Unconditionally Superclose Analysis of a New Mixed Finite Element Method for Nonlinear Parabolic Equation

This paper develops a framework to deal with the unconditional superclose analysis of nonlinear parabolic equation. Taking the finite element pair $Q_{11}/Q_{01} × Q_{10}$ as an example, a new mixed finite element method (FEM) is established and the $τ$ -independent superclose results of the original variable $u$ in $H^1$-norm and the flux variable $\mathop{q} \limits ^{\rightarrow}= −a(u)∇u$ in $L^2$-norm are deduced ($τ$ is the temporal partition parameter). A key to our analysis is an error splitting technique, with which the time-discrete and the spatial-discrete systems are constructed, respectively. For the first system, the boundedness of the temporal errors is obtained. For the second system, the spatial superclose results are presented unconditionally, while the previous literature always only obtain the convergent estimates or require certain time step conditions. Finally, some numerical results are provided to confirm the theoretical analysis, and show the efficiency of the proposed method.     

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.     

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.     

Stevia rebaudiana targeting α-amylase: An in-vitro and in-silico mechanistic study

Diabetes mellitus (DM) is the fastest growing metabolic disorder in the world. Recently, more attention is paid to the study of natural products due to side effects of synthetic drugs. Stevia rebaudiana (Bertoni) is considered an encouraging starting point for the antidiabetic lead development. In the present study, the in vitro α-amylase inhibitory activity of the extracts of S. rebaudiana is investigated. In order to understand the molecular mechanism and future pharmacophore development, in silico study of secondary metabolites isolated from S. rebaudiana was carried out. Results indicated that water extract shows highest α-amylase inhibitory activity as compared to other extracts. Moreover, compound 20 (rebaudioside A) which has been previously reported and isolated from water extract showed the impressive binding profile with α-amylase. Therefore, our study suggests that S. rebaudiana could be used in the development of therapeutic drugs for the treatment of diabetes.     

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.     

QbD approached comparison of reaction mechanism in microwave synthesized gold nanoparticles and their superior catalytic role against hazardous nirto‐dye

Microwave irradiation (MI) process characteristically enables extremely rapid “in‐core” heating of dipoles and ions, in comparison to conventional thermal (conductance) process of heat transfer. During the process of nanoparticles synthesis, MI both modulates functionality behaviors as well as dynamic of reaction in favorable direction. So, MI providing a facile, favorable and alternative approach during nanoparticles synthesis nanoparticles with enhanced catalytic performances. Although, conventionally used reducing and capping reagents of synthetic origin, are usually environmentally hazardous and toxic for living organism. But, in absence of suitable capping agent; stability, shelf life and catalytic activity of metallic nanoparticles adversely affected. However, polymeric templates which emerged as suitable choice of agent for both reducing and capping purposes; bearing additional advantages in terms of catalyst free one step green synthesis process with high degree of biosafety and efficiency. Another aspect of current works was to understand role of process variables in growth mechanism and catalytic performances of microwave processed metallic nanoparticles, as well as comparison of these parameters with conventional heating method. However, due to poor prediction ability with previously published architect OFAT (One factor at a time) design with these nanoparticles as well as random selection of process variables with their different levels, such comparison couldn't be possible. Hence, using gum Ghatti (Anogeissus latifolia) as a model bio‐template and under simulated reaction conditions; architect of QbD design systems were integrated in microwave processed nanoparticles to establish mechanistic role these variables. Furthermore, in comparison to conventional heating; we reported well validated mathematical modeling of process variables on characteristic of nanoparticles as well as synthesized gold nanoparticles of desired and identical dimensions, in both thermal and microwave‐based processes. Interestingly, despite of identical dimension, MI processed gold nanoparticles bearing higher efficiency (kinetic rate) against remediation of hazardous nitro dye (4‐nitrophenol), into safer amino (4‐aminophenol) analogues.