arXiv subjects

Rajeev Kapri

Publications and source records attributed to Rajeev Kapri.

At least 19 recordsLinked to original sources

arXiv2025

Polymer translocation through extended patterned pores in two dimensions: scaling of the total translocation time

We study the translocation of a flexible polymer through extended patterned pores using molecular dynamics (MD) simulations. We consider cylindrical and conical pore geometries that can be controlled by the angle of the pore apex $\alpha$. We obtained the average translocation time $\langle \tau \rangle$ for various chain lengths $N$ and the length of the pores $L_p$ for various values $\alpha$ and found that $\langle \tau \rangle$ scales as $\langle \tau \rangle \sim N^\gamma \mathcal{F}\left( L_p N^\phi \right)$ with exponents $\gamma = 3.00\pm0.05$ and $\phi = 1.50\pm0.05$ for both patterned and unpatterned pores.

cond-mat.soft↗

arXiv2025

Spatial organisation of multiple species of active particles interacting with an interface

We investigate the steady-state organisation of active particles residing on an interface. Particle activity induces interface deformations, while the local shape of the interface guides particle movement. We consider multiple species of particles which can locally pull on the interface or push it. This coupled system exhibits a wide variety of behaviours, including clustering, anti-clustering, diffusion, mixing, demixing, and localisation. Our findings suggest that one can control surface properties by strategically adding or removing specific particle types. Furthermore, by adjusting particle activity levels, we can selectively disperse particle types, enabling precise manipulation of surface movement and geometry.

cond-mat.soft↗

arXiv2024

Packing and ejection dynamics of polymers: Role of confinement, polymer stiffness and activity

The translocation of biopolymers, such as DNA and proteins, across cellular or nuclear membranes is essential for numerous biological processes. The translocation dynamics are influenced by the properties of the polymers, such as polymer stiffness, and the geometry of the capsid. In our study, we aim to investigate the impact of polymer stiffness, activity, and different capsid geometries on the packing and ejection dynamics of both passive and active polymers. We employ Langevin dynamics simulations for a systematic investigation. We observe that flexible polymers exhibit packing times that are faster than those of their semi-flexible counterparts. Interestingly, for large polymers compared to the capsid size, sphere facilitates faster packing and unpacking compared to ellipsoid, mimicking the cell nucleus and suggesting a geometrical advantage for biopolymer translocation. In summary, we observe that increasing activity accelerates both the packing and ejection processes for both flexible and semi-flexible polymers. However, the effect is significantly more pronounced for semi-flexible polymers, highlighting the crucial role of polymer flexibility in these dynamics. These findings deepen our understanding of the intricate interplay between polymer flexibility, capsid geometry, and activity, providing valuable insight into the dynamics of polymer packing and ejection processes.

cond-mat.soft↗

arXiv2023

Stochastic resonance in a model of a periodically driven DNA : Multiple transitions, scaling and sequence dependence

We numerically study stochastic resonance in the unzipping of a model double-stranded DNA by a periodic force. We observe multiple peaks in stochastic resonance in the output signal as the driving force frequency is varied for different force amplitudes, temperature, chain length, and chain heterogeneity. Multiple peaks point to the existence of multiple stable and metastable states, which correspond to dynamical states of partially zipped and unzipped conformations and transitions between them. We quantify such transitions by looking at the time evolution of the fraction of bound base pairs. We obtain phase diagrams in the force amplitude-temperature plane both in the resonance frequency of the primary peak and the output signal at the peak value. We further obtain an excellent scaling behavior of the output signal for changing lengths of the DNA. Resonance behavior is also affected by chain heterogeneity as it depends strongly on which base pair the periodic forcing is applied.

cond-mat.soft↗

arXiv2022

Driven translocation of a semiflexible polymer through a conical channel in the presence of attractive surface interactions

We study the translocation of a semiflexible polymer through a conical channel with attractive surface interactions and a driving force which varies spatially inside the channel. Using the results of the translocation dynamics of a flexible polymer through an extended channel as control, we first show that the asymmetric shape of the channel gives rise to non-monotonic features in the total translocation time as a function of the apex angle of the channel. The waiting time distributions of individual monomer beads inside the channel show unique features strongly dependent on the driving force and the surface interactions. Polymer stiffness results in longer translocation times for all angles of the channel. Further, non-monotonic features in the translocation time as a function of the channel angle changes substantially as the polymer becomes stiffer, which is reflected in the changing features of the waiting time distributions. We construct a free energy description of the system incorporating entropic and energetic contributions in the low force regime to explain the simulation results.

cond-mat.soft↗

arXiv2021

Hysteresis loop area scaling exponents in DNA unzipping by a periodic force: A Langevin dynamics simulation study

