97,390 research outputs found

    A Novel Approach to Discontinuous Bond Percolation Transition

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    We introduce a bond percolation procedure on a DD-dimensional lattice where two neighbouring sites are connected by NN channels, each operated by valves at both ends. Out of a total of NN, randomly chosen nn valves are open at every site. A bond is said to connect two sites if there is at least one channel between them, which has open valves at both ends. We show analytically that in all spatial dimensions, this system undergoes a discontinuous percolation transition in the NN\to \infty limit when γ=lnnlnN\gamma =\frac{\ln n}{\ln N} crosses a threshold. It must be emphasized that, in contrast to the ordinary percolation models, here the transition occurs even in one dimensional systems, albeit discontinuously. We also show that a special kind of discontinuous percolation occurs only in one dimension when NN depends on the system size.Comment: 6 pages, 6 eps figure

    Universal properties of three-dimensional magnetohydrodynamic turbulence: Do Alfv\'en waves matter?

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    We analyse the effects of the propagating Alfv\'en waves, arising due to non-zero mean magnetic fields, on the nonequilibrium steady states of three-dimensional (3d) homogeneous Magnetohydrodynamic (MHD) turbulence. In particular, the effects of Alfv\'en waves on the universal properties of 3dMHD turbulence are studied in a one-loop self-consistent mode-coupling approach. We calculate the kinetic- and magnetic energy-spectra. We find that {\em even} in the presence of a mean magnetic field the energy spectra are Kolmogorov-like, i.e., scale as k5/3k^{-5/3} in the inertial range where k\bf k is a Fourier wavevector belonging to the inertial range. We also elucidate the multiscaling of the structure functions in a log-normal model by evaluating the relevant intermittency exponents, and our results suggest that the multiscaling deviations from the simple Kolmogorov scaling of the structure functions decrease with increasing strength of the mean magnetic field. Our results compare favourably with many existing numerical and observational results.Comment: To appear in JSTAT (2005