Efficient numerical algorithm for stochastic differential equation has been an important object in the research of statistical physics and mathematics for a long time.In this work we study the highly accurate numerica...Efficient numerical algorithm for stochastic differential equation has been an important object in the research of statistical physics and mathematics for a long time.In this work we study the highly accurate numerical algorithm for the overdamped Langevin equation.In particular,our interest is in the behaviour of the numerical schemes for solving the overdamped Langevin equation in the harmonic system.Based on the large friction limit of the underdamped Langevin dynamic scheme,three algorithms for overdamped Langevin equation are obtained.We derive the explicit expression of the stationary distribution of each algorithm by analysing the discrete time trajectory for both one-dimensional case and multi-dimensional case.The accuracy of the stationary distribution of each algorithm is illustrated by comparing with the exact Boltzmann distribution.Our results demonstrate that the“BAOA-limit”algorithm generates an accurate distribution of the harmonic system in a canonical ensemble,within a stable range of time interval.The other algorithms do not produce the exact distribution of the harmonic system.展开更多
The analytical solution of a multidimensional Langevin equation at the overdamping limit is obtained and the probability of particles passing over a two-dimensional saddle point is discussed. These results may break a...The analytical solution of a multidimensional Langevin equation at the overdamping limit is obtained and the probability of particles passing over a two-dimensional saddle point is discussed. These results may break a path for studying further the fusion in superheavy elements synthesis.展开更多
The temperature dependent width of the fission fragment distributions was simulated in the Langevin equation by taking two-parameter exponential form of the fission fragment mass variance at scission point for each fi...The temperature dependent width of the fission fragment distributions was simulated in the Langevin equation by taking two-parameter exponential form of the fission fragment mass variance at scission point for each fission event. The result can reproduce experimental data well, and it permits to make reliable estimate for unmeasured product yields near symmetry fission.展开更多
The quantum thermodynamic functions of a harmonic oscillator coupled to a heat bath through velocity-dependent coupling are obtained analytically. It is shown that both the free energy and the entropy decay fast with ...The quantum thermodynamic functions of a harmonic oscillator coupled to a heat bath through velocity-dependent coupling are obtained analytically. It is shown that both the free energy and the entropy decay fast with the temperature in relation to that of the usual coupling from. This implies that the velocity-dependent coupling helps to ensure the third law of thermodynamics.展开更多
Cell migration plays an essential role in a wide variety of physiological and pathological processes. In this paper we numerically discuss the properties of an anisotropic persistent random walk (APRW) model, in whi...Cell migration plays an essential role in a wide variety of physiological and pathological processes. In this paper we numerically discuss the properties of an anisotropic persistent random walk (APRW) model, in which two different and independent persistent times are assumed for cell migrations in the x-and y-axis directions. An intrinsic orthogonal coordinates with the primary and non-primary directions can be defined for each migration trajectory based on the singular vector decomposition method. Our simulation results show that the decay time of single exponential distribution of velocity auto-correlation function (VACF) in the primary direction is actually the large persistent time of the APRW model, and the small decay time of double exponential VACF in the non-primary direction equals the small persistent time of the APRW model. Thus, we propose that the two persistent times of anisotropic migration of cells can be properly estimated by discussing the VACFs of trajectory projected to the primary and non-primary directions.展开更多
A typical biological cell lives in a small volmne at room temperature; the noise effect on the cell signal transduction pathway may play an important role in its dynamics. Here, using the transforming growth factor-β...A typical biological cell lives in a small volmne at room temperature; the noise effect on the cell signal transduction pathway may play an important role in its dynamics. Here, using the transforming growth factor-β signal transduction pathway as an example, we report our stochastic simulations of the dynamics of the pathway and introduce a linear noise approximation method to calculate the transient intrinsic noise of pathway components. We compare the numerical solutions of the linear noise approximation with the statistic results of chemical Langevin equations, and find that they are quantitatively in agreement with the other. When transforming growth factor-β dose decreases to a low level, the time evolution of noise fluctuation of nuclear Smad2-Smad4 complex indicates the abnormal enhancement in the transient signal activation process.展开更多
