The Motion of Repulsive Brownian Particles in Quenched Disorder

Brownian motion of the particles with repulsive interaction is investigated. When the potential condition is satisfied, the eigenvalue problem of interaction Fokker-Planck equation under certain conditions can be transformed to that of a many-particle Schrödinger equation. Using the Green's function method, we obtain the effective single-variable Fokker-Planck equation in the low density limit. We find that the diffusion of coupled Brownian particles in quenched disorder media is also anomalous in 2D. The Mittag-Leffler relaxation of pancake vortices is investigated by fractional Fokker-Planck equation.     

热核物质中基态关联修正下的单核子势和核子有效质量

以有限温度Brueckner-Hartree-Fock(BHF)方法为基础，利用质量算子的空穴线展开，计算了不同温度和密度下的核物质中单核子势和核子有效质量，特别是研究和讨论了基态关联效应和三体核力贡献对热核物质中单核子势的影响. 研究表明，基态关联和三体核力对单核子势的密度和温度依赖性均有重要影响. 基态关联导致的重排修正具有排斥性，大大减弱了低动量区域单核子势的吸引性，而且基态关联效应对单核子势的贡献随密度增大而增强，随温度升高而减弱. 三体核力对基态关联的影响是导致单核子势中重排项贡献减小. 在高密 关键词： 有限温度BHF方法 质量算子空穴线展开 重排修正 单核子势 有效质量     

Solution of the Fokker-Planck Equation with a Logarithmic Potential

We investigate the diffusion of particles in an attractive one-dimensional potential that grows logarithmically for large |x| using the Fokker-Planck equation. An eigenfunction expansion shows that the Boltzmann equilibrium density does not fully describe the long-time limit of this problem. Instead this limit is characterized by an infinite covariant density. This non-normalizable density yields the mean square displacement of the particles, which for a certain range of parameters exhibits anomalous diffusion. In a symmetric potential with an asymmetric initial condition, the average position decays anomalously slowly. This problem also has applications outside the thermal context, as in the diffusion of the momenta of atoms in optical molasses.     

Vapour-liquid equilibria of the two- and three-dimensional monoatomic classical fluids interacting via double Yukawa potential

We have carried out Monte Carlo simulations in Gibbs ensemble for two-and three-dimensional double Yukawa fluid. We have compared liquid-vapour equilibrium curve with that of Lennard-Jones, when parameters occurring in double Yukawa potential are chosen to fit Lennard-Jones potential. The results are in good agreement. The role of repulsive and attractive contributions for the potential on the liquid-vapour coexistence region as well as on critical temperature and critical density has been studied. The critical temperature is found to be more sensitive than the critical density to the variation in repulsive and attractive parts of the potential. Also, the range of the attractive interaction directly influences range of the liquid vapour coexistence region. It has been found that smaller the values of the attractive parameter, larger is the coexistence region.     

Modulated phases and slow dynamics in attractive colloids

A system with a short-range attraction and a competing long-range screened repulsion is studied by using the self-consistent Hartree approximation and a replica approach. It is shown that by varying the parameters of the repulsive potential and the temperature yields a phase coexistence, a lamellar and a glassy phase. These results, which are confirmed by molecular dynamic simulations on a system of particles interacting via a DLVO potential, provide novel insights in the role of modulated phases in the slow dynamics of charged colloids in polymeric solutions.     

Anomalous diffusion in two-dimensional potentials with hexagonal symmetry

The diffusion process in a Hamiltonian dynamical system describing the motion of a particle in a two-dimensional (2D) potential with hexagonal symmetry is studied. It is shown that, depending on the energy of the particle, various transport processes can exist: normal (Brownian) diffusion, anomalous diffusion, and ballistic transport. The relationship between these transport processes and the underlying structure of the phase space of the Hamiltonian dynamical system is investigated. The anomalous transport is studied in detail in two particular cases: in the first case, inside the chaotic sea there exist self-similar structures with fractal properties while in the second case the transport takes place in the presence of multilayered structures. It is demonstrated that structures of the second type can lead to a physical situation in which the transport becomes ballistic. Also, it is shown that for all cases in which the diffusive transport is anomalous the trajectories of the diffusing particles contain long segments of regular motion, the length of these segments being described by Levy probability density functions. Finally, the numerical values of the parameters which describe the diffusion processes are compared with those predicted by existing theoretical models. (c) 2000 American Institute of Physics.     

Influence of surface affinity of planar walls on effective interaction between the wall and colloids

Using density functional theory, we investigate the effective interaction between a big colloid immersed in a sea of small colloids and a wall which has different affinity to the small colloids. Steele 10-4-3 potential is introduced to mimic both short-range repulsive and long-range attractive interactions between the wall and the small colloids. It is found that the surface affinity of the wall has a significant influence on the effective interaction. In the short-range repulsive case, the repulsion greatly enhances the big colloid-wall effective attraction, which sensitively depends on the concentration of small colloids, and is not sensitive to the repulsive strength. In the long-range attractive case, both the concentration of small colloids and the attractive strength have great effect on the effective interaction, and with an increase of the attractive strength, a strong repulsion may be induced when the big colloid is close to the wall. In low density limit of small colloids, the present results agree well with those of the Asakura and Oosawa(AO) approximation.     

