 2 to 100 days). Moreover, the time evolution and scale dependence of cross correlations between both series are considered. The trends are perfectly anti-correlated. The modes of mean year 3 and 1 year have also negative correlation, whereas higher frequency modes have a much smaller correlation. The estimation of time-dependent intrinsic correlations helps to show patterns of correlations at different scales, for different modes.Comment: 35 pages with 22 figure

From random walk to multifractal random walk in zooplankton swimming behaviour

EDITORIAL OFFICE, TAIPEI, TAIWAN, 11

Prediction of RECRUITment In randomized clinical Trials (RECRUIT-IT)— : —rationale and design for an international collaborative study

Funding: BK has received a project specific grant from the University of Basel to realize this project. In addition, this study is supported by the Swiss National Science Foundation (grant 320030_149496/1) and the Gottfried and Julia Bangerter-Rhyner Foundation. The provided work by BG, JHL, CW, and JY has been supported by the National Cancer Institute Cancer Centre Support Grant P30 CA168524 and used BISR core. The Health Services Research Unit, University of Aberdeen, receives core funding from the Chief Scientist Office of the Scottish Government Health Directorates. DC is supported by a Research Chair from the Canadian Institute for Health Research. The mentioned funding sources have no role in the design and conduct of the study; the collection, management, analysis, and interpretation of the data; the preparation, review, or approval of the manuscript; or the decision to submit the manuscript for publication.Peer reviewedPublisher PD

Code assessment and modelling for Design Basis Accident analysis of the European Sodium Fast Reactor design. Part II: Optimised core and representative transients analysis

The new reactor concepts proposed in the Generation IV International Forum require the development and validation of computational tools able to assess their safety performance. In the first part of this paper the models of the ESFR design developed by several organisations in the framework of the CP-ESFR project were presented and their reliability validated via a benchmarking exercise. This second part of the paper includes the application of those tools for the analysis of design basis accident (DBC) scenarios of the reference design. Further, this paper also introduces the main features of the core optimisation process carried out within the project with the objective to enhance the core safety performance through the reduction of the positive coolant density reactivity effect. The influence of this optimised core design on the reactor safety performance during the previously analysed transients is also discussed. The conclusion provides an overview of the work performed by the partners involved in the project towards the development and enhancement of computational tools specifically tailored to the evaluation of the safety performance of the Generation IV innovative nuclear reactor designs