The non-classical properties of light propagating in four-channel Kerr waveguides, confined in an optical cavity, are studied. The solution to the Hamiltonian of field operators is obtained semi-analytically by using ...The non-classical properties of light propagating in four-channel Kerr waveguides, confined in an optical cavity, are studied. The solution to the Hamiltonian of field operators is obtained semi-analytically by using symmetrically ordered phase-space representation. Full quantum analysis of the input coherent fields displays a strong transition of photon property between the super-Poissonian and sub-Poissonian statistics. It is found that the cavity-assisted multichannel system exhibits enhanced squeezing both in single-and compound-mode. This multichannel system may be utilized as an efficient quantumlight generator.展开更多
The diffusion behavior driven by bounded noise under the influence of a coupled harmonic potential is investigated in a two-dimensional coupled-damped model. With the help of the Laplace analysis we obtain exact descr...The diffusion behavior driven by bounded noise under the influence of a coupled harmonic potential is investigated in a two-dimensional coupled-damped model. With the help of the Laplace analysis we obtain exact descriptions for a particle’s two-time dynamics which is subjected to a coupled harmonic potential and a coupled damping. The time lag is used to describe the velocity autocorrelation function and mean square displacement of the diffusing particle. The diffusion behavior for the time lag is also discussed with respect to the coupled items and the amplitude of bounded noise.展开更多
In order to calculate the electron energy distribution in the fuel rod gap of a VVER- 1000 nuclear reactor, the Fokker-Planck equation (FPE) governing the non-equilibrium behavior of electrons passing through the fu...In order to calculate the electron energy distribution in the fuel rod gap of a VVER- 1000 nuclear reactor, the Fokker-Planck equation (FPE) governing the non-equilibrium behavior of electrons passing through the fuel-rod gap as an absorber has been solved in this paper. Besides, the Monte Carlo Geant4 code was employed to simulate the electron migration in the fuel-rod gap and the energy distribution of electrons was found. As for the results, the accuracy of the FPE was compared to the Geant4 code outcomes and a satisfactory agreement was found. Also, different percentage of the volatile and noble gas fission fragments produced in fission reactions in fuel rod, i.e. Krypton, Xenon, Iodine, Bromine, Rubidium and Cesium were employed so as to investigate their effects on the electrons' energy distribution. The present results show that most of the electrons in the fuel rod's gap were within the thermal energy limitation and the tail of the electron energy distribution was far from a Maxwellian distribution. The interesting outcome was that the electron energy distribution is slightly increased due to the accumulation of fission fragments in the gap. It should be noted that solving the FPE for the energy straggling electrons that are penetrating into the fuel-rod gap in the VVER-1000 nuclear reactor has been carried out for the first time using an analytical approach.展开更多
The pre-scission neutrons measured in the reactions ^16O+^181Ta and ^19F+^178Hf are studied via a Langevin equation coupled with a statistical decay model. We find that because of the mass asymmetry of different ent...The pre-scission neutrons measured in the reactions ^16O+^181Ta and ^19F+^178Hf are studied via a Langevin equation coupled with a statistical decay model. We find that because of the mass asymmetry of different entrance channels, the spin distributions of compound nuclei would be different, consequently, the measured neutrons in these two reactions would also different. This means that the entrance channel will affect the particle emission in the fission process of hot nuclei.展开更多
We applied the four dimensional Langevin dynamical model to investigate the average spin of fission fragments. Elongation, neck thickness, asymmetry parameter, and the orientation degree of freedom(K coordinate)are ...We applied the four dimensional Langevin dynamical model to investigate the average spin of fission fragments. Elongation, neck thickness, asymmetry parameter, and the orientation degree of freedom(K coordinate)are the four dimensions of the dynamical model. We assume that the collective modes depend on the emission angle of the fragments, then different parameters related to the average spin of fission fragments are calculated dynamically.The angle dependence of average spin of fission fragments is investigated by calculating the spin at angles 90?and165?. Also, the obtained results based on the transition state model at scission point are presented. One can obtain better agreement between the results of the dynamical model and experimental data in comparison with the results of the transition state model.展开更多
