Effect of Detachments in Asymmetric Simple Exclusion Processes

Asymmetric simple exclusion processes are important for understanding low-dimensional multi-particle dynamic phenomena. The effect of irreversible detachments of particles on dynamics of asymmetric simple exclusion processes is studied using analytical and computer simulation techniques. In the simplest model, where particles can only detach from a single site in the bulk of the system, a theory is presented and used to calculate explicitly phase diagrams and particle density profiles. The complexity of the phase behavior is discussed in terms of a recent domain-wall theory for driven lattice systems. The theoretical results qualitatively and quantitatively agree with computer Monte Carlo simulations.     

The configurational space of colloidal patchy polymers with heterogeneous sequences

In this work we characterize the configurational space of a short chain of colloidal particles as a function of the range of directional and heterogeneous isotropic interactions. The individual particles forming the chain are colloids decorated with patches that act as interaction sites between them. We show, using computer simulations, that it is possible to sample the relative probability of occurrence of a structure with a sequence in the space of all possible realizations of the chain. The results presented here represent a first attempt to map the space of possible configurations that a chain of colloidal particles may adopt. Knowledge of such a space is crucial for a possible application of colloidal chains as models for designable self-assembling systems.     

Diffusion of particles on a heterogeneous surface: A case of adsorption-induced surface reconstruction

The influence of surface reconstruction on diffusion of particles adsorbed on the surface is investigated in the framework of symmetrical four-position model. The analytical expressions for free energy and diffusion coefficients are obtained assuming the lateral interaction between particles is negligibly small.The critical behavior of the system is described by the Ising spin model. The coverage dependencies of the tracer, jump and chemical diffusion coefficients are calculated for some representative temperatures. The dependencies show clearly strong influence of the surface reconstruction on the thermodynamic and kinetic phenomena: diffusion coefficients become anisotropic on the reconstructed surface. To check the analytical results we have used Monte Carlo simulations of the diffusion on this lattice.     

Three-dimensional finite-element simulation of Zener pinning dynamics

The Zener pinning dynamics of a moving boundary interacting with one or more particles is described by a three-dimensional (3D) finite-element model. The model, based upon a variational formulation for boundary motion by viscous drag, is solved by a finite-element method to obtain the velocity at each node of triangular linear elements on the grain boundary. It is first applied to relatively simple and validated cases, for which analytical and numerical results are available. These cases correspond to an axisymmetrical geometry, in which the grain boundary interacts with a centred particle. A simple analytical pinning criterion is derived from these simulations. The model is then applied to general 3D cases, in which the grain boundary interacts with arbitrarily localized and sized particles. The aim of these 3D simulations is to quantify the influence of the position and the number of particles on the average grain-boundary velocity. It is shown, for example, that the drag effect is enhanced when the particle, or the cluster of particles, is off-centre and that pinning is less efficient with several particles than with a single particle producing the same Zener force.     

Aggregation of colloidal particles with a finite interparticle attraction energy

Aggregation of colloidal particles with a finite attraction energy was investigated with computer simulations and with gold particles coated with a surfactant. Computer simulations were carried out with the Shih-Aksay-Kikuchi (SAK) model, which incorporates a finite nearest-neighbor attraction energy-E into the diffusion-limited-cluster-aggregation (DLCA) model. Both the computer simulations and the experiments showed that (i) with a finite interparticle attraction energy, aggregates can still remain fractal, and (ii) the fractal dimension remains unchanged at large interparticle attraction energies and increases when the interparticle attraction energy is smaller than 4k _B T whereT is the temperature andK _B is the Boltzmann constant. The agreement between the simulations and the experimental results suggests that the reversible aggregation process in a colloidal system can be represented by the SAK model.     

Variational calculation of the angular width of the multiple scattering distribution in foil transmission

A simple formula is derived for calculating the angular width of multiple scattering distributions for atomic particles traversing thin foils. The universal result is obtained by applying the variational method on standard multiple scattering theory. This procedure can be carried through in a straight-forward way, thus saving lengthy series expansions and Fourier transforms. In the case of power cross sections exact analytical expressions can be obtained. A remarkably good agreement is found between our calculation and previous theories, as well as with results from our computer simulations.     

