Binary nanodroplet collisions have received increasing attention, whilst the identification of collision outcomes and the viscous dissipation mechanism have remained poorly understood. Using molecular dynamics simulations, this study investigates binary nanodroplet collisions over wide ranges of Weber number (We), Ohnesorge number (Oh) and off-centre distances. Coalescence, stretching separation and shattering are identified; however, bouncing, reflexive separation and rotational separation reported for millimetre-sized collisions are not observed, which is attributed to the enhanced viscous effect caused by the ‘natural’ high-viscosity characteristics of nanodroplets. Intriguingly, as an intermediate outcome, holes form in retracting films at relatively high We, arising from the vibration and thermal fluctuation of the films. Due to the combined effects of inertial, capillary and viscous forces, binary nanodroplet collisions fall into the cross-over regime, so estimating viscous dissipation becomes extremely important for distinguishing outcome boundaries. Based on the criterion that stretching separation is triggered only when the residual off-centre kinetic energy exceeds the surface energy required for separation, the boundary equation between coalescence and stretching separation is established. Here, viscous dissipation is calculated by the extracted flow feature from simulations, showing that the ratio of viscous dissipation to the initial kinetic energy depends only on Oh, not on We. Because of complex viscous dissipation mechanisms, the same boundary equation in the cross-over regime has also not been satisfactorily revealed for macroscale collisions. Therefore, the proposed equation is tested for wide data sources from both macroscale and nanoscale collisions, and satisfying agreement is achieved, demonstrating the universality of the equation.

Fine mapping and discovery of watermelon rind trait candidate genes are of great significance for modern watermelon breeding and development. In this study, we used the high-resolution genetic mapping and genome-wide genetic variation detection technology, combined with genome survey and sequencing technology, to locate and discover the candidate genes for rind traits of star watermelon varieties ‘Su XuanBai’ and ‘SHLX21’. Firstly, we identified a total of eight quantitative trait loci (QTLs) related to watermelon rind traits on chromosome 6. Secondly, a total of 208,240 single nucleotide polymorphisms and 75,345 small Indels (insertions/deletions) were detected in the two parents by high-coverage re-sequencing, respectively. Based on the genetic variation of the two parents and combined with Gene Ontology (GO) and Kyoto Encyclopedia of Genes and Genomes (KEGG) analysis using the planta database, the QTL region was reduced to 0.02 Mb. Finally, we identified the six potential regulatory factors for watermelon rind traits using real-time quantitative PCR. In conclusion, our results revealed the fine localization of candidate genes for watermelon rind traits and the successful discovery of candidate genes for regulating watermelon rind traits, which is of importance for watermelon rind traits and breeding-improved watermelon varieties.

In this paper, we propose and study an almost periodic reaction–diffusion epidemic model in which disease latency, spatial heterogeneity and general seasonal fluctuations are incorporated. The model is given by a spatially nonlocal reaction–diffusion system with a fixed time delay. We first characterise the upper Lyapunov exponent λ* for a class of almost periodic reaction–diffusion equations with a fixed time delay and provide a numerical method to compute it. On this basis, the global threshold dynamics of this model is established in terms of λ* It is shown that the disease-free almost periodic solution is globally attractive if λ* < 0, while the disease is persistent if λ* > 0. By virtue of numerical simulations, we investigate the effects of diffusion rate, incubation period and spatial heterogeneity on disease transmission.

Porous silicon nitride ceramics are attracting extensive attention due to its high strength and low dielectric loss. However, further strength enhancement at elevated temperatures is hindered by its intergranular phase, forming from sintering additives. This paper describes the fabrication of porous silicon nitride ceramic materials, by using a replacement method of carbothermal nitridation. The initial samples which were obtained from the sintering of mixed powder consisted of 95 wt% Si3N4 and 5 wt% Y2O3. After the removal of the oxide intergranular phase and the infiltration of mixtures of phenolic resins and silica sols, carbothermal nitridation process was carried out at 1550 °C for 2 h under nitrogen. X-ray diffraction and microstructural analysis revealed a complete replacement of oxide intergranular phases by the newly formed Si3N4 intergranular phase. The unmodified ceramic exhibited lower flexural strength at 1400 °C, which was only 50% of the room-temperature strength. Although the modified ceramic attained a slightly lower flexural strength at room temperature after the replacement of intergranular phase, its strength measured at 1400 °C could attain 90% of room-temperature strength.

Several divergent sympatry mtDNA lineages have been described in redlip mullet Liza haematocheilus, and this high inter-lineage divergence raises questions about the taxonomic status of L. haematocheilus lineages in the north-western Pacific. In this study, the amplified fragment length polymorphism technique was employed to examine genetic structure of L. haematocheilus and estimate the level of independence of the different mtDNA lineages in the north-western Pacific. A total of 186 bands were amplified from 91 individuals among 8 populations by 4 primer combinations and the percentage of polymorphic bands was 91.74%. The Unweighted Pair Group Method with Arithmetic Mean tree based on Nei genetic distance revealed two clusters (North Clade and South Clade). Molecular variance analysis and pairwise FST supported the separation of north and south populations of L. haematocheilus in the north-western Pacific. The incongruence between nuclear groups and mitochondrial lineages suggests the three distinct lineages do not represent cryptic species and the presence of divergent mitochondrial lineages in the same sample is a result of secondary contact after an extended period of isolation. The Pleistocene isolation and biological characteristics of species may be responsible for the genetic differentiation of L. haematocheilus.

