Dynamical fluctuations in fragmentation reactions in a Boltzmann–Langevin approach

Based on the isospin-dependent Boltzmann–Langevin model, the dynamical fluctuations in the fragmentation reaction of ¹¹²Sn+¹¹²Sn are investigated. The quadrupole moment and octupole moment with zero magnetic quantum number have large fluctuations in the early time of the collisions. The dynamical fluctuations in momentum space show a strong dependence on the incident energy. The effects of using different fluctuations on the fragment cross sections are also studied in the fragmentation reactions. The results by using Q₂₀ + Q₃₀ fluctuation have a better agreement with the experimental data. Calculations using Q₂₀ + Q₃₀ fluctuation produce more proton-rich and neutron-rich nuclei than those using Q₂₀ fluctuation only. Besides, the difference between the production cross sections of fragments calculated by using Q₂₀ and Q₂₀ + Q₃₀ fluctuations is larger in the vicinity of the projectile. These results present that the dynamical fluctuations may affect the whole dynamical process of fragmentation reactions including the production of fragments, due to the nonlinear nature of the Boltzmann–Langevin equation.     

Langevin dynamic simulation of hysteresis in a field-swept Landau potential

Numerical simulations are done of Langevin dynamics for a uniform-orderparameter, field-swept Landau model,= –|a/2|m ²+|b/4|m ⁴–mh(t) , to study hysteresis effects. The field is swept at a constant rateh(t)=h(0)+ht. The stochastic jump values of the field {h_J from an initially prepared metastable minimumm(0) are recorded, on passage to a global minimum m(). The results are: (a) The mean jump¯h _J(h) increases (hysteresis loop widens) with h, confirming a previous theoretical criterion based on rate competition between field-sweep and inverse mean first-passage time (FPT); (b) The broad jump distribution(h _J,h) is related to intrinsically large FPT fluctuations ( ²–²)/ ² O(1), and can be quantitatively understood. Possible experimental tests of the ideas are indicated.     

朗之万方程及其在蛋白质折叠动力学中的应用

研究了朗之万方程的动力学性质,并用它模拟了蛋白质分子的折叠过程.首先在相空间中对朗之万方程做连续映射,发现做布朗运动的粒子在位置坐标上存在明显的概率分布,这表明蛋白质折叠过程中分子空间构型是非遍历的.此外,本文还通过数值模拟得到了去折叠态蛋白质的紧密度指标,并验证了它与实验结果以及其他理论方法的一致性.本文还提出了一种利用重整化方法研究熔球体状态蛋白质的理论模型,并提供了考虑疏水基影响的蛋白质折叠过程的模拟思路. 关键词： 朗之万方程 蛋白质折叠非遍历性 紧密度指标 重整化     

Numerical distortion and effects of thermostat in molecular dynamics simulations of single-walled carbon nanotubes

In this paper, single-walled carbon nanotubes （SWCNTs） are studied through molecular dynamics （MD） simulation. The simulations are performed at temperatures of 1 and 300K separately, with atomic interactions characterized by the second Reactive Empirical Bond Order （REBO） potential, and temperature controlled by a certain thermostat, i.e. by separately using the velocity scaling, the Berendsen scheme, the Nose-Hoover scheme, and the generalized Langevin scheme. Results for a （5,5） SWCNT with a length of 24.5 nm show apparent distortions in nanotube configuration, which can further enter into periodic vibrations, except in simulations using the generalized Langevin thermostat, which is ascribed to periodic boundary conditions used in simulation. The periodic boundary conditions may implicitly be applied in the form of an inconsistent constraint along the axis of the nanotube. The combination of the inconsistent constraint with the cumulative errors in calculation causes the distortions of nanotubes. When the generalized Langevin thermostat is applied, inconsistently distributed errors are dispersed by the random forces, and so the distortions and vibrations disappear. This speculation is confirmed by simulation in the case without periodic boundary conditions, where no apparent distortion and vibration occur. It is also revealed that numerically induced distortions and vibrations occur only in simulation of nanotubes with a small diameter and a large length-to-diameter ratio. When MD simulation is applied to a system with a particular geometry, attention should be paid to avoiding the numerical distortion and the result infidelity.     

Langevin dynamics simulations of phase separation in a one-component system

Langevin dynamics computer simulations have been performed for a two-dimensional Lennard-Jones fluid quenched into the coexistence region of its liquid-vapor phase diagram. For late stages of the phase-separation process, the average radius of the liquid clusters is found to grow proportional to (time)^1/4. This growth law is analyzed theoretically and compared to recent molecular dynamics and Monte Carlo results. Details of the different simulation methods are critically discussed.     

