A moving grid finite element method applied to a model biological pattern generator

Many problems in biology involve growth. In numerical simulations it can therefore be very convenient to employ a moving computational grid on a continuously deforming domain. In this paper we present a novel application of the moving grid finite element method to compute solutions of reaction–diffusion systems in two-dimensional continuously deforming Euclidean domains. A numerical software package has been developed as a result of this research that is capable of solving generalised Turing models for morphogenesis.     

Initial oxidation kinetics of copper (1 1 0) film investigated by in situ UHV-TEM

Previous studies of the initial stage of oxidation on clean single crystal of Cu(1 0 0) have been extended to the case of the Cu(1 1 0) surface. The dynamic observation of the nucleation and growth of Cu oxide by means of in situ ultra high vacuum transmission electron microscopy (UHV-TEM) shows a highly enhanced oxidation rate on Cu(1 1 0) surface as compared to Cu(1 0 0). The kinetic data on the nucleation and growth of the three-dimensional oxide islands agree well with our heteroepitaxial model of surface diffusion of oxygen.     

Unified Solution of the Expected Maximum of a Discrete Time Random Walk and the Discrete Flux to a Spherical Trap

Two random-walk related problems which have been studied independently in the past, the expected maximum of a random walker in one dimension and the flux to a spherical trap of particles undergoing discrete jumps in three dimensions, are shown to be closely related to each other and are studied using a unified approach as a solution to a Wiener-Hopf problem. For the flux problem, this work shows that a constant c = 0.29795219 which appeared in the context of the boundary extrapolation length, and was previously found only numerically, can be derived analytically. The same constant enters in higher-order corrections to the expected-maximum asymptotics. As a byproduct, we also prove a new universal result in the context of the flux problem which is an analogue of the Sparre Andersen theorem proved in the context of the random walker's maximum.     

The processes of ordering and formation of two-dimensional glasses at metal surfaces

Using the experimental results obtained for the Dy-Mo(1 1 2) system, we discuss the possibilities and mechanisms of formation of two-dimensional (2D) glasses on metal surfaces. It has been found that in the coverage range 0.07 < θ < 0.58, ordered Dy superstructures formed and observed at T < 400 K are irreversibly destroyed by annealing to higher temperatures and turn into an amorphous (glass) structure on cooling. It is supposed that this conversion is caused by the formation, at T > 400 K, of a Dy-Mo surface alloy in which the rate of Dy surface diffusion is strongly reduced in comparison with its value in the absence of alloying. As a result, the mobility of Dy adatoms becomes too low at the temperatures corresponding to the ordered equilibrium state of the surface, and this state cannot be achieved in reasonable relaxation time. This interpretation is corroborated by the experimental data on substantial suppression of surface diffusion in some coadsorbed layers. Since surface glasses contact with ordered (crystalline) substrates, their structure may have a peculiar character different from that of “conventional” metal glasses. Surface glasses can find a number of applications as rather stable systems that combine low dimensionality, specific electronic structure of their constituents and extremely high density of defects.     

Evidence for diffusion-limited kinetics during electromigration-induced step bunching on Si(1 1 1)

We have measured how the initial terrace width l₀ on vicinal Si(1 1 1) surfaces influences the rate of step bunching and the minimum terrace width within a bunch when direct-current heated at 940-1290 °C. A comparison of this data with analytic solutions and numerical simulations of the conventional “sharp-step” model give strong evidence that the kinetic length d is relatively small (d < ∼20 nm) in both temperature regime I (∼850-950 °C) and regime III (∼1200-1300 °C), in which step-down current is required for step bunching. This indicates that surface mass transport is diffusion-limited in both regimes I and III when l₀ > 20 nm, and hence that the adatom attachment- and terrace diffusion-hopping rates are of comparable magnitude. We also observe similar scaling with initial terrace width in temperature regime II (∼1040-1190 °C), in which step-up current is required for bunching, suggesting a similar step bunching mechanism in all three temperature regimes.     