We present astrometric results on two millisecond pulsars, PSR B1257+12 and PSR J1022+1001, as carried out through VLBI. For PSR B1257+12, a model-independent distance of 710−38+43 pc and proper motion of (μα = 46.44 ± 0.08 mas/yr, μδ=−84.87 ± 0.32 mas/yr) were obtained from 5 epochs of VLBA and 4 epochs of EVN observations, spanning about 2 years. The two dimensional proper motion of PSR J1022+1001 (μα~−10.13 mas/yr, μδ~16.89 mas/yr) was also estimated, using 3 epochs of EVN observations. Based on our results, the X-ray efficiency of PSR B1257+12 should be in the same range as other millisecond pulsars, and not as low as previously thought.

This paper is concerned with the stability and instability of standing waves for the quasilinear Schrödinger equation of the formwhich has been derived in many models from mathematical physics. We find the exact threshold depending upon the interplay of quasilinear and nonlinear terms that separates stability and instability. More precisely, we prove that for α ∈ and odd p ∈ , when , the standing wave is stable, and when (where for N ≥ 3 and 2 α ċ 2* = +∞ for N = 2), the standing wave is strongly unstable. Our results show that the quasilinear term 2 α(△|φ|2α)|φ|2α−2φ makes the standing waves more stable, which is consistent with the physical phenomena.

Cryopreservation can cause cumulus cell damage around the immature oocytes, which may result in poor subsequent development. To evaluate the effect of the meiosis stage on the cumulus cell cryoinjury and determine the suitable stage for cryopreservation in immature oocytes, mouse oocytes at germinal vesicle (GV) and germinal vesicle breakdown (GVBD) stages were vitrified using open pulled straw (OPS) method. Cumulus cells damage was scored immediately after thawing by double-fluorescent staining. The survival rate of the oocytes was evaluated and the subsequent development of oocytes was assessed through in vitro culture (IVC) and in vitro fertilization (IVF) separately. After vitrification, a higher proportion of cumulus cells of GV oocytes were damaged than those of GVBD and untreated control groups. The survival rate of vitrified GVBD oocytes (94.1%) was significantly higher (p < 0.05) than that of GV oocytes (85.4%). Oocytes vitrified at GVBD stage (55.7%) showed similar cleavage rate compared to those at GV stage (49.2%), but significantly higher (p < 0.05) blastocyst rate (40.9% vs. 27.4%). These results demonstrate that oocytes at GVBD stage remain better cumulus membrane integrity and developmental ability during vitrification than those at GV stage, indicating they are more suitable for immature oocytes cryopreservation in mice.

We prove the existence of multiple bound states of the nonlinear Schrödinger equation −Δu + V(x)u = f(u). Here the linear potential V is continuous and bounded from below, and the nonlinearity f is of asymptotically linear type. We show that, under certain assumptions on the spectrum of the Schrödinger operator −Δ + V and the asymptotic behaviour of f(u)/u, the above equation has at least four non-trivial solutions, two of them sign changing.

We prove the existence of a positive solution for the Schrödinger-type equation on RN,−Δu + V(x)u = f(u) for u ∈ H1(RN), provided thatThe result is obtained in two cases. (a) lim|x|→ ∞V(x) = V (∞) ∈ (0,∞), f is subcritical and supt>0 2F(t)t−2 < V (∞). (b) There exist V > 0 and R* > 0 such that f(t)t−1 < V ∞ ≤ V (x) for all t > 0 and |x| ≥ R*.

Three-dimensional temperature (T)–pressure (P)–composition (X) phase diagrams of binary carbon-hydrogen (C–H) and carbon-oxygen (C–O) systems for activated low pressure diamond growth have been calculated. Based on an approximation of linear combination between C–H and C–O systems, a projective ternary carbonhydrogen-oxygen (C–H–O) phase diagram has also been obtained. There is always a diamond growth region in each of these phase diagrams. Once a supply of external activating energy stops, the diamond growth region will not exist. Nearly all of the reliable experimental data reported in the literature drop into the possible diamond growth region of the calculated projective ternary C–H–O phase diagram under the conditions of 0.01–100 kPa and above 700 K.

We establish the existence of positive solutions with two peaks being located on the boundary of the domain for the problem −Δu + λu = up in antipodal invariant domains including ball domains with Neumann boundary conditions. Here p is the critical Sobolev exponent (N + 2)/(N − 2). The shape of the solutions and the location of the peaks are also studied.