In this work,Langevin dynamics simulations were carried out to thoroughly investigate the swapping process of composite knots under tension in a cuboid nanochannel.From our analysis,the free energy profiles of knot sw...In this work,Langevin dynamics simulations were carried out to thoroughly investigate the swapping process of composite knots under tension in a cuboid nanochannel.From our analysis,the free energy profiles of knot swapping under different conditions were extracted from the overall probability distribution of the relative distance between the centers of composite knots.In addition,the impact of the stretching force,confinement size,and bending stiffness on the free energy profiles was directly identified.Especially,the influence of topology structure is for the first time reported.The increasing stretching force in a fixed confinement or the confinement size under a constant stretching force does not alter their respective equilibrium populations at the separate state and the entangled state.In contrast,a bending stiffness larger than 15 enhanced the formation of the entangled state.The topology structure of the 51knot,which was different from the 52knot,resulted in forming a metastable state in the free energy profiles.The increasing stretching forces yielded an enhancement of the following free energy barrier.展开更多
The knots frequently occur in biopolymer and their diffusion plays an active role in the gene regulation.In this work,Langevin dynamics simulations were carried out to detect the diffusion behaviours of a knot along a...The knots frequently occur in biopolymer and their diffusion plays an active role in the gene regulation.In this work,Langevin dynamics simulations were carried out to detect the diffusion behaviours of a knot along a tensioned polymer in different spatial constraints.The polymer accommodating a knot was tethered to two macrospheres to block the unravelling of the knot.As a result,the curves for the diffusion coefficients of the knot with different bending stiffness as a function of the tension in different spatial constraints were obtained.In the space without constraints or with weak constraints,the corresponding curves for the knot with relatively large bending stiffness exhibited two turnover behaviours.On the contrary,for the knot with relatively small bending stiffness,the diffusion coefficients were monotonically reduced with increasing tension.However,in a space with strong constraints,all the curves showed one turnover behaviour regardless of the bending stiffness.The turnover behaviours divided the curves into different regimes,and the dominant diffusion mechanisms in the regimes,namely,knot-region breathing,self-reptation,and internal friction,were clearly identified.The effective friction coefficientsξof the knots with 3_(1),4_(1),5_(1) and 5_(2) types as a function of the knot size N at a fixed tension were well fitted by the relationξ∝N.The effective friction coefficients of the knots at relatively large tension f>3 sharply increased with the knot complexity,which is not dependent on the spatial constraints.By contrast,the values of these coefficients at relatively small tension f≤3 were remarkably dependent on the spatial constraints.Our work not only provides valuable simulation results to assist the understanding of the diffusion of DNA knot,but also highlights the single-molecule design for the manipulation of DNA knots in future.展开更多
Langevin simulation of the particles multi-passing over the saddle point is proposed to calculate thermal fission rate. Due to finite friction and the corresponding thermal fluctuation, a backstreaming exists in the p...Langevin simulation of the particles multi-passing over the saddle point is proposed to calculate thermal fission rate. Due to finite friction and the corresponding thermal fluctuation, a backstreaming exists in the process of the particle descent from the saddle to the scission. This leads to that the diffusion behind the saddle point has influence upon the stationary flow across the saddle point. A dynamical correction factor, as a ratio of the flows of multi- and first-overpassing the saddle point, is evaluated analytically. The results show that the fission rate calculated by the particles multi-passing over the saddle point is lower than the one calculated by the particle firstly passing over the saddle point, and the former approaches the results at the scission point.展开更多
We propose an n-order noise,which is realized by driving an n-order linear differential equation with aGaussian white noise.The time-derivative noise is a low-resistant band-passing noise.If the derivative noise is re...We propose an n-order noise,which is realized by driving an n-order linear differential equation with aGaussian white noise.The time-derivative noise is a low-resistant band-passing noise.If the derivative noise is regardedas a thermal one,the system has a vanishing effective friction and it should induce ballistic diffusion of a free particleat long times.The simulation method for the generalized Langevin equation driven by the n-order noise is discussedsystematically.The features of three-order derivative noises are presented when they are applied to a ratchet system.展开更多
