Explore the vast range of titles available.

This paper focuses on the Cauchy problem for a one-dimensional quasilinear hyperbolic–parabolic coupled system with initial data given on a line of parabolicity. The coupled system is derived from the Poiseuille flow of full Ericksen–Leslie model in the theory of nematic liquid crystals, which incorporates the crystal and liquid properties of the materials. The main difficulty comes from the degeneracy of the hyperbolic equation, which makes that the system is not continuously differentiable and then the classical methods for the strictly hyperbolic–parabolic coupled systems are invalid. With a choice of a suitable space for the unknown variable of the parabolic equation, we first solve the degenerate hyperbolic problem in a partial hodograph plane and express the smooth solution in terms of the original variables. Based on the smooth solution of the hyperbolic equation, we then construct an iterative sequence for the unknown variable of the parabolic equation by the fundamental solution of the heat equation. Finally, we verify the uniform convergence of the iterative sequence in the selected function space and establish the local existence and uniqueness of classical solutions to the degenerate coupled problem.

This article focuses on the singularity formation of smooth solutions for a one-dimensional nonlinear degenerate hyperbolic-parabolic coupled system originating from the Poiseuille flow of nematic liquid crystals. Without assuming that the wave speed of the hyperbolic equation is a positive function, we show that its smooth solution will break down in finite time even for an arbitrarily small initial energy. Based on an estimate of the solution for the heat equation, we use the method of characteristics to control the wave speed and its derivative so that the wave speed does not degenerate and its derivative does not change sign in a period of time.

Background The broad-leaved Korean pine mixed forest is an important and typical component of a global temperate forest. Soil microbes are the main driver of biogeochemical cycling in this forest ecosystem and have complex interactions with carbon (C) and nitrogen (N) components in the soil. Results We investigated the vertical soil microbial community structure in a primary Korean pine-broadleaved mixed forest in Changbai Mountain (from 699 to 1177 m) and analyzed the relationship between the microbial community and both C and N components in the soil. The results showed that the total phospholipid fatty acid (PLFA) of soil microbes and Gram-negative bacteria (G-), Gram-positive bacteria (G+), fungi (F), arbuscular mycorrhizal fungi (AMF), and Actinomycetes varied significantly ( p  < 0.05) at different sites (elevations). The ratio of fungal PLFAs to bacterial PLFAs (F/B) was higher at site H1, and H2. The relationship between microbial community composition and geographic distance did not show a distance-decay pattern. The coefficients of variation for bacteria were maximum among different sites (elevations). Total soil organic carbon (TOC), total nitrogen (TN), soil water content (W), and the ratio of breast-height basal area of coniferous trees to that of broad-leaved tree species (RBA) were the main contributors to the variation observed in each subgroup of microbial PLFAs. The structure equation model showed that TOC had a significant direct effect on bacterial biomass and an indirect effect upon bacterial and fungal biomass via soil readily oxidized organic carbon (ROC). No significant relationship was observed between soil N fraction and the biomass of fungi and bacteria. Conclusion The total PLFAs (tPLFA) and PLFAs of soil microbes, including G-, G+, F, AMF, and Actinomycetes, were significantly affected by elevation. Bacteria were more sensitive to changes in elevation than other microbes. Environmental heterogeneity was the main factor affecting the geographical distribution pattern of microbial community structure. TOC, TN, W and RBA were the main driving factors for the change in soil microbial biomass. C fraction was the main factor affecting the biomass of fungi and bacteria and ROC was one of the main sources of the microbial-derived C pool.

This paper focuses on the structure of classical sonic-supersonic solutions near sonic curves for the two-dimensional full Euler equations in gas dynamics. In order to deal with the parabolic degeneracy near the sonic curve, a novel set of dependent and independent variables are introduced to transform the Euler equations into a new system of governing equations which displays a clear regularity-singularity structure. With the help of technical characteristic decompositions, the existence of a local smooth solution for the new system is first established in a weighted metric space by using the iteration method and then expressed in terms of the original physical variables. This is the first construction of a classical sonic-supersonic solution near a sonic curve for the full Euler equations.

This paper is focused on the local well-posedness of initial-boundary value and Cauchy problems to a one-dimensional quasilinear hyperbolic-parabolic coupled system with boundary or far field degenerate initial data. The governing system is derived from the theory of nematic liquid crystals, which couples a hyperbolic equation describing the crystal property and a parabolic equation describing the liquid property of the material. The hyperbolic equation is degenerate at the boundaries or spatial infinity, which results in the classical methods for the strictly hyperbolic-parabolic coupled systems being invalid. We introduce admissible weighted function spaces and apply the parametrix method to construct iteration mappings for these two degenerate problems separately. The local existence and uniqueness of classical solutions of the degenerate initial-boundary value and Cauchy problems are established by the contraction mapping principle in their selected function spaces. Moreover, the solutions have no loss of regularity and their existence times are independent of the spatial variable.

This paper focuses on a degenerate boundary value problem arising from the study of the two-dimensional Riemann problem to the nonlinear wave system. In order to deal with the parabolic degeneracy, we introduce a partial hodograph transformation to transform the nonlinear wave system into a new system, which displays a clear regularity–singularity structure. The local existence of classical solutions for the new system is established in a weighted metric space. Returning the solution to the original variables, we obtain the existence of classical solutions to the degenerate boundary value problem for the nonlinear wave system.