三体核力重排效应对核物质中单核子平均场的贡献

在微观多体Brueckner-Hartree-Fock理论框架内, 实现了三体核力对核物质中单核子势的重排贡献的计算, 研究了三体核力重排贡献对单核子平均势场的动量相关性和密度依赖性的影响. 另外, 还计算了核物质中核子的有效质量并着重讨论了三体核力重排效应的影响. 结果表明: 三体核力对单核子势的重排贡献具有排斥性, 而且三体核力的重排效应随动量和密度的增加而迅速增强; 在高密度和高动量区域这一排斥贡献具有很强的动量相关性并起到了减弱单核子势吸引性和增强单核子势动量相关性的重要作用, 有助于澄清非相对论性BHF平均势场在高密度和高动量区域吸引性过强和动量相关性过弱的问题.     

Spontaneous patterning of quantum dots at the air-water interface

Nanoparticles deposited at the air-water interface are observed to form circular domains at low density and stripes at higher density. We interpret these patterns as equilibrium phenomena produced by a competition between an attraction and a longer-ranged repulsion. Computer simulations of a generic pair potential with attractive and repulsive parts of this kind, reproduce both the circular and stripe patterns. Such patterns have a potential use in nanoelectronic applications.     

A classical density functional approach to depletion interaction of Lennard-Jones binary mixtures

In this article, we apply classical density functional theory to investigate the characteristics of depletion interaction in Lennard-Jones (LJ) binary fluid mixtures. First, to confirm the validity of our adopted density functional formalism, we calculate the radial distribution functions using a theoretical approach and compare them with results obtained by molecular dynamics simulation. Then, this approach is applied to two colloids immersed in LJ solvent systems. We investigate the variation of depletion interaction with respect to the distance of two colloids in LJ binary systems. We find that depletion interaction may be attractive or repulsive, mostly depending on the bulk density of the solvent and the temperature of the binary system. For high bulk densities, the repulsive barrier of depletion force is remarkable when the total excluded volume of colloids touches each other and reaches a maximum. The height of the repulsive barrier is related to the parameters of the LJ potential and bulk density. Moreover, the depletion force may exhibit attractive wells if the bulk density of the solvent is low. The attractive well tends to appear when the surface–surface distance of colloids is half of the size of the polymer and deepens with temperature lowering in a fixed bulk density. In contrast with the hard-sphere system, no oscillation of depletion potential around zero is observed.     

A molecular dynamics study on the role of attractive and repulsive forces in excess heat capacity at constant volume of dense fluids

The curves of experimental heat capacity against density show a minimum around and below the critical temperature (Tc), but at higher temperatures, this minimum is not observed. In this study, the role of attractive and repulsive forces on excess heat capacity of Lennard–Jones (LJ) dense fluids has been investigated using a molecular dynamics simulation technique. LJ potential is divided into attractive and repulsive parts. From the molecular dynamics calculations, potential energy and heat capacities have been obtained for Argon at temperatures of 100–500?K. The repulsive forces play the main role in causing the heat capacities at temperatures greater than critical point. Around and below the critical temperature, the role of repulsion is dominant at high densities, but attraction has the main role at low densities, consequently at middle densities, a minimum is formed.     

The origin of the attraction between like charged hydrophobic and hydrophilic walls confining a near-critical binary aqueous mixture with ions

The effect of ionic solute on a near-critical binary aqueous mixture confined between charged walls with different adsorption preferences is considered within a simple density functional theory. For the near-critical system containing small amounts of ions, a Landau-type functional is derived on the basis of the assumption that the correlation, ξ, and the Debye screening length, κ(-1), are both much larger than the molecular size. The corresponding approximate Euler-Lagrange equations are solved analytically for ions insoluble in the organic solvent. A nontrivial concentration profile of the solvent is found near the charged hydrophobic wall as a result of the competition between the short-range attraction of the organic solvent and the electrostatic attraction of the hydrated ions. An excess of water may be present near the hydrophobic surface for some range of the surface charge and ξκ. As a result, the effective potential between the hydrophilic and the hydrophobic surface can be repulsive far from the critical point, then attractive and again repulsive when the critical temperature is approached, in agreement with a recent experiment (Nellen et al 2011 Soft Matter 7 5360).     

Fluids with highly directional attractive forces. II. Thermodynamic perturbation theory and integral equations

The formalism of statistical thermodynamics developed in the preceding paper is used as a basis for deriving tractable approximations. The system treated is one where repulsion and highly directional attraction due to a single molecular site combine to allow the formation of dimers, but no highers-mers. We derive thermodynamic perturbation theory, using the system interacting with only the repulsive potential as a reference system. Two distinct integral equations for the pair correlation are derived. The first one treats both parts of the interaction approximately; the other one employs the repulsive reference system used in perturbation theory. We show that each of these integral equations permits the calculation of an important thermodynamic function directly from the solution at a single state of density and temperature. In the first case this applies to a pressure consistent with the compressibility relation, in the second to the excess Helmholtz free energy over the reference system.Supported by the NSF under Grant No. CHE-82-11236 and by the U.S. Air Force under Grant No. AFOSR 82-0016A.     

