Three-dimensional Langevin Dynamics Research Articles

Transport of a comb-like polymer across a nanochannel subject to a pulling force.

We investigate the dynamics of comb-like polymer translocation through a nanochannel using three-dimensional Langevin dynamics simulations based on a coarse-grained chain model. A comprehensive set of simulations are performed to examine the effects of system parameters such as the grafting density $\rho$ of the side chains, the polymer chain length, the nanochannel dimensions, and the magnitude of the pulling force on the translocation dynamics. For a given polymer chain length, keeping the backbone length is constant while varying $\rho$, we have found that the dependence of the mean translocation time $\left\langle \tau\right\rangle $ on $\rho$ is non-monotonic, with a maximum translocation time for a specific $\rho$ at which the translocation is the slowest.
The simulation results also show that $\left\langle \tau\right\rangle $ is not significantly affected by the channel width above a certain radius, while the comb-like polymer translocation is hindered by a narrower channel due to increased interactions between the chain monomers and the channel. In addition, $\left\langle \tau\right\rangle $ increases linearly with the nanochannel length.
A linear scaling relationship between the mean translocation time $\left\langle \tau\right\rangle$ and the chain length $N$ of polymer is obtained, $\left\langle \tau\right\rangle \sim N$. Similarly, the dependence of $\left\langle \tau\right\rangle$ on the backbone chain size $N_{bb}$ has a quasi-linear dependence, $\left\langle \tau\right\rangle \sim N_{bb}$. On the other hand, the translocation velocity $v$ follows a power-law relationship with the polymer chain length $N$ as $v \sim N^{-1}$. The mean translocation time also shows an inverse linear relationship with the magnitude of the pulling force $F$, $\left\langle \tau\right\rangle \sim F^{-1}$. The power-law relationships discovered in this study contribute to the fundamental understanding of the comb polymer translocation dynamics and to establishing a framework for further investigations in this field.

Star-shaped polymer translocation into a nanochannel: Langevin dynamics simulations

The dynamics of a star-shaped polymer translocation pulled by a single arm through a nanochannel is investigated using three-dimensional Langevin dynamics simulations. The pulling force is applied on the terminal monomer of the leading arm in order to mimic the motion of chains subject to a combination of magnetic and optical tweezers in real experimental setups. The effect of channel dimensions and magnitude of the pulling force as well as the chain size and functionality on the chain’s translocation dynamics is extensively examined. The variation of the mean translocation time 〈τ〉 with respect to channel length and diameter exhibits a non-trivial behavior characterized by an abrupt change in the translocation dynamics for chains with higher functionalities f. The dependence of 〈τ〉 upon channel aspect ratio yields also a regime change for the transport dynamics for chains with larger functionalities. Moreover, the average exit time with respect to chains total mass N and to the magnitude of the pulling force F are found to follow scaling laws in agreement with theoretical predictions.

Three-dimensional Langevin dynamics of N atom scattering from N-covered Ag(1 1 1)

We analyzed the dynamics of N atom scattering from N -covered Ag(1 1 1), using the generalized Langevin oscillator (GLO) method and a three-dimensional neural network potential energy surface. Two values for the mass of the surface oscillator were considered in the GLO model to account for the energy exchange with the surface, i.e., that of Ag and that of N. For these mass values different trends were found for the dependence of the ratio of the average final divided by the average initial translational energy on the scattering angle. Using the nitrogen mass gives a trend closer to the experimental results for the dependence of the energy of the in-plane scattered atoms on the scattering angle, but worse agreement with experiment for the angular distribution of the in-plane scattered atoms. Two different algorithms are applied to integrate the stochastic equations of motion in the presence of energy dissipation. Our calculations show that a trivially extended Bulirsch-Stoer algorithm is more efficient than an algorithm based on a Langevin Liouville operator splitting technique, in that it yields the same results with a much larger time step.

Dynamics of driven translocation of semiflexible polymers.

