We present a comprehensive extension of the integral of first passage times(IFS)method to investigate the adsorption kinetics of polymers with multiple binding sites on planar surfaces.While effective for single-point...We present a comprehensive extension of the integral of first passage times(IFS)method to investigate the adsorption kinetics of polymers with multiple binding sites on planar surfaces.While effective for single-point adsorption,the original IFS method was limited in capturing the complex kinetics of multi-point adsorption due to inadequate reaction coordinates and theoretical frameworks.Our approach introduces a center-of-mass-based reaction coordinate and a generalized kinetic model that accounts for multi-barrier free energy landscapes characteristic of collective polymer diffusion and binding.This theoretical advancement,implemented using the adaptive bias force method for efficient sampling,enables prediction of adsorption kinetics across timescales from nanoseconds to seconds.Our results demonstrate that adsorption behavior is governed by two key factors:the number of binding monomers primarily controls desorption barriers and long-term stability,while the configuration of pre-adsorbed layers significantly modulates both adsorption and desorption rates.Polymers with three or more binding sites exhibit effectively irreversible adsorption due to exponentially increasing desorption barriers,whereas different adsorbed layer configurations lead to distinct equilibrium coverages and kinetic profiles.This extended IFS framework provides critical insights for designing functional surfaces in nanoscale sensing,macromolecular recognition,and tailored polymeric coatings where precise control over adsorption kinetics is essential.展开更多
An approximate method is presented for obtaining analytical solutions for the conditional first passage probability of systems under modulated white noise excitation. As the method is based on VanMarcke＇s approximati...An approximate method is presented for obtaining analytical solutions for the conditional first passage probability of systems under modulated white noise excitation. As the method is based on VanMarcke＇s approximation, with normalization of the response introduced, the expected decay rates can be evaluated from the second-moment statistics instead of the correlation functions or spectrum density functions of the response of considered structures. Explicit solutions to the second-moment statistics of the response are given. Accuracy, efficiency and usage of the proposed method are demonstrated by the first passage analysis of single-degree-of-freedom （SDOF） linear systems under two special types of modulated white noise excitations.展开更多
The transient properties of a three-level atomic optical bistable system in the presence of multiplicative and additive noises are investigated. The explicit expressions of the mean first-passage time （MFPT） of the ...The transient properties of a three-level atomic optical bistable system in the presence of multiplicative and additive noises are investigated. The explicit expressions of the mean first-passage time （MFPT） of the transition from the high intracavity intensity state to the low one are obtained by numerical computations. The impacts of the intensities of the multiplicative noise DM and the additive noise DA, the intensity of correlation between two noises λ, and the intensity of the incident light y on the MFPT are discussed, respectively. Our results show： （i） for the case of no correlation between two noises （2, = 0.0）, the increase in DM and DA can lead to an increase in the probability of the transition to the low intracavity intensity state, while the increase in y can lead to a retardation of the transition; and （ii） for the case of correlation between two noises （λ≠ 0.0）, the increase in λ can cause an increase in the probability of the transition, and the increase in DA can cause a retardation of the transition firstly and then an increase in the probability of the transition, i.e., the noise-enhanced stability is observed for the case of correlation between two noises.展开更多
An analytical moment-based method was proposed for calculating first passage probability of structures under non-Gaussian stochastic behaviour. In the method, the third-moment standardization that con- stants can be o...An analytical moment-based method was proposed for calculating first passage probability of structures under non-Gaussian stochastic behaviour. In the method, the third-moment standardization that con- stants can be obtained from first three-order response moments was used to map a non-Gaussian structural response into a standard Gaussian process; then the mean up-crossing rates, the mean clump size and the initial passage probability of some critical barrier level by the original structural response were estimated. Finally, the formula for calculating first passage probability was established on the assumption that the corrected up-crossing rates are independent. By a nonlinear single-degree-of-freedom system excited by a stationary Gaussian load, it is demonstrated how the procedure can be used for the type of structures considered. Further, comparisons between the results from the present procedure and those from Monte-Carlo simulation are performed.展开更多
