Fractal walk and walk on fractals

The one-dimensional walk of a particle executing instantaneous jumps between the randomly distributed “atoms” at which it resides for a random time is considered. The random distances between the neighboring atoms and the time intervals between jumps are mutually independent. The asymptotic (t → ∞) behavior of this process is studied in connection with the problem of interpretation of the generalized fractional diffusion equation (FDE). It is shown that the interpretation of the FDE as the equation describing the walk (diffusion) in a fractal medium is incorrect in the model problem considered. The reason is that the FDE implies that the consecutive jumps (fractal walk) are independent, whereas they are correlated in the case under consideration: a particle leaving an atom in the direction opposite to the preceding direction traverses the same path until arriving at the atom.     

Anomalous high resolution N.M.R. line-widths in plastic crystals

An optimized version of the force bias scheme is presented for the Monte Carlo simulation of water in which the random walk of the individual molecule is biased in the direction of the force and torque acting on the molecule. A new criterion is developed to judge the efficiency of sampling the configuration space by studying the translational and rotational diffusion of individual molecules during the random walk. The force bias method is compared with the uniform sampling method using ST2 water as an example, and with molecular dynamics. Similarities and differences between molecular dynamics and Monte Carlo are discussed with respect to pair correlations and energy distributions.     

碳纳米管阀门的分子动力学研究

以Lennard-Jones位能式与Brenner-Tersoff位能式为基础,经由分子动力学模拟,探讨流体分子与碳管间质、能传递的关系.首先在一(5,5)armchair碳管侧面,分别移除不同数目的碳原子,形成阀口(A_av=17.3~116.9Å2),进行模拟.结果显示,常用的自扩散行为在该环境下不足以完全说明物性,即在相同系统温度下,阀口的大小也会改变氢原子逸出速度V_b(Breakthrough velocity).为此,必须考虑麦克斯韦-波尔兹曼能量分布方程(Maxwell-Boltzmann energy distribution)修正,此外,原子释放率与阀口尺寸有明显的相依性.同时研究中亦发现,阀门不同几何尺寸引起位能障(Potential energy barrier)、功函数(Work function)以及能隙(Energy gap)的改变,进而影响粒子通过时流率、流速等动力行为.可利用该特性,作为控制原子、分子流动的纳米阀门、粒子分离或化学反应器等基础设计依据.     

Residence Time Statistics for Normal and Fractional Diffusion in a Force Field

We investigate statistics of occupation times for an over-damped Brownian particle in an external force field, using a backward Fokker–Planck equation introduced by Majumdar and Comtet. For an arbitrary potential field the distribution of occupation times is expressed in terms of solutions of the corresponding first passage time problem. This general relationship between occupation times and first passage times, is valid for normal Markovian diffusion and for non-Markovian sub-diffusion, the latter modeled using the fractional Fokker–Planck equation. For binding potential fields we find in the long time limit ergodic behavior for normal diffusion, while for the fractional framework weak ergodicity breaking is found, in agreement with previous results of Bel and Barkai on the continuous time random walk on a lattice. For non-binding cases, rich physical behaviors are obtained, and classification of occupation time statistics is made possible according to whether or not the underlying random walk is recurrent and the averaged first return time to the origin is finite. Our work establishes a link between fractional calculus and ergodicity breaking.     

Integro-differential equation for joint probability density in phase space associated with continuous-time random walk

We derive an integro-differential equation for the joint probability density function in phase space associated with the continuous-time random walk, with generic waiting time probability density function and external force. This equation permits us to investigate whole diffusion processes covering initial-, intermediate-, and long-time ranges, which can distinguish the evolution details for systems having the same behavior in the long-time limit with different initial- and intermediate-time behaviors. Moreover, we obtained analytic solutions for probability density functions both in velocity and phase spaces, and interesting dynamic behaviors are discovered.     

Discrimination of individual atoms on Ge/Si(1 1 1)-(7 × 7) intermixed surface

We have discriminated individual Ge atoms from the intermixed Ge/Si(1 1 1)-(7 × 7) surface using a non-contact atomic force microscope at a room temperature environment. In fact, Si-Ge (IV-IV) binary system is considered as one of the most difficult systems for atomic discrimination among atoms in the IV group because of the similarities in the electronic and chemical properties. However, in this study, we found one of the most attractive tools to discriminate a specific atom from the others even in the difficult Si-Ge system. Ge atoms are shown as dim spots in comparison to Si atoms with bright spots on the intermixed surface by a weak chemical bonding energy and/or a relaxation effect despite large atomic radius and high spatial position in both variable frequency shift and topographic images. The discrimination of individual atoms with respect to the chemical interaction variation will further provide a chance to manipulate different atomic species and assemble various nanostructures in near future.     

