Searcharxiv⌕ Search

arXiv subjects

Debabrata Panja

Publications and source records attributed to Debabrata Panja.

At least 55 records · Page 3Linked to original sources
arXiv2008

Pore-blockade Times for Field-Driven Polymer Translocation

We study pore blockade times for a translocating polymer of length $N$, driven by a field $E$ across the pore in three dimensions. The polymer performs Rouse dynamics, i.e., we consider polymer dynamics in the absence of hydrodynamical interactions. We find that the typical time the pore remains blocked during a translocation event scales as $\sim N^{(1+2ν)/(1+ν)}/E$, where $ν\simeq0.588$ is the Flory exponent for the polymer. In line with our previous work, we show that this scaling behaviour stems from the polymer dynamics at the immediate vicinity of the pore -- in particular, the memory effects in the polymer chain tension imbalance across the pore. This result, along with the numerical results by several other groups, violates the lower bound $\sim N^{1+ν}/E$ suggested earlier in the literature. We discuss why this lower bound is incorrect and show, based on conservation of energy, that the correct lower bound for the pore-blockade time for field-driven translocation is given by $ηN^{2ν}/E$, where $η$ is the viscosity of the medium surrounding the polymer.

cond-mat.soft↗
arXiv2007

Polymer Translocation out of Planar Confinements

Polymer translocation in three dimensions out of planar confinements is studied in this paper. Three membranes are located at $z=-h$, $z=0$ and $z=h_1$. These membranes are impenetrable, except for the middle one at $z=0$, which has a narrow pore. A polymer with length $N$ is initially sandwiched between the membranes placed at $z=-h$ and $z=0$ and translocates through this pore. We consider strong confinement (small $h$), where the polymer is essentially reduced to a two-dimensional polymer, with a radius of gyration scaling as $R^{\tinytext{(2D)}}_g \sim N^{ν_{\tinytext{2D}}}$; here, $ν_{\tinytext{2D}}=0.75$ is the Flory exponent in two dimensions. The polymer performs Rouse dynamics. Based on theoretical analysis and high-precision simulation data, we show that in the unbiased case $h=h_1$, the dwell-time $τ_d$ scales as $N^{2+ν_{\tinytext{2D}}}$, in perfect agreement with our previously published theoretical framework. For $h_1=\infty$, the situation is equivalent to field-driven translocation in two dimensions. We show that in this case $τ_d$ scales as $N^{2ν_{\tinytext{2D}}}$, in agreement with several existing numerical results in the literature. This result violates the earlier reported lower bound $N^{1+ν}$ for $τ_d$ for field-driven translocation. We argue, based on energy conservation, that the actual lower bound for $τ_d$ is $N^{2ν}$ and not $N^{1+ν}$. Polymer translocation in such theoretically motivated geometries thus resolves some of the most fundamental issues that are the subjects of much heated debate in recent times.

cond-mat.soft↗
arXiv2007

Extreme Associated Functions: Optimally Linking Local Extremes to Large-scale Atmospheric Circulation Structures

We present a new statistical method to optimally link local weather extremes to large-scale atmospheric circulation structures. The method is illustrated using July-August daily mean temperature at 2m height (T2m) time-series over the Netherlands and 500 hPa geopotential height (Z500) time-series over the Euroatlantic region of the ECMWF reanalysis dataset (ERA40). The method identifies patterns in the Z500 time-series that optimally describe, in a precise mathematical sense, the relationship with local warm extremes in the Netherlands. Two patterns are identified; the most important one corresponds to a blocking high pressure system leading to subsidence and calm, dry and sunny conditions over the Netherlands. The second one corresponds to a rare, easterly flow regime bringing warm, dry air into the region. The patterns are robust; they are also identified in shorter subsamples of the total dataset. The method is generally applicable and might prove useful in evaluating the performance of climate models in simulating local weather extremes.