The motion of a lazy Pearson walker is studied with different probability (p) of jump in two and three dimensions. The probability of exit ( ) from a zone of radius is studied as a function of with d...The motion of a lazy Pearson walker is studied with different probability (p) of jump in two and three dimensions. The probability of exit ( ) from a zone of radius is studied as a function of with different values of jump probability p. The exit probability is found to scale as , which is obtained by method of data collapse. The first passage time ( ) i.e., the time required for first exit from a zone is studied. The probability distribution of first passage time was studied for different values of jump probability (p). The probability distribution of first passage time was found to scale as . Where, F and G are two scaling functions and a, b, g and d are some exponents. In both the dimensions, it is found that, , , and .展开更多
First passage time in Markov chains is defined as the first time that a chain passes a specified state or lumped states. This state or lumped states may indicate first passage time of an interesting, rare and amazing ...First passage time in Markov chains is defined as the first time that a chain passes a specified state or lumped states. This state or lumped states may indicate first passage time of an interesting, rare and amazing event. In this study, obtaining distribution of the first passage time relating to lumped states which are constructed by gathering the states through lumping method for a irreducible Markov chain whose state space is finite was deliberated. Thanks to lumping method the chain＇s Markov property has been preserved. Another benefit of lumping method in the way of practice is reduction of the state space thanks to gathering states together. As the obtained first passage distributions are continuous, it may be used in many fields such as reliability and risk analysis展开更多
The first-passage problem of dynamical power system of a single-machine-infinite-bus(SMIB)system under random perturbations is studied.First,the stochastic averaging method for quasi non-integrable generalized Hamilto...The first-passage problem of dynamical power system of a single-machine-infinite-bus(SMIB)system under random perturbations is studied.First,the stochastic averaging method for quasi non-integrable generalized Hamiltonian systems is applied to reduce the equations of the SMIB system under random perturbations to a set of averaged Itequations.Then,the backward Kolmogorov equation governing the conditional reliability function and the Pontryagin equation governing the conditional mean of first passage time are established and solved numerically,respectively.Finally,the proposed method is verified by using the Monte Carlo simulation of the original system.展开更多
This paper is the first attempt to investigate the risk probability criterion in semi-Markov decision processes with loss rates. The goal is to find an optimal policy with the minimum risk probability that the total l...This paper is the first attempt to investigate the risk probability criterion in semi-Markov decision processes with loss rates. The goal is to find an optimal policy with the minimum risk probability that the total loss incurred during a first passage time to some target set exceeds a loss level. First, we establish the optimality equation via a successive approximation technique, and show that the value function is the unique solution to the optimality equation. Second, we give suitable conditions, under which we prove the existence of optimal policies and develop an algorithm for computing ?-optimal policies. Finally, we apply our main results to a business system.展开更多
This paper considers a first passage model for discounted semi-Markov decision processes with denumerable states and nonnegative costs. The criterion to be optimized is the expected discounted cost incurred during a f...This paper considers a first passage model for discounted semi-Markov decision processes with denumerable states and nonnegative costs. The criterion to be optimized is the expected discounted cost incurred during a first passage time to a given target set. We first construct a semi-Markov decision process under a given semi-Markov decision kernel and a policy. Then, we prove that the value function satisfies the optimality equation and there exists an optimal （or ε-optimal） stationary policy under suitable conditions by using a minimum nonnegative solution approach. Further we give some properties of optimal policies. In addition, a value iteration algorithm for computing the value function and optimal policies is developed and an example is given. Finally, it is showed that our model is an extension of the first passage models for both discrete-time and continuous-time Markov decision processes.展开更多
This work is devoted to calculating the first passage probabilities of one-dimensional diffusion processes. For a one-dimensional diffusion process, we construct a sequence of Markov chains so that their absorption pr...This work is devoted to calculating the first passage probabilities of one-dimensional diffusion processes. For a one-dimensional diffusion process, we construct a sequence of Markov chains so that their absorption probabilities approximate the first passage probability of the given diffusion process. This method is especially useful when dealing with time-dependent boundaries.展开更多
The prime concern of this paper is the first passage time of a nonhomogeneous random walk, which is nearest neighbor but able to stay at its position. It is revealed that the branching structure of the walk correspond...The prime concern of this paper is the first passage time of a nonhomogeneous random walk, which is nearest neighbor but able to stay at its position. It is revealed that the branching structure of the walk corresponds to a 2-type non-homogeneous branching process and the first passage time of the walk can be expressed by that branching process. Therefore, one can calculate the mean and variance of the first passage time, though its exact distribution is unknown.展开更多
