arXiv subjects

Takahiro Sakaue

Publications and source records attributed to Takahiro Sakaue.

At least 37 records · Page 2Linked to original sources

arXiv2020

Twist dynamics and buckling instability of ring DNA: Effect of groove asymmetry and anisotropic bending

By combining analytical theory and Molecular Dynamics simulations we study the relaxation dynamics of DNA circular plasmids that initially undergo a local twist perturbation. We identify three distinctive time scales; (I) a rapid relaxation of local bending, (II) the slow twist spreading, and (III) the buckling transition taking place in a much longer time scale. In all of these stages, the twist-bend coupling arising from the groove asymmetry in DNA double helix clearly manifests. In particular, the separation of time scales allows to deduce an effective diffusion equation in stage (II), with a diffusion coefficient influenced by the twist-bend coupling. We also discuss the mapping of the realistic DNA model to the simplest isotropic twistable worm-like chain using the renormalized bending and twist moduli; although useful in many cases, it fails to make a quantitative prediction on the instability mode of buckling transition.

cond-mat.soft↗

arXiv2020

Stabilization of straight longitudinal dune under bimodal wind with large directional variation

It has been observed that the direction in which a sand dune extends its crest line depends on seasonal variation of wind direction; when the variation is small, the crest line develops more or less perpendicularly to the mean wind direction to form a transverse dune with some undulation. In the case of bimodal wind with a large relative angle, however, the dune extends its crest along the mean wind direction and evolves into an almost straight longitudinal dune. Motivated by these observations, we investigate the dynamical stability of isolated dunes using the crest line model, where the dune dynamics is represented by its crest line motion. First, we extend the previous linear stability analysis under the unidirectional wind to the case with non-zero slant angle between the wind direction and the normal direction of the crest line, and show that the stability diagram does not depend on the slant angle. Secondly, we examine how the linear stability is affected by the seasonal changes of wind direction in the case of bimodal wind with equal strength and duration. For the transverse dune, we find that the stability is virtually the same with that for the unidirectional wind as long as the dune evolution during a season is small. On the other hand, in the case of the longitudinal dune, the dispersions of the growth rates for the perturbation are drastically different from those of the unidirectional wind, and we find that the largest growth rate is always located at $k = 0$. This is because the growth of the perturbation with $k \ne 0$ is canceled by the alternating wind from opposite sides of the crest line even though it grows during each duration period of the bimodal wind.

cond-mat.soft↗

arXiv2019

Transition Path Times in Asymmetric Barriers

Biomolecular conformational transitions are usually modeled as barrier crossings in a free energy landscape. The transition paths connect two local free energy minima and transition path times (TPT) are the actual durations of the crossing events. The simplest model employed to analyze TPT and to fit empirical data is that of a stochastic particle crossing a parabolic barrier. Motivated by some disagreement between the value of the barrier height obtained from the TPT distributions as compared to the value obtained from kinetic and thermodynamic analyses, we investigate here TPT for barriers which deviate from the symmetric parabolic shape. We introduce a continuous set of potentials, that starting from a parabolic shape, can be made increasingly asymmetric by tuning a single parameter. The TPT distributions obtained in the asymmetric case are very well-fitted by distributions generated by parabolic barriers. The fits, however, provide values for the barrier heights and diffusion coefficients which deviate from the original input values. We show how these findings can be understood from the analysis of the eigenvalues spectrum of the Fokker-Planck equation and highlight connections with experimental results.

cond-mat.stat-mech↗

arXiv2018

Active dynamics and spatially coherent motion in chromosomes subject to enzymatic force dipoles

Inspired by recent experiments on chromosomal dynamics, we introduce an exactly solvable model for the interaction between a flexible polymer and a set of motor-like enzymes. The enzymes can bind and unbind to specific sites of the polymer and when bound produce a dipolar force on two neighboring monomers. We study the resulting non-equilibrium dynamics of the polymer and find that the motion of the monomers has several properties that were observed experimentally for chromosomal loci: a subdiffusive mean squared displacement and the appearance of regions of correlated motion. We also determine the velocity autocorrelation of the monomers and find that the underlying stochastic process is not fractional Brownian motion. Finally, we show that the active forces swell the polymer by an amount that becomes constant for large polymers.

