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In this paper, we derive the weak form for clamped plates composed of incompressible neo-Hookean material from the uniformly valid asymptotic plate theory. By using the finite-element software COMSOL, we study the numerical solutions of the weak form. We show the accuracy and the efficiency of the weak form by comparing the numerical results for the two-dimensional weak form and a three-dimensional model. As a basis for comparison we choose numerical values of the displacement, the second Piola–Kirchhoff stress, and the Green–Lagrange strain at the bottom. The numerical simulations are performed for three different cases of thickness–span ratios, including (1) very thin plate, (2) thin plate, and (3) moderately thick plate. The results show that the uniformly valid plate theory is a reliable and implementable plate theory for even moderately thick plates with large deformations.

This study was designed to identify the pathogen causing soft rot of Pinellia ternata in Qianjiang of Hubei province and screen out the effective bactericides, so as to provide a theoretical basis for the control of soft rot of P. ternata. In this study, the pathogen was identified based on molecular biology and physiological biochemistry, followed by the detection of pathogenicity and pathogenicity spectrum via plant tissue inoculation in vitro and the indoor toxicity determination using the inhibition zone method to screen out bactericide with good antibacterial effects. The control effect of the bactericide against P. ternata soft rot was verified by the leave and tuber inoculation in vitro. The phylogenetic tree was constructed based on the 16 S rDNA, dnaX gene, and recA gene sequences, respectively, and the result showed that the pathogen belonged to the same branch as the type strain Dickeya fangzhongdai JS5. The physiological and biochemical tests showed that the pathogen was identical to D. fangzhongdai, which proved that the pathogen was D. fangzhongdai. The pathogenicity test indicated that the pathogen could obviously infect leaves at 24 h and tubers in 3 d. As revealed by the indoor toxicity test, 0.3% tetramycin, 5% allicin, and 80% ethylicin had good antibacterial activities, with EC_(50) values all less than 50 mg·L~(-1). Tests in tissues in vitro showed that 5% allicin exhibited the best control effect, followed by 0.3% tetramycin and 10% zhongshengmycin oligosaccharide, and their preventive effects were better than curative effects. Therefore, 5% allicin can be used as the preferred agent for the control of P. ternata soft rot, and 0.3% tetramycin and 10% zhongshengmycin oligosaccharide as the alternatives. This study has provided a certain theoretical basis for the control of P. ternata soft rot.

Corydalis saxicola Bunting (CSB), whose common name in Chinese is Yanhuanglian, is a herb in the family Papaveraceae. When applied in traditional Chinese medicine, it is used to treat various diseases including hepatitis, abdominal pain, and bleeding haemorrhoids. In addition, Corydalis saxicola Bunting injection (CSBI) is widely used against acute and chronic hepatitis. This review aims to provide up-to-date information on the botanical distribution, description, traditional uses, phytochemistry, pharmacology, and clinical applications of CSB. A comprehensive review was implemented on studies about CSB from several scientific databases, such as SciFinder, Elsevier, Springer, ACS Publications, Baidu Scholar, CNKI, and Wanfang Data. Phytochemical studies showed that 81 chemical constituents have been isolated and identified from CSB, most of which are alkaloids. This situation indicates that these alkaloids would be the main bioactive substances and that they have antitumour, liver protective, antiviral, and antibacterial pharmacological activities. CSBI can not only treat hepatitis and liver cancer but can also be used in combination with other drugs. However, the relationships between the traditional uses and modern pharmacological actions, the action mechanisms, quality standards, and the material basis need to be implemented in the future. Moreover, the pharmacokinetics of CSBI in vivo and the toxicology should be further investigated.

A uniformly-valid plate theory, independent of the magnitudes of applied loads, is derived based on the two-dimensional plate theory obtained from series expansions about the bottom surface of a plate. For five different magnitudes of surface loads, it is shown by using asymptotic expansions that this unified plate theory recovers five well-known plate models in the literature to leading-order. This demonstrates its uniform validity. More generally, it provides a uniformly-valid plate model provided that two asymptotic conditions are satisfied, which can be checked as a posteriori. The weak formulation of the uniformly-valid plate equations is furnished, which can be used for finite element implementation.

