Development of a Chitosan/Nickel Phthalocyanine Composite Based Conductometric Micro-sensor for Methanol Detection

Thin-film composite of chitosan/nickel phthalocyanine (NiPc) was electrochemically deposited on the fingers of interdigitated gold electrodes, applying chronoamperometric polymerization technique. The presence of crystallized NiPc in the chitosan was confirmed by EDX and FTIR analysis. Acetone, ethanol, and methanol gas-sensing properties of the films prepared at optimum conditions were studied at atmospheric temperature, through differential measurements at an optimized frequency of 10 kHz, using a lock-in amplifier. The conductometric sensor presents the highest sensitivity of 60.2 μS.cm⁻¹(v/v) for methanol and 700 ppm as the limit of detection. For validation, the methanol content of a commercial rubbing alcohol was determined.     

A nonlinear model for marble sulphation including surface rugosity and mechanical damage

Here we propose and analyze a mathematical model that aims to describe the marble sulphation process occurring in a given material. The model accounts for rugosity as well as for damaging effects. This model is characterized by some technical difficulties that seem hard to overcome from a theoretical viewpoint. Therefore, we introduce some physically reasonable modifications in order to establish the existence of a suitable notion of solution on a given time interval. Numerical simulations are presented and discussed, also in view of further research.     

Evolution of electrical conductivity and semiconductor to metal transition of iron oxides at extreme conditions

Iron oxides are widely found as ores in Earth's crust and are also important constituents of its interiors. Their polymorphism, composition changes, and electronic structures play essential roles in controlling the structure and geodynamic properties of the solid Earth. While all-natural occurring iron oxides are semiconductors or insulators at ambient pressure, they start to metalize under pressure. Here in this work, we review the electronic conductivity and metallization of iron oxides under high-pressure conditions found in Earth's lower mantle. We summarize that the metallization of iron oxides is generally controlled by the pressure-induced bandgap closure near the Fermi level. After metallization, they possess much higher electrical and thermal conductivity, which will facilitate the thermal convection, support a more stable and thicker D^{$\prime\prime$} layer, and formulate Earth's magnetic field, all of which will constrain the large-scale dynamos of the mantle and core.     

Boussinesq方程行波解的存在性

利用平面动力系统方法的分支理论，研究了Boussinesq方程，通过对Boussinesq方程进行行波变换，得到了相应行波系统的首次积分和平衡点，给出了不同参数条件下的相图，证实了Boussinesq方程存在孤立波解和周期波解。     

对称向量拟均衡问题有效解的存在性

利用标量化方法建立对称向量拟均衡问题有效解的存在性定理。作为标量化方法的应用，利用这一方法得到向量变分不等式和拟向量变分不等式有效解的存在性定理。     

Classical solution for a nonlinear hybrid system modeling combustion in a multilayer porous medium

Combustion processes in porous media have been used by the petroleum engineering industry to extract heavy oil from reservoirs. This study focuses on a one-dimensional nonlinear hybrid system consisting of $n$ reaction–diffusion–convection equations coupled with $n$ ordinary differential equations, which models a combustion front moving through a porous medium with $n$ parallel layers. The state variables are the temperature and fuel concentration in each layer. Coupling occurs in both the reaction function and differential operator coefficients. We prove the existence of a classical solution, first locally and then globally over time, to an initial and boundary value problem for the corresponding system. The proof uses a new approach for combustion problems in porous media. The local solution is obtained by defining an operator in a set of Hölder continuous functions and using Schauder’s fixed-point theorem to find a fixed point as the desired solution. Using Zorn’s lemma, we extend the local solution to a global solution, proving that the first-order spatial derivative of the temperature in each layer is a bounded function.