cond-mat.soft↗

arXiv2018

Topological free volume and quasi-glassy dynamics in melt of ring polymers

Motivated by recent observations that non-concatenated ring polymers in their dense solution exhibit a glass-like dynamics, we propose a free volume description of the motion of such rings based on the notion of topological volume. We first construct a phenomenological free energy which enables one to qnaitify the degree of topological crowding measured by the coordination number. Then we pinpoint a key role of the cooperative dynamics of neighboring rings, which is responsible for an anomalous dependence of the global structural relaxation (diffusion) time on ring length. Predictions on molecular weight dependence of both static (ring size, coordination number) and dynamic (relaxation time, diffusion coefficient) quantities are in very good agreement with reported numerical simulations. Throughout the discussion, the entanglement length $N_e$ is assumed to be a unique characteristic length for the topological constraint, hence, all the physical quantities are universally described in terms of the rescaled chain length $N/N_e$. Finally, we discuss how the dense solution of rings is analogous yet different from ordinary glassy systems.

cond-mat.soft↗

arXiv2017

Non-Markovian dynamics of reaction coordinate in polymer folding

We develop a theoretical description of the critical zipping dynamics of a self-folding polymer. We use tension propagation theory and the formalism of the generalized Langevin equation applied to a polymer that contains two complementary parts which can bind to each other. At the critical temperature, the (un)zipping is unbiased and the two strands open and close as a zipper. The number of closed base pairs $n(t)$ displays a subdiffusive motion characterized by a variance growing as $\langle Δn^2(t) \rangle \sim t^α$ with $α< 1$ at long times. Our theory provides an estimate of both the asymptotic anomalous exponent $α$ and of the subleading correction term, which are both in excellent agreement with numerical simulations. The results indicate that the tension propagation theory captures the relevant features of the dynamics and shed some new insights on related polymer problems characterized by anomalous dynamical behavior.

cond-mat.soft↗

arXiv2017

Compressive response and helix formation of a semi flexible polymer confined in a nanochannel

Configurations of a single semiflexible polymer is studied when it is pushed into a nanochannel in the case where the polymer persistence length $l_p$ is much longer than the channel diameter $D$, i.e. $l_p/D \gg 1$. Using numerical simulations, we show that the polymer undergoes a sequence of recurring structural transitions upon longitudinal compression, i.e. random deflection along the channel, helix going around the channel wall, double-fold random deflection, double-fold helix, etc. We find that the helix transition can be understood as buckling of deflection segments, and the initial helix formation takes place at very small compression with no appreciable weak compression regime of the random deflection polymer.

cond-mat.stat-mech↗

arXiv2016

Complementary mode analyses between sub- and super-diffusions

Several sub-diffusive stochastic processes in nature, e.g., motion of tagged monomer in polymers, height fluctuation of interfaces and particle dynamics in single-file diffusion etc. can be described rigorously or approximately by the superposition of various modes whose relaxation times are broadly distributed. In this paper, we propose a mode analysis generating super-diffusion, which is paired or complementary with that for sub-diffusion. The key point in our discussion lies in the identification of a pair of conjugated variables, which undergoes sub- and super-diffusion, respectively. We provide a simple interpretation for the sub- and superdiffusion duality for these variables using the language of polymer physics. The analysis also suggests the usefulness to look at the force fluctuation in experiments, where a polymer is driven by a constant velocity.

