Novel continuum modeling of crystal surface evolution

We propose a novel approach to continuum modeling of the dynamics of crystal surfaces. Our model follows the evolution of an ensemble of step configurations, which are consistent with the macroscopic surface profile. Contrary to the usual approach where the continuum limit is achieved when typical surface features consist of many steps, our continuum limit is approached when the number of step configurations of the ensemble is very large. The model can handle singular surface structures such as corners and facets. It has a clear computational advantage over discrete models.Comment: 4 pages, 3 postscript 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

Non-invertible transformations and spatiotemporal randomness

We generalize the exact solution to the Bernoulli shift map. Under certain conditions, the generalized functions can produce unpredictable dynamics. We use the properties of the generalized functions to show that certain dynamical systems can generate random dynamics. For instance, the chaotic Chua's circuit coupled to a circuit with a non-invertible I-V characteristic can generate unpredictable dynamics. In general, a nonperiodic time-series with truncated exponential behavior can be converted into unpredictable dynamics using non-invertible transformations. Using a new theoretical framework for chaos and randomness, we investigate some classes of coupled map lattices. We show that, in some cases, these systems can produce completely unpredictable dynamics. In a similar fashion, we explain why some wellknown spatiotemporal systems have been found to produce very complex dynamics in numerical simulations. We discuss real physical systems that can generate random dynamics.Comment: Accepted in International Journal of Bifurcation and Chao

The effect of weaning diet type on grey mullet (Mugil cephalus) juvenile performance during the trophic shift from carnivory to omnivory

In captive grey mullet (Mugil cephalus) juveniles, the weaning stage overlaps the period where there are changes in the ontogeny of digestive enzymes as the fry transit from carnivory to omnivory. The aim of this study was to evaluate growth, survival, weight distribution and the activity of pancreatic and brush border digestive enzymes when fry are fed a carnivorous, herbivorous or omnivorous weaning diet. Fifteen 17-L aquaria in a flow through system with 40‰, UV treated, temperature (24.5 ± 0.5 °C) controlled seawater were stocked with eighty-five 23 dph grey mullet larvae per aquarium. This allowed the testing of three weaning dietary treatments, differing in their protein and carbohydrate content, in 5 replicate aquaria per treatment from 24 to 53 dph. Diet 1 was the dried macroalgal species Ulva lactuca and was designated as a low protein: high carbohydrate herbivorous diet. Diet 2 was a commercial microencapsulated starter feed designated as a high protein: low carbohydrate carnivorous diet. Diet 3 was a 1:1 ww mixture of diets 1 and diet 2 representing an omnivorous feeding regime. The average final weight of the omnivorous feeding fish was significantly (P .05). The activity levels of brush border alkaline phosphatase and intracellular leucine alanine peptidase were similar in grey mullet fry fed the carnivorous and omnivorous diets, but were higher than those in fish fed the herbivorous diet (P < .05). The intestinal maturation index exhibited the highest and lowest values in mullet fry fed the carnivorous and herbivorous diets, respectively, whereas those from the omnivorous group showed intermediate values (P = .03). This study broadly suggests that aquaculture feeds for juvenile grey mullet should be designed for omnivorous feeding habits.info:eu-repo/semantics/acceptedVersio

Genetic analysis of four consanguineous multiplex families with inflammatory bowel disease

Background: Family studies support a genetic predisposition to inflammatory bowel diseases (IBD), but known genetic variants only partially explain the disease heritability. Families with multiple affected individuals potentially harbour rare and high-impact causal variants. Long regions of homozygosity due to recent inbreeding may increase the risk of individuals bearing homozygous loss-of-function variants. This study aimed to identify rare and homozygous genetic variants contributing to IBD. Methods: Four families with known consanguinity and multiple cases of IBD were recruited. In a family-specific analysis, we utilised homozygosity mapping complemented by whole-exome sequencing. Results: We detected a single region of homozygosity shared by Crohn's disease cases from a family of Druze ancestry, spanning 2.6 Mb containing the NOD2 gene. Whole-exome sequencing did not identify any potentially damaging variants within the region, suggesting that non-coding variation may be involved. In addition, affected individuals in the families harboured several rare and potentially damaging homozygous variants in genes with a role in autophagy and innate immunity including LRRK1, WHAMM, DENND3, and C5. Conclusion: This study examined the potential contribution of rare, high-impact homozygous variants in consanguineous families with IBD. While the analysis was not designed to achieve statistical significance, our findings highlight genes or loci that warrant further research. Non-coding variants affecting NOD2 may be of importance in Druze patients with Crohn's disease

Profile scaling in decay of nanostructures

The flattening of a crystal cone below its roughening transition is studied by means of a step flow model. Numerical and analytical analyses show that the height profile, h(r,t), obeys the scaling scenario dh/dr = F(r t^{-1/4}). The scaling function is flat at radii r<R(t) \sim t^{1/4}. We find a one parameter family of solutions for the scaling function, and propose a selection criterion for the unique solution the system reaches.Comment: 4 pages, RevTex, 3 eps figure