We study translocation of semiflexible polymers driven by force f_{d} inside a nanometer-scale pore using our three-dimensional Langevin dynamics model. We show that the translocation time τ increases with increasing bending rigidity κ. Similarly, the exponent β for the scaling of τ with polymer length N,τ∼N^{β}, increases with increasing κ as well as with increasing f_{d}. By comparing waiting times between semiflexible and fully flexible polymers we show that for realistic f_{d} translocation dynamics is to a large extent, but not completely, determined by the polymer's elastic length measured in number of Kuhn segments N_{Kuhn}. Unlike in driven translocation of flexible polymers, friction related to the polymer segment on the trans side has a considerable effect on the resulting dynamics. This friction is intermittently reduced by buckling of the polymer segment in the vicinity of the pore opening on the trans side. We show that in the experimentally relevant regime where viscosity is higher than in computer simulation models, the probability for this buckling increases with increasing f_{d}, giving rise to a larger contribution to the trans side friction at small f_{d}. Similarly to flexible polymers, we find significant center-of-mass diffusion of the cis side polymer segment which speeds up translocation. This effect is larger for smaller f_{d}. However, this speedup is smaller than the slowing down due to the trans side friction. At large enough N_{Kuhn}, the roles can be seen to be reversed, and the dynamics of flexible polymers can be reached. However, for example, polymers used in translocation experiments of DNA are elastically so short that the finite-length dynamics outlined here applies.

Linear response approach to active Brownian particles in time-varying activity fields.

In a theoretical and simulation study, active Brownian particles (ABPs) in three-dimensional bulk systems are exposed to time-varying sinusoidal activity waves that are running through the system. A linear response (Green-Kubo) formalism is applied to derive fully analytical expressions for the torque-free polarization profiles of non-interacting particles. The activity waves induce fluxes that strongly depend on the particle size and may be employed to de-mix mixtures of ABPs or to drive the particles into selected areas of the system. Three-dimensional Langevin dynamics simulations are carried out to verify the accuracy of the linear response formalism, which is shown to work best when the particles are small (i.e., highly Brownian) or operating at low activity levels.

Ejection dynamics of semiflexible polymers out of a nanochannel

Using theoretical analysis and three-dimensional Langevin dynamics simulations, we investigate the influence of chain rigidity on the ejection dynamics of polymers from a nanochannel. We find that there exist two distinct dynamical regimes divided by a critical chain length for both flexible and semiflexible chains. At the short chain regime, semiflexible chains eject faster than flexible chains of the same chain length due to the longer occupying length. In contrast, at the long chain regime, semiflexible chains eject slower than flexible ones as the effective entropic driving force decreases. Based on these results, we propose that the nanochannels could be used to separate flexible and semiflexible chains effectively.

Surface-adsorption-induced polymer translocation through a nanopore: Effects of the adsorption strength and the surface corrugation.

The surface corrugation plays an important role in single polymer diffusion on attractive surfaces. However, its effect on dynamics of surface adsorption-induced polymer translocation through a nanopore is not clear. Using three-dimensional Langevin dynamics simulations, we investigate the dynamics of a flexible polymer chain translocation through a nanopore induced by the selective adsorption of translocated segments onto the trans side of the membrane. The translocation probability Ptrans increases monotonically, while the mean translocation time τ has a minimum as a function of the adsorption strength ɛ, which are explained from the perspective of the effective driving force for the translocation. With the surface being smoother, τ as well as the scaling exponent α of τ with the chain length N decreases. Finally, we show that the distributions of the translocation time are non-Gaussian even for strong adsorption at a moderate surface corrugation. A nearly Gaussian distribution of the translocation time is observed only for the smoothest surface we studied.