physics.ao-ph↗
arXiv2007

Anomalous Dynamics of Unbiased Polymer Translocation through a Narrow Pore

We consider a polymer of length $N$ translocating through a narrow pore in the absence of external fields. Characterization of its purportedly anomalous dynamics has so far remained incomplete. We show that the polymer dynamics is anomalous until the Rouse time $τ_{R}\sim N^{1+2ν}$, with a mean square displacement through the pore consistent with $t^{(1+ν)/(1+2ν)}$, with $ν\approx0.588$ the Flory exponent. This is shown to be directly related to a decay in time of the excess monomer density near the pore as $t^{-(1+ν)/(1+2ν)}\exp(-t/τ_{R})$. Beyond the Rouse time translocation becomes diffusive. In consequence of this, the dwell-time $τ_{d}$, the time a translocating polymer typically spends within the pore, scales as $N^{2+ν}$, in contrast to previous claims.

cond-mat.soft↗
arXiv2007

Passage Times for Polymer Translocation Pulled through a Narrow Pore

We study the passage times of a translocating polymer of length $N$ in three dimensions, while it is pulled through a narrow pore with a constant force $F$ applied to one end of the polymer. At small to moderate forces, satisfying the condition $FN^ν/k_BT\lesssim1$, where $ν\approx0.588$ is the Flory exponent for the polymer, we find that $τ_N$, the mean time the polymer takes to leave the pore, scales as $N^{2+ν}$ independent of $F$, in agreement with our earlier result for F=0. At strong forces, i.e., for $FN^ν/k_BT\gg1$, the behaviour of the passage time crosses over to $τ_N\sim N^2/F$. We show here that these behaviours stem from the polymer dynamics at the immediate vicinity of the pore -- in particular, the memory effects in the polymer chain tension imbalance across the pore.

cond-mat.soft↗
arXiv2007

Effect of Anomalous Dynamics on Unbiased Polymer Translocation

In this paper, we investigate the microscopic dynamics of a polymer of length $N$ translocating through a narrow pore. Characterization of its purportedly anomalous dynamics has so far remained incomplete. We show that the polymer dynamics is anomalous until the Rouse time $τ_{R}\sim N^{1+2ν}$, with a mean square displacement through the pore consistent with $t^{(1+ν)/(1+2ν)}$, with $ν\approx0.588$ the Flory exponent. This is shown to be directly related to a decay in time of the excess monomer density near the pore as $t^{-(1+ν)/(1+2ν)}\exp(-t/τ_{R})$. Beyond the Rouse time translocation becomes diffusive. In consequence of this, the dwell-time $τ_{d}$, the time a translocating polymer typically spends within the pore, scales as $N^{2+ν}$, in contrast to previous claims.

cond-mat.soft↗
arXiv2006

Predictability of El Niño as a Nonlinear Stochastic Limit Cycle

The El Niño phenomenon, synonymously El Niño-Southern Oscillation (ENSO), is an anomalous climatic oscillation in the Equatorial Pacific that occurs once every 3-8 years. It affects the earth's climate on a global scale. Whether it is a cyclic or a sporadic event, or whether its apparently random behaviour can be explained by stochastic dynamics have remained matters of debate. Herein ENSO is viewed, unconventionally, as a two-dimensional dynamical system on a desktop. The main features of ENSO: irregularity, interannual variability, and the asymmetry between El Niño and La Niña are captured, simply, comprehensibly, quickly and cheaply, in a nonlinear stochastic limit cycle paradigm. Its predictability for ENSO compares remarkably well with that of the best state-of-the-art complex models from the European and American meteorological centres. Additionally, for the first time, by analyzing subsurface Equatorial Pacific data since 1960, this model finds that long-term variations are not caused by ENSO itself, but by external sources.

nlin.CD↗
arXiv2006

Elasticity from the Force Network Ensemble in Granular Media

Transmission of forces in static granular materials are studied within the framework of the force network ensemble, by numerically evaluating the mechanical response of hexagonal packings of frictionless grains and rectangular packings of frictional grains. In both cases, close to the point of application of the overload, the response is non-linear and displays two peaks, while at larger length-scales it is linear and elastic-like. The cross-over between these two behaviors occurs at a depth that increases with the magnitude of the overload, and decreases with increasing friction.

