The study of melting stage of bulk silicon using molecular dynamics simulation

The melting stage of bulk silicon is studied using classical molecular dynamics simulation. The mean square displacement and diffusion coefficient are focused allowing statistics analysis of the dynamics displacement of each atom. Three stages of the melting processes, premelting, accelerated melting and relaxation, are resolved. The structural development is evaluated through the stages by Lindemann index, non-Gaussian parameter and the second neighbor coordination number. The studies emphasize the observation that premelting occurs in the ideal crystal on melting.     

Theory of diffusion in premelting systems

Summary The diffusion in premelting films and surfaces is described by the Fokker-Planck equation with a periodic potential whose amplitude depends on the temperature and vanishes at the bulk melting temperature. The self-part of the dynamic structure factor is calculated and the results are compared with neutron scattering data from CH₄ premelting films adsorbed on MgO and with atom scattering data from the (110) surface of Pb. In honour of Prof. Fausto Fumi on the occasion of his retirement from teaching.     

Active diffusion of motor particles

The movement of motor particles consisting of one or several molecular motors bound to a cargo particle is studied theoretically. The particles move on patterns of immobilized filaments. Several patterns are described for which the motor particles undergo nondirected but enhanced diffusion. Depending on the walking distance of the particles and the mesh size of the patterns, the active diffusion coefficient exhibits three different regimes. For micrometer-sized motor particles in water, e.g., this diffusion coefficient can be enhanced by 2 orders of magnitude.     

对利用动态光散射法测量颗粒粒径和液体黏度的改进

光散射技术通过测量悬浮液中布朗运动颗粒的平移扩散系数,得到颗粒流体力学直径或液体黏度.本文由单参数模型入手,建立了低颗粒浓度下,单颗粒平移扩散系数与颗粒集体平移扩散系数和颗粒浓度之间的线性依存关系并将其引入光散射法中,从而对现有的测量方法进行了改进.改进后的测量方法可实现纳米尺度球型颗粒标称直径的测量和液体黏度的绝对法测量.以聚苯乙烯颗粒+水和二氧化硅颗粒+乙醇两个分散系为参考样本,通过实验,验证了改进后方法的可行性.此外,还针对上述两个分散系,实验探讨了温度和颗粒浓度对颗粒集体平移扩散系数的影响规律,发现聚苯乙烯颗粒+水分散系中,颗粒间相互作用表现为引力;二氧化硅颗粒+乙醇分散系中,颗粒间相互作用表现为斥力.讨论了颗粒集体平移扩散系数随颗粒浓度变化规律与第二渗透维里系数的关系.     

浓悬浮液中渗透性颗粒的扩散特性研究

本文利用浓悬浮液中渗透性颗粒的短时扩散动力学数值模拟的结论,并结合Cohen-de Schepper近似和Percus-Yevick近似,研究了不同粒径渗透性颗粒的有效扩散系数随体积分数和渗透率的变化关系. 结果表明:对于浓悬浮液中一定粒径的渗透性颗粒,其扩散系数随渗透率的增加而增加,随体积分数的增加而减少;具有相同粒径与流体动力学屏蔽深度比值且波数较大的渗透性颗粒,其粒径对扩散的影响可以忽略. 关键词： 渗透性颗粒 有效扩散系数 体积分数 布朗运动短时区域     

Effect of lateral interactions on tunnel diffusion of adsorbed particles

A way of calculating the chemical diffusion coefficient for tunnel diffusion is discussed. It is shown that the famous “jump rate” formula may be used to describe the tunnel diffusion of interacting particles in the region of coverages and temperatures where phase transitions in the adsorbed overlayer are absent. The dependence of the tunnel diffusion coefficient on coverage is calculated for the square lattice taking into consideration the repulsive lateral interactions of nearest-neighbour particles.     

Hopping on a zig-zag course

We study the diffusion coefficient of Active Brownian particles in two dimensions. In addition to usual attributes of active motion we let the particles turn in preferred directions over random times. This angular motion is modeled by an effective Lorentz force with time dependent frequency switching between two values at exponentially distributed random times. The diffusion coefficient is calculated by the Taylor-Kubo formula where distributions found from a Fokker-Planck equation or from a continuous time random walk approach have been inserted for averaging. Eventually properties of the diffusion coefficient will be discussed.     

Diffusion in flashing periodic potentials

The one-dimensional overdamped Brownian motion in a symmetric periodic potential modulated by external time-reversible noise is analyzed. The calculation of the effective diffusion coefficient is reduced to the mean first passage time problem. We derive general equations to calculate the effective diffusion coefficient of Brownian particles moving in arbitrary supersymmetric potential modulated by: (i) an external white Gaussian noise and (ii) a Markovian dichotomous noise. For both cases the exact expressions for the effective diffusion coefficient are derived. We obtain acceleration of diffusion in comparison with the free diffusion case for fast fluctuating potentials with arbitrary profile and for sawtooth potential in case (ii). In this case the parameter region where this effect can be observed is given. We obtain also a finite net diffusion in the absence of thermal noise. For rectangular potential the diffusion slows down, for all parameters of noise and of potential, in comparison with the case when particles diffuse freely.     