This paper is an attempt to study the minimization problem of the risk probability of piecewise deterministic Markov decision processes(PDMDPs)with unbounded transition rates and Borel spaces.Different from the expect...This paper is an attempt to study the minimization problem of the risk probability of piecewise deterministic Markov decision processes(PDMDPs)with unbounded transition rates and Borel spaces.Different from the expected discounted and average criteria in the existing literature,we consider the risk probability that the total rewards produced by a system do not exceed a prescribed goal during a first passage time to some target set,and aim to find a policy that minimizes the risk probability over the class of all history-dependent policies.Under suitable conditions,we derive the optimality equation(OE)for the probability criterion,prove that the value function of the minimization problem is the unique solution to the OE,and establish the existence ofε(≥0)-optimal policies.Finally,we provide two examples to illustrate our results.展开更多
This paper provides an overview of significant advances in nonlinear stochastic dynamics during the past two decades, including random response, stochastic stability, stochastic bifurcation, first passage problem and ...This paper provides an overview of significant advances in nonlinear stochastic dynamics during the past two decades, including random response, stochastic stability, stochastic bifurcation, first passage problem and nonlinear stochastic control. Topics for future research are also suggested.展开更多
In this paper, a numerical method for correlation sensitivity analysis of a nonlinear random vibration system is presented. Based on the first passage failure model, the probability perturbation method is employed to ...In this paper, a numerical method for correlation sensitivity analysis of a nonlinear random vibration system is presented. Based on the first passage failure model, the probability perturbation method is employed to determine the statistical characteristics of failure modes and the correlation between them. The sensitivity of correlation between failure modes with respect to random parameters characterizing the uncertainty of the hysteretic loop is discussed. In a numerical example, a two-DOF shear structure with uncertain hysteretic restoring force is considered. The statistical characteristics of response, failure modes and the sensitivity of random hysteretic loop parameters are provided, and also compared with a Monte Carlo simulation.展开更多
To understand the dynamic process of polymer detachment, it is necessary to determine the mean detachment time of a single breakable link, which is modeled as a spring. Normally, this time can be viewed as the escape ...To understand the dynamic process of polymer detachment, it is necessary to determine the mean detachment time of a single breakable link, which is modeled as a spring. Normally, this time can be viewed as the escape of a Brownian particle from the potential well of the spring. However, as the free dangling length of the polymer chain increases, the conformational entropy of the chain is affected by geometric confinement. It means that the wall exerts a repulsive force on the chain, resulting in accelerated link detachment from a macroscopic perspective. In this work, we investigate the effect of entropy on the detachment rate in the case where the substrate is spherical. We demonstrate that spherical confinement accelerates chain detachment both inside and outside the sphere. An analytical expression for the mean detachment time of breakable links is given, which includes an additional pre-factor that is related to the partition function. Additionally, we analyze the expressions for entropic forces inside the sphere, outside the sphere, and on a flat wall, comparing their magnitudes to explain the difference in mean detachment time.展开更多
We study the protein folding problem on the base of our quantum approach by considering the model of protein chain with nine amino-acid residues.We introduce the concept of distance space and its projections on a XY-p...We study the protein folding problem on the base of our quantum approach by considering the model of protein chain with nine amino-acid residues.We introduce the concept of distance space and its projections on a XY-plane,and two characteristic quantities,one is called compactness of protein structure and another is called probability ratio involving shortest path.The concept of shortest path enables us to reduce the 388×388 density matrix to a 2×2 one from which the von Neumann entropy reflecting certain quantum coherence feature is naturally defined.We observe the time evolution of average distance and compactness solved from the classical random walk and quantum walk,we also compare the features of the time-dependence of Shannon entropy and von Neumann entropy.All the results not only reveal the fast quantum folding time but also unveil the existence of quantum intelligence hidden behind in choosing protein folding pathways.展开更多
