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 for inelastic partial-wave amplitudes and the high-energy behaviour of multiparticle production

t-channel unitarity equations are derived for n-particle overlap functions. Together with s-channel unitarity they lead to scaling laws for the inelastic s-channel partial-wave amplitudes $\text{?}{}_{\mathrm{l}}{}^{\mathrm{(n)}}\text{(s)}$ in the limits $\text{s → ∞, l → ∞ x = l (}\text{μ}\text{√s}\text{)}{}^3\text{=}\text{fixed}$. Assuming the validity of the scaling law in the whole range, allowed by s-channel unitarity — i.e. for $\text{l > L (s) = (α(4μ}{}^2\text{) ? 1) (}\text{s}\text{4μ}\text{)}\text{log}\text{(}\text{s}\text{s}{}_1\text{)}$ we obtain constant production cross sections σ⁽ⁿ⁾(s) at high energies s → ∞ up to s factors.     

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.     

Thermodynamical approach in high-energy scattering

A non-conventional thermodynamical approach earlier for high-energy collisions is considered in more detail. The approach provides a physical interpretation not only of the shape of the hadron form factor but also of the increase in its radius with energy . A precise analysis of experimental data on elastic scattering for is performed with the formulae derived. Predictions in the multi TeV range and comparison of results with recent data of the E 710 Collaboration for 1.8 TeV are made. Agreement occurs when the experimental t-distribution is scaled up by 11%.     

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 of aquatic locomotion

In recent years studies of aquatic locomotion have provided some remarkable insights into the many features of fish swimming performances. This paper derives a scaling relation of aquatic locomotion CD(Re)~2 =(Sw)~2 and its corresponding log law and power law. For power scaling law,(Sw)~2 = β_nRe~((2-1)/n), which is valid within the full spectrum of the Reynolds number Re=UL/v from low up to high, can simply be expressed as the power law of the Reynolds number Re and the swimming number Sw=ωAL/v as Re ∝ (Sw)~σ,with σ=2 for creeping flows,σ=4/3 for laminar flows, σ=10/9 and σ=14/13 for turbulent flows. For log law this paper has derived the scaling law as Sw ∝ Re=(lnRe+1.287), which is even valid for a much wider range of the Reynolds number Re. Both power and log scaling relationships link the locomotory input variables that describe the swimmer's gait A;ω via the swimming number Sw to the locomotory output velocity U via the longitudinal Reynolds number Re, and reveal the secret input-output relationship of aquatic locomotion at different scales of the Reynolds number.     

The axial isoscalar neutral current from inelastic electron-nuclear scattering

Parity violating effects due to neutral currents in isoscalar 0⁺→1⁺ nuclear transitions induced by electron scattering are enhanced owing to the small isoscalar magnetic dipole strength. A polarization asymmetry of the order 10⁻⁴ is expected at q 100 MeV for the ¹²C transition to the 1⁺(T = 0) state at 12.71 MeV. It would allow to single out the (electron vector current) × (hardonic axial isoscalar current) quantum numbers and couplings of the neutral current interaction.     

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 violation in γγ scattering

An unorthodox model is examined which predicts that scaling violations in structure functions are related to properties of the photon vacuum polarization amplitude. The relationship is approximate, but very useful. It reproduces the leading QCD prediction in all cases, and allows, as for instance in γγ scattering, to fill up on what QCD cannot say by itself. There is a simple formula for the total γγ cross-section, valid for all values of the photon mass. Data frome ⁺ e^? annihilation can be fed into it to obtain a fit to the measured photon structure function. The PLUTO data are not all difficult to reproduce.     

Non-eikonal effects in high-energy scattering IV. Inelastic scattering

We calculate amplitudes of inelastically scattered high-energy projectiles. For the example of scattering on ¹²C (T_p = 1 GeV) we demonstrate sizeable non-eikonal corrections in diffraction extrema even for relatively small q². At least part of the anomaly in the 3-distribution may be due to these non-eikonal effects.     

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.     

Self-consistency requirement in high-energy nuclear scattering

Practically all serious calculations of exclusive particle production in ultrarelativistic nuclear or hadronic interactions are performed in the framework of Gribov-Regge theory or the eikonalized parton model scheme. It is the purpose of this paper to point out serious inconsistencies in the above-mentioned approaches. We demonstrate that requiring theoretical self-consistency reduces the freedom in modeling high-energy nuclear scattering enormously, and we introduce a fully self-consistent formulation of the multiple-scattering scheme in the framework of a Gribov-Regge--type effective theory. In addition, we develop new computational techniques which allow for the first time a satisfactory solution of the problem in the sense that calculations of observable quantities can be done strictly within a self-consistent formalism.     

Pauli anisotropy in high-energy deuteron scattering

Antisymmetrization of the deuteron-nucleus system leads to an effective three-body interaction that is quadrupole in the neutron-proton displacement vector. This can cause anisotropic deuteron breakup or polarization of scatered deutrons. The effect is largest at about 100 MeV. A relation to work by Ioanides and Johnson is indicated.     

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.