cond-mat.soft↗
arXiv2006

Passage Times for Unbiased Polymer Translocation through a Narrow Pore

We study the translocation process of a polymer in the absence of external fields for various pore diameters $b$ and membrane thickness $L$. The polymer performs Rouse and reptation dynamics. The mean translocation time $<τ_t>$ that the polymer needs to escape from a cell, and the mean dwell time $<τ_d>$ that the polymer spends in the pore during the translocation process, obey scaling relations in terms of the polymer length $N$, $L$ and $b/R_g$, where $R_g$ is the radius of gyration for the polymer. We explain these relations using simple arguments based on polymer dynamics and the equilibrium properties of polymers.

cond-mat.soft↗
arXiv2005

Systematic Density Expansion of the Lyapunov Exponents for a Two-dimensional Random Lorentz Gas

We study the Lyapunov exponents of a two-dimensional, random Lorentz gas at low density. The positive Lyapunov exponent may be obtained either by a direct analysis of the dynamics, or by the use of kinetic theory methods. To leading orders in the density of scatterers it is of the form $A_{0}\tilde{n}\ln\tilde{n}+B_{0}\tilde{n}$, where $A_{0}$ and $B_{0}$ are known constants and $\tilde{n}$ is the number density of scatterers expressed in dimensionless units. In this paper, we find that through order $(\tilde{n}^{2})$, the positive Lyapunov exponent is of the form $A_{0}\tilde{n}\ln\tilde{n}+B_{0}\tilde{n}+A_{1}\tilde{n}^{2}\ln\tilde{n} +B_{1}\tilde{n}^{2}$. Explicit numerical values of the new constants $A_{1}$ and $B_{1}$ are obtained by means of a systematic analysis. This takes into account, up to $O(\tilde{n}^{2})$, the effects of {\it all\/} possible trajectories in two versions of the model; in one version overlapping scatterer configurations are allowed and in the other they are not.

nlin.CD↗
arXiv2005

Response of a Hexagonal Granular Packing under a Localized External Force

We study the response of a two-dimensional hexagonal packing of rigid, frictionless spherical grains due to a vertically downward point force on a single grain at the top layer. We use a statistical approach, where each configuration of the contact forces is equally likely. We show that this problem is equivalent to a correlated $q$-model. We find that the response displays two peaks which lie precisely on the downward lattice directions emanating from the point of application of the force. With increasing depth, the magnitude of the peaks decreases, and a central peak develops. On the bottom of the pile, only the middle peak persists. The response of different system sizes exhibits self-similarity.

cond-mat.stat-mech↗
arXiv2005

Response of a Hexagonal Granular Packing under a Localized External Force: Exact Results

We study the response of a two-dimensional hexagonal packing of massless, rigid, frictionless spherical grains due to a vertically downward point force on a single grain at the top layer. We use a statistical approach, where each mechanically stable configuration of contact forces is equally likely. We show that this problem is equivalent to a correlated $q$-model. We find that the response is double-peaked, where the two peaks, sharp and single-grain diameter wide, lie on the two downward lattice directions emanating from the point of the application of the external force. For systems of finite size, the magnitude of these peaks decreases towards the bottom of the packing, while progressively a broader, central maximum appears between the peaks. The response behaviour displays a remarkable scaling behaviour with system size $N$: while the response in the bulk of the packing scales as $\frac{1}{N}$, on the boundary it is independent of $N$, so that in the thermodynamic limit only the peaks on the lattice directions persist. This qualitative behaviour is extremely robust, as demonstrated by our simulation results with different boundary conditions. We have obtained expressions of the response and higher correlations for any system size in terms of integers corresponding to an underlying discrete structure.

cond-mat.stat-mech↗
arXiv2004

Fluctuating Fronts as Correlated Extreme Value Problems: An Example of Gaussian Statistics

