Low-Energy Electron Microscopy Studies of Interlayer Mass Transport Kinetics on TiN(111)

In situ low-energy electron microscopy was used to study interlayer mass transport kinetics during annealing of three-dimensional (3D) TiN(111) mounds, consisting of stacked 2D islands, at temperatures T between 1550 and 1700 K. At each T, the islands decay at a constant rate, irrespective of their initial position in the mounds, indicating that mass is not conserved locally. From temperature-dependent island decay rates, we obtain an activation energy of 2.8+/-0.3 eV. This is consistent with the detachment-limited decay of 2D TiN islands on atomically-flat TiN(111) terraces [Phys. Rev. Lett. 89 (2002) 176102], but significantly smaller than the value, 4.5+/-0.2 eV, obtained for bulk-diffusion-limited spiral step growth [Nature 429, 49 (2004)]. We model the process based upon step flow, while accounting for step-step interactions, step permeability, and bulk mass transport. The results show that TiN(111) steps are highly permeable and exhibit strong repulsive temperature-dependent step-step interactions that vary between 0.003 and 0.076 eV-nm. The rate-limiting process controlling TiN(111) mound decay is surface, rather than bulk, diffusion in the detachment-limited regime.Comment: 26 pages, 5 figure

Decay of one dimensional surface modulations

The relaxation process of one dimensional surface modulations is re-examined. Surface evolution is described in terms of a standard step flow model. Numerical evidence that the surface slope, D(x,t), obeys the scaling ansatz D(x,t)=alpha(t)F(x) is provided. We use the scaling ansatz to transform the discrete step model into a continuum model for surface dynamics. The model consists of differential equations for the functions alpha(t) and F(x). The solutions of these equations agree with simulation results of the discrete step model. We identify two types of possible scaling solutions. Solutions of the first type have facets at the extremum points, while in solutions of the second type the facets are replaced by cusps. Interactions between steps of opposite signs determine whether a system is of the first or second type. Finally, we relate our model to an actual experiment and find good agreement between a measured AFM snapshot and a solution of our continuum model.Comment: 18 pages, 6 figures in 9 eps file

The profile of a decaying crystalline cone

The decay of a crystalline cone below the roughening transition is studied. We consider local mass transport through surface diffusion, focusing on the two cases of diffusion limited and attachment-detachment limited step kinetics. In both cases, we describe the decay kinetics in terms of step flow models. Numerical simulations of the models indicate that in the attachment-detachment limited case the system undergoes a step bunching instability if the repulsive interactions between steps are weak. Such an instability does not occur in the diffusion limited case. In stable cases the height profile, h(r,t), is flat at radii r<R(t)\sim t^{1/4}. Outside this flat region the height profile obeys the scaling scenario \partial h/\partial r = {\cal F}(r t^{-1/4}). A scaling ansatz for the time-dependent profile of the cone yields analytical values for the scaling exponents and a differential equation for the scaling function. In the long time limit this equation provides an exact description of the discrete step dynamics. It admits a family of solutions and the mechanism responsible for the selection of a unique scaling function is discussed in detail. Finally we generalize the model and consider permeable steps by allowing direct adatom hops between neighboring terraces. We argue that step permeability does not change the scaling behavior of the system, and its only effect is a renormalization of some of the parameters.Comment: 25 pages, 18 postscript figure

Fluctuations of elastic interfaces in fluids: Theory and simulation

We study the dynamics of elastic interfaces-membranes-immersed in thermally excited fluids. The work contains three components: the development of a numerical method, a purely theoretical approach, and numerical simulation. In developing a numerical method, we first discuss the dynamical coupling between the interface and the surrounding fluids. An argument is then presented that generalizes the single-relaxation time lattice-Boltzmann method for the simulation of hydrodynamic interfaces to include the elastic properties of the boundary. The implementation of the new method is outlined and it is tested by simulating the static behavior of spherical bubbles and the dynamics of bending waves. By means of the fluctuation-dissipation theorem we recover analytically the equilibrium frequency power spectrum of thermally fluctuating membranes and the correlation function of the excitations. Also, the non-equilibrium scaling properties of the membrane roughening are deduced, leading us to formulate a scaling law describing the interface growth, W^2(L,T)=L^3 g[t/L^(5/2)], where W, L and T are the width of the interface, the linear size of the system and the temperature respectively, and g is a scaling function. Finally, the phenomenology of thermally fluctuating membranes is simulated and the frequency power spectrum is recovered, confirming the decay of the correlation function of the fluctuations. As a further numerical study of fluctuating elastic interfaces, the non-equilibrium regime is reproduced by initializing the system as an interface immersed in thermally pre-excited fluids.Comment: 15 pages, 11 figure