Using Langevin simulations, we study numerically the directional mode-locking of the dynamics of two- dimensional superpararnagnetic colloidal system in a periodic pinning array. When the colloidal particles are initi...Using Langevin simulations, we study numerically the directional mode-locking of the dynamics of two- dimensional superpararnagnetic colloidal system in a periodic pinning array. When the colloidal particles are initially commensurate with the pinning sites, there appear mode-locking steps in the average velocity of colloidal particles along certain directions of the external driving force. With an increase in the pinning strength, the width of the step increases linearly but the velocity at the step decreases parabolically.展开更多
The dynamics of tracers in crowded matrix is of interest in various areas of physics, such as the diffusion of proteins in living cells. By using two-dimensional （2D） Langevin dynamics simulations, we investigate th...The dynamics of tracers in crowded matrix is of interest in various areas of physics, such as the diffusion of proteins in living cells. By using two-dimensional （2D） Langevin dynamics simulations, we investigate the diffusive properties of a tracer of a diameter in crowded environments caused by randomly distributed crowders of a diameter. Results show that the emergence of subdiffusion of a tracer at intermediate time scales depends on the size ratio of the tracer to crowders a. If a falls between a lower critical size ratio and a upper one, the anomalous diffusion occurs purely due to the molecular crowding, tqlrther analysis indicates that the physical origin of subdiffusion is the ＂cage effect＂. Moreover, the subdiffusion exponent α decreases with the increasing medium viscosity and the degree of crowding, and gets a minimum αmin=0.75 at δ=1. At long time scales, normal diffusion of a tracer is recovered. For δ≤1, the relative mobility of tracers is independent of the degree of crowding. Meanwhile, it is sensitive to the degree of crowding for δ〉l. Our results are helpful in deepening the understanding of the diffusive properties of biomacromolecules that lie within crowded intracellular environments, such as proteins, DNA and ribosomes.展开更多
Multivalent polymer chains exhibit excellent prospect in biomedical applications by serving as therapeutic agents. Using three-dimensional （3D） Langevin dynamics simulations, we investigate adsorption behaviors of m...Multivalent polymer chains exhibit excellent prospect in biomedical applications by serving as therapeutic agents. Using three-dimensional （3D） Langevin dynamics simulations, we investigate adsorption behaviors of multivalent polymer chains to a surface with receptors. Multivalent polymer chains display superselective adsorption. Furthermore, the range of density of surface receptors at which a multivalent polymer chain displays a superselective behavior, narrows down for chains with higher density of ligands. Meanwhile, the optimal density of surface receptors where the highest superselectivity is achieved, decreases with increasing the density of ligands. Then, the conformational properties of bound multivalent chains are studied systematically. Interestingly, we find that the equilibrium radius of gyration Rg and its horizontal component have a maximum as a function of the density of surface receptors. The scaling exponents of Rg with the length of chain suggest that with increasing the density of surface receptors., the conformations of a bound multivalent polymer chain first fall in between those of a two-dimensional （2D） and a 3D chain, while it is slightly collapsed subsequently.展开更多
A polymer chain usually contains two or more types of monomeric species from the perspective of polymer chemistry,which poses achallenge to the understanding of structure-property relationships.It is of course true in...A polymer chain usually contains two or more types of monomeric species from the perspective of polymer chemistry,which poses achallenge to the understanding of structure-property relationships.It is of course true in the field of polymer translocation.In the present work,Iinvestigate the translocation dynamics of heterogeneous flexible polymers composed of two types of monomers labeled A and B through ananopore assisted by binding particles(BPs)by using the coarse-grained Langevin dynamics simulations in two-dimensional domains.Specifically,multiblock copolymers with different block lengths and monomeric components are considered.I critically examine how thetranslocation dynamics responds to the variations in the block length and the monomeric content.Interestingly,it is found that the periodicstructure of a multiblock copolymer causes an obvious fingerprint feature in the residence time of individual monomers in which the number ofpeaks is exactly equal to the number of blocks.These findings provide a basic understanding about the sequence-dynamics relationship for theBPs-assisted translocation of heterogeneous flexible polymers.展开更多
