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Abhik Basu

Publications and source records attributed to Abhik Basu.

90 records · Page 5Linked to original sources
arXiv2011

Fluctuations and symmetries in two-dimensional active gels

Motivated by the unique physical properties of {\em biological active matter}, e.g., cytoskeletal dynamics in eukaryotic cells, we set up {\em effective} two-dimensional (2d) coarse-grained hydrodynamic equations for the dynamics of thin {\em active gels} with polar or nematic symmetries. We use the well-known three-dimensional (3d) descriptions [K. Kruse {\em et al}, {\em Eur. Phys. J E}, {\bf 16}, 5 (2005); A. Basu {\em et al}, {\em Eur. Phys. J E}, {\bf 27}, 149 (2008)] for thin active gel samples confined between parallel plates with appropriate boundary conditions to derive the effective 2d constitutive relations between appropriate thermodynamic fluxes and generalised forces for small deviations from equilibrium. We consider three distinct cases, characterised by spatial symmetries and boundary conditions, and show how such considerations dictate the structure of the constitutive relations. We use these to study the linear instabilities, calculate the correlation functions and the diffusion constant of a small tagged particle, and elucidate their dependences on the {\em activity} or nonequilibrium drive.

cond-mat.stat-mech↗
arXiv2009

Scaling and universality in coupled driven diffusive models

Inspired by the physics of magnetohydrodynamics (MHD) a simplified coupled Burgers-like model in one dimension (1d), a generalization of the Burgers model to coupled degrees of freedom, is proposed to describe 1dMHD. In addition to MHD, this model serves as a 1d reduced model for driven binary fluid mixtures. Here we have performed a comprehensive study of the universal properties of the generalized d-dimensional version of the reduced model. We employ both analytical and numerical approaches. In particular, we determine the scaling exponents and the amplitude-ratios of the relevant two-point time-dependent correlation functions in the model. We demonstrate that these quantities vary continuously with the amplitude of the noise cross-correlation. Further our numerical studies corroborate the continuous dependence of long wavelength and long time-scale physics of the model on the amplitude of the noise cross-correlations, as found in our analytical studies. We construct and simulate lattice-gas models of coupled degrees of freedom in 1d, belonging to the universality class of our coupled Burgers-like model, which display similar behavior. We use a variety of numerical (Monte-Carlo and Pseudospectral methods) and analytical (Dynamic Renormalization Group, Self-Consistent Mode-Coupling Theory and Functional Renormalization Group) approaches for our work. The results from our different approaches complement one another. Possible realizations of our results in various nonequilibrium models are discussed.

cond-mat.stat-mech↗
arXiv2005

Symmetries and novel universal properties of turbulent hydrodynamics in a symmetric binary fluid mixture

We elucidate the universal properties of the nonequilibrium steady states (NESS) in a driven symmetric binary fluid mixture, an example of active advection, in its miscible phase. We use the symmetries of the equations of motion to establish the appropriate form of the structure functions which characterise the statistical properties of the NESS of a driven symmetric binary fluid mixture. We elucidate the universal properties described by the scaling exponents and the amplitude ratios. Our results suggest that these exponents and amplitude ratios vary continuously with the degree of crosscorrelations between the velocity and the gradient of the concentration fields. Furthermore, we demonstrate, in agreement with Celani et al, Phys. Rev. Lett., 89, 234502 (2002, that the conventional structure functions as used in passive scalar turbulence studies exhibit only simple scaling in the problem of symmetric binary fluid mixture even in the weak concentration limit. We also discuss possible experimental verifications of our results.

cond-mat.stat-mech↗
arXiv2005

Universal properties of three-dimensional magnetohydrodynamic turbulence: Do Alfvén waves matter?

We analyse the effects of the propagating Alfvén 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 Alfvén 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 $k^{-5/3}$ in the inertial range where $\bf k$ 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.

cond-mat.stat-mech↗
arXiv2004

Dynamo mechanism: Effects of correlations and viscosities

We analyze the effects of the background velocity and the initial magnetic field correlations, and viscosities on the turbulent dynamo and the α-effect. We calculate the α-coefficients for arbitrary magnetic and fluid viscosities, background velocity and the initial magnetic field correlations. We explicitly demonstrate that the general features of the initial growth and late-time saturation of the magnetic fields due to the non-linear feedback are qualitatively independent of these correlations. We also examine the hydrodynamic limit of the magnetic field growth in a renormalization group framework and discuss the possibilities of suppression of the dynamo growth below a critical rotation. We demonstrate that for Kolmogorov- (K41) type of spectra the Ekman number M >1/2 for dynamo growth to occur.

cond-mat.stat-mech↗
arXiv2003

Scaling in a temperature quench in systems with a Lifshitz point: Nonconserved and conserved order parameters

We study the growth of an N-component (including N=1) order parameter when a system with a Lifshitz point is quenched from the homogeneous disordered state to the ordered states. We study the scaling behaviours of the structure factors for both the non-conserved and conserved order parameters in the long time limit after a quench through the Lifshitz point by using the large-N and renormalisation group (RG) methods. We construct the analogues of Allen-Cahn and Lifshitz-Slyzov growth laws for nonconserved and conserved order parameters which agree with our RG results for N=1. By extending our large-N methods to the anisotropic Lifshitz point we show that the anisotropy is relevant for the growth of the nonconserved order parameter, but irrelevant for the conserved case in the large-N limit. We discuss the effects of mode coupling terms on scaling of the structure factor for the conserved order parameter case. We also consider the ordering dynamics after a quench through an off-Lifshitz point. In a large-N set up we calculate the form of the structure factors of a non-conserved order parameter when a system is quenched from the homogeneous paramegnetic to the modulated phase. We show that after a quench from the paramegnetic to the modulated phase the form of the structure factor violates the standard form of dynamical scaling. Our results compare favourably with the available numerical results.

