The epitaxial growth of graphene on copper foils is a complex process, influenced by thermodynamic, kinetic, and growth parameters, often leading to diverse island shapes including dendrites, squares, stars, hexagons, butterflies, and lobes. Here, we introduce a phase-field model that provides a unified description of these diverse growth morphologies and compare the model results with new experiments. Our model explicitly accounts for the anisotropies in the energies of growing graphene edges, kinetics of attachment of carbon at the edges, and the crystallinity of the underlying copper substrate (through anisotropy in surface diffusion). We show that anisotropic diffusion has a very important, counterintuitive role in the determination of the shape of islands, and we present a "phase diagram" of growth shapes as a function of growth rate for different copper facets. Our results are shown to be in excellent agreement with growth shapes observed for high symmetry facets such as (111) and (001) as well as for high-index surfaces such as (221) and (310).

Summary • It is still an open question as to whether genome size (GS) variation is shaped by natural selection. One approach to address this question is a population-level survey that assesses both the variation in GS and the relationship of GS to ecological variants. • We assessed GS in Zea mays, a species that includes the cultivated crop, maize, and its closest wild relatives, the teosintes. We measured GS in five plants of each of 22 maize landraces and 21 teosinte populations from Mexico sampled from parallel altitudinal gradients. • GS was significantly smaller in landraces than in teosintes, but the largest component of GS variation was among landraces and among populations. In maize, GS correlated negatively with altitude; more generally, the best GS predictors were linked to geography. By contrast, GS variation in teosintes was best explained by temperature and precipitation. • Overall, our results further document the size flexibility of the Zea genome, but also point to a drastic shift in patterns of GS variation since domestication. We argue that such patterns may reflect the indirect action of selection on GS, through a multiplicity of phenotypes and life-history traits.

Most angiosperm nuclear DNA is repetitive and derived from silenced transposable elements (TEs). TE silencing requires substantial resources from the plant host, including the production of small interfering RNAs (siRNAs). Thus, the interaction between TEs and siRNAs is a critical aspect of both the function and the evolution of plant genomes. Yet the co-evolutionary dynamics between these two entities remain poorly characterized. Here we studied the organization of TEs within the maize (Zea mays ssp mays) genome, documenting that TEs fall within three groups based on the class and copy numbers. These groups included DNA elements, low copy RNA elements and higher copy RNA elements. The three groups varied statistically in characteristics that included length, location, age, siRNA expression and 24∶22 nucleotide (nt) siRNA targeting ratios. In addition, the low copy retroelements encompassed a set of TEs that had previously been shown to decrease expression within a 24 nt siRNA biogenesis mutant (mop1). To investigate the evolutionary dynamics of the three groups, we estimated their abundance in two landraces, one with a genome similar in size to that of the maize reference and the other with a 30% larger genome. For all three accessions, we assessed TE abundance as well as 22 nt and 24 nt siRNA content within leaves. The high copy number retroelements are under targeted similarly by siRNAs among accessions, appear to be born of a rapid bust of activity, and may be currently transpositionally dead or limited. In contrast, the lower copy number group of retrolements are targeted more dynamically and have had a long and ongoing history of transposition in the maize genome.

In the present article, we introduce a phase-field model for thin-film growth with anisotropic step energy, attachment kinetics, and diffusion, with second-order (thin-interface) corrections. We are mainly interested in the limit in which kinetic anisotropy dominates, and hence we study how the expected shape of a crystallite, which in the long-time limit is the kinetic Wulff shape, is modified by anisotropic diffusion. We present results that prove that anisotropic diffusion plays an important, counterintuitive role in the evolving crystal shape, and we add second-order corrections to the model that provide a significant increase in accuracy for small supersaturations. We also study the effect of different crystal symmetries and discuss the influence of the deposition rate.

