Scaling laws of turbulent dynamos

We consider magnetic fields generated by homogeneous isotropic and parity invariant turbulent flows. We show that simple scaling laws for the dynamo threshold, magnetic energy and Ohmic dissipation can be obtained depending on the value of the magnetic Prandtl number. To cite this article: S. Fauve, F. Pétrélis, C. R. Physique 8 (2007).     

Scaling laws in high-energy electron-nuclear scattering

The approximate scaling behavior suggested by recent measurements of electron scattering form factors and inelastic structure functions of few-body nuclei (mass 2, 3, 4) is discussed in a relativistic impulse approximation model. The model is a straightforward extension incorporating spin of a nucleon parton model introduced in recent works. We present results for electric and magnetic form factors as well as inelastic structure functions near threshold. The important corrections to scaling which are present in the preasymptotic regions are found to be well accounted for by the type of binding effects included in the phenomenologically constructed infinite-momentum frame nuclear wave functions. While predicted form factors are very sensitive to the parameters in the wave functions it does not appear possible to associate unambiguous dynamical meaning to these parameters. We find that spin effects bring significant and useful corrections.     

Scaling laws in aeolian sand transport

We report on wind tunnel measurements on saltating particles in a turbulent boundary layer and provide evidence that over an erodible bed the particle velocity in the saltation layer and the saltation length are almost invariant with the wind strength, whereas over a nonerodible bed these quantities vary significantly with the air friction speed. It results that the particle transport rate over an erodible bed does not exhibit a cubic dependence with the air friction speed, as predicted by Bagnold, but a quadratic one. This contrasts with saltation over a nonerodible bed where the cubic Bagnold scaling holds. Our findings emphasize the crucial role of the boundary conditions at the bed and may have important practical consequences for aeolian sand transport in a natural environment.     

Scaling laws for transverse relaxation times

Simple scaling laws are useful tools in understanding the effect of changing parameters in MRI experiments. In this paper the general scaling behavior of the transverse relaxation times is discussed. We consider the dephasing of spins diffusing around a field inhomogeneity inside a voxel. The strong collision approximation is used to describe the diffusion process. The obtained scaling laws are valid over the whole dynamic range from motional narrowing to static dephasing. The dependence of the relaxation times on the external magnetic field, diffusion coefficients of the surrounding medium, and the characteristic scale of the field inhomogeneity is analyzed. For illustration the generally valid scaling laws are applied to the special case of a capillary, usually used as a model of the myocardial BOLD effect.     

Scaling laws for melting ice avalanches

This Letter describes an investigation of interfacial melting in ice-bearing granular flows. It is proposed that energy associated with granular collisions causes melting at an ice particle's surface, which can thus occur at temperatures well below freezing. A laboratory experiment has been designed that allows quantification of this process and its effect on the dynamics of a granular shear flow of ice spheres. This experiment employs a rotating drum, half filled with ice particles, situated in a temperature controlled laboratory. Capillary forces between the wetted melted particle surfaces lead to the clumping of particles and enhanced flow speeds, in turn leading to further melting. Dimensional analysis defines a parameter space for further experimentation.     

Scaling laws and the modern city

The inter-relations and the complexity of modern urban spaces are difficult to analyse in a way that allows improving living conditions or help to ascertain optimal decisions for saving energy or improving sustainability. Carefully designed decisions and guidelines might produce unexpected results because of particularities, or complex sets of reactions from residents or economic counterparts. Complexity tends to increase with size, such as when, for instance, services tend to concentrate in large agglomerations, and transportation needs take on critical importance. Complex systems such as living organisms are known to follow approximate relationships as scaling laws between the variables that describe them. Some of these kinds of relationships are tested in relation to modern developed urban spaces, in which it is possible to find a reasonable continuity with the types of scales seen in living organisms, and some preliminary conclusions are drawn.     

Scaling laws for oxygen discharge plasmas

A fluid model is used to simulate ICP discharges in oxygen for a wide range of conditions under which commercial plasma-chemical reactors typically operate. Simple scaling laws are constructed with which different parameters of discharge plasmas in electronegative gases can be readily estimated from the given external parameters—the specific input power W and the product pL of the gas pressure and the characteristic plasma dimension.     

Scaling laws of complex band random matrices

We study a model of complex band random matrices capable of describing the transitions between three different ensembles of Hermitian matrices: Gaussian orthogonal, Gaussian unitary and Poissonian. Analyzing numerical data we observe new scaling relations based on the generalized localization length of eigenvectors. We show that during transitions between canonical ensembles of random matrices the changes of statistical properties of eigenvalues and eigenvectors are correlated.     