cond-mat.stat-mech↗

arXiv2016

Miscibility Phase Diagram of Ring Polymer Blends: A Topological Effect

The miscibility of polymer blends, a classical problem in polymer science, may be altered, if one or both of the component do not have chain ends. Based on the idea of {\it topological volume}, we propose a mean-field theory to clarify how the topological constraints in ring polymers affect the phase behavior of the blends. While the large enhancement of the miscibility is expected for ring-linear polymer blends, the opposite trend toward demixing, albeit comparatively weak, is predicted for ring-ring polymer blends. Scaling formulas for the shift of critical point for both cases are derived. We discuss the valid range of the present theory, and the crossover to the linear polymer blends behaviors, which is expected for short chains. These analysis put forward a view that the topological constraints could be represented as an effective excluded-volume effects, in which the topological length plays a role of the screening factor.

cond-mat.soft↗

arXiv2016

Torque-Induced Rotational Dynamics in Polymers: Torsional Blobs and Thinning

By using the blob theory and computer simulations, we investigate the properties of a linear polymer performing a stationary rotational motion around a long impenetrable rod. In particular, in the simulations the rotation is induced by a torque applied to the end of the polymer that is tethered to the rod. Three different regimes are found, in close analogy with the case of polymers pulled by a constant force at one end. For low torques the polymer rotates maintaining its equilibrium conformation. At intermediate torques the polymer assumes a trumpet shape, being composed by blobs of increasing size. At even larger torques the polymer is partially wrapped around the rod. We derive several scaling relations between various quantities as angular velocity, elongation and torque. The analytical predictions match the simulation data well. Interestingly, we find a "thinning" regime where the torque has a very weak (logarithmic) dependence on the angular velocity. We discuss the origin of this behavior, which has no counterpart in polymers pulled by an applied force.

cond-mat.soft↗

arXiv2015

Driven Anomalous Diffusion: An example from Polymer Stretching

The way tension propagates along a chain is a key to govern many of anomalous dynamics in macromolecular systems. After introducing the weak and the strong force regimes of the tension propagation, we focus on the latter, in which the dynamical fluctuations of a segment in a long polymer during its stretching process is investigated. We show that the response, i.e., average drift, is anomalous, which is characterized by the nonlinear memory kernel, and its relation to the fluctuation is nontrivial. These features are discussed on the basis of the generalized Langevin equation, in which the role of the temporal change in spring constant due to the stress hardening is pinpointed. We carried out the molecular dynamics simulation, which supports our theory.

cond-mat.soft↗

arXiv2014

Dynamical Scaling of Polymerized Membranes

Monte Carlo simulations have been performed to analyze the sub-diffusion dynamics of a tagged monomer in self-avoiding polymerized membranes in the flat phase. By decomposing the mean square displacement into the out-of-plane ($\parallel$) and the in-plane ($\perp$) components, we obtain good data collapse with two distinctive diffusion exponents $2 α_{\parallel} = 0.36 \pm 0.01$ and $2 α_{\perp} = 0.21 \pm 0.01$, and the roughness exponents $ζ_{\parallel} = 0.6 \pm 0.05$ and $ζ_{\perp} = 0.25 \pm 0.05 $, respectively for each component. Their values are consistent with the relation from the rotational symmetry. We derive the generalized Langevin equations to describe the sub-diffusional behaviors of a tagged monomer in the intermediate time regime where the collective effect of internal modes in the membrane dominate the dynamics to produce negative memory kernels with a power-law. We also briefly discuss how the long-range hydrodynamic interactions alter the exponents.

cond-mat.soft↗

arXiv2014

Dynamics and electro-rheology of sheared immiscible fluid mixtures

We analyze the electro-rheological effect in immiscible fluid mixtures with dielectric mismatch. By taking the electric field effect into account, which couples to the dynamics of domain morphology under flow, we propose a set of electro-rheological constitutive equations valid under the condition where the relative magnitude of the flow field is stronger than that of the electric field. Through the comparison with recent experiment, we point out a unique dynamical stress response inherent in situations, where the cross-coupling between different fields is essential.