The Master equation is considered the gold standard for modeling the stochastic mechanisms of gene regulation in molecular detail, but it is too complex to solve exactly in most cases, so approximation and simulation ...The Master equation is considered the gold standard for modeling the stochastic mechanisms of gene regulation in molecular detail, but it is too complex to solve exactly in most cases, so approximation and simulation methods are essential. However, there is still a lack of consensus about the best way to carry these out. To help clarify the situation, we review Master equation models of gene regulation, theoretical approximations based on an expansion method due to N.G. van Kampen and R. Kubo, and simulation algorithms due to D.T. Gillespie and P. Langevin. Expansion of the Master equation shows that for systems with a single stable steady-state, the stochastic model reduces to a deterministic model in a first-order approximation. Additional theory, also due to van Kampen, describes the asymptotic behavior of multistable systems. To support and illustrate the theory and provide further insight into the complex behavior of multistable systems, we perform a detailed simulation study comparing the various approximation and simulation methods applied to synthetic gene regulatory systems with various qualitative characteristics. The simulation studies show that for large stochastic systems with a single steady-state, deterministic models are quite accurate, since the probability distribution of the solution has a single peak tracking the deterministic trajectory whose variance is inversely proportional to the system size. In multistable stochastic systems, large fluctuations can cause individual trajectories to escape from the domain of attraction of one steady-state and be attracted to another, so the system eventually reaches a multimodal probability distribution in which all stable steady- states are represented proportional to their relative stability. However, since the escape time scales exponentially with system size, this process can take a very long time in large systems.展开更多
By calculating the excess of the evaporation residue cross sections of the ^200Pb nucleus over that predicted by the standard statistical model as a function of nuclear viscosity coefficient using a Langevin equation ...By calculating the excess of the evaporation residue cross sections of the ^200Pb nucleus over that predicted by the standard statistical model as a function of nuclear viscosity coefficient using a Langevin equation combined with a statistical decay model, it is found that high angular momentum not only amplifies the dissipation effects on the excess of the evaporation residue cross sections, but also considerably increases the sensitivity of this excess to the nuclear viscosity coefficient. These results suggest that on the experimental side, to accurately obtain the information of nuclear dissipation inside the saddle point by measuring the evaporation residue cross section, it had better populate those compound systems with high spins.展开更多
The excitation functions of the evaporation residue formation probability of three heavy nuclei ^194pb, ^200Pb and ^206pb are calculated by using a Langevin equation coupled with a statistical decay model. The results...The excitation functions of the evaporation residue formation probability of three heavy nuclei ^194pb, ^200Pb and ^206pb are calculated by using a Langevin equation coupled with a statistical decay model. The results show that the neutron-to-proton ratio (N/Z) of a compound nucleus has an effect on survival probability and this effect becomes larger with increasing N/Z. This is because the fission barrier and the pre-saddle particle emission depend on the N/Z ratio of the system.展开更多
A dynamical Langevin model is employed to calculate the excess of the evaporation residue cross sections of the ^194Pb nucleus over that predicted by the standard statistical model as a function of nuclear dissipation...A dynamical Langevin model is employed to calculate the excess of the evaporation residue cross sections of the ^194Pb nucleus over that predicted by the standard statistical model as a function of nuclear dissipation strength. It is shown that large excitation energy can increase the effects of nuclear dissipation on the excess of the evaporation residues and the sensitivity of this excess to the dissipation strength,and that more higher excitation energies have little contribution to further raising this sensitivity. These results suggest that on the experimental side,producing those compound systems with moderate excitation energy is sucient for a good determination of the pre-saddle nuclear dissipation strength by measuring the evaporation residue cross section,and that forming an extremely highly excited system does not considerably improve the sensitivity of evaporation residues to the dissipation strength.展开更多
We prove a fluctuating limit theorem of a sequence of super-stable processes overR with a single point catalyst.The weak convergence of the processes on the space of Schwartz distributions is established.The limiting ...We prove a fluctuating limit theorem of a sequence of super-stable processes overR with a single point catalyst.The weak convergence of the processes on the space of Schwartz distributions is established.The limiting process is an Ornstein–Uhlenbeck type process solving a Langevin type equation driven by a one-dimensional stable process.展开更多
Three different kinds of fluctuation limits (high density fluctuation, small branching fluctuation and large scale fluctuation) of the measure-vained immigration diffusion process are studied,which lead to the general...Three different kinds of fluctuation limits (high density fluctuation, small branching fluctuation and large scale fluctuation) of the measure-vained immigration diffusion process are studied,which lead to the generalized Ornstein-Uhlenbeck diffusion defined by a Langevin equation ofthe type of [1]. The fluctuation limit theorems cover all dimension numbers and give physicalinterpretations to the parameters appearing in the equation.展开更多
