Pressure and intermittency in passive vector turbulence

We investigate the scaling properties a model of passive vector turbulence with pressure and in the presence of a large-scale anisotropy. The leading scaling exponents of the structure functions are proven to be anomalous. The anisotropic exponents are organized in hierarchical families growing without bound with the degree of anisotropy. Nonlocality produces poles in the inertial-range dynamics corresponding to the dimensional scaling solution. The increase with the P\'{e}clet number of hyperskewness and higher odd-dimensional ratios signals the persistence of anisotropy effects also in the inertial range.Comment: 4 pages, 1 figur

The H2+_2^+ molecular ion: a solution

Combining the WKB expansion at large distances and Perturbation Theory at small distances it is constructed a compact uniform approximation for eigenfunctions. For lowest states 1s\si_{g} and 2p\si_{u} this approximation provides the relative accuracy $\lesssim 10^{-5}$ (5 s.d.) for any real $x$ in eigenfunctions and for total energy $E(R)$ it gives 10-11 s.d. for internuclear distances $R \in [0,50]$. Corrections to proposed approximations are evaluated. Separation constants and the oscillator strength for the transition 1s\si_{g} \rar 2p\si_{u} are calculated and compared with existing data.Comment: 16 pages, 4 figures, 6 tables, typos are corrected and small additions are inserted, to be published at JPB (fast track comm

On Prospects for Exploration of Supersymmetry in Double Beta Decay Experiments

We analyze constraints on the parameters of the R-parity violating supersymmetry which can be extracted from non-observation of the neutrinoless nuclear double beta decay ($0\nu\beta\beta$) at a given half-life lower bound. Our analysis covers a large class of phenomenologically viable R-parity violating SUSY models. We introduce special characteristics: the SUSY sensitivity of a $\beta\beta$ decaying isotope and the SUSY reach of a $0\nu\beta\beta$ experiment. The former provides a physical criterion for a selection of the most promising isotopes for SUSY searches and the latter gives a measure of success for a $0\nu\beta\beta$ experiment in exploring the R-parity violating SUSY parameter space. On this basis we discuss prospects for exploration of supersymmetry in various $0\nu\beta\beta$ experiments.Comment: 11 pages, 5 Postscript figures. Modified and updated version is printed also in Proc. of NANP97 (JINR, Dubna, July 7--11, 1997): Phys. Atom Nucl, 1998, 61, vol. 6, p.1092--109

Renormalization group in the infinite-dimensional turbulence: third-order results

The field theoretic renormalization group is applied to the stochastic Navier-Stokes equation with the stirring force correlator of the form k^(4-d-2\epsilon) in the d-dimensional space, in connection with the problem of construction of the 1/d expansion for the fully developed fluid turbulence beyond the scope of the standard epsilon expansion. It is shown that in the large-d limit the number of the Feynman diagrams for the Green function (linear response function) decreases drastically, and the technique of their analytical calculation is developed. The main ingredients of the renormalization group approach -- the renormalization constant, beta function and the ultraviolet correction exponent omega, are calculated to order epsilon^3 (three-loop approximation). The two-point velocity-velocity correlation function, the Kolmogorov constant C_K in the spectrum of turbulent energy and the inertial-range skewness factor S are calculated in the large-d limit to third order of the epsilon expansion. Surprisingly enough, our results for C_K are in a reasonable agreement with the existing experimental estimates.Comment: 30 pages with EPS figure