Soil microorganisms are one of the important biological indictors of soil quality and can reflct the comprehensive ecological environment characteristics of the soil. The research of soil microbial diversity is the key to know the ecological functions and balance with soil. In this paper, high-throughput sequencing on PCR-amplified 16 S rRNA gene V3-V4 fragments was used to determine the bacterial diversity in rhizosphere soil of A. macrocephala under the treatment with BZJN1 or streptoprofen. The results showed that there were no significant differences of the bacteria in A. macrocephala rhizosphere soil of the streptoprofen treatment group and the biocontrol BZJN1 treatment group. All the soil bacteria was classified into 25 categories,67 classes, 108 orders, 167 families and 271 generas, except some unidentified bacteria. Proteobacteria(30.7%-34.8%) was the dominant phylum, of which Alphaproteobacteria(16.8%-18.5%) was the dominant subgroup. Compared with the control group, the relative abundance of multiple phylums bacteria in the rhizosphere soil of A. macrocephala was significantly changed in the streptoprofen treatment group and the biocontrol BZJN1 treatment group. In addition, RDA analysis showed that there was connection with different environmental factors and microbial communities. The abundance of the three genera in the rhizosphere soil of A. macrocephala was significantly positively correlated with Invertase, Urease and AP. PICRUSt function prediction results showed that BZNJ1 could enhance some bacterial functions and promote the plant growth. Biocontrol is a new type of green and safety control pest method. BZNJ1 significantly enhances some bacterial functions on the basis of effectively preventing root rot of A. macrocephala and promoting plant growth, and has no significant effect on the soil bacterial community structure. All the results can provide theoretical support for popularization of BZNJ1.

In this paper, a consistent finite-strain plate theory for growth-induced large deformations is developed. The three-dimensional (3D) governing system of the plate model is formulated through the variational approach, which is composed of the mechanical equilibrium equation and the constraint equation of incompressibility. Then, series expansions of the unknown functions in terms of the thickness variable are adopted. By using the 3D equilibrium equations and the surface boundary conditions, recursion relations for the expansion coefficients are successfully established. As a result, a 2D vector plate equation with three unknowns is obtained and the associated edge boundary conditions are proposed. It can be verified that the plate equation ensures the required asymptotic order for all the terms in the variations of the total energy functional. The weak formulation of the plate equation has also been derived for future numerical calculations. As applications of the plate theory, two examples regarding the growth-induced deformations and instabilities in thin hyperelastic plates are studied. Some analytical results are obtained in these examples, which can be used to describe the large deformations and reveal the bifurcation properties of the thin plates. Furthermore, the results obtained from the current plate theory are compared with those obtained from the classical Foppl-von Karman plate theory, from which the efficiencies and advantages of the current plate theory can be demonstrated.

Three novel lignans (1, 5 and 6) and two novel quinic acids (16 and 17) along with 15 known phenylpropanoids were obtained from the ethanol extract of Zanthoxylum nitidum var. tomentosum (Rutaceae). Their structures were confirmed by comprehensive spectroscopic data (NMR and HRESIMS), and the absolute configurations of all novel compounds were elucidated based on electronic circular dichroism (ECD) spectroscopic data. The production of nitric oxide (NO) in BV-2 microglial cells induced through lipopolysaccharide (LPS) was used to evaluate in vitro anti-neuroinflammatory activity of compounds 1–20. Compound 2, 3, 7 and 16 showed excellent inhibition of LPS-induced NO production. The structure-activity relationships of the isolates were investigated. In addition, the mechanism of action of 2 was elucidated by RT-PCR and Western blotting analysis, which indicated that it reduced neuroinflammatory mainly through NLRP3/caspase1 signaling pathways in LPS-induced BV2 microglial cells.

In this paper, we study the buckling and post-buckling of a compressible hyperelastic slab under both axial compressive force and distributed force on two lateral surfaces. The combined series-asymptotic expansions method is used to obtain the simplified model equations. We further assume that the lateral load is uniformly distributed and is a constant. We discuss three cases: (I) axial compression dominant, (II) lateral compression dominant and (III) uniform compression. In case (I), the lateral stress is given as a constant and no buckling bifurcation will occur when the axial stress is not imposed. In this case, the lateral stress may be compressive or tensile stress. In case (II), the axial compressive stress is given as a constant and no buckling bifurcation will occur when the lateral compressive stress is not imposed. In case (III), the slab is uniformly compressed at two lateral boundaries and two ends of the slab. For all three cases, with sliding-sliding end conditions at two ends, we obtain the approximate expressions of the critical stress values and mode numbers from linear bifurcation analysis and obtain the approximate analytical post-buckling solutions by using the method of multiple scales. We find both supercritical and subcritical bifurcations may occur depending on the material constants, slenderness ratio of the slab and bifurcation modes. The analytical post-buckling solutions are compared with the numerical solutions of the model equations and good agreements are found.