We consider the escape of the particles multi-state noise. It is shown that, the noise can make over fluctuating potential barrier for a system only driven by a the particles escape over the fluctuating potential barr...We consider the escape of the particles multi-state noise. It is shown that, the noise can make over fluctuating potential barrier for a system only driven by a the particles escape over the fluctuating potential barrier in some circumstances; but in other circumstances, it can not. If the noise can make the particle escape over the fluctuating potential barrier, the mean first passage time （MFPT） can display the phenomenon of multi-resonant-activation. For this phenomenon, there are two kinds of resonant activation to appear. One is resonant activation for the MFPTs as the function of the flipping rates of the fluctuating potential barrier; the other is that for the MFPTs as the functions of the transition rates of the multi-state noise.展开更多
The phenomenon of the resonant activation （RA） of a particle over a fluctuating potential barrier with a four-value noise is investigated. It is shown that the mean first passage time （MFPT） displays six minima as...The phenomenon of the resonant activation （RA） of a particle over a fluctuating potential barrier with a four-value noise is investigated. It is shown that the mean first passage time （MFPT） displays six minima as the function of the transition rates γ1, γ2, γ3, γ4, γ5, and 76 of the four-value noise, respectively. In addition, the effect of other parameters of the system, such as the noise strength D of the additive Gaussian white noise and the parameter value a, b, c, and d of the four-value noise, on the RAs is also investigated.展开更多
In this paper, we present an asymmetry conformational potential with a reflecting boundary and an absorbing boundary, in which the diffusive search of the free head of kinesin motor can be biased toward its forward bi...In this paper, we present an asymmetry conformational potential with a reflecting boundary and an absorbing boundary, in which the diffusive search of the free head of kinesin motor can be biased toward its forward binding site. Under a wide range of condition, using first-passage time analysis we perform numerical simulation to the Langevin equation, and obtain the dependence of the dwell time for forward steps on the load force. And we calculate the expression for the dwell time by the Laplace transform method. Both numerical and analytical results show that the dwell times exponentially depend on the load force, which provide a simple physical explanation for experimental data. Our results suggest that ATP binding-conformation change in the neck linker plays an important role in unidirectional steps during kinesin＇s mechanochemical cycle.展开更多
This paper studies the mean first passage time （or exit time, or escape time） over the non-fluctuating potential harrier for a system driven only by a dichotomous noise. It finds that the dichotomous noise can make ...This paper studies the mean first passage time （or exit time, or escape time） over the non-fluctuating potential harrier for a system driven only by a dichotomous noise. It finds that the dichotomous noise can make the particles escape over the potential barrier, in some circumstances; but in other circumstances, it can not. In the case that the particles escape over the potential harrier, a resonant activation phenomenon for the mean first passage time over the potential barrier is obtained.展开更多
基金financially supported by the National Natural Science Foundation of China(No.12374207)the Natural Science Foundation of Jiangsu Province(No.BK20233001)supported by the Big Data Computing Center of Southeast University。
文摘We present a comprehensive extension of the integral of first passage times(IFS)method to investigate the adsorption kinetics of polymers with multiple binding sites on planar surfaces.While effective for single-point adsorption,the original IFS method was limited in capturing the complex kinetics of multi-point adsorption due to inadequate reaction coordinates and theoretical frameworks.Our approach introduces a center-of-mass-based reaction coordinate and a generalized kinetic model that accounts for multi-barrier free energy landscapes characteristic of collective polymer diffusion and binding.This theoretical advancement,implemented using the adaptive bias force method for efficient sampling,enables prediction of adsorption kinetics across timescales from nanoseconds to seconds.Our results demonstrate that adsorption behavior is governed by two key factors:the number of binding monomers primarily controls desorption barriers and long-term stability,while the configuration of pre-adsorbed layers significantly modulates both adsorption and desorption rates.Polymers with three or more binding sites exhibit effectively irreversible adsorption due to exponentially increasing desorption barriers,whereas different adsorbed layer configurations lead to distinct equilibrium coverages and kinetic profiles.This extended IFS framework provides critical insights for designing functional surfaces in nanoscale sensing,macromolecular recognition,and tailored polymeric coatings where precise control over adsorption kinetics is essential.
基金supported by the National Natural Science Foundation of China (No. 50478017)
文摘An approximate method is presented for obtaining analytical solutions for the conditional first passage probability of systems under modulated white noise excitation. As the method is based on VanMarcke＇s approximation, with normalization of the response introduced, the expected decay rates can be evaluated from the second-moment statistics instead of the correlation functions or spectrum density functions of the response of considered structures. Explicit solutions to the second-moment statistics of the response are given. Accuracy, efficiency and usage of the proposed method are demonstrated by the first passage analysis of single-degree-of-freedom （SDOF） linear systems under two special types of modulated white noise excitations.