Using Langevin dynamics simulations, we study the hysteresis in unzipping of longer double stranded DNA chains whose ends are subjected to a time dependent periodic force with frequency $ω$ and amplitude $G$ keeping the other end fixed. We find that the area of the hysteresis loop, $A_{loop}$, scales as $1/ω$ at higher frequencies, whereas it scales as $(G-G_c)^αω^β$ with exponents $α=1$ and $β=1.25$ in the low frequency regime. These values are same as the exponents obtained in Monte Carlo simulation studies of a directed self avoiding walk model of a homopolymer DNA [R. Kapri, Phys. Rev. E 90, 062719 (2014)], and the block copolymer DNA [R. K. Yadav and R. Kapri, Phys. Rev. E 103, 012413 (2021)] on a square lattice, and differs from the values reported earlier using Langevin dynamics simulation studies on a much shorter DNA hairpins.

cond-mat.soft↗

arXiv2021

Driven translocation of a flexible polymer through an interacting conical pore

We study the driven translocation of a flexible polymer through an interacting conical pore using Langevin dynamics simulations. We find that, for a fixed value of externally applied force and pore polymer interaction strength, the mean residence time of monomers inside the pore shows non-monotonic variations with pore apex angle $α$. We explain this behavior using a free energy argument by explicitly accounting for pore-polymer interactions and external drive. Our theoretical observations are corroborated by the simulation results of the mean translocation times as the pore-polymer interactions and external driving force are varied.

cond-mat.soft↗

arXiv2021

Unzipping of a double-stranded block copolymer DNA by a periodic force

Using Monte Carlo simulations, we study the hysteresis in unzipping of a double stranded block copolymer DNA with $-A_n B_n-$ repeat units. Here $A$ and $B$ represent two different types of base pairs having two- and three-bonds, respectively, and $2n$ represents the number of such base pairs in a unit. The end of the DNA are subjected to a time dependent periodic force with frequency ($ω$) and amplitude ($g_0$) keeping the other end fixed. We find that the equilibrium force-temperature phase diagram for the static force is independent of the DNA sequence. For the periodic force case, the results are found to be dependent on the block copolymer DNA sequence and also on the base pair type on which the periodic force is acting. We observe hysteresis loops of various shapes and sizes and obtain the scaling of loop area both at low and high frequency regimes.

cond-mat.soft↗

arXiv2019

Unzipping DNA by a periodic force: Hysteresis loops, Dynamical order parameter, Correlations and Equilibrium curves

The unzipping of a double stranded DNA whose ends are subjected to a time dependent periodic force with frequency $ω$ and amplitude $G$ is studied using Monte Carlo simulations. We obtain the dynamical order parameter, $Q$, defined as the time average extension between the end monomers of two strands of the DNA over a period, and its probability distributions $P(Q)$ at various force amplitudes and frequencies. We also study the time autocorrelations of extension and the dynamical order parameter for various chain lengths. The equilibrium force-distance isotherms were also obtained at various frequencies by using non-equilibrium work measurements.

cond-mat.soft↗

arXiv2018

Sequencing of semiflexible polymers of varying bending rigidity using patterned pores

We study the translocation of a semiflexible polymer through extended pores with patterned stickiness, using Langevin dynamics simulations. We find that the consequence of pore patterning on the translocation time dynamics is dramatic and depends strongly on the interplay of polymer stiffness and pore-polymer interactions. For heterogeneous polymers with periodically varying stiffness along their lengths, we find that variation of the block size of the sequences and the orientation, results in large variations in the translocation time distributions. We show how this fact may be utilized to develop an effective sequencing strategy. This strategy involving multiple pores with patterned surface energetics, can predict heteropolymer sequences having different bending rigidity to a high degree of accuracy.

cond-mat.soft↗

arXiv2015

Order parameter scaling in fluctuation dominated phase ordering

In systems exhibiting fluctuation-dominated phase ordering, a single order parameter does not suffice to characterize the order, and it is necessary to monitor a larger set. For hard-core sliding particles (SP) on a fluctuating surface and the related coarse-grained depth (CD) models, this set comprises the long-wavelength Fourier components of the density profile. We study both static and dynamic scaling laws obeyed by the Fourier modes $Q_m$ and find that the mean value obeys the static scaling law $\langle Q_m \rangle \sim L^{-ϕ}f(m/L)$ with $ϕ\simeq2/3$ and $ϕ\simeq 3/5$ with Edwards-Wilkinson (EW) and Kardar-Parisi-Zhang (KPZ) surface evolution respectively. The full probability distribution $P(Q_m)$ exhibits scaling as well. Further, time-dependent correlation functions such as the steady state auto-correlation and cross-correlations of order parameter components are scaling functions of $t/L^z$, where $L$ is the system size and $z$ is the dynamic exponent with $z=2$ for EW and $z=3/2$ for KPZ surface evolution. In addition we find that the CD model shows temporal intermittency, manifested in the dynamical structure functions of the density and a weak divergence of the flatness as the scaled time approaches zero.