Inflammation is a very common and important basic pathological process. There is still a great need for the isolation of effective anti-inflammatory agents from plants. In this paper, five new isobutylamides, zanthoxylumamides E-I (1-5), and four known isobutylamides (6-9) were isolated from Zanthoxylum nitidum var. tomentosum (Rutaceae). Chiral resolution of seven racemic isobutylamides (1-4 and 6-8) was successfully performed, and the absolute configurations of two stereoisomers of 1-4 were validated by ECD and NMR. The obtained isobutylamides were evaluated in vitro anti-inflammatory activity with the lipopolysaccharide (LPS)-stimulated production of nitric oxide (NO) in murine macrophage RAW264.7 cells. Compound 8 exhibited significant inhibition of LPS-induced NO production. The underlying molecular mechanisms of the anti-inflammatory activity of 8 revealed that it suppressed the NO production through the modulation of myeloid differentiation factor 88 (MyD88) and interferon regulatory factor 3 (IRF3) signaling pathways.

In order to examine the effects of nanoscale zero-valent iron (nZVI) on the performance of denitrifying granular sludge (DGS) in a continuous flow model, the variations of nitrogen removal efficiency in the reactor, sludge morphology, and denitrifying characteristics at different influent nZVI concentrations were investigated in an upflow sludge bed (USB). The results showed that nZVI concentrations lower than 5 mg·L

This paper studies the axisymmetric deformations of a nonlinearly hyperelastic tube subjected to axial compression. We aim at investigating the critical buckling stresses and modes, deriving the analytical solutions for the post-bifurcation deformations and studying the imperfection sensitivity. For a general isotropic hyperelastic tube, a coupled series-asymptotic method is utilized to derive two simplified model equations with specified constraints on the tube geometry. Then, we specialize to the Blatz–Ko material. With greased end conditions, through linear bifurcation analysis, we obtain the critical stress values and the corresponding mode numbers. The analytical solutions for the post-bifurcation states are constructed by the multiple scales method. By examining the solution behavior in the post-bifurcation regime, it is found that a thick tube could be considerably softer than a thin one. The singularities theory is used to consider the imperfection sensitivity, which reveals the mechanism is the existence of two modes corresponding to the same critical stress. Numerical solutions are also obtained which confirm the validity of the analytical solutions.

In this paper, we study the equilibrium states of a compressible hyperelastic layer under compression after the primary and secondary bifurcations. Starting from the two-dimensional field equations for a compressible hyperelastic material, we use a methodology of coupled series-asymptotic expansions developed earlier to derive two coupled non-linear ordinary differential equations (ODEs) as the model equations. The critical buckling stresses are determined by a linear bifurcation analysis, which are in agreement with the results in the literature. The method of multiple scales is used to solve the model equations to obtain the second-order asymptotic solutions after the primary bifurcations. An analytical formula for the post-buckling amplitudes is derived. Two kinds of numerical solutions are also obtained, the numerical solutions of the model equations by a difference method and those of the two-dimensional field equations by the finite elements method. Comparisons among the analytical solutions, numerical solutions and solutions obtained by the Lyapunov–Schmidt–Koiter (LSK) method in the literature are made and good agreements for the displacements are found. It is also found that at some places the axial strain is tensile, although the layer is under compression. To consider the secondary bifurcation, we superimpose a small deformation on the state after the primary bifurcation. With the analytical solution of the primary bifurcation, we manage to reduce the problem of the secondary bifurcation to one of the first bifurcations governed by a second order variable-coefficient ODE. And, our analysis identifies an explicit function and from the existence/non-existence of its zero one can immediately judge whether a secondary bifurcation can take place or not. The zero corresponds to a turning point of the governing ODE, which leads to non-trivial solutions. Further, by the WKB method the equation (in a very simple form) for determining the critical stress for the secondary bifurcation is derived. We further use AUTO to compute the secondary bifurcation point numerically, which confirms the validity of our analytical results. The numerical solution in the secondary bifurcation branch is also computed by AUTO. It is found that the secondary bifurcation induces a “wave number doubling” phenomenon and also the shape of the layer has a convexity change along the axial direction.