Study on the polymer translocation induced blockade ionic current inside a nanopore by Langevin dynamics simulation

The blockade ionic current inside a nanopore due to polymer translocation is studied using a three-dimensional Langevin dynamics method. The blockade current IB is dependent on the polymer length N, polymer configuration, polymer–pore interaction, and charge of the polymer. The behavior of IB can be explained using four factors: (1) the volume vacancy fraction fV inside the pore; (2) the conformation of the polymer; (3) the location of the polymer inside the pore; and (4) the total charge Ztot inside the pore. We find that IB increases with fV but decreases with increasing |Ztot|. The influence of the polymer’s conformation is complex, dependent on the size of polymer RG and the cross-sectional size of the pore s. A compact conformation can decrease IB when RG > s but increase IB when RG < s. For the latter case, the conformation of the polymer is too small to block the pore, thus providing a broad passage for the ions. At the same fV, monomers will locate close to the surface with a large polymer–pore attraction, which also provides a large IB.

Polymer translocation in solid-state nanopores: Dependence of scaling behavior on pore dimensions and applied voltage

We investigate unforced and forced translocation of a Rouse polymer (in the absence of hydrodynamic interactions) through a silicon nitride nanopore by three-dimensional Langevin dynamics simulations, as a function of pore dimensions and applied voltage. Our nanopore model consists of an atomistically detailed nanopore constructed using the crystal structure of β-Si(3)N(4). We also use realistic parameters in our simulation models rather than traditional dimensionless quantities. When the polymer length is much larger than the pore length, we find the translocation time versus chain length scales as τ ∼ N(2+ν) for the unforced case and as τ ∼ N((1+2ν)/(1+ν)) for the forced case. Our results agree with theoretical predictions which indicate that memory effects and tension on the polymer chain play an important role during the translocation process. We also find that the scaling exponents are highly dependent on the applied voltage (force). When the length of the polymer is on the order of the length of the pore, we do not find a continuous scaling law, but rather scaling exponents that increase as the length of the polymer increases. Finally, we investigate the scaling behavior of translocation time versus applied voltage for different polymer and pore lengths. For long pores, we obtain the theoretical scaling law of τ ∼ 1/V(α), where α ≅ 1 for all voltages and polymer lengths. For short pores, we find that α decreases for very large voltages and/or small polymer lengths, indicating that the value of α = 1 is not universal. The results of our simulations are discussed in the context of experimental measurements made under different conditions and with differing pore geometries.

Translocation of closed polymers through a nanopore under an applied external field

The dynamic behaviours of the translocations of closed circular polymers and closed knotted polymers through a nanopore, under the driving of an applied field, are studied by three-dimensional Langevin dynamics simulations. The power-law scaling of the translocation time τ with the chain length N and the distribution of translocation time are investigated separately. For closed circular polymers, a crossover scaling of translocation time with chain length is found to be τ ≃ Nα, with the exponent α varying from α = 0.71 for relatively short chains to α = 1.29 for longer chains under driving force F = 5. The scaling behaviour for longer chains is in good agreement with experimental results, in which the exponent α = 1.27 for the translocation of double-strand DNA. The distribution of translocation time D(τ) is close to a Gaussian function for duration time τ < τp and follows a falling exponential function for duration time τ > τp. For closed knotted polymers, the scaling exponent α is 1.27 for small field force (F = 5) and 1.38 for large field force (F = 10). The distribution of translocation time D(τ) remarkably features two peaks appearing in the case of large driving force. The interesting result of multiple peaks can conduce to the understanding of the influence of the number of strands of polymers in the pore at the same time on translocation dynamic process and scaling property.

Fast single-stranded desoxyribonucleic acid sequencing between polynucleotide molecules

The dynamics of the translocation of single-stranded desoxyribonucleic acid (DNA) chains through a nanopore under the driving of an applied field is studied by three-dimensional Langevin dynamics simulations. It was found that different monomers correspond to different residence times. With the increase of the length of nanopore, the difference in residence time becomes smaller and smaller. Based on the simplified model, a new method is proposed to discriminate between the poly(dA) and poly(dC) of single-stranded DNA chains by recording the residence time of monomer. The method is utilized to predict the sequence of seventeen different chains, and the average accuracy is about 951%. If the residence time of monomer can be well recorded in the DNA translocation experiment, the sequence of the whole DNA will be predicted once and for all. With the improvement of the method, it will provide a low-cost high-throughput way to predict the sequence of DNA.