基金supported by the Natural Science Foundation of Yunnan Province of China (Grant No. 2010CD031)the Key Project of Research Fund of Education Department of Yunnan Province of China (Grant No. 2001Z011)the Candidate Talents Training Fund of Yunnan Province, China (Grant No. 2012HB009)
文摘The transient properties of a three-level atomic optical bistable system in the presence of multiplicative and additive noises are investigated. The explicit expressions of the mean first-passage time （MFPT） of the transition from the high intracavity intensity state to the low one are obtained by numerical computations. The impacts of the intensities of the multiplicative noise DM and the additive noise DA, the intensity of correlation between two noises λ, and the intensity of the incident light y on the MFPT are discussed, respectively. Our results show： （i） for the case of no correlation between two noises （2, = 0.0）, the increase in DM and DA can lead to an increase in the probability of the transition to the low intracavity intensity state, while the increase in y can lead to a retardation of the transition; and （ii） for the case of correlation between two noises （λ≠ 0.0）, the increase in λ can cause an increase in the probability of the transition, and the increase in DA can cause a retardation of the transition firstly and then an increase in the probability of the transition, i.e., the noise-enhanced stability is observed for the case of correlation between two noises.
基金the National Natural Science Foundation of China (No. 50478017)
文摘An analytical moment-based method was proposed for calculating first passage probability of structures under non-Gaussian stochastic behaviour. In the method, the third-moment standardization that con- stants can be obtained from first three-order response moments was used to map a non-Gaussian structural response into a standard Gaussian process; then the mean up-crossing rates, the mean clump size and the initial passage probability of some critical barrier level by the original structural response were estimated. Finally, the formula for calculating first passage probability was established on the assumption that the corrected up-crossing rates are independent. By a nonlinear single-degree-of-freedom system excited by a stationary Gaussian load, it is demonstrated how the procedure can be used for the type of structures considered. Further, comparisons between the results from the present procedure and those from Monte-Carlo simulation are performed.
文摘The motion of a lazy Pearson walker is studied with different probability (p) of jump in two and three dimensions. The probability of exit ( ) from a zone of radius is studied as a function of with different values of jump probability p. The exit probability is found to scale as , which is obtained by method of data collapse. The first passage time ( ) i.e., the time required for first exit from a zone is studied. The probability distribution of first passage time was studied for different values of jump probability (p). The probability distribution of first passage time was found to scale as . Where, F and G are two scaling functions and a, b, g and d are some exponents. In both the dimensions, it is found that, , , and .
文摘First passage time in Markov chains is defined as the first time that a chain passes a specified state or lumped states. This state or lumped states may indicate first passage time of an interesting, rare and amazing event. In this study, obtaining distribution of the first passage time relating to lumped states which are constructed by gathering the states through lumping method for a irreducible Markov chain whose state space is finite was deliberated. Thanks to lumping method the chain＇s Markov property has been preserved. Another benefit of lumping method in the way of practice is reduction of the state space thanks to gathering states together. As the obtained first passage distributions are continuous, it may be used in many fields such as reliability and risk analysis
基金supported by the National Natural Science Foundation of China(Grant Nos.10772159 and 10932009)Zhejiang Provincial Natural Science Foundation of China(Grant No.Y7080070)the Research&Development Start Grant of Huaqiao University(Grant No.09BS622)
文摘The first-passage problem of dynamical power system of a single-machine-infinite-bus(SMIB)system under random perturbations is studied.First,the stochastic averaging method for quasi non-integrable generalized Hamiltonian systems is applied to reduce the equations of the SMIB system under random perturbations to a set of averaged Itequations.Then,the backward Kolmogorov equation governing the conditional reliability function and the Pontryagin equation governing the conditional mean of first passage time are established and solved numerically,respectively.Finally,the proposed method is verified by using the Monte Carlo simulation of the original system.
基金supported by National Natural Science Foundation of China(Grant Nos.61374067 and 11471341)
文摘This paper is the first attempt to investigate the risk probability criterion in semi-Markov decision processes with loss rates. The goal is to find an optimal policy with the minimum risk probability that the total loss incurred during a first passage time to some target set exceeds a loss level. First, we establish the optimality equation via a successive approximation technique, and show that the value function is the unique solution to the optimality equation. Second, we give suitable conditions, under which we prove the existence of optimal policies and develop an algorithm for computing ?-optimal policies. Finally, we apply our main results to a business system.