To explore the potential stressing effect of nanoscale zero-valent iron (nZVI) on denitrifying granular sludge (DGS), the evolution of DGS denitrifying performance under different C/N ratios was investigated in this study, by carrying out batch tests of eight successive periods with the nZVI shock-loading. The results showed that the specific denitrification rate of µ value decreased when the nZVI dosage was higher than 5 mg · L⁻¹. Meanwhile, a positive correlation between the inhibition ratio (IR) of µ value and substrate C/N ratios or nZVI dosage was observed. When the nZVI dosage reached 100 mg · L⁻¹, both extracellular protein and polysaccharides concentrations decreased obviously. It would be beneficial to promote the recovery of DGS denitrifying activity and reduce the COD demanding to remove unit mass of nitrate, by increasing external carbon source with C/N ratios of higher than 4. On the basis of Freundlich and Langmuir adsorption isotherms, when higher C/N ratio was provided, stronger bioadsorption of nZVI would be achieved. During the recovery period, a significant improvement of DCS denitrifying performance under the high C/N ratio was expected, due to the continuous washout of total iron in sludge phase (Qe), while the µ value would reach or approach the one of the control group when Qe was lower than 0.4 mg · g⁻¹.

In this paper, we study the buckling of an incompressible hyperelastic rectangular layer due to compression with sliding end conditions. The combined series-asymptotic expansions method is used to derive two-coupled nonlinear ordinary differential equations (ODEs) governing the leading order of the axial strain W and shear strain G. Linear analysis yields the critical stress values of buckling. For the nonlinearly coupled system, by introducing a small parameter, the approximate analytical solutions for post-buckling deformations are obtained by using the method of multiple scales. The amplitude of buckling is expressed explicitly by the aspect ratio, the incremental dimensionless engineering stress and the mode of buckling. To the authors' best knowledge, it is the first time that such an analytical formula is obtained within the framework of two-dimensional field equations for nonlinearly elastic materials (including both geometric and material nonlinearity). Numerical computations of the coupled system are also carried out. Good agreements between the numerical and analytical solutions are found when the amplitudes of buckling are moderate. Finally, some energy analysis regarding material failure is made.

The problem of uniaxial compression of an incompressible 2D thin rectangle is studied in this paper. We consider the case where the two ends of the rectangle are welded to two rigid bodies. The focus is on the bifurcation analysis and post-buckling solutions. The combined series-asymptotic expansion method is used to derive two coupled non-linear ordinary differential equations (ODEs), which govern the leading-order axial strain and shear strain. Through an analysis on the linearized equations, an algebraic equation for determining the critical stress values of buckling is obtained. For the non-linear coupled ODEs, the numerical solutions of the non-trivial solutions are obtained by providing proper initial guesses. Energy analysis shows that for the first mode of buckling material failure may first happen at the middle point of the bottom surface.

In the two experiments by Beatty and his coauthors on the compressions of elastic rectangles/bars, it was found that there is a transition region of the aspect ratio which separates buckling from b...

In this paper, we study the corner-like formation in a slender nonlinearly elastic cylinder due to compression. Mathematically, this is a very challenging problem: one needs to study the bifurcation of the nonlinear field equations (complicated nonlinear partial differential equations) and show that there is a bifurcation leading to a solution with a corner-like profile. We also aim to obtain the asymptotic expression for this post-bifurcation solution. As far as we know, there is no available analytical method to obtain the post-bifurcation solution of nonlinear partial differential equation(s). Here we use a novel approach to tackle the present problem. Through a method of coupled series–asymptotic expansions, we manage to derive the normal form equation of the original nonlinear field equations, which can be written as a singular ordinary differential equation (ODE) system (the vector field has a singularity at one point). With welding end conditions, the problem is reduced to study the boundary-value problem of a singular ODE system. It seems that such a boundary-value problem of a singular ODE system was not formulated or studied before in the context of the present problem. With the help of phase planes, we manage to solve such a boundary-value problem. It turns out that there is a vertical singular line in phase planes, which causes the bifurcation to a corner-like solution. The expression for this post-bifurcation solution is also obtained. From the analytical results obtained, we reveal that the coupling effect of the material nonlinearity and geometrical size is the physical mechanism that causes the formation of a corner-like profile.

