Mean field limits for nonlinear spatially extended Hawkes processes with exponential memory kernels

We consider spatially extended systems of interacting nonlinear Hawkes processes modeling large systems of neurons placed in ${\mathbb{R}}^d$ and study the associated mean field limits. As the total number of neurons tends to infinity, we prove that the evolution of a typical neuron, attached to a given spatial position, can be described by a nonlinear limit differential equation driven by a Poisson random measure. The limit process is described by a neural field equation. As a consequence, we provide a rigorous derivation of the neural field equation based on a thorough mean field analysis.     

Semi-concurrent vector fields in Finsler geometry

In the present paper, we give an answer to a question which is closely related to doubly warped product of Finsler metrics: ‘‘For each n, is there an n-dimensional Finsler manifold $(M,F)$, admitting a non-constant smooth function f on M such that $\frac{\partial f}{\partial x^i}\frac{\partial g^{ij}}{\partial y^k}=0$?”. We relate the preceding mentioned condition to different concepts appeared and studied in Finsler geometry. We introduce and investigate the notion of a semi concurrent vector field on a Finsler manifold. We show that some special Finsler manifolds admitting such vector fields turn out to be Riemannian. We prove that Tachibana's characterization of Finsler manifolds admitting a concurrent vector field leads to Riemannian metrics. Various examples for conic Finsler spaces that admit semi-concurrent vector field are presented.     

Inhibition effect of butan-1-ol on the corrosion behavior of austenitic stainless steel (Type 304) in dilute sulfuric acid

The electrochemical behavior of austenitic stainless steel (Type 304) in 3 M sulfuric acid with 3.5% recrystallized sodium chloride at specific concentrations of butan-1-ol was investigated with the aid of potentiodynamic polarization, open circuit measurement and weight loss technique. Butan-1-ol effectively inhibited the steel corrosion with a maximum inhibition efficiency of 78.7% from weight-loss analysis and 80.9% from potentiodynamic polarization test at highest concentration studied. Adsorption of the compound obeyed the Freundlich isotherm. Thermodynamic calculations reveal physiochemical interactions and spontaneous adsorption mechanism. Surface characterizations showed the absence of corrosion products and topographic modifications of the steel. Statistical analysis depicts the overwhelming influence and statistical significance of inhibitor concentration on the inhibition performance.     

Synthesis and Structures of Arene Ruthenium (II)–NHC Complexes: Efficient Catalytic α‐alkylation of ketones via Hydrogen Auto Transfer Reaction

A panel of six new arene Ru (II)‐NHC complexes 2a‐f , (NHC = 1,3‐diethyl‐(5,6‐dimethyl)benzimidazolin‐2‐ylidene 1a , 1,3‐dicyclohexylmethyl‐(5,6‐dimethyl)benzimidazolin‐2‐ylidene 1b and 1,3‐dibenzyl‐(5,6‐dimethyl)benzimidazolin‐2‐ylidene 1c ) were synthesized from the transmetallation reaction of Ag‐NHC with [(η⁶‐arene)RuCl₂]₂ and characterized. The ruthenium (II)‐NHC complexes 2a‐f were developed as effective catalysts for α‐alkylation of ketones and synthesis of bioactive quinoline using primary/amino alcohols as coupling partners respectively. The reactions were performed with 0.5 mol% catalyst load in 8 h under aerobic condition and the maximum yield was up to 96%. Besides, the different alkyl wingtips on NHC and arene moieties were studied to differentiate the catalytic robustness of the complexes in the transformations.     

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。     

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.