基金Project supported by the Basic and Applied Basic Research Foundation of Guangdong Province,China(Grant No.2021A1515010328)the Key-Area Research and Development Program of Guangdong Province,China(Grant No.2020B010183001)the National Natural Science Foundation of China(Grant No.12074126)。
文摘Efficient numerical algorithm for stochastic differential equation has been an important object in the research of statistical physics and mathematics for a long time.In this work we study the highly accurate numerical algorithm for the overdamped Langevin equation.In particular,our interest is in the behaviour of the numerical schemes for solving the overdamped Langevin equation in the harmonic system.Based on the large friction limit of the underdamped Langevin dynamic scheme,three algorithms for overdamped Langevin equation are obtained.We derive the explicit expression of the stationary distribution of each algorithm by analysing the discrete time trajectory for both one-dimensional case and multi-dimensional case.The accuracy of the stationary distribution of each algorithm is illustrated by comparing with the exact Boltzmann distribution.Our results demonstrate that the“BAOA-limit”algorithm generates an accurate distribution of the harmonic system in a canonical ensemble,within a stable range of time interval.The other algorithms do not produce the exact distribution of the harmonic system.
基金Supported by National Natural Science Foundation of China (10575075, 10447006)
文摘The analytical solution of a multidimensional Langevin equation at the overdamping limit is obtained and the probability of particles passing over a two-dimensional saddle point is discussed. These results may break a path for studying further the fusion in superheavy elements synthesis.
基金Supported by Knowledge Innovation Program of Chinese Academy of Sciences (55010701)National Support Plan of Science and Technology of China (2006BAI08B04-7)+2 种基金973 Program (2007CB815004)Shanghai Development Foundation from Science and Technology (06JC14082)National Natural Science Foundation of China (10775167)
文摘The temperature dependent width of the fission fragment distributions was simulated in the Langevin equation by taking two-parameter exponential form of the fission fragment mass variance at scission point for each fission event. The result can reproduce experimental data well, and it permits to make reliable estimate for unmeasured product yields near symmetry fission.
基金Supported by the National Natural Science Foundation of China under Grant No 1067401, and the Specialized Research Foundation for the Doctoral Program of Higher Education under Grant No 20050027001.
文摘The quantum thermodynamic functions of a harmonic oscillator coupled to a heat bath through velocity-dependent coupling are obtained analytically. It is shown that both the free energy and the entropy decay fast with the temperature in relation to that of the usual coupling from. This implies that the velocity-dependent coupling helps to ensure the third law of thermodynamics.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.31370830,11675134,11474345,and 11604030)the State Key Development Program for Basic Research of China(Grant No.2013CB837200)+1 种基金the 111 Project,China(Grant No.B16029)the China Postdoctoral Science Foundation(Grant No.2016M602071)
文摘Cell migration plays an essential role in a wide variety of physiological and pathological processes. In this paper we numerically discuss the properties of an anisotropic persistent random walk (APRW) model, in which two different and independent persistent times are assumed for cell migrations in the x-and y-axis directions. An intrinsic orthogonal coordinates with the primary and non-primary directions can be defined for each migration trajectory based on the singular vector decomposition method. Our simulation results show that the decay time of single exponential distribution of velocity auto-correlation function (VACF) in the primary direction is actually the large persistent time of the APRW model, and the small decay time of double exponential VACF in the non-primary direction equals the small persistent time of the APRW model. Thus, we propose that the two persistent times of anisotropic migration of cells can be properly estimated by discussing the VACFs of trajectory projected to the primary and non-primary directions.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10721403)the National Basic Research Program of China (Grant No. 2009CB918500)
文摘A typical biological cell lives in a small volmne at room temperature; the noise effect on the cell signal transduction pathway may play an important role in its dynamics. Here, using the transforming growth factor-β signal transduction pathway as an example, we report our stochastic simulations of the dynamics of the pathway and introduce a linear noise approximation method to calculate the transient intrinsic noise of pathway components. We compare the numerical solutions of the linear noise approximation with the statistic results of chemical Langevin equations, and find that they are quantitatively in agreement with the other. When transforming growth factor-β dose decreases to a low level, the time evolution of noise fluctuation of nuclear Smad2-Smad4 complex indicates the abnormal enhancement in the transient signal activation process.
