A note on confined diffusion

The random motion of a Brownian particle confined in some finite domain is considered. Quite generally, the relevant statistical properties involve infinite series, whose coefficients are related to the eigenvalues of the diffusion operator. Because the latter depend on space dimensionality and on the particular shape of the domain, an analytical expression is in most circumstances not available. In this article, it is shown that the series may in some circumstances sum up exactly. Explicit calculations are performed for 2D diffusion restricted to a circular domain and 3D diffusion inside a sphere. In both cases, the short-time behaviour of the mean square displacement is obtained.     

异质原子在Cu（001）表面扩散的分子动力学模拟

采用分子动力学方法模拟单个增原子Ag,Pd和Cu在Cu（001）表面上的扩散过程.通过对自扩散和异质扩散过程中扩散机制的观察,统计三种不同的增原子在不同温度下的扩散频率,拟合给出扩散势垒和扩散频率的指前因子,并与扩散势垒的静力学计算结果进行比较.结果表明：在800 K以下时,三种增原子均以简单跳跃机制为主扩散,与衬底不互溶的Ag增原子的跳跃频率最大,与衬底互溶的Pd增原子的跳跃频率最小.同质增原子与异质增原子的扩散频率和温度的关系均较好地符合Arrhenius公式,由Arrhenius公式拟合给出的三种不同增原子的扩散势垒与表面结构和增原子表面结合能有关.Pd和Cu增原子从跳跃机制为主向交换机制为主的转换温度分别在825和937 K左右. 关键词： 表面扩散 分子动力学模拟     

分子动力学模拟Gd原子在Cu(110)表面的扩散过程

为了分析Gd吸附原子在Cu(110)表面的扩散机理，用分子动力学对该扩散过程进行模拟.模拟 结果表明在［1 1 0］方向Gd原子通过跳跃机理扩散，而且多步跳跃频率很高.而在［0 0 1］方向则通过交换机理扩散.吸附原子在［1 1 0］方向的扩散能力要比［0 0 1］ 方向强.通过对扩散频率的拟合，发现两种扩散机理都符合Arrhenius公式，从而确定了跳跃 机理的扩散势垒为0.097eV，交换机理的扩散势垒为0.33eV.另外还用能量弛豫的方法确定了 跳跃机理的扩散势垒. 关键词： 分子动力学 表面扩散 跳跃机理 交换机理 扩散势垒     

The diffusion constant for two-state brownons

We calculate the diffusion constant for two-state brownons when the change of state is not, as usually assumed, Markovian. The correction to the non-interchanging species result is found to be exactly expressible in terms of the Laplace transforms of the sojourn time densities.     

气体-表面相互作用的分子动力学模拟研究

采用分子动力学模拟方法研究了气体分子Ar在光滑和粗糙Pt表面上的散射规律.提出了一种速度抽样方法,计算了不同温度条件下气体分子对光滑和粗糙表面的切向动量适应系数和吸附概率.结果显示：光滑表面条件下,气体分子的切向动量系数和吸附概率都随着温度的升高而降低;粗糙度对气体分子切向动量与表面的适应具有极大的促进作用,当粗糙度足够大时,切向动量适应系数的大小趋近于1.0,对温度的敏感性也逐渐降低.采用粒子束方法对气体分子在光滑和粗糙表面上的散射规律进行了定量分析.总结了散射过程中气体分子的典型轨迹和动量变化规律,将气体分子在光滑表面的散射分为两种类型：单次碰撞后散射和多次碰撞后散射.单次碰撞后散射的气体分子平均切向动量有所减小,而经过多次碰撞后散射的气体分子则倾向于保持原有的平均切向动量.对于粗糙表面,粗糙度的存在使气体分子与表面间的动量和能量适应更加充分,导致气体分子在较粗糙表面上散射后的平均切向动量大幅减小并接近于0,且气体分子在表面上经历的碰撞次数越多,其散射后的能量损失越严重.     

Molecular dynamics simulation of nanoscale surface diffusion of heterogeneous adatoms clusters

Molecular dynamics simulation employing the embedded atom method potential is utilized to investigate nanoscale surface diffusion mechanisms of binary heterogeneous adatoms clusters at 300 K, 500 K, and 700 K. Surface diffusion of heterogeneous adatoms clusters can be vital for the binary island growth on the surface and can be useful for the formation of alloy-based thin film surface through atomic exchange process. The results of the diffusion process show that at 300 K, the diffusion of small adatoms clusters shows hopping, sliding, and shear motion; whereas for large adatoms clusters(hexamer and above), the diffusion is negligible. At 500 K, small adatoms clusters, i.e., dimer, show almost all possible diffusion mechanisms including the atomic exchange process; however no such exchange is observed for adatoms clusters greater than dimer. At 700 K, the exchange mechanism dominates for all types of clusters, where Zr adatoms show maximum tendency and Ag adatoms show minimum or no tendency toward the exchange process. Separation and recombination of one or more adatoms are also observed at 500 K and 700 K. The Ag adatoms also occupy pop-up positions over the adatoms clusters for short intervals. At 700 K, the vacancies are also generated in the vicinity of the adatoms cluster,vacancy formation, filling, and shifting can be observed from the results.     

