Wright-Fisher diffusion bridges

The trajectory of the frequency of an allele which begins at $x$ at time $0$ and is known to have frequency $z$ at time $T$ can be modelled by the bridge process of the Wright-Fisher diffusion. Bridges when $x=z=0$ are particularly interesting because they model the trajectory of the frequency of an allele which appears at a time, then is lost by random drift or mutation after a time $T$. The coalescent genealogy back in time of a population in a neutral Wright-Fisher diffusion process is well understood. In this paper we obtain a new interpretation of the coalescent genealogy of the population in a bridge from a time $t\in (0,T)$. In a bridge with allele frequencies of 0 at times 0 and $T$ the coalescence structure is that the population coalesces in two directions from $t$ to $0$ and $t$ to $T$ such that there is just one lineage of the allele under consideration at times $0$ and $T$. The genealogy in Wright-Fisher diffusion bridges with selection is more complex than in the neutral model, but still with the property of the population branching and coalescing in two directions from time $t\in (0,T)$. The density of the frequency of an allele at time $t$ is expressed in a way that shows coalescence in the two directions. A new algorithm for exact simulation of a neutral Wright-Fisher bridge is derived. This follows from knowing the density of the frequency in a bridge and exact simulation from the Wright-Fisher diffusion. The genealogy of the neutral Wright-Fisher bridge is also modelled by branching P\'olya urns, extending a representation in a Wright-Fisher diffusion. This is a new very interesting representation that relates Wright-Fisher bridges to classical urn models in a Bayesian setting. This paper is dedicated to the memory of Paul Joyce

Temperature-Dependent Friction-Induced Surface Amorphization Mechanism of Crystal Silicon

Friction-induced surface amorphization of silicon is one of the most important surface wear and damage forms, changing the material properties and harming the reliability of silicon-based devices. However, knowledge regarding the amorphization mechanisms as well as the effects of temperature is still insufficient, because the experimental measurements of the crystal–amorphous interface structures and evolutions are extremely difficult. In this work, we aim to fully reveal the temperature dependence of silicon amorphization behaviors and relevant mechanisms by using reactive molecular dynamics simulations. We first show that the degree of amorphization is suppressed by the increasing temperature, contrary to our initial expectations. Then, we further revealed that the observed silicon amorphization behaviors are attributed to two independent processes: One is a thermoactivated and shear-driven amorphization process where the theoretical amorphization rate shows an interesting valley-like temperature dependence because of the competition between the increased thermal activation effect and the reduction of shear stress, and another one is a thermoactivated recrystallization process which shows a monotonically increasing trend with temperature. Thus, the observed reduction of amorphization with temperature is mainly due to the recrystallization effect. Additionally, analytical models are proposed in this work to describe both the amorphization and the recrystallization processes. Overall, the present findings provide deep insights into the temperature-dependent amorphization and recrystallization processes of silicon, benefiting the further development of silicon-based devices and technologies

Graphene Failure under MPa: Nanowear of Step Edges Initiated by Interfacial Mechanochemical Reactions

The low wear resistance of macroscale graphene coatings does not match the ultrahigh mechanical strength and chemical inertness of the graphene layer itself; however, the wear mechanism responsible for this issue at low mechanical stress is still unclear. Here, we demonstrate that the susceptibility of the graphene monolayer to wear at its atomic step edges is governed by the mechanochemistry of frictional interfaces. The mechanochemical reactions activated by chemically active SiO2 microspheres result in atomic attrition rather than mechanical damage such as surface fracture and folding by chemically inert diamond tools. Correspondingly, the threshold contact stress for graphene edge wear decreases more than 30 times to the MPa level, and mechanochemical wear can be described well with the mechanically assisted Arrhenius-type kinetic model, i.e., exponential dependence of the removal rate on the contact stress. These findings provide a strategy for improving the antiwear of graphene-based materials by reducing the mechanochemical interactions at tribological interfaces

Additional file 4: Table S3. of Identification and differential regulation of microRNAs in response to methyl jasmonate treatment in Lycoris aurea by deep sequencing

Conserved miRNA and miRNA families identified by similarity. (XLSX 105 kb

Inverse Relationship between Thickness and Wear of Fluorinated Graphene: “Thinner Is Better”