文摘The non-classical properties of light propagating in four-channel Kerr waveguides, confined in an optical cavity, are studied. The solution to the Hamiltonian of field operators is obtained semi-analytically by using symmetrically ordered phase-space representation. Full quantum analysis of the input coherent fields displays a strong transition of photon property between the super-Poissonian and sub-Poissonian statistics. It is found that the cavity-assisted multichannel system exhibits enhanced squeezing both in single-and compound-mode. This multichannel system may be utilized as an efficient quantumlight generator.
基金supported by the National Natural Science Foundation of China(11101333 and 11302172)the Natural Science Foundation of Shaanxi(2011GQ1018)the Northwestern Polytechnical University Foundation for Fundamental Research(JC201152)
文摘The diffusion behavior driven by bounded noise under the influence of a coupled harmonic potential is investigated in a two-dimensional coupled-damped model. With the help of the Laplace analysis we obtain exact descriptions for a particle’s two-time dynamics which is subjected to a coupled harmonic potential and a coupled damping. The time lag is used to describe the velocity autocorrelation function and mean square displacement of the diffusing particle. The diffusion behavior for the time lag is also discussed with respect to the coupled items and the amplitude of bounded noise.
文摘In order to calculate the electron energy distribution in the fuel rod gap of a VVER- 1000 nuclear reactor, the Fokker-Planck equation (FPE) governing the non-equilibrium behavior of electrons passing through the fuel-rod gap as an absorber has been solved in this paper. Besides, the Monte Carlo Geant4 code was employed to simulate the electron migration in the fuel-rod gap and the energy distribution of electrons was found. As for the results, the accuracy of the FPE was compared to the Geant4 code outcomes and a satisfactory agreement was found. Also, different percentage of the volatile and noble gas fission fragments produced in fission reactions in fuel rod, i.e. Krypton, Xenon, Iodine, Bromine, Rubidium and Cesium were employed so as to investigate their effects on the electrons' energy distribution. The present results show that most of the electrons in the fuel rod's gap were within the thermal energy limitation and the tail of the electron energy distribution was far from a Maxwellian distribution. The interesting outcome was that the electron energy distribution is slightly increased due to the accumulation of fission fragments in the gap. It should be noted that solving the FPE for the energy straggling electrons that are penetrating into the fuel-rod gap in the VVER-1000 nuclear reactor has been carried out for the first time using an analytical approach.
基金National Natural Science Foundation of China (10405007)
文摘The pre-scission neutrons measured in the reactions ^16O+^181Ta and ^19F+^178Hf are studied via a Langevin equation coupled with a statistical decay model. We find that because of the mass asymmetry of different entrance channels, the spin distributions of compound nuclei would be different, consequently, the measured neutrons in these two reactions would also different. This means that the entrance channel will affect the particle emission in the fission process of hot nuclei.
文摘We applied the four dimensional Langevin dynamical model to investigate the average spin of fission fragments. Elongation, neck thickness, asymmetry parameter, and the orientation degree of freedom(K coordinate)are the four dimensions of the dynamical model. We assume that the collective modes depend on the emission angle of the fragments, then different parameters related to the average spin of fission fragments are calculated dynamically.The angle dependence of average spin of fission fragments is investigated by calculating the spin at angles 90?and165?. Also, the obtained results based on the transition state model at scission point are presented. One can obtain better agreement between the results of the dynamical model and experimental data in comparison with the results of the transition state model.