Nuclear scission and fission-fragment kinetic-energy distribution: Study within three-dimensional Langevin dynamics

A multi-dimensional stochastic approach based on three-dimensional Langevin equations is applied for calculation of the first four moments of the kinetic-energy distribution of fission fragments in a wide range of Coulomb parameter 700 < Z 2 / A 1 / 3 < 1700 . A modified one-body mechanism of nuclear dissipation with reduction factor k s = 0.25 and different scission criteria widely used in modern fission theory are applied: zero-neck-radius R N = 0 and finite-neck-radius R N = 0.3 R 0 . A probabilistic scission criterion has been proposed also for the description of the scission process of compound nucleus. All of these scission criteria result in a good description of experimental data of the first moment of the kinetic-energy distribution. At the same time all the scission criteria provide satisfactory description of the second, third and fourth moments of the energy distribution. On the basis of theoretical calculations we cannot discriminate scission criterion, which scission criterion gives the best agreement with the experimental data. A possible way to improve the theoretical description of the experimental data could be introduction of additional collective coordinates, which could provide more flexible shapes of compound nucleus during the descent from saddle to scission.

Dynamical description of the moments of the energy distribution of fission fragments and scission of a fissile nucleus

A multidimensional stochastic approach to fission dynamics on the basis of three-dimensional Langevin equations is applied systematically to calculating the first four moments of the energy distribution of fission fragments over a broad range of Coulomb parameter values (700 < Z2/A1/3 < 1700). For the scission of a fissile nucleus into fragments, use was made of various criteria traditional in modern fission theory: the vanishing of the neck radius at the scission instant and the equality of the neck radius to about 0.3R0 at this instant. In calculating the energy distribution, both of the criteria used lead to a fairly good description of experimental data on the first two moments and to a satisfactory description of data on the third and fourth moments of the distribution. However, the quality of the description of available experimental data is insufficiently good for giving preference to any of these criteria. Within three-dimensional Langevin dynamics, it is shown that the vanishing-radius criterion leads to unexpectably good agreement with experimental data on the first four moments of the energy distribution. A modified version of one-body dissipation where the coefficient that takes into account the reduction of the wall-formula contribution was set to ks = 0.25 was used in the calculations.

Dynamical treatment of fission fragment angular distribution

A dynamical approach to the treatment of fission fragment angular distribution is developed. The approach is based on three-dimensional Langevin dynamics for shape collective coordinates joined with the Monte Carlo algorithm for the degree of freedom associated with the projection K of the total angular momentum of the fissioning system on the symmetry axis. The relaxation time of the tilting mode τK is estimated. From fits to experimental data on the fission fragment angular distribution of heavy fissioning compound systems, the K equilibration time is deduced to be ∼4 × 10−21 s for temperatures ∼1–2 MeV. A modified one-body mechanism of nuclear viscosity with the reduction coefficient of the contribution from the ‘wall’ formula ks = 0.25 has been used in calculations.

Dynamical interpretation of average fission-fragment kinetic energy systematics and nuclear scission