Transposable elements (TEs) compose the majority of angiosperm DNA. Plants counteract TE activity by silencing them epigenetically. One form of epigenetic silencing requires 21–22 nt small interfering RNAs that act to degrade TE mRNA and may also trigger DNA methylation. DNA methylation is reinforced by a second mechanism, the RNA-dependent DNA methylation (RdDM) pathway. RdDM relies on 24 nt small interfering RNAs and ultimately establishes TEs in a quiescent state. These host factors interact at a systems level, but there have been no system level analyses of their interactions. Here, we define a deterministic model that represents the propagation of active TEs, aspects of the host response and the accumulation of silenced TEs. We describe general properties of the model and also fit it to biological data in order to explore two questions. The first is why two overlapping pathways are maintained, given that both are likely energetically expensive. Under our model, RdDM silenced TEs effectively even when the initiation of silencing was weak. This relationship implies that only a small amount of RNAi is needed to initiate TE silencing, but reinforcement by RdDM is necessary to efficiently counter TE propagation. Second, we investigated the reliance of the host response on rates of TE deletion. The model predicted that low levels of deletion lead to few active TEs, suggesting that silencing is most efficient when methylated TEs are retained in the genome, thereby providing one explanation for the large size of plant genomes.

A global bifurcation of the blue sky catastrophe type has been found in a small Prandtl number binary mixture contained in a laterally heated cavity. The system has been studied numerically applying the tools of bifurcation theory. The catastrophe corresponds to the destruction of an orbit which, for a large range of Rayleigh numbers, is the only stable solution. This orbit is born in a global saddle-loop bifurcation and becomes chaotic in a period doubling cascade just before its disappearance at the blue sky catastrophe.PACS numbers: 47.27. Te, 47.20.Ky, 44.25.+f Bifurcation theory has long been a very helpful tool in the analysis of complex dynamics of nonlinear systems [1,2]. Whereas different devised scenarios have been found in theoretical models with a few variables, there is a growing interest both in relating real systems with that kind of models (e.g. projecting their dynamics to some relevant degrees of freedom [3]) and in directly analyzing the behavior of these systems in terms of dynamical systems theory (by studying them either experimentally or by realistic models). In this context a great deal of work has been devoted to convection in fluids. Qualitative changes in the dynamics of fluxes maintained out of equilibrium by imposed thermal gradients have provided examples of most of the known bifurcations, and have become a main subject in the area of nonlinear dynamics.In this letter we will show the occurrence of a blue sky catastrophe [BSC] in double diffusive convection. The BSC is a codimension-1 bifurcation that consists in the destruction of a stable periodic orbit as its length and period tend to infinity, while the cycle remains bounded and located at a finite distance from all the equilibrium solutions [1,4]. This destruction is caused by the collision with a non-hyperbolic cycle that appears at the bifurcation point. While approaching the bifurcation the orbit increasingly coils in the zone where the new cycle will appear, which originates the divergence in both period and length. In that point the original cycle becomes an orbit homoclinic to the new cycle. This type of bifurcation is relatively exotic, but can easily be found in slow-fast (i.e. singularly perturbed) systems with at least two fast variables [5].We are interested in double-diffusive fluxes that occur when convection is driven by simultaneous thermal and concentration gradients in a binary mixture [6]. Doublediffusive convection in cavities with imposed vertical gradients exhibits very rich dynamics, and has been used as a system to study pattern formation [7] and transition to chaos [8]. The case of horizontal gradients, which arises naturally in applications such as crystal growth [9] or oceanography [6], has received less attention. In this work we numerically study this latter configuration for a small Prandtl number binary mixture. We consider the case when thermal and solutal buoyancy forces exactly compensate each other, which allows the existence of a quiescent (conductive) state [10,11,12,13]. We have found th...

The dynamics of a small Prandtl number binary mixture in a laterally heated cavity is studied numerically. By combining temporal integration, steady state solving and linear stability analysis of the full PDE equations, we have been able to locate and characterize a codimension-three degenerate Takens-Bogdanov point whose unfolding describes the dynamics of the system for a certain range of Rayleigh numbers and separation ratios near S=-1.Comment: 8 pages, 5 figure

In this study, we present a phase-field model that describes the process of intercalation of Li ions into a layer of an amorphous solid such as amorphous silicon (a-Si). The governing equations couple a viscous Cahn-Hilliard-Reaction model with elasticity in the framework of the Cahn-Larché system. We discuss the parameter settings and flux conditions at the free boundary that lead to the formation of phase boundaries having a sharp gradient in lithium ion concentration between the initial state of the solid layer and the intercalated region. We carry out a matched asymptotic analysis to derive the corresponding sharp-interface model that also takes into account the dynamics of triple points where the sharp interface intersects the free boundary of the Si layer. We numerically compare the interface motion predicted by the sharp-interface model with the long-time dynamics of the phase-field model.