Inertial- and Dissipation-Range Asymptotics in Fluid Turbulence

We propose and verify a wave-vector-space version of generalized extended self similarity and broaden its applicability to uncover intriguing, universal scaling in the far dissipation range by computing high-order (\leq 20\/) structure functions numerically for: (1) the three-dimensional, incompressible Navier Stokes equation (with and without hyperviscosity); and (2) the GOY shell model for turbulence. Also, in case (2), with Taylor-microscale Reynolds numbers 4 \times 10^{4} \leq Re_{\lambda} \leq 3 \times 10^{6}\/, we find that the inertial-range exponents (\zeta_{p}\/) of the order - p\/ structure functions do not approach their Kolmogorov value p/3\/ as Re_{\lambda}\/ increases.Comment: RevTeX file, with six postscript figures. epsf.tex macro is used for figure insertion. Packaged using the 'uufiles' utilit

Electromagnetic Polarizabilities of Nucleons bound in 40^{40}Ca, 16^{16}O and 4^4He

Differential cross sections for elastic scattering of photons have been measured for $^{40}$Ca at energies of 58 and 74 MeV and for $^{16}$O and $^4$He at 61 MeV, in the angular range from 45$^o$ to 150$^o$. Evidence is obtained that there are no significant in-medium modifications of the electromagnetic polarizabilities except for those originating from meson exchange currents.Comment: 20 pages including 5 Figure

Hydrodynamics of the Kuramoto-Sivashinsky Equation in Two Dimensions

The large scale properties of spatiotemporal chaos in the 2d Kuramoto-Sivashinsky equation are studied using an explicit coarse graining scheme. A set of intermediate equations are obtained. They describe interactions between the small scale (e.g., cellular) structures and the hydrodynamic degrees of freedom. Possible forms of the effective large scale hydrodynamics are constructed and examined. Although a number of different universality classes are allowed by symmetry, numerical results support the simplest scenario, that being the KPZ universality class.Comment: 4 pages, 3 figure

Anomalous Scaling in the N-Point Functions of Passive Scalar

A recent analysis of the 4-point correlation function of the passive scalar advected by a time-decorrelated random flow is extended to the N-point case. It is shown that all stationary-state inertial-range correlations are dominated by homogeneous zero modes of singular operators describing their evolution. We compute analytically the zero modes governing the N-point structure functions and the anomalous dimensions corresponding to them to the linear order in the scaling exponent of the 2-point function of the advecting velocity field. The implications of these calculations for the dissipation correlations are discussed.Comment: 16 pages, latex fil

Quark-meson coupling model for finite nuclei

A Quark-Meson Coupling (QMC) model is extended to finite nuclei in the relativistic mean-field or Hartree approximation. The ultra-relativistic quarks are assumed to be bound in non-overlapping nucleon bags, and the interaction between nucleons arises from a coupling of vector and scalar meson fields to the quarks. We develop a perturbative scheme for treating the spatial nonuniformity of the meson fields over the volume of the nucleon as well as the nucleus. Results of calculations for spherical nuclei are given, based on a fit to the equilibrium properties of nuclear matter. Several possible extensions of the model are also considered.Comment: 33 pages REVTeX plus 2 postscript figure

Neutron polarizabilities investigated by quasi-free Compton scattering from the deuteron

Measuring Compton scattered photons and recoil neutrons in coincidence, quasi-free Compton scattering by the neutron has been investigated at MAMI (Mainz) at $theta^{lab}_\gamma=136^o$ in an energy range from 200 to 400 MeV. From the data a polarizability difference of $\alpha_n - \beta_n = 9.8 \pm 3.6(stat)^{+2.1}_{-1.1}(syst)\pm 2.2(model)$ in units of $10^{-4}fm^3$ has been determined. In combination with the polarizability sum $\alpha_n+\beta_n= 15.2\pm 0.5$ deduced from photo absorption data, the neutron electric and magnetic polarizabilities, $\alpha_n=12.5\pm 1.8(stat)^{+1.1}_{-0.6}(syst)\pm 1.1(model)$ and $\beta_n = 2.7\mp 1.8(stat)^{+0.6}_{-1.1}(syst)\mp 1.1(model)$, are obtained

Passive Scalar: Scaling Exponents and Realizability

An isotropic passive scalar field $T$ advected by a rapidly-varying velocity field is studied. The tail of the probability distribution $P(\theta,r)$ for the difference $\theta$ in $T$ across an inertial-range distance $r$ is found to be Gaussian. Scaling exponents of moments of $\theta$ increase as $\sqrt{n}$ or faster at large order $n$, if a mean dissipation conditioned on $\theta$ is a nondecreasing function of $|\theta|$. The $P(\theta,r)$ computed numerically under the so-called linear ansatz is found to be realizable. Some classes of gentle modifications of the linear ansatz are not realizable.Comment: Substantially revised to conform with published version. Revtex (4 pages) with 2 postscript figures. Send email to [email protected]

Dynamic Scaling of Ion-Sputtered Surfaces

We derive a stochastic nonlinear equation to describe the evolution and scaling properties of surfaces eroded by ion bombardment. The coefficients appearing in the equation can be calculated explicitly in terms of the physical parameters characterizing the sputtering process. We find that transitions may take place between various scaling behaviors when experimental parameters such as the angle of incidence of the incoming ions or their average penetration depth, are varied.Comment: 13 pages, Revtex, 2 figure

Renormalization Group Analysis of a Noisy Kuramoto-Sivashinsky Equation

We have analyzed the Kuramoto-Sivashinsky equation with a stochastic noise term through a dynamic renormalization group calculation. For a system in which the lattice spacing is smaller than the typical wavelength of the linear instability occurring in the system, the large-distance and long-time behavior of this equation is the same as for the Kardar-Parisi-Zhang equation in one and two spatial dimensions. For the $d=2$ case the agreement is only qualitative. On the other hand, when coarse-graining on larger scales the asymptotic flow depends on the initial values of the parameters.Comment: 8 pages, 5 figures, revte

Sharp Lower Bounds for the Dimension of the Global Attractor of the Sabra Shell Model of Turbulence

In this work we derive a lower bounds for the Hausdorff and fractal dimensions of the global attractor of the Sabra shell model of turbulence in different regimes of parameters. We show that for a particular choice of the forcing and for sufficiently small viscosity term $\nu$, the Sabra shell model has a global attractor of large Hausdorff and fractal dimensions proportional to $\log_\lambda \nu^{-1}$ for all values of the governing parameter $\epsilon$, except for $\epsilon=1$. The obtained lower bounds are sharp, matching the upper bounds for the dimension of the global attractor obtained in our previous work. Moreover, we show different scenarios of the transition to chaos for different parameters regime and for specific forcing. In the ``three-dimensional'' regime of parameters this scenario changes when the parameter $\epsilon$ becomes sufficiently close to 0 or to 1. We also show that in the ``two-dimensional'' regime of parameters for a certain non-zero forcing term the long-time dynamics of the model becomes trivial for any value of the viscosity