Interface collisions.

We provide a theoretical framework to analyze the properties of frontal collisions of two growing interfaces considering different short-range interactions between them. Due to their roughness, the collision events spread in time and form rough domain boundaries, which defines collision interfaces in time and space. We show that statistical properties of such interfaces depend on the kinetics of the growing interfaces before collision, but are independent of the details of their interaction and of their fluctuations during the collision. Those properties exhibit dynamic scaling with exponents related to the growth kinetics, but their distributions may be nonuniversal. Our results are supported by simulations of lattice models with irreversible dynamics and local interactions. Relations to first passage processes are discussed and a possible application to grain-boundary formation in two-dimensional materials is suggested.

Trends in colorectal cancer in the Caribbean: A population-based study in Martinique, 1982-2011.

BACKGROUND: We aimed to describe incidence and mortality from colorectal cancer, and temporal trends between 1982 and 2011 in Martinique (French West-Indies). METHODS: This was a descriptive, longitudinal, observational study based on data from the Martinique cancer registry. The study included all incident cases of colorectal cancer between 1982 and 2011. We recorded sociodemographic data and clinical variables (histology, site according to the WHO classification). Cancer cases were recorded in strict conformity with the international standards. Annual rate of change was calculated, direct standardisation was used for incidence and mortality age standardised rates (ASR). The comparative incidence figure and comparative mortality figure (95% confidence intervals) were calculated. RESULTS: In total, 2530 patients were included in our study; 1243 died. In the period 2007-2011, a considerable increase in incidence was observed, making colorectal cancer the second leading cause of cancer deaths in both sexes (8.9% and 10.5%). In men, ASR for incidence increased from 9.6/100,000 person-years in the period 1982-1986 to 27.2/100,000 person-years in the period 2007-2011, with a notable acceleration of the increase. In women, ASR increased from 8.4 to 19.8/100,000 person-years over the same periods. For the latest period 2007-2011, mortality rates were 9.9 and 7.6/100,000 person-years for men and for women respectively. Regardless of the sex, there was a strong increase in the incidence of right colon cancer, which became the most common colorectal site in women in Martinique. CONCLUSION: Our findings confirm the increase in the incidence of colorectal cancer that started in the 2000s. Trends observed reflect a salient epidemiological transition of the Caribbean.

Controlling the wetting transitions of nanoparticles on nanopatterned substrates using an electric current.

We study the behavior of a nanoparticle under electromigration on a nanopatterned surface. We show that electromigration allows one to control the wetting transitions of the nanoparticle. Suitable surface electromigration conditions to observe these transitions can be achieved with electric currents larger than 1 µA. Using kinetic Monte Carlo simulations and analytical modeling, we determine the phase diagram of the wetting states, showing how wetting multistability is affected by electromigration. In addition, we show that the dynamics of the transitions is controlled by surface diffusion in our simulations, and we provide a quantitative expression for the transition time.

Wetting of elastic solids on nanopillars.

Solids and liquids are both known to exhibit Cassie-Baxter states, where a drop or a solid nanoparticle is maintained on top of pillars due to wetting forces. We point out that due to elastic strain, solid nanocrystals exhibit a behavior different from that of liquids. First, the equilibrium Cassie-Baxter state on a single pillar exhibits a spontaneous symmetry breaking due to elastic effects. The second consequence of elasticity is the existence of stable partially impaled states, resulting from a compromise between wetting forces which favor impalement and elastic strain which resists impalement. Based on kinetic Monte Carlo simulations which include elastic strain, we discuss these effects and we propose a global phase diagram for the stability of nanocrystals on nanopillars.

Anisotropy and coarsening in the instability of solid dewetting fronts.

We report on the destabilization of the film edge during the dewetting of ultrathin solid films. An unusual coarsening behavior is found within the linear instability regime. In addition, we find that the instability is suppressed along faceted orientations. Our results are obtained via kinetic Monte Carlo simulations. An analytical model based on diffusion-limited mass transport on the rim and nucleation-limited increase of the rim height provides a good description of kinetic Monte Carlo simulations. Our results are consistent with recent experimental observations.