Suppression of diffusion by a weak external field in periodic potentials

Diffusion of overdamped Brownian particles in sawtooth potentials subject to a spatially uniform tilt is studied focusing on the influence of a small bias. It is shown that in the potentials with an asymmetry in the direction of tilting force, the application of a weak external force leads to a suppression of diffusive motion: the diffusion coefficient as a function of bias passes through a minimum which precedes an increase of diffusion caused by delocalization of particles. In the weak noise limit the effect can be understood as a competition between the forward and backward escape rates over potential barriers determining the behaviour of the diffusion coefficient in a weak external field. The asymptotic lower border for the reduction of spreading of particles at fixed temperature is established. The decrease of diffusion is accompanied by more rapid increase of current.     

固定化细胞的制备以及性能实验研究

本文对固定化光合细胞的制备工艺以及包埋细菌时固定化颗粒的结构、扩散性能作了初步的研究,采用PVA和海藻酸纳为包埋剂为可视化实验制作了一种完全透明的固定化颗粒,采用吸渗法测其孔隙率,并测定了颗粒中葡萄糖的扩散系数.     

核磁共振中多量子相干扩散行为的理论表述和计算机模拟

改进了Warren所提出的CRAZED脉冲序列以研究分子间多量子相干的扩散过程 ,讨论了利用核磁共振测量分子内和分子间多量子相干表观自扩散系数的理论表述 ,采用粒子的随机行走模型模拟其扩散行为 .在短脉冲近似和长脉冲梯度场两种实验条件下 ,分别获得了因扩散引起的不同相干阶数的相对信号衰减强度随梯度场脉冲间隔时间的变化曲线 ,由此得到分子内多量子相干和分子间多量子相干的表观扩散率与溶液分子扩散系数的关系 .还将计算机模拟结果与理论预测进行分析和比较 ,发现二者能很好地吻合 .研究结果表明 ,分子间多量子相干的表观扩散率与常规的分子内多量子相干的表观扩散率明显不同 ,因此 ,分子间多量子相干的表观扩散率可能提供一种新的核磁共振成像的对比度机理     

Simulations of anomalous ion diffusion in experimentally measured turbulent potential

The diffusion of plasma impurities in tokamak-edge-plasma turbulence is investigated numerically. The time-dependent potential governing particle motion was measured by 2D array of 8×8 Langmuir probes in edge region of CASTOR tokamak. The diffusion of particles is found to be classical in the radial direction, but it can be of an anomalous Lévy-walk type in the poloidal direction. The diffusion is found to be dependent on the ratio of particles’ mass and charge. When this ratio grows, the diffusion coefficient in radial direction grows as well, whereas poloidal diffusion coefficient drops down. Moreover, movement of particles in the time-frozen snapshot of this potential is investigated showing that also the time-independent potential is much more favorable for the particle diffusion in poloidal direction than in radial one. In the case of single ionized carbon ions the poloidal diffusion in time-independent potential transits to the Lévy-walk type for temperatures greater than 25 eV, for radial diffusion Lévy-walk was not observed even for 500 eV.     

On the effects of noise and drift on diffusion in fluids

We discuss some aspects of the intriguing problem of interplay between molecular diffusion and the geometry of the velocity field in the diffusion of test particles. By simple arguments one can understand how the diffusion coefficient can have a large enhancement from the combined effects of the noise and the drift terms in the Langevin equation ruling the motion of test particles. The same effects give rise to the superdiffusive transport observed in media with correlated random velocity fields.     

Noise-induced transport with low randomness

We study the transport of overdamped Brownian particles in periodic potentials subject to a spatially modulated Gaussian white noise. We derive an analytical expression for the diffusion coefficient of particles. By means of velocity, diffusion coefficient, and their ratio (Péclet number) we discuss (a) symmetric potential and modulation of noise intensity and (b) a ratchet profile with strong noise modulation. It is shown that state dependent fluctuations may not only induce directed transport, but also a pronounced coherence of transport if the potential exhibits a strong asymmetry.     

Self-diffusion in granular gases: Green-Kubo versus Chapman-Enskog

We study the diffusion of tracers (self-diffusion) in a homogeneously cooling gas of dissipative particles, using the Green-Kubo relation and the Chapman-Enskog approach. The dissipative particle collisions are described by the coefficient of restitution epsilon which for realistic material properties depends on the impact velocity. First, we consider self-diffusion using a constant coefficient of restitution, epsilon=const, as frequently used to simplify the analysis. Second, self-diffusion is studied for a simplified (stepwise) dependence of epsilon on the impact velocity. Finally, diffusion is considered for gases of realistic viscoelastic particles. We find that for epsilon=const both methods lead to the same result for the self-diffusion coefficient. For the case of impact-velocity dependent coefficients of restitution, the Green-Kubo method is, however, either restrictive or too complicated for practical application, therefore we compute the diffusion coefficient using the Chapman-Enskog method. We conclude that in application to granular gases, the Chapman-Enskog approach is preferable for deriving kinetic coefficients.     