运用CTRW-Metropolis模型数值研究亚稳势中粒子逃逸问题

基于连续时间随机行走(CTRW)理论,实现反常扩散条件下对跳跃步长和等待时间分布函数的抽样,改进Metropolis抽样判定方法以适用于存在非线性势的情况.数值研究布朗粒子在亚稳势下的逃逸速率.结果显示,稳定逃逸速率γ_st随反常指数α非单调变化,在超扩散条件下存在极大值和位垒相消现象.     

Binuclear atom as the bound state of a proton and a heavy atom

The existence of a bound state of a proton and a heavy atom is predicted. The atom is described by the Thomas-Fermi method. The electrons screen the field of the proton, which suppresses the repulsive force between the proton and the atomic nucleus. On the other hand, the force of attraction between the proton and the electrons is directed along the electron density gradient (i.e., towards the nucleus). It is concluded that for Z = 80, the two forces are balanced at a distance from the nucleus of about 0.6 of the Bohr radius. It is found that the potential energy minimum of the proton with a depth of several tens of electronvolts lies in the range of negative energies (attraction). It is proposed that such a system be referred to as a binuclear atom. It is emphasized that, in contrast to molecules, in which binding with the hydrogen atom is ensured by a rearrangement of the states of the outer-shell (valence) electrons, a binuclear atom is formed as a result of the collective response of the system of inner electrons to the proton potential.     

Molecular Dynamics Simulations of Liquid Phosphorus at High Temperature and Pressure

By performing ab initio molecular dynamics simulations, we have investigated the microstructure, dynamical and electronic properties of liquid phosphorus （P） under high temperature and pressure. In our simulations, the calculated coordination number （CN） changes discontinuously with density, and seems to increase rapidly after liquid P is compressed to 2.5 g/cm3. Under compression, liquid P shows the first-order liquid-liquid phase transition from the molecular liquid composed of the tetrahedral P4 molecules to complex polymeric form with three-dimensional network structure, accompanied by the nonmetal to metal transition of the electronic structure. The order parameters Q6 and Q4 are sensitive to the microstructural change of liquid P. By calculating diffusion coefficients, we show the dynamical anomaly of liquid P by compression. At lower temperatures, a maximum exists at the diffusion coefficients as a function of density; at higher temperatures, the anomalous behavior is weakened. The excess entropy shows the same phenomena as the diffusion coefficients. By analysis of the angle distribution functions and angular limited triplet correlation functions, we can clearly find that the Peierls distortion in polymeric form of liquid P is reduced by further compression.     

Molecular dynamical calculations of the transport properties of a square-well fluid: V. The coefficient of self-diffusion

The diffusivity of a system, consisting of square-well molecules, has been determined by means of the dynamical computer simulation technique. The calculations offer a systematic investigation of the diffusivity covering almost the whole fluid region. It is found that at low and intermediate densities, the addition of a square negative potential on hard spheres lowers the diffusion coefficient but that at high densities, an increase can also be found, depending on the choice of the potential parameters. A negative first-order and a positive second-order density dependence of the product of density and diffusion coefficient has been found, which is in qualitative correspondence with results of real experiments.     

计算平均力势的理论方法

提出了一个用于计算平均力势的普适性的理论框架,方法克服了以前的方法的缺陷,仅仅需要溶剂粒子在单个溶质粒子附近的密度分布作为输入.计算了两个大尺寸溶质粒子浸在小尺寸硬球溶剂浴中的平均力势,理论预言与可能的模拟数据符合.调查了溶剂-溶质相互作用势、溶剂密度、溶质粒子尺寸对过量平均力势的影响.结论是:溶剂粒子在单个溶质粒子附近的减少导致吸引的过量平均力势,而溶剂粒子在单个溶质粒子附近的聚集导致排斥的过量平均力势,高溶剂密度与大溶质粒子尺寸能强化这种趋势.讨论了这种空耗吸引-聚集排斥与生物学中的疏水吸引-水化排斥的联系.     

Pattern formation and glassy phase in the phi4 theory with a screened electrostatic repulsion

We study analytically the structural properties of a system with a short-range attraction and a competing long-range screened repulsion. This model contains the essential features of the effective interaction potential among charged colloids in polymeric solutions and provides novel insights on the equilibrium phase diagram of these systems. Within the self-consistent Hartree approximation and by using a replica approach, we show that varying the parameters of the repulsive potential and the temperature yields a phase coexistence, a lamellar, and a glassy phase. Our results strongly suggest that the cluster phase observed in charged colloids might be the signature of an underlying equilibrium lamellar phase, hidden on experimental time scales.