arXiv subjects

Harshwardhan H. Katkar

Publications and source records attributed to Harshwardhan H. Katkar.

4 recordsLinked to original sources

arXiv2026

Thermodynamics and Kinetics of a Three-Arm Star Polymer Translocating through a Nanopore

In this work, voltage-driven translocation of uniformly charged long linear and three-arm star polymers through narrow nanopores is investigated. Langevin dynamics simulation is performed using a coarse-grained model of the polymer and a semi-implicit representation of the nanopore. The mean translocation time of a linear polymer is found to be inversely proportional to the applied voltage over a wide range of voltages. In contrast, the mean translocation time of a three-arm star polymer of the same molecular weight exhibits a pronounced deviation from this scaling relation below a threshold voltage. The threshold voltage is found to be nearly independent of the molecular weight of the polymer, but depends on the size of the nanopore and salt concentration. Metadynamics simulation is used to estimate the free-energy landscape for the translocation of the three-arm star polymer. Below the threshold voltage, the free energy exhibits a pronounced second barrier resulting from an entropic contribution and electrostatic interactions between segments of the trailing arm inside the nanopore. A Fokker-Planck model developed using the estimated free-energy accurately predicts the deviation from the scaling relation below the threshold voltage and shows a remarkable agreement with the Langevin dynamics simulation results using a voltage-independent fitting parameter. The agreement between the theory and the Langevin dynamics simulation results is seen for different nanopore radii, molecular weights of the polymer and salt concentrations studied. A simple extension of the free energy landscape is suggested to predict translocation kinetics for higher molecular weights of the polymer without performing additional computationally expensive simulations.

cond-mat.soft↗

arXiv2025

Free Energy and Diffusivity in the Fokker-Planck Theory of Polymer Translocation

We revisit the Fokker-Planck based theory of driven polymer translocation through a narrow nanopore. A bead-spring model of a uniformly charged polyelectrolyte chain translocating through a semi-implicit model of a nanopore embedded in a membrane are used to gain insights into the underlying free energy landscape and kinetics of translocation. The free energy landscape is predicted using metadynamics simulation, an enhanced sampling method. A direct comparison with the theoretical free energy formulation proposed in the literature allows us to introduce a modification related to the entropic contribution in the theory. Additional classical Langevin dynamics simulation runs are performed to obtain the translocation time distribution for polymers of lengths $N$ driven by voltages $V$ through nanopores of radii $r_p$. In agreement with earlier reports, a scaling of the mean translocation time $\langle τ_\text{LD} \rangle \sim N^α/V$ is observed, with $α\sim 1.40 - 1.48$ depending on the nanopore size. Fitting the mean first passage time given by the Fokker-Planck theory, $\langle τ_\text{FP}\rangle$,to simulation results helps gain insights into the diffusivity $k_\text{FP}$ used in the theory. We report a scaling of $k_\text{FP}\sim N^β$. The $r_p-$dependent values of the exponent $β$ significantly deviate from the Rouse theory prediction of $β= -1$ for center-of-mass diffusivity of a polymer chain.

cond-mat.soft↗

arXiv2017

Role of Non-Equilibrium Conformations on Driven Polymer Translocation

One of the major theoretical methods in understanding polymer translocation through a nanopore is the Fokker-Planck formalism based on the assumption of quasi-equilibrium of polymer conformations. The criterion for applicability of the quasi-equilibrium approximation for polymer translocation is that the average translocation time per Kuhn segment, $\langle τ\rangle/N_K$ is longer than the relaxation time $τ_0$ of the polymer. Towards an understanding of conditions that would satisfy this criterion, we have performed coarse-grained three dimensional Langevin dynamics and multi-particle collision dynamics simulations. We have studied the role of initial conformations of a polyelectrolyte chain (which were artificially generated with a flow field) on the kinetics of its translocation across a nanopore under the action of an externally applied transmembrane voltage $V$ (in the absence of the initial flow field). Stretched (out-of-equilibrium) polyelectrolyte chain conformations are deliberately and systematically generated and used as initial conformations in translocation simulations. Independent simulations are performed to study the relaxation behavior of these stretched chains and a comparison is made between the relaxation timescale and the mean translocation time ($\langle τ\rangle$). For such artificially stretched initial states, $\langle τ\rangle/N_K < τ_0$, demonstrating the inapplicability of the quasi-equilibrium approximation. Nevertheless, we observe a scaling of $\langle τ\rangle \sim 1/V$ over the entire range of chain stretching studied, in agreement with the predictions of the Fokker-Planck model. On the other hand, for realistic situations where initial artificially imposed flow field is absent, a comparison of experimental data reported in the literature with the theory

cond-mat.soft↗

arXiv2014

Bifurcation in a thin liquid film flowing over a locally heated surface

We investigate the non-linear dynamics of a two-dimensional film flowing down a finite heater, for a non-volatile and a volatile liquid. An oscillatory instability is predicted beyond a critical value of Marangoni number using linear stability theory. Continuation along the Marangoni number using non-linear evolution equation is used to trace bifurcation diagram associated with the oscillatory instability. Hysteresis, a characteristic attribute of a sub-critical Hopf bifurcation, is observed in a critical parametric region. The bifurcation is universally observed for both, a non-volatile film and a volatile film.

physics.flu-dyn↗