分子动力学方法研究金属Ti中He小团簇的迁移

采用分子动力学方法模拟了不同温度下He原子及He团簇在金属Ti中的迁移特性,并计算了扩散前系数和激活能. 研究发现这种扩散的各向异性非常显著,具体表现在He原子及He团簇在不同方向上扩散系数的前系数完全不同,但它们的激活能却相同. 研究表明:在预测金属中He的扩散行为时,必须采用动态模拟方法才能得到准确的前系数,仅仅考虑势垒的静态模拟方法是不行的. 另外,还发现一个不同于直觉的现象,即较低温度下He二聚物的扩散系数比单个He原子的扩散系数大;此外,在所模拟的温度范围内Arrhenius方程能够很好地描述它们的扩散. 这说明动力学模拟对预测金属中He的扩散行为具有重要的意义. 关键词： 分子动力学 扩散系数 各向异性 氦     

Ge diffusion on Si surfaces

Ge diffusion on Si(100), (111), and (110) surfaces has been studied by Auger electron spectroscopy and low energy electron diffraction in the temperature range from 600 to 800 °C. Surface diffusion coefficients versus temperature have been measured.     

二元Lennard-Jones液体的相分离过程及其扩散性质的分子动力学研究

采用分子动力学(MD)模拟方法,研究了二元体系中相分离过程、粒子的扩散系数以及相分离域尺寸大小随温度的变化规律.发现,相分离域随温度的生长过程可以分为两个阶段,分别是温度比较高的快速生长阶段和低温时的稳定生长阶段;相分离体系中系统的扩散激活能不是常数,而是一个随温度变化的函数,并且当温度高于60 K时,满足关系式E(T)=a+bT^c.讨论了组元尺寸的变化对相分离过程的影响.结果表明,随两组元中某一组元 关键词： 相分离 扩散 分子动力学模拟     

First passage time statistics of Brownian motion with purely time dependent drift and diffusion

Systems where resource availability approaches a critical threshold are common to many engineering and scientific applications and often necessitate the estimation of first passage time statistics of a Brownian motion (Bm) driven by time-dependent drift and diffusion coefficients. Modeling such systems requires solving the associated Fokker-Planck equation subject to an absorbing barrier. Transitional probabilities are derived via the method of images, whose applicability to time dependent problems is shown to be limited to state-independent drift and diffusion coefficients that only depend on time and are proportional to each other. First passage time statistics, such as the survival probabilities and first passage time densities are obtained analytically. The analysis includes the study of different functional forms of the time dependent drift and diffusion, including power-law time dependence and different periodic drivers. As a case study of these theoretical results, a stochastic model of water resources availability in snowmelt dominated regions is presented, where both temperature effects and snow-precipitation input are incorporated.     

Non-Markovian diffusion equations and processes: Analysis and simulations

In this paper we introduce and analyze a class of diffusion type equations related to certain non-Markovian stochastic processes. We start from the forward drift equation which is made non-local in time by the introduction of a suitable chosen memory kernel K(t). The resulting non-Markovian equation can be interpreted in a natural way as the evolution equation of the marginal density function of a random time process l(t). We then consider the subordinated process Y(t)=X(l(t)) where X(t) is a Markovian diffusion. The corresponding time evolution of the marginal density function of Y(t) is governed by a non-Markovian Fokker-Planck equation which involves the memory kernel K(t). We develop several applications and derive the exact solutions. We consider different stochastic models for the given equations providing path simulations.     

Collective diffusion of Brownian particles with square well and hydrodynamic interaction

The low wavenumber collective diffusion coefficient of a semi-dilute suspension of spherical Brownian particles interacting via square well potential and hydrodynamic pair interaction is considered. The first two nonvanishing terms of an expansion in powers of the wavenumber are calculated. Analytical expressions are found for extremely narrow wells and in the limit of large well diameters.     

Brownian surfaces with boundary and Deligne cohomology

We define differentiable random surfaces, which realize a kind of generalized parallel transport for line bundles over the loop space. This gives a realization of one of the axioms of Segal of conformal field theory.     

Definition of percolation thresholds on self-affine surfaces

We study the percolation transition on a two-dimensional substrate with long-range self-affine correlations. We find that the position of the percolation threshold on a correlated lattice is no longer unique and depends on the spanning rule employed. Numerical results are provided for spanning across the lattice in specified (horizontal or vertical), either or both directions.     