Historical note: On the simulation of dispersive wave propagation by elasticity models

Attention is called to E. Schrödinger's elegant analytical solution [Annalen der Physik 44 (1914) p.916] of the initial-value problem for the Born–von Kármán model of an infinite one-dimensional chain of uniformly spaced particles of mass M with nearest-neighbour coupling by harmonic springs. This model has recently served as the starting point for a computer study of the transition to partial differential equations describing dispersive wave propagation in inhomogeneous media [Askes et al., Phil. Mag. 88 (2008) p.3415]. Schrödinger's solution allows the main features of the limit process involved in this transition to be studied in a straightforward way.     

Reaction kinetics of diffusing particles injected into a reactive substrate

We analyze the kinetics of trapping (A+B-->B) and annihilation (A+B-->0) processes on a one-dimensional substrate with homogeneous distribution of immobile B particles while the A particles are supplied by a localized source. For the imperfect reaction case, we analyze both problems by means of a stochastic model and compare the results with numerical simulations. In addition, we present the exact analytical results of the stochastic model for the case of perfect trapping.     

An anchoring transition at surfaces with grafted liquid-crystalline chain molecules

The anchoring of nematic liquid crystals on surfaces with grafted liquid-crystalline chain molecules is studied by computer simulations and within a mean-field approach. The computer simulations show that a swollen layer of collectively tilted chains may induce untilted homeotropic (perpendicular) alignment in the nematic fluid. The results can be understood within a simple theoretical model. The anchoring on a layer of mutually attractive chains is determined by the structure of the interface between the layer of chain molecules and the solvent. It is controlled by an interplay between the attractive chain interactions, the translational entropy of the solvent and its elasticity. A second-order anchoring transition driven by the grafting density from tilted-to-homeotropic alignment is predicted. Received 5 July 2001 and Received in final form 16 November 2001     

New cooperative effects in ballistic deposition of hard disks

In this Letter, we analyze the problem of monolayer formation onto a flat surface by deposition of hard particles. Our detailed computer simulations of ballistic deposition of hard disks show significant deviations from the classical analytical solution obtained by J. Talbot [Phys. Rev. Lett. 68, 958 (1992)]. These deviations are due to cooperative adsorption induced by particles trapped above the adsorbed layer. We show that not only the adsorption kinetics but also the jamming (saturation) coverage of the surface depends on the volume fraction of the suspension, a prediction which is completely new. These new cooperative effects cannot be neglected even in the case of very diluted suspensions.     

Risk Estimate of Diseases in Scale-Free Networks

We investigate the effect of risk estimate on the spread of diseases by the standard susceptible-infected- susceptible （SIS） model. The perception of the risk of being infected is explained as cutting off links among individuals, either healthy or infected, We study this simple dynamics on scale-free networks by analytical methods and computer simulations. We obtain the self-consistency form for the infection prevalence in steady states. For a given transmission rate, there exists a linear relationship between the reciprocal of the density of infected nodes and the estimate parameter. We confirm all the results by sufficient numerical simulations.     

Structurization of ferrofluids in the absence of an external magnetic field

Structural transformations in a model ferrofluid in the absence of an external magnetic field have been theoretically studied. The results agree with well-known laboratory experiments and computer simulations in showing that, if the concentration of particles and their magnetic interaction energy are below certain critical values, most particles form separate linear chains. If these parameters exceed the critical values, most particles concentrate so as to form branched network structures. The passage from chains to network has a continuous character rather than represents a discontinuous first-order phase transition.     

Lattice phonons in the presence of non-linear excitations

We examine the interaction between linear (phonon-like) and non linear (kink, soliton-like) excitations of the classical, discrete, ?⁴ chain in the displacive regime. The discreteness of the lattice manifests itself (a) in the asymptotic phonon phase shift, (b) in partial reflection occurring near the Brillouin zone edge and (c) in the spatial shift suffered by a kink due to its collision with a phonon wavepacket. Our analytical results are confirmed by computer simulations.     

