Upper critical dimension of the KPZ equation

Numerical results for the Directed Polymer model in 1+4 dimensions in various types of disorder are presented. The results are obtained for system size considerably larger than that considered previously. For the extreme strong disorder case (Min-Max system), associated with the Directed Percolation model, the expected value of the meandering exponent, zeta = 0.5 is clearly revealed, with very week finite size effects. For the week disorder case, associated with the KPZ equation, finite size effects are stronger, but the value of seta is clearly seen in the vicinity of 0.57. In systems with "strong disorder" it is expected that the system will cross over sharply from Min-Max behavior at short chains to weak disorder behavior at long chains. This is indeed what we find. These results indicate that 1+4 is not the Upper Critical Dimension (UCD) in the week disorder case, and thus 4+1 does not seem to be the upper critical dimension for the KPZ equation

Classical and quantum regimes of the superfluid turbulence

We argue that turbulence in superfluids is governed by two dimensionless parameters. One of them is the intrinsic parameter q which characterizes the friction forces acting on a vortex moving with respect to the heat bath, with 1/q playing the same role as the Reynolds number Re=UR/\nu in classical hydrodynamics. It marks the transition between the "laminar" and turbulent regimes of vortex dynamics. The developed turbulence described by Kolmogorov cascade occurs when Re >> 1 in classical hydrodynamics, and q << 1 in the superfluid hydrodynamics. Another parameter of the superfluid turbulence is the superfluid Reynolds number Re_s=UR/\kappa, which contains the circulation quantum \kappa characterizing quantized vorticity in superfluids. This parameter may regulate the crossover or transition between two classes of superfluid turbulence: (i) the classical regime of Kolmogorov cascade where vortices are locally polarized and the quantization of vorticity is not important; and (ii) the quantum Vinen turbulence whose properties are determined by the quantization of vorticity. The phase diagram of the dynamical vortex states is suggested.Comment: 12 pages, 1 figure, version accepted in JETP Letter

1000 GeV gamma rays from Cygnus X-3: An update

Measurements of 1000 GeV gamma-rays from Cygnus X-3 made with the University of Durham facility at Dugway, Utah in 1981/82 are reviewed. The light curve of the 4.8 hour modulated emission is updated and shows evidence significant at the 4.4 sigma level for strong emission (9% of the cosmic ray rate) at phase 0.625 and less significant (1.4 sigma level) indications of weaker emission (3% of the cosmic ray rate) at phase 0.125. The effect constituting the excess on the few nights showing the strongest emission appears to arise from the smallest Cerenkov light signals suggesting a steep gamma-ray spectrum. The 1982 data have been searched unsuccessfully for evidence of emission at phase 0.2, in coincidence with the results from the ultra-high energy (extensive Air Showers (EAS) measurements in 1979-1982. A systematic investigation of a long term variation in the strength of the peak of the 4.8 hr modulated 1000 GeV gamma-ray emission has been made. We find that in addition to the approximately 34 d variation reported by us previously, a stronger effect exists at around 19d

The 1000 GeV gamma rays from ms pulsars

The detection of 1000 GeV gamma-rays with the characteristic 6.1 ms periodicity of the radio pulsar PSR 1953 +29 is reported. This result, significant at the 5.4 beta level, provides the first direct evidence for the association of the 6 ms radio pulsar PSR1953+29 with the gamma-ray source 2CG065+0. Extensive observations of the 1.5 ms pulsar PSR 1937 are also reported

Locality and stability of the cascades of two-dimensional turbulence

We investigate and clarify the notion of locality as it pertains to the cascades of two-dimensional turbulence. The mathematical framework underlying our analysis is the infinite system of balance equations that govern the generalized unfused structure functions, first introduced by L'vov and Procaccia. As a point of departure we use a revised version of the system of hypotheses that was proposed by Frisch for three-dimensional turbulence. We show that both the enstrophy cascade and the inverse energy cascade are local in the sense of non-perturbative statistical locality. We also investigate the stability conditions for both cascades. We have shown that statistical stability with respect to forcing applies unconditionally for the inverse energy cascade. For the enstrophy cascade, statistical stability requires large-scale dissipation and a vanishing downscale energy dissipation. A careful discussion of the subtle notion of locality is given at the end of the paper.Comment: v2: 23 pages; 4 figures; minor revisions; resubmitted to Phys. Rev.