cond-mat.stat-mech↗

arXiv2015

Unzipping DNA by a periodic force: Hysteresis loop area and its scaling

Using Monte Carlo simulations, we study the hysteresis in unzipping of a double stranded DNA whose ends are subjected to a time dependent periodic force with frequency ($ω$) and amplitude ($G$). For the static force, i.e., $ω\to 0$, the DNA is in equilibrium with no hysteresis. On increasing $ω$, the area of the hysteresis loop initially increases and becomes maximum at frequency $ω^{*}(G)$, which depends on the force amplitude $G$. If the frequency is further increased, we find that for lower amplitudes the loop area decreases monotonically to zero, but for higher amplitudes it has an oscillatory component. The height of subsequent peaks decrease and finally the loop area becomes zero at very high frequencies. The number of peaks depends on the length of the DNA. We give a simple analysis to estimate the frequencies at which maxima and minima occurs in the loop area. We find that the area of the hysteresis loop scales as $1/ω$ in high-frequency regime whereas, it scales as $G^α ω^β$ with exponents $α=1$ and $β= 5/4$ at low-frequencies. The values of the exponents $α$ and $β$ are different from the exponents reported earlier based on the hysteresis of small hairpins.

cond-mat.soft↗

arXiv2012

Hysteresis and nonequilibrium work theorem for DNA unzipping

We study by using Monte Carlo simulations the hysteresis in unzipping and rezipping of a double stranded DNA (dsDNA) by pulling its strands in opposite directions in the fixed force ensemble. The force is increased, at a constant rate from an initial value $g_0$ to some maximum value $g_m$ that lies above the phase boundary and then decreased back again to $g_{0}$. We observed hysteresis during a complete cycle of unzipping and rezipping. We obtained probability distributions of work performed over a cycle of unzipping and rezipping for various pulling rates. The mean of the distribution is found to be close (the difference being within 10%, except for very fast pulling) to the area of the hysteresis loop. We extract the equilibrium force versus separation isotherm by using the work theorem on repeated non-equilibrium force measurements. Our method is capable of reproducing the equilibrium and the non-equilibrium force-separation isotherms for the spontaneous rezipping of dsDNA.

cond-mat.soft↗

arXiv2012

Scalable ultra-sensitive detection of heterogeneity via coupled bistable dynamics

We demonstrate how the collective response of $N$ globally coupled bistable elements can strongly reflect the presence of very few non-identical elements in a large array of otherwise identical elements. Counter-intuitively, when there are a small number of elements with natural stable state different from the bulk of the elements, {\em all} the elements of the system evolve to the stable state of the minority due to strong coupling. The critical fraction of distinct elements needed to produce this swing shows a sharp transition with increasing $N$, scaling as $1/\sqrt{N}$. Furthermore, one can find a global bias that allows robust {\em one bit} sensitivity to heterogeneity. Importantly, the time needed to reach the attracting state does not increase with the system size. We indicate the relevance of this ultra-sensitive generic phenomenon for massively parallelized search applications.

nlin.AO↗

arXiv2009

Asymptotic shape of the region visited by an Eulerian Walker

We study an Eulerian walker on a square lattice, starting from an initially randomly oriented background using Monte Carlo simulations. We present evidence that, that, for large number of steps $N$, the asymptotic shape of the set of sites visited by the walker is a perfect circle. The radius of the circle increases as $N^{1/3}$, for large $N$, and the width of the boundary region grows as $N^{α/ 3}$, with $α= 0.40 \pm .05$. If we introduce stochasticity in the evolution rules, the mean square displacement of the walker, $ \sim N^{2ν}$, shows a crossover from the Eulerian ($ν= 1/3$) to a simple random walk ($ν=1/2$) behaviour.

cond-mat.stat-mech↗

arXiv2009

Can a double stranded DNA be unzipped by pulling a single strand?: Phases of adsorbed DNA

We study the unzipping of a double stranded DNA (dsDNA) by applying an external force on a single strand while leaving the other strand free. We find that the dsDNA can be unzipped to two single strands if the external force exceeds a critical value. We obtain the phase diagram which is found to be different from the phase diagram of unzipping by pulling both the strands in opposite directions. In the presence of an attractive surface near DNA, the phase diagram gets modified drastically and shows richer surprises including a critical end point and a triple point.

cond-mat.soft↗

arXiv2008

Manipulating a single adsorbed DNA for a critical endpoint

We show the existence of a critical endpoint in the phase diagram of unzipping of an adsorbed double-stranded (ds) polymer like DNA. The competition of base pairing, adsorption and stretching by an external force leads to the critical end point. From exact results, the location of the critical end point is determined and its classical nature established.

cond-mat.soft↗

arXiv2007

Randomly forced DNA

We study the effect of random forces on a double stranded DNA in unzipping the two strands, analogous to the problem of an adsorbed polymer under a random force. The ground state develops bubbles of various lengths as the random force fluctuation is increased. The unzipping phase diagram is shown to be drastically different from the pure case.

cond-mat.soft↗