One-Dimensional Steady Transport by Molecular Dynamics Simulation：Non-Boltzmann Position Distribution and Non-Arrhenius Dynamical Behavior

A non-equilibrium steady state can be characterized by a nonzero but stationary flux driven by a static external force. Under a weak external force, the drift velocity is difficult to detect because the drift motion is feeble and submerged in the intense thermal diffusion. In this article, we employ an accurate method in molecular dynamics simulation to determine the drift velocity of a particle driven by a weak external force in a one-dimensional periodic potential. With the calculated drift velocity, we found that the mobility and diffusion of the particle obey the Einstein relation, whereas their temperature dependences deviate from the Arrhenius law. A microscopic hopping mechanism was proposed to explain the non-Arrhenius behavior. Moreover, the position distribution of the particle in the potential well was found to deviate from the Boltzmann equation in a non-equilibrium steady state. The non-Boltzmann behavior may be attributed to the thermostat which introduces an effective "viscous" drag opposite to the drift direction of the particle.     

A Brownian motion version of the directed polymer problem

Consider a Brownian particle in three dimensions in a random environment. The environment is determined by a potential random in space and time. It is shown that at small noise the large-time behavior of the particle is diffusive. The diffusion constant depends on the environment. This work generalizes previous results for random walk in a random environment. In these results the diffusion constant does not depend on the environment.     

Self-motile colloidal particles: from directed propulsion to random walk

The motion of an artificial microscale swimmer that uses a chemical reaction catalyzed on its own surface to achieve autonomous propulsion is fully characterized experimentally. It is shown that at short times it has a substantial component of directed motion, with a velocity that depends on the concentration of fuel molecules. At longer times, the motion reverts to a random walk with a substantially enhanced diffusion coefficient. Our results suggest strategies for designing artificial chemotactic systems.     

Two-state random walk model of diffusion. 2. Oscillatory diffusion

Continuing our study of interrupted diffusion, we consider the problem of a particle executing a random walk interspersed with localized oscillations during its halts (e.g., at lattice sites). Earlier approaches proceedvia approximation schemes for the solution of the Fokker-Planck equation for diffusion in a periodic potential. In contrast, we visualize a two-state random walk in velocity space with the particle alternating between a state of flight and one of localized oscillation. Using simple, physically plausible inputs for the primary quantities characterising the random walk, we employ the powerful continuous-time random walk formalism to derive convenient and tractable closed-form expressions for all the objects of interest: the velocity autocorrelation, generalized diffusion constant, dynamic mobility, mean square displacement, dynamic structure factor (in the Gaussian approximation), etc. The interplay of the three characteristic times in the problem (the mean residence and flight times, and the period of the ‘local mode’) is elucidated. The emergence of a number of striking features of oscillatory diffusion (e.g., the local mode peak in the dynamic mobility and structure factor, and the transition between the oscillatory and diffusive regimes) is demonstrated.     

MANIPULATION OF ATOMS, MOLECULES AND CLUSTERS FOR CONSTRUCTION OF NANOSYSTEMS

Controlled manipulations with the scanning tunneling microscope (STM) down to the scale of small molecules and single atoms allow to built molecular and atomic nanosystems, leading to the fascinating possibility of creating manmade structures on atomic scale. Here we present a short review on atomic scale manipulation investigations. Upon soft lateral manipulation of adsorbed species, in which only tip/particle forces are used, three different manipulation modes (pushing, pulling, sliding) can be discerned. We show that even the manipulation of highly coordinated native substrate atoms is possible and we demonstrate how this can be applied as local analytic and synthetic chemistry tools, with important consequences on surface structure research. Vertical manipulation of Xe and CO is demonstrated, leading to improved imaging with functionalized tips. With CO deliberately transferred to the tip, we have also succeeded to perform vibrational spectroscopy on single molecules. Furthermore, we describe how we have reproduced a full chemical reaction with single molecules, whereby all basic steps, namely preparation of the reactants, diffusion and association, are induced with the STM tip. Finally, we have extended the manipulation techniques to large specially designed molecules by performing lateral manipulation in constant height and realizing the principle of a conformational molecular switch.     

First principles calculation of the interdiffusion coefficient in binary alloys

The atomic mechanisms of diffusion in alloys are complex due to the variations of migration energies with environment and the correlations induced by short-range order between the different components. We present a first-principles approach for calculating vacancy-mediated diffusion coefficients in crystalline binary alloys and apply it to obtain the interdiffusion coefficient of Al(1-x)Lix. The rigorous treatment of atomic migration indicates that short- and long-range order induces strongly correlated migration mechanisms that deviate from random walk behavior.     