The effect of viscosity of non-translocated(cis)side,ηcis,on the driven translocation of charged polymers through nanopores is investigated using Langevin dynamics simulation.Results show that the translocation of po...The effect of viscosity of non-translocated(cis)side,ηcis,on the driven translocation of charged polymers through nanopores is investigated using Langevin dynamics simulation.Results show that the translocation of polymer chains can be regulated by changingηcis.Asηcis decreases,the translocation timeτdecreases,and the exponentδin the scaling relation with driving force f,τ~f-δ,increases whereasαin the scaling relation with chain length N,τ~Nα,decreases.Simultaneously,the conformation of the polymer chain at the cis side gravitates towards an equilibrium state.The results imply a relationship between the translocation and the conformation of polymer chains.To verify this hypothesis,we change the conformation of polymer by artificially relaxing the translocating polymer via adding an additional relaxation time in the simulation.A sufficient large additional relaxation time for the translocating polymer chain at the cis side only or at both cis and trans sides results in exponentsαandδboth close to 1,in contrast toα=1.36 andδ=0.8 for the translocation without the additional relaxation.The additional relaxation for the polymer chain at the cis side accelerates the translocation and plays a more important role than that for polymer chain at the trans side.展开更多
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 dist...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.展开更多
Transport of passive particles induced by chiral-active particles in microchannel is investigated by using the overdamped Langevin dynamics simulation in a two-dimensional model system. Due to the chirality of active ...Transport of passive particles induced by chiral-active particles in microchannel is investigated by using the overdamped Langevin dynamics simulation in a two-dimensional model system. Due to the chirality of active particles and special structure of microchannel, effective ratchet transport of passive particles is achieved. Effective transport of passive particles depends on the width of microchannel（d）, the density（ρ）, and the angular velocity（ω） of chiral-active particles.There exist optimal parameters for d and ω at which the transport efficiency for passive particles takes its maximal value.This investigation can help us understand the necessity of active motion for living systems to maintain a number of vital processes such as materials transport inside cells and the foraging dynamics of mobile organisms.展开更多
Langevin dynamics simulations are employed to explore the effects of chain stiffness and electrostatic interaction(EI) on the conformational behavior of a circular semiflexible polyelectrolyte(CSPE) in presence of tri...Langevin dynamics simulations are employed to explore the effects of chain stiffness and electrostatic interaction(EI) on the conformational behavior of a circular semiflexible polyelectrolyte(CSPE) in presence of trivalent counterions.We investigate the effect of bending energy b and the dimensionless Bjerrum length A on the conformational behavior of the CSPE with a fixed chain length.The competition among the EIs,chain stiffness and entropy of the system leads to rich conformations for the CSPE.As the b is less than or equal to 50,The shape of the CSPE changes from a oblate ring to a rod at small A,then to a toroid at intermediate A,and finally to a globule at very large A.However,the globular conformation is not observed for large b.In addition,we find that the number of torus ring increases with A increase,while decreases with b increase.This study should be helpful in gaining insight into the conformational behaviour of charged biopolymer.展开更多
Langevin molecular dynamics simulations reveal the impact of confinement strength on the structure and dynamics of a two-dimensional complex plasma under constant shear force.Structural analysis via Voronoi diagrams a...Langevin molecular dynamics simulations reveal the impact of confinement strength on the structure and dynamics of a two-dimensional complex plasma under constant shear force.Structural analysis via Voronoi diagrams and the local bond-order parameter|Ψ6|shows that stronger confinement enhances hexagonal order and mitigates shear-induced disorder.Dynamical properties,determined by mean-square displacement(MSD)and the velocity autocorrelation function(VACF),indicate that the shear-induced superdiffusion weakens with increasing confinement strength.The entropy change(?S)shows that strong confinement(ω>1)balances particle dynamics between shear and shear-free regions,thereby stabilizing the system.These findings highlight the interplay between confinement and shear force.展开更多
We investigate the time-dependent probability for a Brownian particle passing over the barrier to stay at a metastable potential pocket against escaping over the barrier. This is related to the whole fusion-fission dy...We investigate the time-dependent probability for a Brownian particle passing over the barrier to stay at a metastable potential pocket against escaping over the barrier. This is related to the whole fusion-fission dynamical process and can be called the reverse Kramers problem. By the passing probability over the saddle point of an inverse harmonic potential multiplying the exponential decay factor of a particle in the metastable potential, we present an approximate expression for the modified passing probability over the barrier, in which the effect of the reflection boundary of the potential is taken into account. Our analytical result and Langevin Monte-Carlo simulation show that the probability of passing and against escaping over the barrier is a non-monotonous function of time and its maximal value is less than the stationary result of the passing probability over the saddle point of an inverse harmonic potential.展开更多