cond-mat.soft↗

arXiv2014

Nano-pore based characterization of branched polymers

We propose a novel characterization method of randomly branched polymers based on the geometrical property of such objects in confined spaces. The central idea is that randomly branched polymers exhibit passing/clogging transition across the nano-channel as a function of the channel size. This critical channel size depends on the degree of the branching, whereby allowing the extraction of the branching information of the molecule.

cond-mat.soft↗

arXiv2013

Hamilton-Jacobi method for molecular distribution function in a chemical oscillator

Using the Hamilton-Jacobi method, we solve chemical Fokker-Planck equations within the Gaussian approximation and obtain a simple and compact formula for a conditional probability distribution. The formula holds in general transient situations, and can be applied not only for a steady state but also for a oscillatory state. By analyzing the long time behavior of the solution in the oscillatory case, we obtain the phase diffusion constant along the periodic orbit and the steady distribution perpendicular to it. A simple method for numerical evaluation of these formulas are devised, and they are compared with Monte Carlo simulations in the case of Brusselator as an example. Some results are shown to be identical to previously obtained expressions.

cond-mat.stat-mech↗

arXiv2013

Cis-Trans Dynamical Asymmetry in Driven Polymer Translocation

During polymer translocation driven by e.g. voltage drop across a nanopore, the segments in the cis-side is incessantly pulled into the pore, which are then pushed out of it into the trans-side. This pulling and pushing polymer segments are described in the continuum level by nonlinear transport processes known, respectively, as fast and slow diffusions. By matching solutions of both sides through the mass conservation across the pore, we provide a physical basis for the cis and trans dynamical asymmetry, a feature repeatedly reported in recent numerical simulations. We then predict how the total driving force is dynamically allocated between cis (pulling) and trans (pushing) sides, demonstrating that the trans-side event adds a finite-chain length effect to the dynamical scaling, which may become substantial for weak force and/or high pore friction cases.

cond-mat.soft↗

arXiv2013

Inelastic collapse in one-dimensional driven systems under gravity

We study the inelastic collapse in the one-dimensional $N$-particle systems in the situation where the system is driven from below under the gravity. We investigate the hard-sphere limit of the inelastic soft-sphere systems by numerical simulations to find how the collision rate per particle $n_{coll}$ increases as a function of the elastic constant of the sphere $k$ when the restitution coefficient $e$ is kept constant. For the systems with large enough $N \agt 20$, we find three regimes in $e$ depending on the behavior of $n_{coll}$ in the hard-sphere limit: (i) uncollapsing regime for $1 \ge e > e_{c1}$, where $n_{coll}$ converges to a finite value, (ii) logarithmically collapsing regime for $e_{c1} > e > e_{c2}$, where $n_{coll}$ diverges as $n_{coll} \sim \log k$, and (iii) power-law collapsing regime for $e_{c2} > e > 0$, where $n_{coll}$ diverges as $n_{coll} \sim k^α$ with an exponent $α$ that depends on $N$. The power-law collapsing regime shrinks as $N$ decreases and seems not to exist for the system with N=3 while, for large $N$, the size of the uncollapsing and the logarithmically collapsing regime decreases as $e_{c1} \simeq 1-2.6/N$ and $e_{c2} \simeq 1-3.0/N$. We demonstrate that this difference between large and small systems exists already in the inelastic collapse without the external drive and the gravity.

cond-mat.soft↗

arXiv2012

Two phase picture in driven polymer translocation

Two phase picture is a simple and effective methodology to capture the nonequilibrium dynamics of polymer associated with tension propagation. When applying it to the driven translocation process, there is a point to be noted, as briefly discussed in our recent article [Phys. Rev. E 85, 061803 (2012)]. In this article, we address this issue in detail and modify our previous prediction [Euro. Phys. J. E 34, 135 (2011)] by adopting an alternative steady-state ansatz. The modified scaling prediction turns out to be the same as that of the iso-flux model recently proposed by Rowghanian and Grosberg [J. Phys. Chem. B 115, 14127-14135 (2011)].

cond-mat.soft↗