cond-mat.stat-mech↗
arXiv2003

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.

cond-mat.stat-mech↗
arXiv2002

Dynamo effect beyond the kinematic approximation: suppression of linear instabilities by non-linear feedback

The turbulent dynamo effect, which describes the generation of magnetic fields in astrophysical objects, is described by the dynamo equation. This, in the kinematic (linear) approximation gives an unbounded exponential growth of the long wavelength part of the magnetic fields. Here we, in a systematic diagrammatic, perturbation theory, show how non-linear effects suppress the linear instability and bring down the growth rate to zero in the large time limit. We work with diffferent background velicity spectrum and initial magnetic field correlations. Our results indicate the robustness and very general nature of dynamo growth: It is qualitatively independent of the background velicty and intial magnetic field spectra. We also argue that our results can be justified within the framework of the first order smoothing approximation, as applicable for the full non-linear problem. We discuss our results from the view points of renormalisation group analysis.

nlin.CD↗
arXiv2001

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

We review recent progress in understanding the full phase diagram of a one-dimensional, driven, two-species lattice model [Lahiri and Ramaswamy, PRL 79 (1997) 1150] in which the mobility of each species depends on the density of the other. The model shows three phases. The first is characterised by phase separation of an exceptionally robust sort, termed Strong Phase Separation, which survives at all temperature. The second phase has trivial static correlations, but density fluctuations are transported by a pair of kinematic waves involving both species. In the most interesting case, the two linearised eigenmodes, although nonlinearly coupled, have different dynamic exponents. The third ``phase'' arises at the phase boundary between the first two. Here, the first species evolves autonomously, but its fluctuations influence the evolution of the second, as in the passive scalar problem. The second species then shows phase separation of a delicate sort, with density fluctuations persisting even 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.

cond-mat.stat-mech↗
arXiv2000

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 R.Lahiri and S.Ramaswamy [{\em Phys. Rev. Lett.} {\bf 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 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.

cond-mat↗
arXiv2000

Scaling and noise-crosscorrelations in a Burgers-like model for Magnetohydrodynamics

We study the effects of crosscorrelations of noises on the scaling properties of the correlation functions in a reduced model for Magnetohydrodynamic (MHD) turbulence [A. Basu, J.K Bhattacharjee and S. Ramaswamy [{\em Eur. Phys. J B} {\bf 9}, 725 (1999)]. We show that in {\em dimension d} crosscorrelations with sufficient long wavelength singularity become relevant and take the system to the long range noise fixed point. The crosscorrelations also affect the ratio of energies of the magnetic and velocity fields ($E_b/E_v$) in the strong coupling phase. In dimension $d=1$ the fluctuation-dissipation theorem (FDT) does not hold in presence of short range crosscorrelations. We discuss the possible effects of crosscorrelations on the scaling properties of fully developed MHD turbulence.

nlin.CD↗
arXiv2000

Phase transitions and noise crosscorrelations in a model of directed polymers in a disordered medium

We show that effective interactions mediated by disorder between two directed polymers can be modelled as the crosscorrelation 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 details 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.

cond-mat↗
arXiv1999

Inequivalence of Dynamical Ensembles in a Generalised Driven Diffusive Lattice Gas

We generalise the Driven Diffusive Lattice Gas (DDLG) model by using a combination of Kawasaki and Glauber dynamics. We find via Monte Carlo simulations and perturbation studies that the simplest possible generalisation of the equivalence of the canonical and grand-canonical ensembles, which holds in equilibrium, does not apply for this class of nonequilibrium systems.

cond-mat↗
arXiv1999

Decaying magnetohydrodynamics: effects of initial conditions

We study the effects of homogenous and isotropic initial conditions on decaying Magnetohydrodynamics (MHD). We show that for an initial distribution of velocity and magnetic field fluctuations, appropriately defined structure functions decay as power law in time. We also show that for a suitable choice of initial cross-correlations between velocity and magnetic fields even order structure functions acquire anomalous scaling in time where as scaling exponents of the odd order structure functions remain unchanged. We discuss our results in the context of fully developed MHD turbulence.

chao-dyn↗
arXiv1998

The dynamo effect - A dynamic renormalisation group approach

The Dynamo effect is used to describe the generation of magnetic fields in astrophysical objects. However, no rigorous derivation of the dynamo equation is available. We justify the form of the equation using an Operator Product Expansion (OPE) of the relevant fields. We also calculate the coefficients of the OPE series using a dynamic renormalisation group approach and discuss the time evolution of the initial conditions on the initial seed magnetic field.

cond-mat↗
arXiv1998

Mean Magnetic Field and Noise Cross-Correlation in Magnetohydrodynamic Turbulence: Results from a One-Dimensional Model

We show that a recently proposed [J. Fleischer and P.H. Diamond, {\em Phys. Rev. E}{\bf 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.

cond-mat↗
arXiv1997

Multiscaling in Models of Magnetohydrodynamic Turbulence

From a direct numerical simulation of the MHD equations we show, for the first time, that velocity and magnetic-field structure functions exhibit multiscaling, extended self similarity (ESS), and generalized extended self similarity (GESS). We also propose a new shell model for homogeneous and isotropic MHD turbulence, which preserves all the invariants of ideal MHD, reduces to a well-known shell model for fluid turbulence for zero magnetic field, has no adjustable parameters apart from Reynolds numbers, and exhibits the same multiscaling, ESS, and GESS as the MHD equations. We also study dissipation-range asymptotics and the inertial- to dissipation-range crossover.

chao-dyn↗