Ocean swell within the kinetic equation for water waves

Effects of wave-wave interactions on ocean swell are studied. Results of extensive simulations of swell evolution within the duration-limited setup for the kinetic Hasselmann equation at long times up to $10^6$ seconds are presented. Basic solutions of the theory of weak turbulence, the so-called Kolmogorov-Zakharov solutions, are shown to be relevant to the results of the simulations. Features of self-similarity of wave spectra are detailed and their impact on methods of ocean swell monitoring are discussed. Essential drop of wave energy (wave height) due to wave-wave interactions is found to be pronounced at initial stages of swell evolution (of order of 1000 km for typical parameters of the ocean swell). At longer times wave-wave interactions are responsible for a universal angular distribution of wave spectra in a wide range of initial conditions.Comment: Submitted to Journal of Geophysical Research 18 July 201

Hopping Conductivity of a Nearly-1d Fractal: a Model for Conducting Polymers

We suggest treating a conducting network of oriented polymer chains as an anisotropic fractal whose dimensionality D=1+\epsilon is close to one. Percolation on such a fractal is studied within the real space renormalization group of Migdal and Kadanoff. We find that the threshold value and all the critical exponents are strongly nonanalytic functions of \epsilon as \epsilon tends to zero, e.g., the critical exponent of conductivity is \epsilon^{-2}\exp (-1-1/\epsilon). The distribution function for conductivity of finite samples at the percolation threshold is established. It is shown that the central body of the distribution is given by a universal scaling function and only the low-conductivity tail of distribution remains $\epsilon$-dependent. Variable range hopping conductivity in the polymer network is studied: both DC conductivity and AC conductivity in the multiple hopping regime are found to obey a quasi-1d Mott law. The present results are consistent with electrical properties of poorly conducting polymers.Comment: 27 pages, RevTeX, epsf, 5 .eps figures, to be published in Phys. Rev.

Dimensionally Reduced SYM_4 as Solvable Matrix Quantum Mechanics

We study the quantum mechanical model obtained as a dimensional reduction of N=1 super Yang-Mills theory to a periodic light-cone "time". After mapping the theory to a cohomological field theory, the partition function (with periodic boundary conditions) regularized by a massive term appears to be equal to the partition function of the twisted matrix oscillator. We show that this partition function perturbed by the operator of the holonomy around the time circle is a tau function of Toda hierarchy. We solve the model in the large N limit and study the universal properties of the solution in the scaling limit of vanishing perturbation. We find in this limit a phase transition of Gross-Witten type.Comment: 29 pages, harvmac, 1 figure, formulas in appendices B and C correcte

Stationary states of an electron in periodic structures in a constant uniform electrical field

On the basis of the transfer matrix technique an analytical method to investigate the stationary states, for an electron in one-dimensional periodic structures in an external electrical field, displaying the symmetry of the problem is developed. These solutions are shown to be current-carrying. It is also shown that the electron spectrum for infinite structures is continuous, and the corresponding wave functions do not satisfy the symmetry condition of the problem.Comment: 10 pages (Latex), no figures, in the revised variant some mistakes in the English text are corrected and also the first two paragraphs in the Conclusion are refined (Siberian physical-technical institute at the Tomsk state university, Tomsk, Russia