arXiv subjects

Dibyendu Das

Publications and source records attributed to Dibyendu Das.

At least 55 records · Page 3Linked to original sources

arXiv2012

Spatial Structures and Giant Number Fluctuations in Models of Active Matter

The large scale fluctuations of the ordered state in active matter systems are usually characterised by studying the "giant number fluctuations" of particles in any finite volume, as compared to the expectations from the central limit theorem. However, in ordering systems, the fluctuations in density ordering are often captured through their structure functions deviating from Porod law. In this paper we study the relationship between giant number fluctuations and structure functions, for different models of active matter as well as other non-equilibrium systems. A unified picture emerges, with different models falling in four distinct classes depending on the nature of their structure functions. For one class, we show that experimentalists may find Porod law violation, by measuring subleading corrections to the number fluctuations.

cond-mat.soft↗

arXiv2011

Dynamics of a flexible polymer in planar mixed flow

We present exact spatio-temporal correlation functions of a Rouse polymer chain submerged in a fluid having planar mixed flow, in the steady state. Using these correlators, determination of the time scale distribution functions associated with the first-passage tumbling events is difficult in general; it was done recently in Phys. Rev. Lett.,101, 188301 (2008), for the special case of "simple shear" flow. We show here that the method used in latter paper fails for the general mixed flow problem. We also give many new estimates of the exponent $θ$ associated with the exponential tail of the angular tumbling time distribution in the case of simple shear

cond-mat.stat-mech↗

arXiv2011

Intrinsic noise induced resonance in presence of sub-threshold signal in Brusselator

In a system of non-linear chemical reactions called the Brusselator, we show that {\it intrinsic noise} can be regulated to drive it to exhibit resonance in the presence of a sub-threshold signal. The phenomena of periodic stochastic resonance and aperiodic stochastic resonance, hitherto studied mostly with extrinsic noise, is demonstrated here to occur with inherent systemic noise using exact stochastic simulation algorithm due to Gillespie. The role of intrinsic noise in a couple of other phenomena is also discussed.

physics.chem-ph↗

arXiv2011

Coarse grained dynamics of the freely cooling granular gas in one dimension

We study the dynamics and structure of clusters in the inhomogeneous clustered regime of a freely cooling granular gas of point particles in one dimension. The coefficient of restitution is modeled as $r_0<1$ or 1 depending on whether the relative speed is greater or smaller than a velocity scale $δ$. The effective fragmentation rate of a cluster is shown to rise sharply beyond a $δ$ dependent time scale. This crossover is coincident with the velocity fluctuations within a cluster becoming order $δ$. Beyond this crossover time, the cluster size distribution develops a nontrivial power law distribution, whose scaling properties are related to those of the velocity fluctuations. We argue that these underlying features are responsible behind the recently observed nontrivial coarsening behaviour in the one dimensional freely cooling granular gas.

cond-mat.soft↗

arXiv2011

Lattice models for ballistic aggregation in one-dimension

We propose two lattice models in one dimension, with stochastically hopping particles which aggregate on contact. The hops are guided by "velocity rates" which themselves evolve according to the rules of ballistic aggregation as in a sticky gas in continuum. Our lattice models have both velocity and density fields and an appropriate real time evolution, such that they can be compared directly with event driven molecular dynamics (MD) results for the sticky gas. We demonstrate numerically that the long time and large distance behavior of the lattice models are identical to that of the MD, and some exact results known for the sticky gas. In particular, the exactly predicted form of the non-Gaussian tail of the velocity distribution function is clearly exhibited. This correspondence of the lattice models and the sticky gas in continuum is nontrivial, as the latter has a deterministic dynamics with local kinematic constraint, in contrast with the former; yet the spatial velocity profiles (with shocks) of the lattice models and the MD have striking match.

cond-mat.stat-mech↗

arXiv2009

Predicting the coherence resonance curve using a semi-analytical treatment

Emergence of noise induced regularity or Coherence Resonance in nonlinear excitable systems is well known. We explain theoretically why the normalized variance ($V_{N}$) of inter spike time intervals, which is a measure of regularity in such systems, has a unimodal profile. Our semi-analytic treatment of the associated spiking process produces a general yet simple formula for $V_{N}$, which we show is in very good agreement with numerics in two test cases, namely the FitzHugh-Nagumo model and the Chemical Oscillator model.

cond-mat.stat-mech↗

arXiv2009

On the equivalence of the freely cooling granular gas to the sticky gas

A freely cooling granular gas with velocity dependent restitution coefficient is studied in one dimension. The restitution coefficient becomes near elastic when the relative velocity of the colliding particles is less than a velocity scale $δ$. Different statistical quantities namely density distribution, occupied and empty cluster length distributions, and spatial density and velocity correlation functions, are obtained using event driven molecular dynamic simulations. We compare these with the corresponding quantities of the sticky gas (inelastic gas with zero coefficient of restitution). We find that in the inhomogeneous cooling regime, for times smaller than a crossover time $t_1$ where $t_1 \sim δ^{-1}$, the behaviour of the granular gas is equivalent to that of the sticky gas. When $δ\rt 0$, then $t_1 \rt \infty$ and hence, the results support an earlier claim that the freely cooling inelastic gas is described by the inviscid Burgers equation. For a real granular gas with finite $δ$, the existence of the time scale $t_1$ shows that, for large times, the granular gas is not described by the inviscid Burgers equation.