Atomically thin two-dimensional (2D) materials are excellent candidates for utilization as a solid lubricant or additive at all length scales from macro-scale mechanical devices to micro/nano-electromechanical systems (MEMS/NEMS). In such applications, wear resistance of ultrathin 2D materials is critical for sustained lubrication performance. Here, we investigated the wear of fluorinated graphene (FG) nanosheets deposited on silicon surfaces using atomic force microscopy (AFM) and discovered that the wear resistance of FG improves as the FG thickness decreases from 4.2 to 0.8 nm (corresponding to seven layers to single layer) and the surface energy of the substrate underneath the FG nanosheets increases. On the basis of density function theory (DFT) calculations, the negative correlation of wear resistance to FG thickness and the positive correlation to substrate surface energy could be explained with the degree of interfacial charge transfer between FG and substrate which affects the strength of FG adhesion to the substrate

Additional file 6: Table S5. of Identification and differential regulation of microRNAs in response to methyl jasmonate treatment in Lycoris aurea by deep sequencing

Validation and comparative relative expression of differentially expressed miRNAs between the CK and MJ100 libraries in L. aurea. (XLSX 19 kb

Nanoscale Wear Triggered by Stress-Driven Electron Transfer

Wear of sliding contacts causes device failure and energy costs; however, the microscopic principle in activating wear of the interfaces under stress is still open. Here, the typical nanoscale wear, in the case of silicon against silicon dioxide, is investigated by single-asperity wear experiments and density functional theory calculations. The tests demonstrate that the wear rate of silicon in ambient air increases exponentially with stress and does not obey classical Archard’s law. Series calculations of atomistic wear reactions generally reveal that the mechanical stress linearly drives the electron transfer to activate the sequential formation and rupture of interfacial bonds in the atomistic wear process. The atomistic wear model is thus resolved by combining the present stress-driven electron transfer model with Maxwell–Boltzmann statistics. This work may advance electronic insights into the law of nanoscale wear for understanding and controlling wear and manufacturing of material surfaces

Influence of Interfacial Chemistry and Oxygen on Graphene Step Edges as Antiwear Coatings

Graphene has been widely applied to assemble antiwear coatings due to its ultrahigh mechanical strength and intrinsically lubricating properties; however, the ubiquitous atomic step edges as typical defects in coating are vulnerable to wear depending on the environment atmosphere. Here, we reported atomic attrition of the mechanically exfoliated graphene step edge and its silicon substrate against a Si probe initiating at a much lower threshold load in room air in comparison with peel-induced rupture as a dominant failure behavior at high loads in vacuum. Further investigations indicate that the atomic attrition of the graphene step edge should mainly originate from the interfacial chemical reactions with the chemically active Si probe associated with surrounding oxygen. Oxygen facilitates the atomic wear of graphene edges, whereas water molecules adsorbed at the step edge as a lubricating layer suppress edge damage. Even under oxygen conditions, only peel-induced rupture as a mechanical wear of the graphene edge was observed when scratched with an inert diamond probe. This study elucidates the two wear mechanisms operating at the graphene step edges and provides a strategy to enhance the wear resistance of graphene coatings by reducing ambient oxygen levels and minimizing interfacial chemical interactions

Layer-Dependent Nanowear of Graphene Oxide

The mechanical performance and surface friction of graphene oxide (GO) were found to inversely depend on the number of layers. Here, we demonstrate the non-monotonic layer-dependence of the nanowear resistance of GO nanosheets deposited on a native silicon oxide substrate. As the thickness of GO increases from ∼0.9 nm to ∼14.5 nm, the nanowear resistance initially demonstrated a decreasing and then an increasing tendency with a critical number of layers of 4 (∼3.6 nm in thickness). This experimental tendency corresponds to a change of the underlying wear mode from the overall removal to progressive layer-by-layer removal. The phenomenon of overall removal disappeared as GO was deposited on an H-DLC substrate with a low surface energy, while the nanowear resistance of thicker GO layers was always higher. Combined with density functional theory calculations, the wear resistance of few-layer GO was found to correlate with the substrate’s surface energy. This can be traced back to substrate-dependent adhesive strengths of GO, which correlated with the GO thickness originating from differences in the interfacial charge transfer. Our study proposes a strategy to improve the antiwear properties of 2D layered materials by tuning their own thickness and/or the interfacial interaction with the underlying substrate