基金The National Natural Science Foundation of China under Grant Nos.11864006,11874309,12164007,and 12204118。
文摘In this work,Langevin dynamics simulations were carried out to thoroughly investigate the swapping process of composite knots under tension in a cuboid nanochannel.From our analysis,the free energy profiles of knot swapping under different conditions were extracted from the overall probability distribution of the relative distance between the centers of composite knots.In addition,the impact of the stretching force,confinement size,and bending stiffness on the free energy profiles was directly identified.Especially,the influence of topology structure is for the first time reported.The increasing stretching force in a fixed confinement or the confinement size under a constant stretching force does not alter their respective equilibrium populations at the separate state and the entangled state.In contrast,a bending stiffness larger than 15 enhanced the formation of the entangled state.The topology structure of the 51knot,which was different from the 52knot,resulted in forming a metastable state in the free energy profiles.The increasing stretching forces yielded an enhancement of the following free energy barrier.
基金The National Natural Science Foundation of China under Grant Nos.11864006, 11874309, 12164007, and 12204118
文摘The knots frequently occur in biopolymer and their diffusion plays an active role in the gene regulation.In this work,Langevin dynamics simulations were carried out to detect the diffusion behaviours of a knot along a tensioned polymer in different spatial constraints.The polymer accommodating a knot was tethered to two macrospheres to block the unravelling of the knot.As a result,the curves for the diffusion coefficients of the knot with different bending stiffness as a function of the tension in different spatial constraints were obtained.In the space without constraints or with weak constraints,the corresponding curves for the knot with relatively large bending stiffness exhibited two turnover behaviours.On the contrary,for the knot with relatively small bending stiffness,the diffusion coefficients were monotonically reduced with increasing tension.However,in a space with strong constraints,all the curves showed one turnover behaviour regardless of the bending stiffness.The turnover behaviours divided the curves into different regimes,and the dominant diffusion mechanisms in the regimes,namely,knot-region breathing,self-reptation,and internal friction,were clearly identified.The effective friction coefficientsξof the knots with 3_(1),4_(1),5_(1) and 5_(2) types as a function of the knot size N at a fixed tension were well fitted by the relationξ∝N.The effective friction coefficients of the knots at relatively large tension f>3 sharply increased with the knot complexity,which is not dependent on the spatial constraints.By contrast,the values of these coefficients at relatively small tension f≤3 were remarkably dependent on the spatial constraints.Our work not only provides valuable simulation results to assist the understanding of the diffusion of DNA knot,but also highlights the single-molecule design for the manipulation of DNA knots in future.
基金The project supported by National Natural Science Foundation of China under Grant Nos.10075007 and 10235020
文摘Langevin simulation of the particles multi-passing over the saddle point is proposed to calculate thermal fission rate. Due to finite friction and the corresponding thermal fluctuation, a backstreaming exists in the process of the particle descent from the saddle to the scission. This leads to that the diffusion behind the saddle point has influence upon the stationary flow across the saddle point. A dynamical correction factor, as a ratio of the flows of multi- and first-overpassing the saddle point, is evaluated analytically. The results show that the fission rate calculated by the particles multi-passing over the saddle point is lower than the one calculated by the particle firstly passing over the saddle point, and the former approaches the results at the scission point.
文摘We propose an n-order noise,which is realized by driving an n-order linear differential equation with aGaussian white noise.The time-derivative noise is a low-resistant band-passing noise.If the derivative noise is regardedas a thermal one,the system has a vanishing effective friction and it should induce ballistic diffusion of a free particleat long times.The simulation method for the generalized Langevin equation driven by the n-order noise is discussedsystematically.The features of three-order derivative noises are presented when they are applied to a ratchet system.