In this paper, we study a three-dimensional axisymmetric boundary-value problem of a slender cylinder composed of a nonlinearly elastic material subjected to an axial force. Starting from the field equations, after a transformation and proper scalings, we identify a small variable and two small parameters, which characterize the present problem. Then, by an approach involving compound series-asymptotic expansions, a nonlinear ODE is derived, which governs the axial strain (the first-term in the series expansion). By imposing the zero radial displacement conditions at two ends, we manage to get the analytical solution of the axial strain, from which all other physical quantities can be deduced and thus the three-dimensional displacement field can be determined. Graphical results are presented, which show that there are two boundary layers near the two ends while the middle part is in a state of almost uniform extension. The asymptotic structure of the analytical solution is derived, which offers clear explanations to the structure of the deformed configuration and shows that the thickness of both boundary layers is of the order of the radius. We also point out the relevance of the present results to the St. Venant’s problem. In particular, we obtain the explicit uniformly-valid exponentially small error term, when the obtained deformed configuration is compared to the configuration of a uniform extension.

In this Note, we study the corner instabilities in a slender cylinder constituted by a nonlinearly elastic material. Starting from the three-dimensional nonlinear field equations, we derive, through a novel method, a singular dynamical system as the normal form equation. It is shown that this system can capture the corner instabilities. We are also able to obtain analytical expressions of the solutions. The mechanism that causes corner formations is also found. To cite this article: H.-H. Dai, F.-F. Wang, C. R. Acad. Sci. Paris, Ser. I 345 (2007).

Two anaerobic baffled reactors (ABR) were compared for anaerobic ammonium oxidation (ANAMMOX) enrichment using synthetic wastewater with different inoculated sludge, the mixed anaerobic flocculent sludge/granular sludge (R1) and anaerobic activated sludge (R2). The research showed the ANAMMOX activity occurred in both reactors allowing continuous removal of ammonium and nitrite, in which the ammonia and nitrite nitrogen loading was about 54.5-68.0 g (m3 x d)(-1), when maintaining the temperature at 30-35 degrees C, pH at 7.5 +/- 0.5 and HRT at 26 h. However, the ANAMMOX reaction was successfully started after 120 d and 125 d, respectively. The removal rules of the two reactors were basically similar, and the enrichment processes occurred in both reactors could be divided into 4 phases, which were sluggish phase, expressive phase, enhanced phase and steady phase. In the steady phase, the average removal rates of NH4+ -N, NO2- -N were higher than 90%, and the average removal load achieved 57.3-67.9 g x (m3 x d)(-1). Moreover, the ammonium removal load in R1 was slightly higher than that in R2. Additionally, more than 90% of nitrogen was dramatically removed in the first compartment of ABR. Meanwhile, the color of sludge gradually changed from brown, litter bed brown to black along with the flow direction, which was similar to the removal rule of nitrogen. In a word, the results showed the different inoculated sludge did not cause obvious differences in the starting rule and the removal characteristics of ANAMMOX reactor.

In this paper, by constructing N-fold Darboux transformations, we obtain new solutions of the generalized coupled modified Korteweg-de Vries (GC-mKdV) equation, the mKdV equation and the coupled integrable dispersionless equation. Particularly, we get single and two-kink solutions, single and two-hyperbolic soliton solutions, single and two-parabola soliton solutions, respectively.

From the Levi spectral problem, we obtain the (1+1)-dimensional Burgers' equation and the (2+1)-dimensional modified Kadomtsev–Petviashvili equation. Through the Miura transformation, the modified Kadomtsev–Petviashvili equation is transformed into the Kadomtsev–Petviashvili equation. Then by constructing some new Darboux transformations, we obtain new soliton solutions of Burgers' equation and find solitons fusion. By solving two (1+1)-dimensional soliton equations, new soliton solutions of the modified Kadomtsev–Petviashvili equation are obtained. And then explicit solutions of the Kadomtsev–Petviashvili equation are also obtained through the Miura transformation.