In this paper, we view fluctuating fronts made of particles on a one-dimensional lattice as an extreme value problem. The idea is to denote the configuration for a single front realization at time $t$ by the set of co-ordinates $\{k_i(t)\}\equiv[k_1(t),k_2(t),...,k_{N(t)}(t)]$ of the constituent particles, where $N(t)$ is the total number of particles in that realization at time $t$. When $\{k_i(t)\}$ are arranged in the ascending order of magnitudes, the instantaneous front position can be denoted by the location of the rightmost particle, i.e., by the extremal value $k_f(t)=\text{max}[k_1(t),k_2(t),...,k_{N(t)}(t)]$. Due to interparticle interactions, $\{k_i(t)\}$ at two different times for a single front realization are naturally not independent of each other, and thus the probability distribution $P_{k_f}(t)$ [based on an ensemble of such front realizations] describes extreme value statistics for a set of correlated random variables. In view of the fact that exact results for correlated extreme value statistics are rather rare, here we show that for a fermionic front model in a reaction-diffusion system, $P_{k_f}(t)$ is Gaussian. In a bosonic front model however, we observe small deviations from the Gaussian.

cond-mat.stat-mech↗
arXiv2004

Clustering in a One-dimensional Inelastic Lattice Gas

We analyze a lattice model closely related to the one-dimensional inelastic gas with periodic boundary condition. The one-dimensional inelastic gas tends to form high density clusters of particles with almost the same velocity, separated by regions of low density; plotted as a function of particle indices, the velocities of the gas particles exhibit sharp gradients, which we call shocks. Shocks and clusters are seen to form in the lattice model too, although no true positions of the particles are taken into account. The locations of the shocks in terms of the particle index show remarkable independence on the coefficient of restitution and the sequence of collisions used to update the system, but they do depend on the initial configuration of the particle velocities. We explain the microscopic origin of the shocks. We show that dynamics of the velocity profile inside a cluster satisfies a simple continuum equation, thereby allowing us to study cluster-cluster interactions at late times.

cond-mat.soft↗
arXiv2003

Effects of Fluctuations on Propagating Fronts

Propagating fronts are seen in varieties of non-equilibrium pattern forming systems in Physics, Chemistry and Biology. In the last two decades, many researchers have contributed to the understanding of the underlying dynamics of the propagating fronts. Of these, the deterministic and mean-field dynamics of the fronts were mostly understood in late 1980s and 1990s. On the other hand, although the earliest work on the effect of fluctuations on propagating fronts dates back to early 1980s, the subject of fluctuating fronts did not reach its adolescence until the mid 1990s. From there onwards the last few years witnessed a surge in activities in the effect of fluctuations on propagating fronts. Scores of papers have been written on this subject since then, contributing to a significant maturity of our understanding, and only recently a full picture of fluctuating fronts has started to emerge. This review is an attempt to collect all the works on fluctuating (propagating) fronts in a coherent and cogent manner in proper perspective. It is based on the idea of making our knowledge in this field available to a broader audience, and it is also expected to help to collect bits and pieces of loose thread-ends together for possible further investigation.

cond-mat.stat-mech↗
arXiv2003

Asymptotic Scaling of the Diffusion Coefficient of Fluctuating "Pulled" Fronts

We present a (heuristic) theoretical derivation for the scaling of the diffusion coefficient $D_f$ for fluctuating ``pulled'' fronts. In agreement with earlier numerical simulations, we find that as $N\to\infty$, $D_f$ approaches zero as $1/\ln^3N$, where $N$ is the average number of particles per correlation volume in the stable phase of the front. This behaviour of $D_f$ stems from the shape fluctuations at the very tip of the front, and is independent of the microscopic model.

cond-mat.stat-mech↗
arXiv2003

Front Propagation and Diffusion in the A <--> A + A Hard-core Reaction on a Chain

We study front propagation and diffusion in the reaction-diffusion system A $\leftrightharpoons$ A + A on a lattice. On each lattice site at most one A particle is allowed at any time. In this paper, we analyze the problem in the full range of parameter space, keeping the discrete nature of the lattice and the particles intact. Our analysis of the stochastic dynamics of the foremost occupied lattice site yields simple expressions for the front speed and the front diffusion coefficient which are in excellent agreement with simulation results.

cond-mat.stat-mech↗