Abhik Basu

Weak and strong dynamic scaling in a one-dimensional driven coupled-field model: effects of kinematic waves.

We study the coupled dynamics of the displacement fields in a one-dimensional coupled-field model for drifting crystals, first proposed by Lahiri and Ramaswamy [Phys. Rev. Lett. 79, 1150 (1997)]. We present some exact results for the steady state and the current in the lattice version of the model for a special subspace in the parameter space, within the region where the model displays kinematic waves. We use these results to construct the effective continuum equations corresponding to the lattice model. These equations decouple at the linear level in terms of the eigenmodes. We examine the long-time, large-distance properties of the correlation functions of the eigenmodes by using symmetry arguments, Monte Carlo simulations, and self-consistent mode-coupling methods. For most parameter values, the scaling exponents of the Kardar-Parisi-Zhang equation are obtained. However, for certain symmetry-determined values of the coupling constants the two eigenmodes, although nonlinearly coupled, are characterized by two distinct dynamic exponents. We discuss the possible application of the dynamic renormalization group in this context.

Statistical properties of driven magnetohydrodynamic turbulence in three dimensions: Novel universality

We analyse the universal properties of nonequilibrium steady states of driven magnetohydrodynamic (MHD) turbulence in three dimensions (3d). We elucidate the dependence of various phenomenologically important dimensionless constants on the symmetries of the two-point correlation functions. We, for the first time, also suggest the intriguing possibility of multiscaling universality class varying continuously with certain dimensionless parameters. The experimental and theoretical implications of our results are discussed.

Mean magnetic field and noise cross-correlation in magnetohydrodynamic turbulence: results from a one-dimensional model

Abstract:We show that a recently proposed [J. Fleischer, P.H. Diamond, Phys. Rev. E 58, R2709 (1998)] one-dimensional Burgers-like model for magnetohydrodynamics (MHD) is in effect identical to existing models for drifting lines and sedimenting lattices. We use the model to demonstrate, contrary to claims in the literature, that the energy spectrum of MHD turbulence should be independent of mean magnetic field and that cross-correlations between the noise sources for the velocity and magnetic fields cannot change the structure of the equations under renormalisation. We comment on the scaling and the multiscaling properties of the stochastically forced version of the model.

Coupled nonequilibrium growth equations: self-consistent mode coupling using vertex renormalization

We find that studying the simplest of the coupled nonequilibrium growth equations of Barabasi by self-consistent mode coupling requires the use of dressed vertices. Using the vertex renormalization, we find a roughening exponent which already in the leading order is quite close to the numerical value.

Phase Diagram of a Two-Species Lattice Model with a Linear Instability

We discuss the properties of a one-dimensional lattice model of a driven system with two species of particles in which the mobility of one species depends on the density of the other. This model was introduced by Lahiri and Ramaswamy ( Phys . Rev. Lett ., 79 , 1150 (1997)) in the context of sedimenting colloidal crystals, and its continuum version was shown to exhibit an instability arising from linear gradient couplings. In this paper we review recent progress in understanding the full phase diagram of the model. There are three phases. In the first, the steady state can be determined exactly along a representative locus using the condition of detailed balance. The system shows phase separation of an exceptionally robust sort, termed strong phase separation, which survives at all temperatures. The second phase arises in the threshold case where the first species evolves independently of the second, but the fluctuations of the first influence the evolution of the second, as in the passive scalar problem. The second species then shows phase separation of a delicate sort, in which long-range order coexists with fluctuations which do not damp down in the large-size limit. This fluctuation-dominated phase ordering is associated with power law decays in cluster size distributions and a breakdown of the Porod law. The third phase is one with a uniform overall density, and along a representative locus the steady state is shown to have product measure form. Density fluctuations are transported by two kinematic waves, each involving both species and coupled at the nonlinear level. Their dissipation properties are governed by the symmetries of these couplings, which depend on the overall densities. In the most interesting case, the dissipation of the two modes is characterized by different critical exponents, despite the nonlinear coupling.

Phase transitions and noise cross-correlations in a model of directed polymers in a disordered medium

We show that effective interactions mediated by disorder between two directed polymers can be modeled as the cross-correlation of noises in the Kardar-Parisi-Zhang (KPZ) equations satisfied by the respective free energies of these polymers. When there are two polymers, disorder introduces attractive interactions between them. We analyze the phase diagram in detail and show that these interactions lead to new phases in the phase diagram. We show that, even in dimension d=1, the two directed polymers see the attraction only if the strength of the disorder potential exceeds a threshold value. We extend our calculations to show that if there are m polymers in the system, then m-body interactions are generated in the disorder averaged effective free energy.

Dynamo mechanism: Effects of correlations and viscosities

Abstract.We analyze the effects of the background velocity and the initial magnetic field correlations, and viscosities on the turbulent dynamo and the

Decaying magnetohydrodynamics: Effects of initial conditions

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The dynamo effect?a dynamic renormalisation group approach

-effect. We calculate the

MULTISCALING IN MODELS OF MAGNETOHYDRODYNAMIC TURBULENCE

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