Existence of strong minimizers for the Griffith static fracture model in dimension two

We consider the Griffith fracture model in two spatial dimensions, and prove existence of strong minimizers, with closed jump set and continuously differentiable deformation fields. One key ingredient, which is the object of the present paper, is a generalization to the vectorial situation of the decay estimate by De Giorgi, Carriero, and Leaci. This is based on replacing the coarea formula by a method to approximate $SB{D}^p$ functions with small jump set by Sobolev functions, and is restricted to two dimensions. The other two ingredients will appear in companion papers and consist respectively in regularity results for vectorial elliptic problems of the elasticity type and in a method to approximate in energy $GSB{D}^p$ functions by $SB{V}^p$ ones.     

NUMERICAL SIMULATION OF FIBROBLAST DUROTAXIS MIGRATION INDUCED BY STIFFNESS GRADIENT OF SUBSTRATE1)

建立了一种细胞趋硬性迁移的理论模型和有限元分析框架,为连续变刚度人工基质的试验设计提供理论依据。考虑了细胞体的黏弹性属性,以及细胞与基质间的配受体动态反应过程,并以配受体合成时间为时间步长,将细胞运动方程化为静力学形式进行求解。对有限元过程提出一种动约束,便于消除其结构矩阵的奇异性。结果表明,模型能够模拟黏着斑内部力的快速波动现象,细胞的运动速度与观测数据一致,可有效模拟20,h以上的长时程问题。     

Polymer nanoparticles with a sensitive CO2‐responsive hydrophilic/hydrophobic surface

Poly(methyl methacrylate) (PMMA) nanoparticles with a sensitive CO₂‐responsive hydrophilic/hydrophobic surface that confers controlled dispersion and aggregation in water were prepared by emulsion polymerization at 50 °C under CO₂ bubbling using amphiphilic diblock copolymers of 2‐dimethylaminoethyl methacrylate (DMAEMA) and N‐isopropyl acrylamide (NIPAAm) as an emulsifier. The amphiphilicity of the hydrophobic–hydrophilic diblock copolymer at 50 °C was triggered by CO₂ bubbling in water and enabled the copolymer to serve as an emulsifier. The resulting PMMA nanoparticles were spherical, approximately 100 nm in diameter and exhibited sensitive CO₂/N₂‐responsive dispersion/aggregation in water. Using copolymers with a longer PNIPAAm block length as an emulsifier resulted in smaller particles. A higher concentration of copolymer emulsifier led to particles with a stickier surface. Given its simple preparation and reversible CO₂‐triggered amphiphilic behavior, this newly developed block copolymer emulsifier offers a highly efficient route toward the fabrication of sensitive CO₂‐stimuli responsive polymeric nanoparticle dispersions. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019, 57, 2149–2156     

Thermal decomposition of model compound of algal biomass

This contribution investigates thermal decomposition of leucine, as a representative model compound for amino acids in algal biomass. We map out potential energy surface for a wide array of unimolecular and self-condensation reactions operating in the decomposition of leucine. Decarboxylation and dehydration of leucine ensues by eliminating CO₂ and –OH, respectively, from the –COOH group attached to the α-carbon. The molecular channel for deamination involves cleavage of NH₂ from α-carbon of leucine. The activation energies for direct elimination of CO₂, NH₃, and H₂O from a leucine molecule lie within 20.7 kJ/mol of each other. Activation energies for these decomposition pathways reside below the bond dissociation enthalpy of H–C(α) of 323.1 kJ/mol. The decarboxylation, deamination, and dehydration pathways, via radical-prompted pathways, systematically require lower energy barriers, in reference to closed-shell reaction corridors. Detailed computations at the CBS-QB3 level provide the Arrhenius rate parameters for the unimolecular and bimolecular reactions, and standard enthalpies of formation, standard entropies, and heat capacities for all the products and intermediates. A kinetic analysis of gas-phase reactions, within the context of a plug-flow reactor model, accounts qualitatively for the formation of major products observed experimentally in the thermal degradation of the condensed-phase leucine. Among notable N-containing species, the model predicts the prevailing of NH₃ over HCN and HNCO, in addition to corresponding appreciable concentrations of amines, imines, and nitriles. Our detailed kinetic investigation illustrates a negligible contribution of the self-condensation reactions of leucine in the gas phase.     

Nonintrusive data-based learning of a switched control heating system using POD,DMD and ANN

The aim of this work is to derive an accurate model of two-dimensional switched control heating system from data generated by a Finite Element solver. The nonintrusive approach should be able to capture both temperature fields, dynamics and the underlying switching control rule. To achieve this goal, the algorithm proposed in this paper will make use of three main ingredients: proper orthogonal decomposition (POD), dynamic mode decomposition (DMD) and artificial neural networks (ANN). Some numerical results will be presented and compared to the high-fidelity numerical solutions to demonstrate the capability of the method to reproduce the dynamics.     

Global strong solution of 3D tropical climate model with damping

We establish the global well-posedness of a strong solution to the 3D tropical climate model with damping. We prove that there exists the global and unique solution for α, β, γ satisfying one of the following three conditions: (1) \alpha ,\beta \ge \mathrm{4}; (2) ; (3) .     

单重工作休假M/M/c排队驱动的流体模型分析

该文在M/M/c排队驱动系统中加入工作休假策略,研究了单重工作休假多服务台排队驱动的流体模型.利用拟生灭过程和矩阵几何解法得到驱动系统稳态队长分布.构建净输入率结构,导出流体模型的稳态联合分布函数满足的的矩阵微分方程组,进而利用Laplace-Stieltjes变换(LST)方法得到稳态下缓冲器库存量的空库概率及均值表达式.最后,给出模型在多信道无线Mesh网下的应用,通过数值例子展示参数变化对系统性能指标的影响.