Molecular dynamics simulations of the nano-droplet impact process on hydrophobic surfaces

Large-scale molecular dynamics simulations are used to study the dynamic processes of a nano-droplet impacting on hydrophobic surfaces at a microscopic level. Both the impact phenomena and the velocity distributions are recorded and analyzed. According to the simulation results, similar phenomena are obtained to those in macro-experiments. Impact velocity affects the spread process to a greater degree than at a level of contact angle when the velocity is relatively high. The velocity distribution along the X axis during spread is wave-like, either W- or M-shaped, and the velocity at each point is oscillatory; while the edges have the highest spread velocity and there are crests in the distribution curve which shift toward the edges over time. The distribution along the Y axis is 〈- or 〉-shaped, and the segments above the middle have the lowest decrease rate in the spreading process and the highest increase rate in the retraction process.     

Brownian diffusion in a nonuniform gas

An analysis is made of the effects on the diffusion of Brownian particles whose Knudsen number is large compared to unity, of nonuniformities in the host gas. As examples, in one type of nonuniformity of the host gas, the Chapman-Enskog velocity distribution function for the gas molecules is used; in the other, the host gas is a free-molecule Couette flow. In both cases, a new force on the Brownian particles appears. Two techniques are used (extending Kramers' method and utilizing the Chapman-Enskog method) to transform the new Fokker-Planck equation into generalized Smoluchowski and convective diffusion equations. In these equations, the diffusion coefficient appears as a second-order tensor. Thus, it is demonstrated that Brownian diffusion in a nonuniform gas is anisotropic.The work of Slinn was financially supported in part by Battelle Memorial Institute and in part by U.S. Atomic Energy Commission Contract AT(45-1)-1830. The work of Shen was supported in part by U.S. Air Force Office of Scientific Research Contract 49(638)-1346.     

Molecular dynamics simulations of diffusion of carbon into iron

Molecular dynamics (MD) simulations of diffusion couple tests were conducted between carbon (diamond/graphite) and iron at three different temperatures (300, 800 and 1600 K) and contact times (0, 40 and 80 ps) to investigate the chemical interaction between carbon and iron. Two different carbon structures, namely, diamond (cubic) and graphite (hexagonal), were considered. Diffusion of carbon into iron was observed only when a graphite interlayer was added to the diamond surface. When diamond alone was used, no diffusion was observed. This result provides corroborating evidence that diamond tool wear in the machining of iron occurs via a mechanism that involves an initial graphitization of diamond followed by diffusion of the newly formed graphite into the iron workpiece.     

Molecular dynamics study of self-diffusion in Zr

We employed a recently developed semi-empirical Zr potential to determine the diffusivities in hcp and bcc Zr via molecular dynamics simulation. The point defect concentration was determined directly from molecular dynamics (MD) simulation rather than from theoretical methods using T = 0 calculations. Our MD simulation indicates that the diffusion proceeds via the interstitial mechanism in hcp Zr, and both vacancy and interstitial mechanisms contribute to diffusivity in bcc Zr. The agreement with the experimental data is excellent for hcp Zr and rather good for bcc Zr at high temperatures, but there is considerable disagreement at low temperatures.     

Formation of ordered nanodroplet chains on a solid surface by enhanced surface diffusion and shadow effect

We report on a mechanism that under an off-normal incident ion beam, ordered nanodroplets may emerge spontaneously from a flat solid surface and line-up into chains perpendicular to the beam direction, forming a highly ordered hexagonal pattern. This behavior is in contrast to the general belief that an off-normal bombardment produces surface ripples, while the formation of dots requires either normal bombardment or off-normal bombardment with simultaneous sample rotation. The self-assembled nanodroplets reveal a mechanism different from the usual sputtering process. We propose a continuum theory which shows that the balance of mass flux plays an important role for the hexagonal pattern formation while the shadow effect causes the droplets to align into chains. The simulations suggest that the fundamental mechanism may be applicable to other systems, which may lead to an effective approach for nanofabrication.     

Molecular dynamics simulation of oxygen diffusion in dry and water-containing brown coal

Moisture content of brown coal has a pronounced impact on O₂ diffusion during coal oxidation. The transport behaviour of O₂ in dry and hydrated brown coal matrix with 10, 20, and 30?wt% moisture contents have been studied by molecular dynamics (MD) simulations at 298.15?K and 0.1?MPa. By analysing the diffusion characteristics of O₂, it is found that the diffusion process results from jumps of O₂ molecules between adjacent cavities in the coal matrix. With the increase of moisture content, the swelling extent of coal matrix increases in the range of 10–30?wt%, resulting in increased cavity volume, cavity interconnectivity, and mobility of coal macromolecule. These factors are all beneficial to the transport process of O₂ molecule. In addition, O₂ molecule prefers to reside in the available water-poor coal cavity and unoccupied region of water-rich cavity according to the estimated binding energies.