Pattern-induced thermal unbinding of filaments.

Substrate patterning is shown to be a convenient method to control the adhesion of filaments. The pattern not only permits a control of adhesion, it also leads to an unbinding transition at finite temperatures. The dimensionality of transverse fluctuations controls the continuity of the transition, and in some cases, re-entrant binding is observed as temperature is increased. Unbinding on patterns is found to be easier to observe than unbinding on flat substrates. Finally, experimental conditions under which unbinding could be observable are discussed.

Dewetting of ultrathin solid films.

Ultrathin crytalline solid films are found to dewet with a faceted rim. In the case of heterogeneous dewetting initiated from a linear trench or from periodically arranged holes, the dewetted area expands either with a faceted multilayer rim or in a layer-by-layer fashion. In the case of homogeneous dewetting, holes are accompanied with multilayer rims and the uncoverage increases as a power law of time. Results of kinetic Monte Carlo simulations are elucidated within the frame of nucleation theory and surface diffusion limited dynamics.

Adhesion of membranes and filaments on rippled surfaces.

Adhesion of membranes and filaments on periodic rippled surfaces is studied by means of a one-dimensional model. The adhesion behavior is found to depend crucially on the shape of the ripples. Fakir-carpet and sinusoidal patterns are studied in detail. Infinite staircases of periodic ground states are found, with a periodicity diverging at a transition line. Moreover, the boundaries of the regions of existence of metastable states form a complex sequence on the fakir-carpet surface. This is inferred to lead to an unbinding transition by progressive stages when fluctuations are negligible. The occurrence of adhesion transitions for graphene, carbon nanotubes, and lipidic membranes is discussed quantitatively.

Dewetting of a solid monolayer.

We report on the dewetting of a monolayer on a solid substrate, where mass transport occurs via surface diffusion. For a wide range of parameters, a labyrinthine pattern of bilayer islands is formed. An irreversible regime and a thermodynamic regime are identified. In both regimes, the velocity of a dewetting front, the wavelength of the bilayer island pattern, and the rate of nucleation of dewetted zones are obtained. We also point out the existence of a scaling behavior, which is analyzed by means of a geometrical model.

Stiff knots.

We report on the geometry and mechanics of knotted stiff strings. We discuss both closed and open knots. Our two main results are that (i) their equilibrium energy as well as the equilibrium tension for open knots depends on the type of knot as the square of the bridge number and (ii) braid localization is found to be a general feature of stiff string entanglements, while angle and knot localizations are forbidden. Moreover, we identify a family of knots for which the equilibrium shape is a circular braid. Two other equilibrium shapes are found from Monte Carlo simulations. These three shapes are confirmed by rudimentary experiments. Our approach is also extended to the problem of the minimization of the length of a knotted string with a maximum allowed curvature.

Birth and morphological evolution of step bunches under electromigration.

We analyze the dynamics of electromigration-induced step bunching in the absence of desorption. We show that, even when the instability occurs at long wavelength, hinting to a smooth morphology, the surface suddenly splits into bunches escorted with wide terraces, in agreement with several observations. As the size of the bunches increases, a nonstandard regime is exhibited, namely, the bunches do not match tangentially to the facet, as would the classical Pokrosvky-Talapov shape dictate. This Letter presents a complete scenario of evolution of bunches from their birth up to their ultimate stage.

Local electromigration model for crystal surfaces.

The dynamics of crystal surfaces in the presence of electromigration is analyzed. From a phase field model with a migration force which depends on the local geometry, a step model with additional contributions is derived in the kinetic boundary conditions. These contributions trigger various surface instabilities, such as step meandering, bunching, and pairing on vicinal surfaces. Experiments are discussed.

Kinetic step pairing.