基金Supported by the Scientific Research Foundation of Graduate School of Zhengzhou Universitythe Natural Science Research Foundation of Henan Provincial Department of Science and Technology under Grant No. 112300410151
文摘Using Langevin simulations, we study numerically the directional mode-locking of the dynamics of two- dimensional superpararnagnetic colloidal system in a periodic pinning array. When the colloidal particles are initially commensurate with the pinning sites, there appear mode-locking steps in the average velocity of colloidal particles along certain directions of the external driving force. With an increase in the pinning strength, the width of the step increases linearly but the velocity at the step decreases parabolically.
基金This work is supported by the National Natural Science Foundation of China （No.21225421 and No.21474099）, the National Basic Research Program of China （No.2014CB845605）.
文摘The dynamics of tracers in crowded matrix is of interest in various areas of physics, such as the diffusion of proteins in living cells. By using two-dimensional （2D） Langevin dynamics simulations, we investigate the diffusive properties of a tracer of a diameter in crowded environments caused by randomly distributed crowders of a diameter. Results show that the emergence of subdiffusion of a tracer at intermediate time scales depends on the size ratio of the tracer to crowders a. If a falls between a lower critical size ratio and a upper one, the anomalous diffusion occurs purely due to the molecular crowding, tqlrther analysis indicates that the physical origin of subdiffusion is the ＂cage effect＂. Moreover, the subdiffusion exponent α decreases with the increasing medium viscosity and the degree of crowding, and gets a minimum αmin=0.75 at δ=1. At long time scales, normal diffusion of a tracer is recovered. For δ≤1, the relative mobility of tracers is independent of the degree of crowding. Meanwhile, it is sensitive to the degree of crowding for δ〉l. Our results are helpful in deepening the understanding of the diffusive properties of biomacromolecules that lie within crowded intracellular environments, such as proteins, DNA and ribosomes.
文摘Multivalent polymer chains exhibit excellent prospect in biomedical applications by serving as therapeutic agents. Using three-dimensional （3D） Langevin dynamics simulations, we investigate adsorption behaviors of multivalent polymer chains to a surface with receptors. Multivalent polymer chains display superselective adsorption. Furthermore, the range of density of surface receptors at which a multivalent polymer chain displays a superselective behavior, narrows down for chains with higher density of ligands. Meanwhile, the optimal density of surface receptors where the highest superselectivity is achieved, decreases with increasing the density of ligands. Then, the conformational properties of bound multivalent chains are studied systematically. Interestingly, we find that the equilibrium radius of gyration Rg and its horizontal component have a maximum as a function of the density of surface receptors. The scaling exponents of Rg with the length of chain suggest that with increasing the density of surface receptors., the conformations of a bound multivalent polymer chain first fall in between those of a two-dimensional （2D） and a 3D chain, while it is slightly collapsed subsequently.
基金This work was finanailly supported by the China Postdoctoral Science Foundation(No.2015M581998).
文摘A polymer chain usually contains two or more types of monomeric species from the perspective of polymer chemistry,which poses achallenge to the understanding of structure-property relationships.It is of course true in the field of polymer translocation.In the present work,Iinvestigate the translocation dynamics of heterogeneous flexible polymers composed of two types of monomers labeled A and B through ananopore assisted by binding particles(BPs)by using the coarse-grained Langevin dynamics simulations in two-dimensional domains.Specifically,multiblock copolymers with different block lengths and monomeric components are considered.I critically examine how thetranslocation dynamics responds to the variations in the block length and the monomeric content.Interestingly,it is found that the periodicstructure of a multiblock copolymer causes an obvious fingerprint feature in the residence time of individual monomers in which the number ofpeaks is exactly equal to the number of blocks.These findings provide a basic understanding about the sequence-dynamics relationship for theBPs-assisted translocation of heterogeneous flexible polymers.