Multi-Particle Collision Dynamics -- a Particle-Based Mesoscale Simulation Approach to the Hydrodynamics of Complex Fluids

In this review, we describe and analyze a mesoscale simulation method for fluid flow, which was introduced by Malevanets and Kapral in 1999, and is now called multi-particle collision dynamics (MPC) or stochastic rotation dynamics (SRD). The method consists of alternating streaming and collision steps in an ensemble of point particles. The multi-particle collisions are performed by grouping particles in collision cells, and mass, momentum, and energy are locally conserved. This simulation technique captures both full hydrodynamic interactions and thermal fluctuations. The first part of the review begins with a description of several widely used MPC algorithms and then discusses important features of the original SRD algorithm and frequently used variations. Two complementary approaches for deriving the hydrodynamic equations and evaluating the transport coefficients are reviewed. It is then shown how MPC algorithms can be generalized to model non-ideal fluids, and binary mixtures with a consolute point. The importance of angular-momentum conservation for systems like phase-separated liquids with different viscosities is discussed. The second part of the review describes a number of recent applications of MPC algorithms to study colloid and polymer dynamics, the behavior of vesicles and cells in hydrodynamic flows, and the dynamics of viscoelastic fluids

Biological versus chronological ovarian age:implications for assisted reproductive technology

<p>Abstract</p> <p>Background</p> <p>Women have been able to delay childbearing since effective contraception became available in the 1960s. However, fertility decreases with increasing maternal age. A slow but steady decrease in fertility is observed in women aged between 30 and 35 years, which is followed by an accelerated decline among women aged over 35 years. A combination of delayed childbearing and reduced fecundity with increasing age has resulted in an increased number and proportion of women of greater than or equal to 35 years of age seeking assisted reproductive technology (ART) treatment.</p> <p>Methods</p> <p>Literature searches supplemented with the authors' knowledge.</p> <p>Results</p> <p>Despite major advances in medical technology, there is currently no ART treatment strategy that can fully compensate for the natural decline in fertility with increasing female age. Although chronological age is the most important predictor of ovarian response to follicle-stimulating hormone, the rate of reproductive ageing and ovarian sensitivity to gonadotrophins varies considerably among individuals. Both environmental and genetic factors contribute to depletion of the ovarian oocyte pool and reduction in oocyte quality. Thus, biological and chronological ovarian age are not always equivalent. Furthermore, biological age is more important than chronological age in predicting the outcome of ART. As older patients present increasingly for ART treatment, it will become more important to critically assess prognosis, counsel appropriately and optimize treatment strategies. Several genetic markers and biomarkers (such as anti-Müllerian hormone and the antral follicle count) are emerging that can identify women with accelerated biological ovarian ageing. Potential strategies for improving ovarian response include the use of luteinizing hormone (LH) and growth hormone (GH). When endogenous LH levels are heavily suppressed by gonadotrophin-releasing hormone analogues, LH supplementation may help to optimize treatment outcomes for women with biologically older ovaries. Exogenous GH may improve oocyte development and counteract the age-related decline of oocyte quality. The effects of GH may be mediated by insulin-like growth factor-I, which works synergistically with follicle-stimulating hormone on granulosa and theca cells.</p> <p>Conclusion</p> <p>Patients with biologically older ovaries may benefit from a tailored approach based on individual patient characteristics. Among the most promising adjuvant therapies for improving ART outcomes in women of advanced reproductive age are the administration of exogenous LH or GH.</p