cond-mat.soft↗

arXiv2008

Accurate statistics of a flexible polymer chain in shear flow

We present exact and analytically accurate results for the problem of a flexible polymer chain in shear flow. Under such a flow the polymer tumbles, and the probability distribution of the tumbling times $τ$ of the polymer decays exponentially as $\sim \exp(-ατ/τ_0)$ (where $τ_0$ is the longest relaxation time). We show that for a Rouse chain, this nontrivial constant $α$ can be calculated in the limit of large Weissenberg number (high shear rate) and is in excellent agreement with our simulation result of $α\simeq 0.324$. We also derive exactly the distribution functions for the length and the orientational angles of the end-to-end vector of the polymer.

cond-mat.stat-mech↗

arXiv2008

Critical behavior of loops and biconnected clusters on fractals of dimension d < 2

We solve the O(n) model, defined in terms of self- and mutually avoiding loops coexisting with voids, on a 3-simplex fractal lattice, using an exact real space renormalization group technique. As the density of voids is decreased, the model shows a critical point, and for even lower densities of voids, there is a dense phase showing power-law correlations, with critical exponents that depend on n, but are independent of density. At n=-2 on the dilute branch, a trivalent vertex defect acts as a marginal perturbation. We define a model of biconnected clusters which allows for a finite density of such vertices. As n is varied, we get a line of critical points of this generalized model, emanating from the point of marginality in the original loop model. We also study another perturbation of adding local bending rigidity to the loop model, and find that it does not affect the universality class.

cond-mat.stat-mech↗

arXiv2007

Violation of Porod law in a freely cooling granular gas in one dimension

We study a model of freely cooling inelastic granular gas in one dimension, with a restitution coefficient which approaches the elastic limit below a relative velocity scale v. While at early times (t << 1/v) the gas behaves as a completely inelastic sticky gas conforming to predictions of earlier studies, at late times (t >> 1/v) it exhibits a new fluctuation dominated phase ordering state. We find distinct scaling behavior for the (i) density distribution function, (ii) occupied and empty gap distribution functions, (iii) the density structure function and (iv) the velocity structure function, as compared to the completely inelastic sticky gas. The spatial structure functions (iii) and (iv) violate the Porod law. Within a mean-field approximation, the exponents describing the structure functions are related to those describing the spatial gap distribution functions.

cond-mat.stat-mech↗

arXiv2007

Persistence of a Rouse polymer chain under transverse shear flow

We consider a single Rouse polymer chain in two dimensions in presence of a transverse shear flow along the $x$ direction and calculate the persistence probability $P_0(t)$ that the $x$ coordinate of a bead in the bulk of the chain does not return to its initial position up to time $t$. We show that the persistence decays at late times as a power law, $P_0(t)\sim t^{-θ}$ with a nontrivial exponent $θ$. The analytical estimate of $θ=0.359...$ obtained using an independent interval approximation is in excellent agreement with the numerical value $θ\approx 0.360\pm 0.001$.

cond-mat.stat-mech↗

arXiv2006

Motion of a random walker in a quenched power law correlated velocity field

We study the motion of a random walker in one longitudinal and d transverse dimensions with a quenched power law correlated velocity field in the longitudinal x-direction. The model is a modification of the Matheron-de Marsily (MdM) model, with long-range velocity correlation. For a velocity correlation function, dependent on transverse co-ordinates y as 1/(a+|{y_1 - y_2}|)^alpha, we analytically calculate the two-time correlation function of the x-coordinate. We find that the motion of the x-coordinate is a fractional Brownian motion (fBm), with a Hurst exponent H = max [1/2, (1- alpha/4), (1-d/4)]. From this and known properties of fBM, we calculate the disorder averaged persistence probability of x(t) up to time t. We also find the lines in the parameter space of d and alpha along which there is marginal behaviour. We present results of simulations which support our analytical calculation.