基金Supported by the Natural Science Foundation of China(No.60874004,60736028)Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme(2010)
文摘This paper considers a first passage model for discounted semi-Markov decision processes with denumerable states and nonnegative costs. The criterion to be optimized is the expected discounted cost incurred during a first passage time to a given target set. We first construct a semi-Markov decision process under a given semi-Markov decision kernel and a policy. Then, we prove that the value function satisfies the optimality equation and there exists an optimal （or ε-optimal） stationary policy under suitable conditions by using a minimum nonnegative solution approach. Further we give some properties of optimal policies. In addition, a value iteration algorithm for computing the value function and optimal policies is developed and an example is given. Finally, it is showed that our model is an extension of the first passage models for both discrete-time and continuous-time Markov decision processes.
基金This work was supported in part by the National Natural Science Foundation of Ghina （Grant Nos. 11301030, 11431014）, the 985-Project, and the Beijing Higher Education Young Elite Teacher Project.
文摘This work is devoted to calculating the first passage probabilities of one-dimensional diffusion processes. For a one-dimensional diffusion process, we construct a sequence of Markov chains so that their absorption probabilities approximate the first passage probability of the given diffusion process. This method is especially useful when dealing with time-dependent boundaries.
文摘The prime concern of this paper is the first passage time of a nonhomogeneous random walk, which is nearest neighbor but able to stay at its position. It is revealed that the branching structure of the walk corresponds to a 2-type non-homogeneous branching process and the first passage time of the walk can be expressed by that branching process. Therefore, one can calculate the mean and variance of the first passage time, though its exact distribution is unknown.
基金supported by the National Natural Science Foundation of China(Nos.11931018,11961005)Guangdong Province Key Laboratory of Computational Science at the Sun Yat-sen University(No.2020B1212060032)the Natural Science Foundation of Guangxi Province(No.2020GXNSFAA297196)。
文摘This paper is an attempt to study the minimization problem of the risk probability of piecewise deterministic Markov decision processes(PDMDPs)with unbounded transition rates and Borel spaces.Different from the expected discounted and average criteria in the existing literature,we consider the risk probability that the total rewards produced by a system do not exceed a prescribed goal during a first passage time to some target set,and aim to find a policy that minimizes the risk probability over the class of all history-dependent policies.Under suitable conditions,we derive the optimality equation(OE)for the probability criterion,prove that the value function of the minimization problem is the unique solution to the OE,and establish the existence ofε(≥0)-optimal policies.Finally,we provide two examples to illustrate our results.
基金The project supported by the National Natural Science Foundation of China (19972059)
文摘This paper provides an overview of significant advances in nonlinear stochastic dynamics during the past two decades, including random response, stochastic stability, stochastic bifurcation, first passage problem and nonlinear stochastic control. Topics for future research are also suggested.
基金National Natural Science Foundation of ChinaUnder Grant No: 50535010
文摘In this paper, a numerical method for correlation sensitivity analysis of a nonlinear random vibration system is presented. Based on the first passage failure model, the probability perturbation method is employed to determine the statistical characteristics of failure modes and the correlation between them. The sensitivity of correlation between failure modes with respect to random parameters characterizing the uncertainty of the hysteretic loop is discussed. In a numerical example, a two-DOF shear structure with uncertain hysteretic restoring force is considered. The statistical characteristics of response, failure modes and the sensitivity of random hysteretic loop parameters are provided, and also compared with a Monte Carlo simulation.