Weak disorder: anomalous transport and diffusion are normal yet again

We carry out a detailed study of the motion of particles driven by a constant external force over a landscape consisting of a periodic potential corrugated by a small amount of spatial disorder. We observe anomalous behavior in the form of subdiffusion and superdiffusion and even subtransport over very long time scales. Recent studies of transport over slightly random landscapes have focused only on parameters leading to normal behavior, and while enhanced diffusion has been identified when the external force approaches the critical value associated with the transition from locked to running solutions, the regime of anomalous behavior had not been recognized. We provide a qualitative explanation for the origin of these anomalies, and make connections with a continuous time random walk approach.     

Surface diffusion of Si,Ge and C adatoms on Si （001） substrate studied the molecular dynamics simulation

Depositions of Si, Ge and C atoms onto a preliminary Si (001) substrate at different temperatures are investigated by using the molecular dynamics method. The mechanism of atomic self-assembling occurring locally on the flat terraces between steps is suggested. Diffusion and arrangement patterns of adatoms at different temperatures are observed. At 900 K, the deposited atoms are more likely to form dimers in the perpendicular [110] direction due to the more favourable movement along the perpendicular [110] direction. C adatoms are more likely to break or reconstruct the dimers on the substrate surface and have larger diffusion distances than Ge and Si adatoms. Exchange between C adatoms and substrate atoms are obvious and the epitaxial thickness is small. Total potential energies of adatoms and substrate atoms involved in the simulation cell are computed. When a newly arrived adatom reaches the stable position, the potential energy of the system will decrease and the curves turns into a ladder-like shape. It is found that C adatoms can lead to more reduction of the system energy and the potential energy of the system will increase as temperature increases.     

Mechanism of chemisorption and interface penetration in reactive systems at low temperatures

In the transport mechanism discussed it is demonstrated that in the large gradients of the chemical potential that exist in reactive systems gas atoms should be able to migrate in a perpendicular direction up to several atomic distances below the surface by non-activated processes. The exponential decrease in the sticking probability s observed after an initial stage with a constant s value of about unity is correlated with the increase of the activation energy barrier between molecules in the gas phase and in the chemisorbed state on the surface. Quantitative experimental results of the kinetic of chemisorption processes recently obtained for oxygen and nitrogen systems support the qualitative and semiquantitative statements of the mechanism proposed.     

Biased diffusion in a piecewise linear random potential

We study the biased diffusion of particles moving in one direction under the action of a constant force in the presence of a piecewise linear random potential. Using the overdamped equation of motion, we represent the first and second moments of the particle position as inverse Laplace transforms. By applying to these transforms the ordinary and the modified Tauberian theorem, we determine the short- and long-time behavior of the mean-square displacement of particles. Our results show that while at short times the biased diffusion is always ballistic, at long times it can be either normal or anomalous. We formulate the conditions for normal and anomalous behavior and derive the laws of biased diffusion in both these cases.     

Internal emission of hot electrons at the metal surface in reaction atomic collisions: Pd/n-Si nano-Schottky diode

The internal emission of hot electrons from a metal (Pd) surface is studied. The electrons gain energy from chemical atomic collisions with the thermal energy hydrogen atoms or with H₂ + O₂ molecules. A Pd(15 nm)/n-Si(111) nano-Schottky diode is used as a detector of hot electrons in which chemicurrents (and chemo-emf) are generated. The efficiency of entering of chemo-electrons into the external circuit per act of interaction (or per product molecule) is determined.     

Nonstochastic behavior of atomic surface diffusion on Cu(111) down to low temperatures

Atomic diffusion is usually understood as a succession of random, independent displacements of an adatom over the surface's potential energy landscape. Nevertheless, an analysis of molecular dynamics simulations of self-diffusion on Cu(111) demonstrates the existence of different types of correlations in the atomic jumps at all temperatures. Thus, the atomic displacements cannot be correctly described in terms of a random walk model. This fact has a profound impact on the determination and interpretation of diffusion coefficients and activation barriers.     

Active Brownian motion tunable by light

Active Brownian particles are capable of taking up energy from their environment and converting it into directed motion; examples range from chemotactic cells and bacteria to artificial micro-swimmers. We have recently demonstrated that Janus particles, i.e.?gold-capped colloidal spheres, suspended in a critical binary liquid mixture perform active Brownian motion when illuminated by light. In this paper, we investigate in more detail their swimming mechanism, leading to active Brownian motion. We show that the illumination-borne heating induces a local asymmetric demixing of the binary mixture, generating a spatial chemical concentration gradient which is responsible for the particle's self-diffusiophoretic motion. We study this effect as a function of the functionalization of the gold cap, the particle size and the illumination intensity: the functionalization determines what component of the binary mixture is preferentially adsorbed at the cap and the swimming direction (towards or away from the cap); the particle size determines the rotational diffusion and, therefore, the random reorientation of the particle; and the intensity tunes the strength of the heating and, therefore, of the motion. Finally, we harness this dependence of the swimming strength on the illumination intensity to investigate the behavior of a micro-swimmer in a spatial light gradient, where its swimming properties are space-dependent.