Scaling Properties Of Spectra Research Articles

On two-dimensional magnetohydrodynamic turbulence

Numerical studies of decaying two-dimensional (2D) magnetohydrodynamic (MHD) turbulence are presented. Results concern mainly the decay laws of integral quantities and the scaling properties of spectra and structure functions. The self-similarity of the decay is characterized by the invariance of the ratios of resistive and viscous dissipation rates, kinetic and magnetic energies, and mean parallel and perpendicular velocities. The energy decay rate is primarily determined by the conservation of the mean-square magnetic potential, but the process is somewhat retarded at intermediate times by current density condensation in the magnetic eddies. In contrast to the 3D case, the energy spectrum agrees with the Iroshnikov–Kraichnan (IK) law Ek∼k−3/2, but is modified by a strong anomalous bottleneck effect. Structure functions of the Elsässer fields satisfy the property of extended self-similarity, which provides accurate values of the relative scaling exponents. Also the structure functions themselves show clear scaling properties, particularly at the highest Reynolds numbers studied. The scaling exponent ζ2 is consistent with the IK spectrum, but ζ3 and ζ4 remain distinctly below unity, which is surprising in view of an exact relation suggesting ζ3=1. Finally, the role of the tearing mode in 2D MHD turbulence is revisited.

Scaling properties of spectra and eigenfunctions for quantum dynamical and disordered systems

A short review of recent results on quantum chaos and band random matrices is given. Main attention is paid to spectrum statistics and structure of eigenfunctions for the case of strong influence of localization. The relation between level curvature for an ensemble of periodic band random matrices and conductance for quasi one-dimensional disordered models is discussed.

Whole-Region Formula for Single-Particle Distributions and Two-Body Reactions at All Angles

A formula for inclusive distributions ab-?cX is proposed, which incorporates large Pr scaling with power fall-off in pr, limiting behaviour in fragmentation region and approach from below to Feynman scaling in central region. By taking ex­ clusive limit X =d of formula, differential cross section for ab-?cd at all angles is obtained, which exhibits both fixed-angle scaling at large angles and Regge-like be­ haviour at small angles. The parameters in formula are determined by bond numbers of urbaryon lines connecting a, b, c and X (or d). The formula is closely related to structure functions of colliding hadrons. Construction of formula from certain factors assigned to urbaryon lines is suggested. § 1. Introduction and summary The quantum number dependence of inclusive spectra is one of pro­ minent features at large transverse momenta,2l quite similarly to those at small ones. 8l This fact indicates that quantum number flow in hadron collisions is. closely related to energy-momentum flow, reflecting dynamical structure of hadrons. In previous papers,'l we discussed that longitudinal spectra are characterized by flow of urbaryon lines from colliding hadrons to produced ones, and proposed the interpolation formula 5l which gives. a unified description of shapes and scaling properties of spectra in small PT region. In this paper, we attempt to extend formula so as to be able to describe single­ particle distributions in whole kinematical region, including two-body re­ actions at exclusive limit. Our starting bases are following. We define valence urbaryons as ones which characterize internal quantum number of hadrons, and denote number of valence urbaryons in a hadron i by ni.*l. Assuming quark model description of internal quantum numbers of hadrons, we have ni = 2 and 3 for a meson and a baryon, respectively. We take a view that hadron reactions are characterized by bond number niJ which denotes number of valence urbaryons connecting i and j. In general, there may be infinite numbers of urbaryon pairs and gluons in a hadron. The above view implies that