基金financially supported by the National Natural Science Foundation of China (No.51965057)Xinjiang Tianchi Ph D Project (No.TCBS202113)+3 种基金the Natural Science Foundation of Xinjiang (No.2022D01C34)Xinjiang Basic Research Funds for Universities (No.XJEDU2022P017)Robot-Intelligent Equipment Technology Innovation (No.2022D14002)Xinjiang Tianshan Science Technology Innovation Leading Talents Program (No.2022TSYCLJ0044)。
文摘To understand the dynamic process of polymer detachment, it is necessary to determine the mean detachment time of a single breakable link, which is modeled as a spring. Normally, this time can be viewed as the escape of a Brownian particle from the potential well of the spring. However, as the free dangling length of the polymer chain increases, the conformational entropy of the chain is affected by geometric confinement. It means that the wall exerts a repulsive force on the chain, resulting in accelerated link detachment from a macroscopic perspective. In this work, we investigate the effect of entropy on the detachment rate in the case where the substrate is spherical. We demonstrate that spherical confinement accelerates chain detachment both inside and outside the sphere. An analytical expression for the mean detachment time of breakable links is given, which includes an additional pre-factor that is related to the partition function. Additionally, we analyze the expressions for entropic forces inside the sphere, outside the sphere, and on a flat wall, comparing their magnitudes to explain the difference in mean detachment time.
基金Project supported by the National Key Research and Development Program of China(Grant No.2017YFA0304304)the National Natural Science Foundation of China(Grant No.11935012)
文摘We study the protein folding problem on the base of our quantum approach by considering the model of protein chain with nine amino-acid residues.We introduce the concept of distance space and its projections on a XY-plane,and two characteristic quantities,one is called compactness of protein structure and another is called probability ratio involving shortest path.The concept of shortest path enables us to reduce the 388×388 density matrix to a 2×2 one from which the von Neumann entropy reflecting certain quantum coherence feature is naturally defined.We observe the time evolution of average distance and compactness solved from the classical random walk and quantum walk,we also compare the features of the time-dependence of Shannon entropy and von Neumann entropy.All the results not only reveal the fast quantum folding time but also unveil the existence of quantum intelligence hidden behind in choosing protein folding pathways.
基金Supported by National Natural Science Foundation of China under Grant No. 10975079by K.C. Wong Magna Fund of Ningbo University in Chinaby the Ningbo Natural Sciences Foundation in China
文摘We consider the escape of the particles multi-state noise. It is shown that, the noise can make over fluctuating potential barrier for a system only driven by a the particles escape over the fluctuating potential barrier in some circumstances; but in other circumstances, it can not. If the noise can make the particle escape over the fluctuating potential barrier, the mean first passage time （MFPT） can display the phenomenon of multi-resonant-activation. For this phenomenon, there are two kinds of resonant activation to appear. One is resonant activation for the MFPTs as the function of the flipping rates of the fluctuating potential barrier; the other is that for the MFPTs as the functions of the transition rates of the multi-state noise.
基金National Natural Science Foundation of China under Grant No.10375009K.C.Wong Magna Fund in Ningbo University of ChinaNational Natural Science Foundation of China under Grant No.10647134
文摘The phenomenon of the resonant activation （RA） of a particle over a fluctuating potential barrier with a four-value noise is investigated. It is shown that the mean first passage time （MFPT） displays six minima as the function of the transition rates γ1, γ2, γ3, γ4, γ5, and 76 of the four-value noise, respectively. In addition, the effect of other parameters of the system, such as the noise strength D of the additive Gaussian white noise and the parameter value a, b, c, and d of the four-value noise, on the RAs is also investigated.
基金Supported by Beijing National Science Foundation under Grant No. 4102031
文摘In this paper, we present an asymmetry conformational potential with a reflecting boundary and an absorbing boundary, in which the diffusive search of the free head of kinesin motor can be biased toward its forward binding site. Under a wide range of condition, using first-passage time analysis we perform numerical simulation to the Langevin equation, and obtain the dependence of the dwell time for forward steps on the load force. And we calculate the expression for the dwell time by the Laplace transform method. Both numerical and analytical results show that the dwell times exponentially depend on the load force, which provide a simple physical explanation for experimental data. Our results suggest that ATP binding-conformation change in the neck linker plays an important role in unidirectional steps during kinesin＇s mechanochemical cycle.
基金supported by the Scientific Research Foundation (SRF) for the Returned Overseas Chinese Scholars (ROCS), State Education Ministry (SEM), and by K. C. Wong Magna Fund in Ningbo University
文摘This paper studies the mean first passage time （or exit time, or escape time） over the non-fluctuating potential harrier for a system driven only by a dichotomous noise. It finds that the dichotomous noise can make the particles escape over the potential barrier, in some circumstances; but in other circumstances, it can not. In the case that the particles escape over the potential harrier, a resonant activation phenomenon for the mean first passage time over the potential barrier is obtained.