A dynamical interpretation of the well-known systematics for average total kinetic energy of fission fragments $\ensuremath{\langle}{E}_{K}\ensuremath{\rangle}$ over a wide range of the Coulomb parameter ($600&lt;{Z}^{2}/{A}^{1/3}&lt;2200$) is given. Different scission criteria traditionally employed in fission theory---at zero neck radius and at finite neck radius---have been applied in dynamical calculations. Both have resulted in a fairly good description of the dependence of $\ensuremath{\langle}{E}_{K}\ensuremath{\rangle}$ on the Coulomb parameter. The results of dynamical calculations of $\ensuremath{\langle}{E}_{K}\ensuremath{\rangle}$ within three-dimensional Langevin dynamics show that the mean distance between the centers of mass of nascent fragments at the scission configuration increases linearly with the parameter ${Z}^{2}/{A}^{1/3}$. This distance changes approximately from $2.35{R}_{0}$ for $^{119}\mathrm{Xe}$ to $2.6{R}_{0}$ for $^{256}\mathrm{Fm}$. In spite of this increase in mean distance between future fragments at scission, the linear dependence of $\ensuremath{\langle}{E}_{K}\ensuremath{\rangle}$ on the parameter ${Z}^{2}/{A}^{1/3}$ remains approximately valid over a wide range of the Coulomb parameter ${Z}^{2}/{A}^{1/3}$.

Langevin fission dynamics of hot rotating nuclei: Systematic application to Z 2/A=34–42 heavy nuclei

A stochastic approach that treats fission dynamics on the basis of three-dimensional Langevin equations is used to calculate the mass-energy distributions of fragments originating from the fission of compound nuclei whose fissility parameter lies in the range Z 2 /A =3 4-42. In these calculations, use was made of the liquid-drop model allowing for finite-range nuclear forces and the diffuseness of the nuclear surface in calculating the potential energy and a modified one-body mechanism of viscosity in describing dissipation. The emission of light prescission particles is taken into account on the basis of the statistical model. The calculations performed within three-dimensional Langevin dynamics reproduce well all parameters of the experimental mass-energy distributions of fission fragments and all parameters of the prefission-neutron multiplicity for various parameters of the compound nucleus. The inclusion of the third collective coordinate in the Langevin equations leads to a considerable increase (by up to 40-50% )i n the variances of mass-energy distributions in relation to what was previously obtained from two-dimensional Langevin calculations. For the parameters of the mass-energy distributions of fission fragments and the parameters of the prefission-neutron multiplicity to be reproduced simultaneously, the reduction coefficient ks must be diminished at least by a factor of 2 (0.2 ≤ ks ≤ 0.5) in relation to that in the case of total one- body viscosity (ks =1 ). c � 2002 MAIK "Nauka/Interperiodica".

Mass-energy distribution of fragments from the fission of excited nuclei within three-dimensional Langevin dynamics

Two-dimensional mass-energy distributions of fission fragments are calculated for the first time on the basis of three-dimensional stochastic Langevin equations. In these calculations, the emission of light prescission particles is taken into account within the statistical model. The results demonstrate that calculations within three-dimensional Langevin dynamics make it possible to describe most compre-hensively the properties of the mass-energy distribution of fission fragments and the mean multiplicity of prescission neutrons.

Three-dimensional Langevin calculations of fission fragment mass-energy distribution from excited compound nuclei

A stochastic approach to fission dynamics based on three-dimensional Langevin equations was applied to calculate fission fragment mass-energy distribution from a number of excited compound nuclei formed in reactions induced by heavy ions. Evaporation of prescission light particles along Langevin fission trajectories from the ground state of the compound nucleus to its scission has been taken into account using a Monte Carlo simulation technique. Inclusion of the third collective coordinate in Langevin dynamics leads to a considerable increase of the variance of the mass and the kinetic-energy distributions of fission fragments as compared with two-dimensional Langevin calculations. A liquid-drop model with finite range of nuclear forces and a modified one-body mechanism for nuclear dissipation have been used in the calculations. The results of the calculations are compared with the available experimental data. The calculations performed using the three-dimensional Langevin dynamics reproduce sufficiently well all the parameters of the two-dimensional fission fragment mass-energy distribution and their dependence on various parameters of the compound nucleus. The mean prescission neutron multiplicities are also reproduced with good accuracy. In order to reproduce simultaneously the measured prescission neutron multiplicities and the variance of the fission fragment mass-energy distribution, the reduction coefficient of the contribution from a wall formula has to be decreased at least by half of the one-body dissipation strength $(0.25&lt;~{k}_{s}&lt;~0.5).$