In order to scientifically judge the quality status and management effect of stand, the multi-indicator comprehensive evaluation method of stand quality was studied. Based on the principles of comprehensiveness, scientificity and operability, this research selected nine evaluation contents from two aspects of stand structure and stand vitality, including vertical structure, horizontal structure, age structure, tree species composition, stand density, stand growth, stand regeneration, large-diameter tree and tree health. Firstly, the specific evaluation indicators were given to each content to form the stand quality evaluation system, and then a bran-new stand quality comprehensive evaluation index ( FQ ) was constructed based on the unit circle method. By comparing the stand quality of typical forest types in 27 plots of 7 regions in China, the validity, scientificity and accuracy of the index were demonstrated. The results were as follows: (1) The stand quality of natural mixed forests was significantly better than that of natural pure forests, and the stand quality of artificial mixed forests was generally better than that of artificial pure forests; (2) The stand quality grades of natural mixed forests were all ≥ grade II, among which the stand quality grades of some natural mixed forests were grade I; (3) The stand quality grades of artificial mixed forests mainly were grade III, the stand quality of natural mixed forests was significantly better than that of artificial mixed forests; (4) In pure forests, only part of the natural pure forest stand quality grades were grade III, the quality grades of other pure forests were grade IV, especially the quality grades of artificial pure forests were grade IV. In comparison, the stand quality of artificial pure forests was the worst. The evaluation results obtained by the index constructed in this research were intuitive and reliable, which were in line with the objective reality and universal law of the actual stands. It could be seen that the multi-indicator comprehensive evaluation method of stand quality proposed in this research could scientifically and fairly evaluate the stand quality of different forest types in different regions. At the same time, it also provided an important theoretical basis and analysis tool for the problem diagnosis of stand quality, the accurate improvement of stand quality and the decision-making of forest management.

The Chinese pine (Pinus tabulaeformis Carr.) is an ecologically and economically important evergreen coniferous tree which dominates warm temperate forests throughout northern China. We established two permanent plots within the Chinese pine forest in the Jiulong Mountains, Beijing, China. To understand the structural characteristics and dynamics of these plots, we analyzed the spatial structural characteristics within nearest-neighbor relationships using the bivariate distributions of the stand spatial structural parameters: uniform angle index, W; mingling index, M; dominance index, U; and crowding index, C. Results revealed that most trees in the forest were randomly distributed. The predominant individuals and randomly arranged trees were in very dense areas and surrounded by the same species. In addition, both plots exhibited a uniform size differentiation pattern. The two plots differed mainly in the level of species mixture and dominance. The majority of reference trees in the pure Chinese pine forest (plot 1) exhibited poor species mingling and low dominance, whereas trees in the mixed Chinese pine forest (plot 2) were evenly distributed in each mingling class and most trees were of intermediate dominance. The study results are useful for optimizing forest management activities in the studied stands, promoting tree growth, regeneration and habitat diversity, and improving forest quality at a fine scale.

BackgroundWater shortage can limit plant growth, which can be ameliorated by arbuscular mycorrhizal (AM) symbiosis through physiological and metabolic regulations. Deciphering which physiological and metabolic processes are central for AM-mediated regulations is essential for applications of mycorrhizal biotechnology in dryland agriculture.MethodologyIn this study, the influence of AM symbiosis on growth performance, photosynthesis, and organ accumulation of key C and N metabolites were assessed by growing maize (Mo17, Lancaster Sure Crop) seedlings inoculated with or without AM fungus (Rhizophagus irregularis Schenck & Smith BGC AH01) under different water regimes in greenhouse.ResultsDrought stress reduced shoot growth, while AM symbiosis significantly improved growth performances, with significant changes of photochemical processes and organ concentration of the key metabolites. AM symbiosis increased root levels of the metabolites in ornithine cycle and unsaturation of fatty acids regardless of water conditions. Root putrescine (Put) concentration was higher in AM than non-inoculated (NM) plants under well-watered conditions; the conversion of Put via diamine oxidase to γ-aminobutyric acid (GABA) occurred in roots of AM plants under drought stress. Leaf concentration of Put, the tricarboxylic acids, and soluble sugars significantly increased in AM plants under drought stress, showing higher values compared to that of NM plants. Moreover, photosystem II efficiency and chlorophyll concentration were higher in AM than NM plants regardless of water status.ConclusionFatty acid- and ornithine cycle-related metabolites along with soluble sugars, Put, and GABA were the key metabolites of AM-mediated regulations in response to drought stress.

Negative conspecific density dependence is one of the principal mechanisms affecting plant performance and community spatial patterns. Although many studies identified the prevalence of density dependent effects in various vegetation types by analyzing conspecific spatial dispersal patterns (spatial patterning) of forest trees, interactions between individuals and heterospecific neighboring trees caused by density-dependent effects are often neglected. The effects of negative density dependence lead us to expect that neighbourhood species segregation would increase with increasing tree size and that larger trees would be surrounded by more heterospecific neighbours than would smaller trees. We studied four mapped 1-Ha plots on Changbaishan Mountain in North-eastern China and used marked point pattern analysis to explore whether trees of different sizes exhibited differences in neighbourhood species segregation; we also determined whether larger trees were more likely to have heterospecific neighbours than smaller trees were. Our results show that bigger trees generally have higher species mingling levels. Neighborhood species segregation ranged from lower than expected levels to random or nearly random patterns at small scales as tree size classes increased under heterogeneous Poisson null model tests. This study provides some evidence in support of negative density dependent effects in temperate forests.