Langevin simulation of scalar fields: Additive and multiplicative noises and lattice renormalization

We consider the Langevin lattice dynamics for a spontaneously broken λ?⁴$\lambda {?}^4$ scalar field theory where both additive and multiplicative noise terms are incorporated. The lattice renormalization for the corresponding stochastic Ginzburg–Landau–Langevin and the subtleties related to the multiplicative noise are investigated.     

半刚性聚电解质链与带相反电荷颗粒复合体系的动力学模拟

用Langevin动力学研究了半刚性聚电解质链与带相反电荷球状颗粒在溶液中的复合体系，并研究了链的拉伸性质.具体考察了带电颗粒的电量以及溶液中盐离子浓度对复合体系的影响.链两端没有施加外力的情况下，当溶液中盐离子浓度较低时，复合体系呈现一种串珠状结构；当溶液中盐离子浓度较高时，复合体系转变为一种聚集态结构.链的两端施加外力的情况下，带电颗粒从链上脱落的过程可以分为两步. 关键词： 聚电解质链 Langevin动力学 Debye-Hückel长度     

Positivity of entropy production in the presence of a random thermostat

We study nonequilibrium statistical mechanics in the presence of a thermostat acting by random forces, and propose a formula for the rate of entropy productione() in a state . When is a natural nonequilibrium steady state we show thate()0, and sometimes we can provee()>0.     

Temperature dependent fission fragment distribution in the Langevin equation

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.     

Study on the multifrequency Langevin ultrasonic transducer

Langevin ultrasonic transducers are widely used in high-power ultrasonics and underwater sound. In ultrasonic cleaning, a matching metal horn rather than a metal cylinder is used as the radiator in order to enhance the radiating surface and improve the acoustic matching between the transducer and the processed medium. To raise the effect of ultrasonic cleaning, the standing wave in the cleaning tank should be eliminated. One method to eliminate the standing wave in the tank is to use the multifrequency ultrasonic transducer. In this paper, the Langevin ultrasonic horn transducer, with two resonance frequencies, is studied. The transducer consists of two groups of piezoelectric ceramic elements: the back metal cylinder, the middle metal cylinder and the front matching metal horn. The vibrational modes of the transducer are analysed, and resonance frequency equations of the transducer in the half-wave and the all-wave vibrational modes are derived. According to the resonance frequency equations, transducers with two resonance frequencies are designed and made. The resonance frequencies, the effective electromechanical coupling coefficients and the equivalent electric impedances of the transducers are measured. It is shown that the measured resonance frequencies are in good agreement with the computed results, and the transducer can be excited to vibrate at two resonance frequencies, which correspond to the half-wave and the all-wave vibrational modes of the transducer.     

Temperature dependent fission fragment distribution in the Langevin equation

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.     

Langevin dynamics of an interface near a wall

We study dynamical contact angles and precursor films using Langevin dynamics for SOS type models, near a wall which favors spreading. We first solve exactly the Gaussian model and discuss various asymptotic regimes. This is only appropriate to partial wetting. We then consider more general models. Using local equilibrium and scaling arguments, we derive the shape of the dynamical profile and the speed of the precursor film which exists when the spreading coefficient is strictly positive. Long-range potentials lead to a layered structure of the precursor film. We also consider the case of a meniscus in a capillary.     

Stochastic equations of the Langevin type under a weakly dependent perturbation

Asymptotic expansions for the probability density of the solution of a stochastic differential equation under a weakly dependent perturbation are proposed. In particular, linear partial differential equations for the first two terms of the correlation time expansion are derived. It is shown that in these expansions the boundary layer part appears and non-Gaussianity of the perturbation is important for the Fokker-Planck approximation correction.     

Temporal breakdown and Borel resummation in the complex Langevin method

We reexamine the Parisi–Klauder conjecture for complex e^iθ/2?⁴$e^{i\theta /2}{?}^4$ measures with a Wick rotation angle 0≤θ/2≤π/2$0\le \theta /2\le \pi /2$ interpolating between Euclidean signature and Lorentzian signature. Our main result is that the asymptotics for short stochastic times t$t$ encapsulates information also about the equilibrium aspects. The moments evaluated with the complex measure and with the real measure defined by the stochastic Langevin equation have the same t→0$t\to 0$ asymptotic expansion which is shown to be Borel summable. The Borel transform correctly reproduces the time dependent moments of the complex measure for all t$t$, including their t→∞$t\to \infty$ equilibrium values. On the other hand the results of a direct numerical simulation of the Langevin moments are found to disagree from the ‘correct’ result for t$t$ larger than a finite t_c$t_c$. The breakdown time t_c$t_c$ increases powerlike for decreasing strength of the noise’s imaginary part but cannot be excluded to be finite for purely real noise. To ascertain the discrepancy we also compute the real equilibrium distribution for complex noise explicitly and verify that its moments differ from those obtained with the complex measure.     