基金financially supported by the National Natural Science Foundation of China (No. 11974305)
文摘The effect of viscosity of non-translocated(cis)side,ηcis,on the driven translocation of charged polymers through nanopores is investigated using Langevin dynamics simulation.Results show that the translocation of polymer chains can be regulated by changingηcis.Asηcis decreases,the translocation timeτdecreases,and the exponentδin the scaling relation with driving force f,τ~f-δ,increases whereasαin the scaling relation with chain length N,τ~Nα,decreases.Simultaneously,the conformation of the polymer chain at the cis side gravitates towards an equilibrium state.The results imply a relationship between the translocation and the conformation of polymer chains.To verify this hypothesis,we change the conformation of polymer by artificially relaxing the translocating polymer via adding an additional relaxation time in the simulation.A sufficient large additional relaxation time for the translocating polymer chain at the cis side only or at both cis and trans sides results in exponentsαandδboth close to 1,in contrast toα=1.36 andδ=0.8 for the translocation without the additional relaxation.The additional relaxation for the polymer chain at the cis side accelerates the translocation and plays a more important role than that for polymer chain at the trans side.
基金financially supported by the National Natural Science Foundation of China(Nos.21225421 and 21474099)the 973 Program of Ministry of Science and Technology of China(MOST)(No.2014CB845605)+1 种基金the Fundamental Research Funds for the Central Universities(No.WK2060200020)the China Postdoctoral Science Foundation(No.2015M581998)
文摘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.
基金supported by the National Natural Science Foundation of China(Grant Nos.21374102,21674096,and 21674082)
文摘Transport of passive particles induced by chiral-active particles in microchannel is investigated by using the overdamped Langevin dynamics simulation in a two-dimensional model system. Due to the chirality of active particles and special structure of microchannel, effective ratchet transport of passive particles is achieved. Effective transport of passive particles depends on the width of microchannel（d）, the density（ρ）, and the angular velocity（ω） of chiral-active particles.There exist optimal parameters for d and ω at which the transport efficiency for passive particles takes its maximal value.This investigation can help us understand the necessity of active motion for living systems to maintain a number of vital processes such as materials transport inside cells and the foraging dynamics of mobile organisms.
基金financially supported by the National Natural Science Foundation of China (Nos. 21863003, 22173080, 21873082, 21674096 and 61762048)the Jiangxi Provincial Natural Science Foundation (No.20202BABL203015)。
文摘Langevin dynamics simulations are employed to explore the effects of chain stiffness and electrostatic interaction(EI) on the conformational behavior of a circular semiflexible polyelectrolyte(CSPE) in presence of trivalent counterions.We investigate the effect of bending energy b and the dimensionless Bjerrum length A on the conformational behavior of the CSPE with a fixed chain length.The competition among the EIs,chain stiffness and entropy of the system leads to rich conformations for the CSPE.As the b is less than or equal to 50,The shape of the CSPE changes from a oblate ring to a rod at small A,then to a toroid at intermediate A,and finally to a globule at very large A.However,the globular conformation is not observed for large b.In addition,we find that the number of torus ring increases with A increase,while decreases with b increase.This study should be helpful in gaining insight into the conformational behaviour of charged biopolymer.
基金supported by the National Natural Science Foundation of China(Grant No.12075315)。
文摘Langevin molecular dynamics simulations reveal the impact of confinement strength on the structure and dynamics of a two-dimensional complex plasma under constant shear force.Structural analysis via Voronoi diagrams and the local bond-order parameter|Ψ6|shows that stronger confinement enhances hexagonal order and mitigates shear-induced disorder.Dynamical properties,determined by mean-square displacement(MSD)and the velocity autocorrelation function(VACF),indicate that the shear-induced superdiffusion weakens with increasing confinement strength.The entropy change(?S)shows that strong confinement(ω>1)balances particle dynamics between shear and shear-free regions,thereby stabilizing the system.These findings highlight the interplay between confinement and shear force.
基金Supported by National Natural Science Foundation of China(11175021)Specialized Research Fund for the Doctoral Program of Higher Education(20120003110025)
文摘We investigate the time-dependent probability for a Brownian particle passing over the barrier to stay at a metastable potential pocket against escaping over the barrier. This is related to the whole fusion-fission dynamical process and can be called the reverse Kramers problem. By the passing probability over the saddle point of an inverse harmonic potential multiplying the exponential decay factor of a particle in the metastable potential, we present an approximate expression for the modified passing probability over the barrier, in which the effect of the reflection boundary of the potential is taken into account. Our analytical result and Langevin Monte-Carlo simulation show that the probability of passing and against escaping over the barrier is a non-monotonous function of time and its maximal value is less than the stationary result of the passing probability over the saddle point of an inverse harmonic potential.