We report on the theoretical and experimental discovery of pairing of identical crystal steps. We first show that step bunching always occurs at long wavelength in the vicinity of an instability threshold when step dynamics is local. But an instability towards a stable train of pairs can be obtained when steps dynamics is nonlocal. This instability is shown to occur for transparent steps under electromigration. Observations on Si(111) under electromigration around 1230 degrees C show stable trains of pairs. By controlling both supersaturation and electromigration, we establish an experimental morphology diagram, from which we conclude that the transparency kinetic coefficient is negative.

Peculiar effects of anisotropic diffusion on dynamics of vicinal surfaces.

We report on peculiar behaviors due to anisotropic terrace diffusion on step meandering on a vicinal surface. We find that anisotropy triggers tilted ripples. In addition, if the fast diffusion direction is perpendicular to the steps, the instability is moderate and coarsening is absent, while in the opposite case the instability is promoted, and interrupted coarsening may be observed. Strong enough anisotropy restabilizes the step for almost all step orientations. These findings point to the nontrivial effect of anisotropy and open promising lines of inquiries in the design of surface architectures.

Interrupted coarsening of anisotropic step meander.

We report on the effect of anisotropy on the step meandering instability on vicinal surfaces during molecular beam epitaxy growth. A scenario of interrupted coarsening is found: the lateral length scale of the structure first significantly increases with time and then freezes at a larger length scale. The wavelength selection mechanism results from a nontrivial nonlinear effect of anisotropy. Anisotropy also leads to solutions which drift sideways, resulting from the loss of the back-front symmetry of the meander and the nonvariational character of dynamics.

Phase field models for step flow.

The relation between phase field and discontinuous models for crystal steps is analyzed. Different formulations of the kinetic boundary conditions of the discontinuous model are first presented. We show that (i) step transparency, usually interpreted as the possibility for adatoms to jump through steps, may be seen as a modification of the equilibrium concentration engendered by step motion. (ii) The interface definition (i.e., the position of the dividing line) intervenes in the expression of the kinetic coefficients only in the case of fast attachment kinetics. (iii) We also identify the thermodynamically consistent reference state for kinetic boundary conditions. Asymptotic expansions of the phase field models in the limit where the interface width is small, lead to various discontinuous models. (1) A phase field model with one global concentration field and variable mobility is shown to lead to a discontinuous model with fast step kinetics. (2) A phase field model with one concentration field per terrace allows one to recover arbitrary step kinetics (i.e., arbitrarily strong Ehrlich-Schwoebel effect and step transparency). Quantitative agreement is found, in both the linear and nonlinear regimes, between the numerical solution of the phase field models and the analytical solution of the discontinuous model.

Continuum model for low temperature relaxation of crystal steps.

High and low temperature relaxation of crystal steps are described in a unified picture, using a continuum model based on a modified expression of the step-free energy. Results are in agreement with experiments and Monte Carlo simulations of step fluctuations and monolayer cluster diffusion and relaxation. In an extended model where mass exchange with neighboring terraces is allowed, step transparency and a low temperature regime for unstable step meandering are found.

Oscillatory driving of crystal surfaces: a route to controlled pattern formation.

We show that the oscillatory driving of crystal surfaces can induce pattern formation or smoothening. Depending on driving conditions, step bunching and meandering, mound formation, or surface smoothening may be seen in the presence of a kinetic asymmetry at the steps or kinks. We employ a step model to calculate the induced mass flux along misoriented surfaces, which accounts for surface dynamics and stability. Slope selection, surface metastability, and frequency-dependent surface stability are found. Quantitative predictions for pattern formation on metal surfaces in an electrolyte are provided.

Unstable step meandering with elastic interactions.

We report on theoretical investigations of the influence of step interactions due to elasticity on unstable step meandering during molecular beam homoepitaxy. It is shown that elasticity causes coarsening of the cellular structure of the meander found in a previous work. The time dependence of step roughness is found to be robust, behaving as t(1/2). The lateral length scale coarsening is shown to be sensitive to the underlying physical mechanisms. In particular, the typical length follows the law t(alpha), with alpha = 1/6 or 1/4 depending on whether line diffusion is negligibly small or not.