A study on the distribution of adsorbed nanoparticles

We use Monte Carlo simulation to calculate the distributions of particles under adsorption force near planar and cylindrical surfaces,respectively.Both hard sphere interaction and repulsive Yukawa (screened coulomb) interaction are employed in our simulations.We study the influence of the inter-particle potentials.The difference between the MC simulation results and the analytical results of ideal gas model shows that the interaction between particles plays an important role in the density distribution under external fields.Moreover,the 2-dimensional constructions of particles close to the surface are studied and show relations of the interaction between particles.These results may indicate us how to improve the methods of building nanoparticle coatings and nano-scale patterns.     

A study on the distribution of adsorbed nanoparticles

We use Monte Carlo simulation to calculate the distributions of particles under adsorption force near planar and cylindrical surfaces, respectively. Both hard sphere interaction and repulsive Yukawa (screened coulomb) interaction are employed in our simulations. We study the influence of the inter-particle potentials. The difference between the MC simulation results and the analytical results of ideal gas model shows that the interaction between particles plays an important role in the density distribution under external fields. Moreover, the 2-dimensional constructions of particles close to the surface are studied and show relations of the interaction between particles. These results may indicate us how to improve the methods of building nanoparticle coatings and nano-scale patterns.     

Phase Separation of Penetrable Core Mixtures

A two-component system of penetrable particles interacting via a gaussian core potential is considered, which may serve as a crude model for binary polymer solutions. The pair structure and thermodynamic properties are calculated within the random phase approximation (RPA) and the hypernetted chain (HNC) integral equation. The analytical RPA predictions are in semi-quantitative agreement with the numerical solutions of the HNC approximation, which itself is very accurate for gaussian core systems. A fluid-fluid phase separation is predicted to occur for a broad range of potential parameters. The pair structure exhibits a nontrivial clustering behaviour of the minority component. Similiar conclusions hold for the related model of parabolic core mixtures, which is frequently used in dissipative particle dynamics (DPD) simulations.     

The reflection of light swift particles from heavy solid targets

The reflection of light particles bombarding heavy targets has been investigated with the single-collision model, which assumes straight line trajectories between the surface and the large angle scattering event upon incidence and exit of the swift particle. This model allows analytical integration, under some approximations, to yield energy and angular distributions of reflected particles as well as particle and energy reflection coefficients in terms of analytical formulae. The results are compared with data from the Monte Carlo computer program TRIM for H and He incident on Au. This comparison shows that the model can be applied for reduced energies larger thanε=5, and that it is well suited for any higher energy up to relativistic energies, in contrast to previous theoretical or empirical formulae.     

Analytical solution to the Lipari-Szabo model based on the reduced spectral density approximation offers a novel protocol for extracting motional parameters.

An analytical solution to the Lipari-Szabo model is derived for isotropic overall tumbling. The parameters of the original Lipari-Szabo model, the order parameter S2 and the effective internal correlation time tau(e), are calculated from two values of the spectral density function. If additionally the spectral density value J(0) is known, the exchange contribution R(ex) term can also be determined. The overall tumbling time tau(c) must be determined in advance, for example, from T1/T2 ratios. The required spectral density values are obtained by reduced spectral density mapping from T1, T2, and NOE measurements. Our computer simulations show that the reduced spectral density mapping is a very good approximation in almost all cases in which the Lipari-Szabo model is applicable. The robustness of the analytical formula to experimental errors is also investigated by extensive computer simulations and is found to be similar to that of the fitting procedures. The derived formulas were applied to the experimental 15N relaxation data of ubiquitin. Our results agree well with the published parameter values of S2 and tau(e), which were obtained from standard fitting procedures. The analytical approach to extract parameters of molecular motions may be more robust than standard analyses and provides a safeguard against spurious fitting results, especially for determining the exchange contribution R(ex).