Non-monotonous dependence of surface roughness on factors influencing energy of adatoms during thin island film growth

Many experimental results show that surface roughness of thin films can increase, decrease, stay constant or pass through the minimum with the change in substrate temperature, energy of arriving atoms or assisted beam (electrons, photons, ions), depending on material and interval of variation of those parameters. The aim of this paper is to explain and analyze this non-monotonous behavior of surface roughness by proposed kinetic model. The model is based on rate equations and includes processes of surface diffusion of adatoms, nucleation, growth and coalescence of islands in the case of thin films growth in Volmer-Weber mode. It is shown by modeling that non-monotonous dependence of surface roughness on the factors influencing energy of adatoms (e.g. temperature, assisted beam irradiation, accelerating voltage) occurs as a result of interplay between diffusion length of adatoms and size of islands, because both parameters depend on energy of adatoms. Variation of island size and diffusion length results in atomic jumps from islands forming rougher or smoother surface. The functions of surface roughness, island size, island density on diffusion length of adatoms and on other parameters are calculated and analyzed in this work.     

Electrical detection of nuclear spin echoes

We show, via a straightforward calculation, that it is feasible to detect nuclear spin echoes in a ferromagnetic thin film by electrical means. The detection scheme is based on the deflection of the electronic magnetization when the nuclear magnetization reforms during an echo. This deflection is observed as a time-dependent magnetoresistive signal.     

Structural, morphological, wettability and thermal resistance properties of hydro-oleophobic thin films prepared by a wet chemical process

The structural properties of fluorine containing polymer compounds make them highly attractive materials for hydro-oleophobic applications. However, most of these exhibit low surface energy and poor adhesion on the substrates. In the present investigation, crack free, smooth and uniform thin films of poly[4,5-difluoro-2,2-bis(trifluoromethyl)-1,3-dioxole]-co-tetrafluoroethylene (TFD-co-TFE) with good adhesion have been deposited by wet chemical spin-coating technique on polished AISI 440C steel substrates. The as-deposited films (xerogel films) have been subjected to annealing for 1 h at different temperatures ranging from 100 to 500 °C in an argon atmosphere. The size growth of the nano-hemispheres increased from 8 nm for xerogel film to 28 nm for film annealed at 400 °C. It was found that as the annealing temperature increased from 100 to 400 °C, nano-hemisphere-like structures were formed, which in turn have shown increase in the water contact angle from 122° to 147° and oil (peanut) contact angle from 85° to 96°. No change in the water contact angle (122°) has been observed when the films deposited at room temperature were heated in air from 30 to 80 °C as well as exposed to steam for 8 days for 8 h/day indicating thermal stability of the film.     

Dimension-Splitting for Simplifying Diffusion in Lattice-Gas Models

We introduce a simplified technique for incorporating diffusive phenomena into lattice-gas molecular dynamics models. In this method, spatial interactions take place one dimension at a time, with a separate fractional timestep devoted to each dimension, and with all dimensions treated identically. We show that the model resulting from this technique is equivalent to the macroscopic diffusion equation in the appropriate limit. This technique saves computational resources and reduces the complexity of model design, programming, debugging, simulation and analysis. For example, a reaction-diffusion simulation can be designed and tested as a one-dimensional system, and then directly extended to two or more dimensions. We illustrate the use of this approach in constructing a microscopically reversible model of diffusion-limited aggregation as well as in a model of growth of biological films.     

Co-Segregation Effects on Boundary Migration

We analyze the effect of co-segregation on the mobility of grain boundaries within the framework of the impurity drag theory originally proposed by Cahn and Lücke and Stüwe for an ideal solution. The new derivation extends this model to the case where there are two types of impurities (or three components in the alloy). Since the resultant expression for the boundary mobility is complicated, numerical solutions were obtained for several cases to show how co-segregation affects the boundary mobility. Depending on the relative diffusivities of the two impurities which are both attracted to the boundary, the mobility may either increase or decrease with increasing concentration of one of the impurities. When one of the impurities is attracted to the boundary and the other repelled from the boundary, increasing the concentration of the attractive impurity can lead to a sharp decrease in the boundary mobility.