Magnetically controlled ballistic deposition. A model of polydisperse granular packing

The flow and deposition of polydisperse granular materials is simulated through the Magnetic Diffusion Limited Aggregation (MDLA) model. The random walk undergone by an entity in the MDLA model is modified such that the trajectories are ballistic in nature, leading to a magnetically controlled ballistic deposition (MBD) model. This allows to obtain important ingredients about a difficult problem that of the nonequilibrium segregation of polydisperse sandpiles and heterogeneous adsorption of a binary distribution of particles which can interact with each other and with an external field. Our detailed results from many simulations of MBD clusters on a two dimensional triangular lattice above a flat surface in a vertical finite size box for binary systems indicates intriguing variations of the density, ''magnetization'', types of clusters, and fractal dimensions. We derive the field and grain interaction dependent susceptibility and compressibility. We deduce a completely new phase diagram for binary granular piles and discuss its complexity inherent to different grain competition and cluster growth probabilities.Comment: 11 pages, 18 figures, submitted to Physica

Granular Matter: a wonderful world of clusters in far-from-equilibrium systems

In this paper, we recall various features of non equilibrium granular systems. Clusters with specific properties are found depending on the packing density, going from loose (a granular gas) to sintered (though brittle) polycrystalline materials. The phase space available can be quite different. Unexpected features, with respect to standard or expected ones in classical fluids or solids, are observed, - like slow relaxation processes or anomalous electrical and thermoelectrical transport property dependences. The cases of various pile structures and the interplay between classical phase transitions and self-organized criticality for avalanches are also outlined.Comment: 7 figures, 37 refs., to be published in Physica

Shock waves in superconducting cosmic strings: growth of current

Intrinsic equations of motion of superconducting cosmic string may admit solutions in the shock-wave form that implies discontinuity of the current term \chi. The hypersurface of discontinuity propagates at finite velocity determined by finite increment \Delta \chi =\chi_+ -\chi_-. The current increases \chi_+>\chi_- in stable shocks but transition between spacelike (\chi >0) and timelike (\chi<0) currents is impossible.Comment: 13 pages, 3 figure

Asymptotic near optimality of the bisection method

Journal ArticleThe bisection method is shown to possess the nearly best rate of convergence for infinitely differentiable functions having zeros of arbitrary multiplicity. If the multiplicity of zeros is bounded, methods are known which have asymptotically at least quadratic rate of convergence

Asymptotic Optimality of the Bisection Method

The bisection method is shown to possess the asymptotically best rate of convergence for infinitely differentiable functions having zeros of arbitrary multiplicity. If the multiplicity of zeros is bounded methods are known which have asymptotically at least quadratic rate of convergence