cond-mat.stat-mech↗

arXiv2005

Critical Dynamics of Dimers: Implications for the Glass Transition

The Adam-Gibbs view of the glass transition relates the relaxation time to the configurational entropy, which goes continuously to zero at the so-called Kauzmann temperature. We examine this scenario in the context of a dimer model with an entropy vanishing phase transition, and stochastic loop dynamics. We propose a coarse-grained master equation for the order parameter dynamics which is used to compute the time-dependent autocorrelation function and the associated relaxation time. Using a combination of exact results, scaling arguments and numerical diagonalizations of the master equation, we find non-exponential relaxation and a Vogel-Fulcher divergence of the relaxation time in the vicinity of the phase transition. Since in the dimer model the entropy stays finite all the way to the phase transition point, and then jumps discontinuously to zero, we demonstrate a clear departure from the Adam-Gibbs scenario. Dimer coverings are the "inherent structures" of the canonical frustrated system, the triangular Ising antiferromagnet. Therefore, our results provide a new scenario for the glass transition in supercooled liquids in terms of inherent structure dynamics.

cond-mat.stat-mech↗

arXiv2004

Persistence of Randomly Coupled Fluctuating Interfaces

We study the persistence properties in a simple model of two coupled interfaces characterized by heights h_1 and h_2 respectively, each growing over a d-dimensional substrate. The first interface evolves independently of the second and can correspond to any generic growing interface, e.g., of the Edwards-Wilkinson or of the Kardar-Parisi-Zhang variety. The evolution of h_2, however, is coupled to h_1 via a quenched random velocity field. In the limit d\to 0, our model reduces to the Matheron-de Marsily model in two dimensions. For d=1, our model describes a Rouse polymer chain in two dimensions advected by a transverse velocity field. We show analytically that after a long waiting time t_0\to \infty, the stochastic process h_2, at a fixed point in space but as a function of time, becomes a fractional Brownian motion with a Hurst exponent, H_2=1-β_1/2, where β_1 is the growth exponent characterizing the first interface. The associated persistence exponent is shown to be θ_s^2=1-H_2=β_1/2. These analytical results are verified by numerical simulations.

cond-mat.stat-mech↗

arXiv2004

Landau theory of glassy dynamics

An exact solution of a Landau model of an order-disorder transition with activated critical dynamics is presented. The model describes a funnel-shaped topography of the order parameter space in which the number of energy lowering trajectories rapidly diminishes as the ordered ground-state is approached. This leads to an asymmetry in the effective transition rates which results in a non-exponential relaxation of the order-parameter fluctuations and a Vogel-Fulcher-Tammann divergence of the relaxation times, typical of a glass transition. We argue that the Landau model provides a general framework for studying glassy dynamics in a variety of systems.

cond-mat.stat-mech↗

arXiv2003

Two-dimensional O(n) model in a staggered field

Nienhuis' truncated O(n) model gives rise to a model of self-avoiding loops on the hexagonal lattice, each loop having a fugacity of n. We study such loops subjected to a particular kind of staggered field w, which for n -> infinity has the geometrical effect of breaking the three-phase coexistence, linked to the three-colourability of the lattice faces. We show that at T = 0, for w > 1 the model flows to the ferromagnetic Potts model with q=n^2 states, with an associated fragmentation of the target space of the Coulomb gas. For T>0, there is a competition between T and w which gives rise to multicritical versions of the dense and dilute loop universality classes. Via an exact mapping, and numerical results, we establish that the latter two critical branches coincide with those found earlier in the O(n) model on the triangular lattice. Using transfer matrix studies, we have found the renormalisation group flows in the full phase diagram in the (T,w) plane, with fixed n. Superposing three copies of such hexagonal-lattice loop models with staggered fields produces a variety of one or three-species fully-packed loop models on the triangular lattice with certain geometrical constraints, possessing integer central charges 0 <= c <= 6. In particular we show that Benjamini and Schramm's RGB loops have fractal dimension D_f = 3/2.

cond-mat.stat-mech↗

arXiv2002

Trap dominated dynamics of classical dimer models

We consider dynamics of classical dimer models undergoing a phase transition to an ordered, frozen state. Relaxation processes are dominated by traps which are entropic in origin and can be traced to the locally jammed nature of the dimer states. Depending on the nature of the phase transition, critical dynamics are characterized either by an exponential, or sub-exponential in time relaxation of the order parameter. In the latter case relaxation time scales diverge {\em exponentially} as the critical point is approached, following the Vogel-Fulcher law.

cond-mat.stat-mech↗

arXiv2002

Aggregate formation in a system of coagulating and fragmenting particles with mass-dependent diffusion rates

The effect of introducing a mass dependent diffusion rate ~ m^{-alpha} in a model of coagulation with single-particle break up is studied both analytically and numerically. The model with alpha=0 is known to undergo a nonequilibrium phase transition as the mass density in the system is varied from a phase with an exponential distribution of mass to a phase with a power-law distribution of masses in addition to a single infinite aggregate. This transition is shown to be curbed, at finite densities, for all alpha > 0 in any dimension. However, a signature of this transition is seen in finite systems in the form of a large aggregate and the finite size scaling implications of this are characterized. The exponents characterizing the steady state probability that a randomly chosen site has mass m are calculated using scaling arguments. The full probability distribution is obtained within a mean field approximation and found to compare well with the results from numerical simulations in one dimension.

cond-mat.stat-mech↗