Scaling laws of complex band random matrices

We study a model of complex band random matrices capable of describing the transitions between three different ensembles of Hermitian matrices: Gaussian orthogonal, Gaussian unitary and Poissonian. Analyzing numerical data we observe new scaling relations based on the generalized localization length of eigenvectors. We show that during transitions between canonical ensembles of random matrices the changes of statistical properties of eigenvalues and eigenvectors are correlated.     

Scaling laws for plasma armatures in railguns

A methodology for deriving the electrical and thermodynamic properties of plasma armatures in railgun launchers is presented. The methodology is based on the solution to the one-dimensional, quasi-steady equations for the plasma armature. It is shown that the thermodynamic and transport properties for typical armature materials can be adequately represented by power-law curve fits in the temperature and pressure regimes of interest. To illustrate the methodology, detailed computations for both copper and aluminum armatures are performed. Some discussion is also presented for hydrogen armatures. It is shown that the armature properties predicted by the scaling laws agree very well with those derived from more detailed numerical solutions to the governing differential equations. It is shown that, for both aluminum and copper armatures, the electrical conductivity is a strong function of the current per unit rail height and a weak function of launcher geometry. This dependence is shown to be in reasonable agreement with experimental data compiled over a wide range of gun bore dimensions and operating conditions     

Scaling laws in evolution of large computer programs

The approach is based on a paradigm of self-organized criticality proposed for experimental investigation and theoretical modeling of software evolution. The dynamics of modifications is studied for three free, open source programs Mozilla, Free-BSD, and Emacs using the data from version control systems. Scaling laws typical for the self-organization criticality are found. The model of software evolution presenting the natural selection principle is proposed. The results of numerical and analytical investigation of the model are presented. They are in good agreement with the data collected for the real-world software. The text was submitted by the authors in English.     

Scaling laws for the decay of multiqubit entanglement

We investigate the decay of entanglement of generalized N-particle Greenberger-Horne-Zeilinger (GHZ) states interacting with independent reservoirs. Scaling laws for the decay of entanglement and for its finite-time extinction (sudden death) are derived for different types of reservoirs. The latter is found to increase with N. However, entanglement becomes arbitrarily small, and therefore useless as a resource, much before it completely disappears, around a time which is inversely proportional to the number of particles. We also show that the decay of multiparticle GHZ states can generate bound entangled states.     

Scaling laws in NMR scattering via dipolar fields

Breaking translational symmetry in magnetostatics imparts a scale dependence that is commonly investigated in physics (W. Warren et al., 1993, Science 262, 2005-2008). An interesting and important example arises in nuclear magnetic resonance studies involving the dipolar mean field of adjacent nuclear spins where the scattering (transfer of spatial spin gratings) via intermolecular macroscopic fields carries a signature of the local spatial distribution of the spin density. For arbitrary geometry, the inverse problem of extracting this spin distribution from experiments is intractable. Here we point out a simple, universal crossover in the scaling behavior at the sample's characteristic length scale, xi, of the species fluctuations in the sample along the measurement direction. This behavior is observed experimentally in an oil-water emulsion, an important representation of complex, heterogeneous, soft matter.     

Scaling laws,logarithmic corrections and inner field

Relations for the indices of the logarithmic corrections to the power singularities analogous to the scaling laws for the power indices are presented. Some predictions on values of the logarithmic indices for the d = 4 ferromagnets are made, and the question on the critical behaviour of the d = 2 Ising model specific heat along the critical isotherm is raised.     

Scaling laws in the vortex lattice model of turbulence

The lattice vortex model of the intertial range in turbulence theory is reviewed; the model consists of an array of vortex tubes whose axes coincide with the bonds on a regular lattice, subjected to random stretching and successive scaling, and constrained by conservation laws for energy, specific volume, circulation, helicity, and an energy/vorticity relation. The scaling laws for vorticity are examined in detail, a Hausdorff dimension for the active portion of the vortex array is calculated, the origin of intermittency is exhibited, and it is pointed out that the Kolmogorov — 5/3 power law already accounts for intermittency effects.Partially supported by the Office of Energy Research, U.S. Department of Energy, under contract DE-AC03-76SF0098, and in part by the Office of Naval Research under contract N00014-76-C-0316