A hybrid formalism combining fluctuating hydrodynamics and generalized Langevin dynamics for the simulation of nanoparticle thermal motion in an incompressible fluid medium

A novel hybrid scheme based on Markovian fluctuating hydrodynamics of the fluid and a non-Markovian Langevin dynamics with the Ornstein-Uhlenbeck noise perturbing the translational and rotational equations of motion of the nanoparticle is employed to study the thermal motion of a nanoparticle in an incompressible Newtonian fluid medium. A direct numerical simulation adopting an arbitrary Lagrangian-Eulerian (ALE) based finite element method (FEM) is employed in simulating the thermal motion of a particle suspended in the fluid confined in a cylindrical vessel. The results for thermal equilibrium between the particle and the fluid are validated by comparing the numerically predicted temperature of the nanoparticle with that obtained from the equipartition theorem. The nature of the hydrodynamic interactions is verified by comparing the velocity autocorrelation function (VACF) and mean squared displacement (MSD) with well-known analytical results. For nanoparticle motion in an incompressible fluid, the fluctuating hydrodynamics approach resolves the hydrodynamics correctly but does not impose the correct equipartition of energy based on the nanoparticle mass because of the added mass of the displaced fluid. In contrast, the Langevin approach with an appropriate memory is able to show the correct equipartition of energy, but not the correct short- and long-time hydrodynamic correlations. Using our hybrid approach presented here, we show for the first time, that we can simultaneously satisfy the equipartition theorem and the (short- and long-time) hydrodynamic correlations. In effect, this results in a thermostat that also simultaneously preserves the true hydrodynamic correlations. The significance of this result is that our new algorithm provides a robust computational approach to explore nanoparticle motion in arbitrary geometries and flow fields, while simultaneously enabling us to study carrier adhesion mediated by biological reactions (receptor-ligand interactions) at the vessel wall at a specified finite temperature.     

蛋白质构型变化的二维广义郎之万方程描述

采用二维广义郎之万方程描述蛋白质构型的随机变化,并与电子输运过程的原子密度填充模型相协调. 假设通过键和通过空间的两类电子输运路径分别受到高斯分数噪声和高斯白噪声的影响. 推导了电子转移给体-受体距离涨落和荧光寿命涨落自相关函数的一般表达式. 采用数值拉普拉斯反变换计算了蛋白质构型涨落动力学,并详尽讨论了长时间和短时间行为的渐近解析. 最后,明确了基于二维广义郎之万方程的蛋白质构型描述与一维描述之间的关系.     

Return to thermal equilibrium by the solution of a quantum Langevin equation

A quantum-mechanical treatment of the evolution of an anharmonic oscillator coupled to a heat bath is given. It is shown that for a certain class of anharmonic potentials the heat bath drives the oscillator to an equilibrium state, close to the quantum Gibbs state associated to the potential. Thus a partial proof is provided for a conjecture of R. Benguria and M. Kac.This paper contains part of the author's Ph.D. work, done at the Institute for Theoretical Physics of Groningen State University, Groningen, the Netherlands.     

The Langevin equation on Lie algebras: Maxwell-Boltzmann is not always the equilibrium

We give a geometric formulation of the Fokker-Planck-Kramer equations for a particle moving on a Lie algebra under the influence of a dissipative and a random force. Special cases of interest are fluid mechanics, the Stochastic Loewner equation and the rigid body. We find that the Boltzmann distribution, although a static solution, is not normalizable when the algebra is not unimodular. This is because the invariant measure of integration in momentum space is not the standard one. We solve the special case of the upper half-plane (hyperboloid) explicitly: there is another equilibrium solution to the Fokker-Planck equation, which is integrable. It breaks rotation invariance.     

Derivation of a Fokker–Planck equation for generalized Langevin dynamics

A Fokker–Planck equation describing the statistical properties of Brownian particles acted upon by long-range stochastic forces with power-law correlations is derived. In contrast with previous approaches (Wang, Phys. Rev. A 45 (1992) 2), it is shown that the distribution of Brownian particles after release from a point source is broader than Gaussian and described by a Fox function. Transport is shown to be ballistic at short times and either sub-diffusive or super-diffusive at large times. The imposition of occasional trapping events onto the Brownian dynamics can result in confined diffusion (d/dtx²→0) at long times when the mean trapping time is divergent. It is suggested that such dynamics describe protein motions in cell membranes.