Diffusion in different models of active Brownian motion

Active Brownian particles (ABP) have served as phenomenological models of self-propelled motion in biology. We study the effective diffusion coefficient of two one-dimensional ABP models (simplified depot model and Rayleigh-Helmholtz model) differing in their nonlinear friction functions. Depending on the choice of the friction function the diffusion coefficient does or does not attain a minimum as a function of noise intensity. We furthermore discuss the case of an additional bias breaking the left-right symmetry of the system. We show that this bias induces a drift and that it generally reduces the diffusion coefficient. For a finite range of values of the bias, both models can exhibit a maximum in the diffusion coefficient vs. noise intensity.     

On the depolarized Rayleigh scattering from macromolecular and colloidal solutions — Anisotropy of the diffusional broadening

The width of the depolarized Rayleigh line for the light scattered from a solution of non-spherical particles is calculated from a generalized diffusion equation. Due to the correlation between the translational motion and the orientation of the particles, the diffusional contribution to the width is anisotropic, i.e. the relevant effective diffusion coefficient depends on the scattering angle and on the polarization vectors. This anisotropy is related to the shape of the particles.     

Dynamic Light Scattering Measurement of Nanometer Particles in Liquids

Dynamic light scattering (DLS) techniques for studying sizes and shapes of nanoparticles in liquids are reviewed. In photon correlation spectroscopy (PCS), the time fluctuations in the intensity of light scattered by the particle dispersion are monitored. For dilute dispersions of spherical nanoparticles, the decay rate of the time autocorrelation function of these intensity fluctuations is used to directly measure the particle translational diffusion coefficient, which is in turn related to the particle hydrodynamic radius. For a spherical particle, the hydrodynamic radius is essentially the same as the geometric particle radius (including any possible solvation layers). PCS is one of the most commonly used methods for measuring radii of submicron size particles in liquid dispersions. Depolarized Fabry-Perot interferometry (FPI) is a less common dynamic light scattering technique that is applicable to optically anisotropic nanoparticles. In FPI the frequency broadening of laser light scattered by the particles is analyzed. This broadening is proportional to the particle rotational diffusion coefficient, which is in turn related to the particle dimensions. The translational diffusion coefficient measured by PCS and the rotational diffusion coefficient measured by depolarized FPI may be combined to obtain the dimensions of non-spherical particles. DLS studies of liquid dispersions of nanometer-sized oligonucleotides in a water-based buffer are used as examples.     

Dramatic change of the self-diffusions of colloidal ellipsoids by hydrodynamic interactions in narrow channels

The self-diffusion problem of Brownian particles under the constraint of quasi-one-dimensional(q1 D) channel has raised wide concern.The hydrodynamic interaction(HI) plays an important role in many practical problems and two-body interactions remain dominant under q1D constraint.We measure the diffusion coefficient of individual ellipsoid when two ellipsoidal particles are close to each other by video-microscopy measurement.Meanwhile, we obtain the numerical simulation results of diffusion coefficient using finite element software.We find that the self-diffusion coefficient of the ellipsoid decreases exponentially with the decrease of their mutual distance X when X X_0, where X_0 is the maximum distance of the ellipsoids to maintain their mutual influence, X_0 and the variation rate are related to the aspect ratio p = a/b.The mean squared displacement(MSD) of the ellipsoids indicates that the self-diffusion appears as a crossover region, in which the diffusion coefficient increases as the time increases in the intermediate time regime, which is proven to be caused by the spatial variations affected by the hydrodynamic interactions.These findings indicate that hydrodynamic interaction can significantly affect the self-diffusion behavior of adjacent particles and has important implications to the research of microfluidic problems in blood vessels and bones, drug delivery, and lab-on-chip.     

Chaotic diffusion for particles moving in a time dependent potential well

The chaotic diffusion for particles moving in a time dependent potential well is described by using two different procedures: (i) via direct evolution of the mapping describing the dynamics and; (ii) by the solution of the diffusion equation. The dynamic of the diffusing particles is made by the use of a two dimensional, nonlinear area preserving map for the variables energy and time. The phase space of the system is mixed containing both chaos, periodic regions and invariant spanning curves limiting the diffusion of the chaotic particles. The chaotic evolution for an ensemble of particles is treated as random particles motion and hence described by the diffusion equation. The boundary conditions impose that the particles can not cross the invariant spanning curves, serving as upper boundary for the diffusion, nor the lowest energy domain that is the energy the particles escape from the time moving potential well. The diffusion coefficient is determined via the equation of the mapping while the analytical solution of the diffusion equation gives the probability to find a given particle with a certain energy at a specific time. The momenta of the probability describe qualitatively the behavior of the average energy obtained by numerical simulation, which is investigated either as a function of the time as well as some of the control parameters of the problem.