文摘The Master equation is considered the gold standard for modeling the stochastic mechanisms of gene regulation in molecular detail, but it is too complex to solve exactly in most cases, so approximation and simulation methods are essential. However, there is still a lack of consensus about the best way to carry these out. To help clarify the situation, we review Master equation models of gene regulation, theoretical approximations based on an expansion method due to N.G. van Kampen and R. Kubo, and simulation algorithms due to D.T. Gillespie and P. Langevin. Expansion of the Master equation shows that for systems with a single stable steady-state, the stochastic model reduces to a deterministic model in a first-order approximation. Additional theory, also due to van Kampen, describes the asymptotic behavior of multistable systems. To support and illustrate the theory and provide further insight into the complex behavior of multistable systems, we perform a detailed simulation study comparing the various approximation and simulation methods applied to synthetic gene regulatory systems with various qualitative characteristics. The simulation studies show that for large stochastic systems with a single steady-state, deterministic models are quite accurate, since the probability distribution of the solution has a single peak tracking the deterministic trajectory whose variance is inversely proportional to the system size. In multistable stochastic systems, large fluctuations can cause individual trajectories to escape from the domain of attraction of one steady-state and be attracted to another, so the system eventually reaches a multimodal probability distribution in which all stable steady- states are represented proportional to their relative stability. However, since the escape time scales exponentially with system size, this process can take a very long time in large systems.
基金National Natural Science Foundation of China(10405007)
文摘By calculating the excess of the evaporation residue cross sections of the ^200Pb nucleus over that predicted by the standard statistical model as a function of nuclear viscosity coefficient using a Langevin equation combined with a statistical decay model, it is found that high angular momentum not only amplifies the dissipation effects on the excess of the evaporation residue cross sections, but also considerably increases the sensitivity of this excess to the nuclear viscosity coefficient. These results suggest that on the experimental side, to accurately obtain the information of nuclear dissipation inside the saddle point by measuring the evaporation residue cross section, it had better populate those compound systems with high spins.
基金Supported by National Natural Science Foundation of China(10405007)
文摘The excitation functions of the evaporation residue formation probability of three heavy nuclei ^194pb, ^200Pb and ^206pb are calculated by using a Langevin equation coupled with a statistical decay model. The results show that the neutron-to-proton ratio (N/Z) of a compound nucleus has an effect on survival probability and this effect becomes larger with increasing N/Z. This is because the fission barrier and the pre-saddle particle emission depend on the N/Z ratio of the system.
基金Supported by National Natural Science Foundation of China (10405007)
文摘A dynamical Langevin model is employed to calculate the excess of the evaporation residue cross sections of the ^194Pb nucleus over that predicted by the standard statistical model as a function of nuclear dissipation strength. It is shown that large excitation energy can increase the effects of nuclear dissipation on the excess of the evaporation residues and the sensitivity of this excess to the dissipation strength,and that more higher excitation energies have little contribution to further raising this sensitivity. These results suggest that on the experimental side,producing those compound systems with moderate excitation energy is sucient for a good determination of the pre-saddle nuclear dissipation strength by measuring the evaporation residue cross section,and that forming an extremely highly excited system does not considerably improve the sensitivity of evaporation residues to the dissipation strength.
基金Supported by National Natural Science Foundation of China(Grant No.11126052)
文摘We prove a fluctuating limit theorem of a sequence of super-stable processes overR with a single point catalyst.The weak convergence of the processes on the space of Schwartz distributions is established.The limiting process is an Ornstein–Uhlenbeck type process solving a Langevin type equation driven by a one-dimensional stable process.
文摘Three different kinds of fluctuation limits (high density fluctuation, small branching fluctuation and large scale fluctuation) of the measure-vained immigration diffusion process are studied,which lead to the generalized Ornstein-Uhlenbeck diffusion defined by a Langevin equation ofthe type of [1]. The fluctuation limit theorems cover all dimension numbers and give physicalinterpretations to the parameters appearing in the equation.