Isotropisation at small scales of rotating helically-driven turbulence

We present numerical evidence of how three-dimensionalization occurs at small scale in rotating turbulence with Beltrami (ABC) forcing, creating helical flow. The Zeman scale $\ell_{\Omega}$ at which the inertial and eddy turn-over times are equal is more than one order of magnitude larger than the dissipation scale, with the relevant domains (large-scale inverse cascade of energy, dual regime in the direct cascade of energy $E$ and helicity $H$, and dissipation) each moderately resolved. These results stem from the analysis of a large direct numerical simulation on a grid of $3072^3$ points, with Rossby and Reynolds numbers respectively equal to 0.07 and $2.7\times 10^4$. At scales smaller than the forcing, a helical wave-modulated inertial law for the energy and helicity spectra is followed beyond $\ell_{\Omega}$ by Kolmogorov spectra for $E$ and $H$. Looking at the two-dimensional slow manifold, we also show that the helicity spectrum breaks down at $\ell_{\Omega}$, a clear sign of recovery of three-dimensionality in the small scales.Comment: 13 pages, 6 figure

A methodology for the selection of manufacturing processes based on the design of the Manufacturing Matrix

This study proposes a decision method to help designers and engineers select the manufacturing process that meet the production performances, including environmental impacts. It has intended to make a decision on manufacturing parameters such as quality, time, cost and environmental impact. The methodology is structured and supported by a matrix called the manufacturing matrix. It is used to evaluate the relationships between the manufacturing process of each product attribute and the process parameters. The method is in 4 steps: create the manufacturing matrix, generate the solutions, evaluate the solutions and select the manufacturing process. The methodology is applied on an industrial case study in the leather good industry. It is able to help practically designers and engineers select the suitable manufacturing process

Compliance error compensation in robotic-based milling

The paper deals with the problem of compliance errors compensation in robotic-based milling. Contrary to previous works that assume that the forces/torques generated by the manufacturing process are constant, the interaction between the milling tool and the workpiece is modeled in details. It takes into account the tool geometry, the number of teeth, the feed rate, the spindle rotation speed and the properties of the material to be processed. Due to high level of the disturbing forces/torques, the developed compensation technique is based on the non-linear stiffness model that allows us to modify the target trajectory taking into account nonlinearities and to avoid the chattering effect. Illustrative example is presented that deals with robotic-based milling of aluminum alloy

Intermittency in the Joint Cascade of Energy and Helicity

The statistics of the energy and helicity fluxes in isotropic turbulence are studied using high resolution direct numerical simulation. The scaling exponents of the energy flux agree with those of the transverse velocity structure functions through refined similarity hypothesis, consistent with Kraichnan's prediction \cite{Kr74}. The helicity flux is even more intermittent than the energy flux and its scaling exponents are closer to those of the passive scalar. Using Waleffe's helical decomposition, we demonstrate that the existence of positive mean helicity flux inhibits the energy transfer in the negative helical modes, a non-passive effect

Theory of Adiabatic fluctuations : third-order noise

We consider the response of a dynamical system driven by external adiabatic fluctuations. Based on the `adiabatic following approximation' we have made a systematic separation of time-scales to carry out an expansion in $\alpha |\mu|^{-1}$, where $\alpha$ is the strength of fluctuations and $|\mu|$ is the damping rate. We show that probability distribution functions obey the differential equations of motion which contain third order terms (beyond the usual Fokker-Planck terms) leading to non-Gaussian noise. The problem of adiabatic fluctuations in velocity space which is the counterpart of Brownian motion for fast fluctuations, has been solved exactly. The characteristic function and the associated probability distribution function are shown to be of stable form. The linear dissipation leads to a steady state which is stable and the variances and higher moments are shown to be finite.Comment: Plain Latex, no figures, 28 pages; to appear in J. Phys.

Stochastic processes with finite correlation time: modeling and application to the generalized Langevin equation

The kangaroo process (KP) is characterized by various forms of the covariance and can serve as a useful model of random noises. We discuss properties of that process for the exponential, stretched exponential and algebraic (power-law) covariances. Then we apply the KP as a model of noise in the generalized Langevin equation and simulate solutions by a Monte Carlo method. Some results appear to be incompatible with requirements of the fluctuation-dissipation theorem because probability distributions change when the process is inserted into the equation. We demonstrate how one can construct a model of noise free of that difficulty. This form of the KP is especially suitable for physical applications.Comment: 22 pages (RevTeX) and 4 figure

Determination of Matter Surface Distribution of Neutron-rich Nuclei

We demonstrate that the matter density distribution in the surface region is determined well by the use of the relatively low-intensity beams that become available at the upcoming radioactive beam facilities. Following the method used in the analyses of electron scattering, we examine how well the density distribution is determined in a model-independent way by generating pseudo data and by carefully applying statistical and systematic error analyses. We also study how the determination becomes deteriorated in the central region of the density, as the quality of data decreases. Determination of the density distributions of neutron-rich nuclei is performed by fixing parameters in the basis functions to the neighboring stable nuclei. The procedure allows that the knowledge of the density distributions of stable nuclei assists to strengthen the determination of their unstable isotopes.Comment: 41 pages, latex, 27 figure