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.     

Photosensitive organic-inorganic hybrid structures based on porous silicon

Abstract

In this study, the photovoltaic organic-inorganic structures were created by deposition of poly(3,4-ethylenedioxythiophene) film doped by poly(styrenesulfonate) and reduced graphene oxide on the porous silicon/silicon substrate. Formation of the hybrid structure was confirmed by means of atomic-force microscopy and Fourier transform infrared spectroscopy. The current-voltage characteristics of the obtained structures were studied. It was found the increase of electrical conductivity and photo-induced signal in organic-inorganic structures. Temporal parameters and spectral characteristics of photoresponse in the 400–1100?nm wavelength range were investigated. The widening of spectral photosensitivity in a short-wavelength range due to light absorption in various layers of the multijunction structure in comparison with single crystal silicon was revealed.     

Porous Molybdenum Carbide Nanostructures Synthesized on Carbon Cloth by CVD for Efficient Hydrogen Production

Molybdenum carbide (Mo₂C) is a promising noble-metal-free electrocatalyst for the hydrogen evolution reaction (HER), due to its structural and electronic merits, such as high conductivity, metallic band states and wide pH applicability. Here, a simple CVD process was developed for synthesis of a Mo₂C on carbon cloth (Mo₂C@CC) electrode with carbon cloth as carbon source and MoO₃ as the Mo precursor. XRD, Raman, XPS and SEM results of Mo₂C@CC with different amounts of MoO₃ and growth temperatures suggested a two-step synthetic mechanism, and porous Mo₂C nanostructures were obtained on carbon cloth with 50 mg MoO₃ at 850 °C (Mo₂C-850(50)). With the merits of unique porous nanostructures, a low overpotential of 72 mV at current density of 10 mA cm⁻² and a small Tafel slope of 52.8 mV dec⁻¹ was achieved for Mo₂C-850(50) in 1.0 m KOH. The dual role of carbon cloth as electrode and carbon source resulted into intimate adhesion of Mo₂C on carbon cloth, offering fast electron transfer at the interface. Cyclic voltammetry measurements for 5000 cycles revealed that Mo₂C@CC had excellent electrochemical stability. This work provides a novel strategy for synthesizing Mo₂C and other efficient carbide electrocatalysts for HER and other applications, such as supercapacitors and lithium-ion batteries.     

Synthesis of Organosilyl-Functionalized Cage-Type Germanoxanes Containing Fluoride Ions

Eight corners of a double-four ring cage-type germanoxane, containing a fluoride ion, were successfully silylated by the combination of chlorosilanes and silazanes. Three different silyl groups, trimethylsilyl, dimethylsilyl, and dimethylvinylsilyl, were attached on the corners of germanoxane cage. The solubility and reactivity of the cage modified with dimethylvinylsilyl groups were significantly increased, allowing for further reaction. Hydrosilylation reaction between dimethylvinylsilylated cage geramanoxanes and dimethylsilylated cage siloxanes afforded porous solids. Functionalization of the corners of germanoxanes with silyl groups should provide valuable building blocks in various functional materials.     

Highly Proton-Conductive Zinc Metal-Organic Framework Based On Nickel(II) Porphyrinylphosphonate

The design of new solid-state proton-conducting materials is a great challenge for chemistry and materials science. Herein, a new anionic porphyrinylphosphonate-based MOF ( IPCE-1Ni ), which involves dimethylammonium (DMA) cations for charge compensation, is reported. As a result of its unique structure, IPCE-1Ni exhibits one of the highest value of the proton conductivity among reported proton-conducting MOF materials based on porphyrins (1.55×10⁻³ S cm⁻¹ at 75 °C and 80 % relative humidity).     

Self-Assembly of C3 Symmetric Rigid Macrolactams into Very Polar and Porous Trigonal Crystals

Cyclohexane and cyclotri-β-alanyl have been used as scaffolds for the design of new C₃-symmetric rings incorporating conjugated alkenes and dienes. All three C₃-symmetric lactams share the same triangular shape and their crystal system is trigonal. They all belong to the R3 space group, R3m, R3 and R3c, for the increasingly large 12-, 18- and 24-membered rigid rings, respectively. All lactams stack on top of each other, through H-bonds and van der Waals noncovalent interactions, leading to endless supramolecular cylinders and tubes. The largest member of the family leads to tubes, the central pores of which is wide enough to let water in. A common feature of all the lactams is their very large dipole, of around 9 D, according to DFT calculations. Surprisingly, all the resulting cylinders and tubes pack side by side in the crystals, with all the dipoles pointing to the same direction. As a result, all three crystals are anisotropic and appear to be the first members of a new kind of highly polar crystals.     

Seeded Polymerization of an Amide-Functionalized Diketopyrrolopyrrole Dye in Aqueous Media

The self-assembly of an amide-functionalized dithienyldiketopyrrolopyrrole (DPP) dye in aqueous media was achieved through seed-initiated supramolecular polymerization. Temperature- and time-dependent studies showed that the spontaneous polymerization of the DPP derivative was temporally delayed upon cooling the monomer solution in a methanol/water mixture. Theoretical calculations revealed that an amide-functionalized DPP derivative adopts an energetically favorable folded conformation in the presence of water molecules due to hydration. This conformational change is most likely responsible for the trapping of monomers in the initial stage of the cooperative supramolecular polymerization in aqueous media. However, the monomeric species can selectively interact with externally added fragmented aggregates as seeds through concerted π-stacking and hydrogen-bonding interactions. Consequently, the time course of the supramolecular polymerization and the morphology of the aggregated state can be controlled, and one-dimensional fibers that exhibit a J-aggregate-like bathochromically shifted absorption band can be obtained.     

Resonances in bounded media: Nonlinear and boundary effects

We study the response of nonlinear wave systems in bounded domains at or near resonance. There are typically two qualitatively distinct types of response which may be observed relating to whether or not higher harmonics are themselves resonant. We introduce a variety of nonlinear model problems at or near resonance and study the subsequent response. We explain how the features of this problem such as the form of nonlinearity, boundary conditions, and the nature of spectrum play a fundamental role in the qualitative nature of the response. Numerical simulations are carried out to provide further explanation and comparison with analytic approximations. The results of this study provide a better understanding of the impact and interplay between nonlinear and boundary effects and thus in turn will contribute to providing new insights into various physically motivated problems in acoustics and other settings.     

Media pressures on Welsh language preservation

Despite compulsory school instruction in the Welsh language and strong cultural incentives to acquire the language, the most recent UK Census showed a downward trend in the number of speakers. The asymmetry in explicit language acquisition incentives is here considered to be offset by the media dominance of the English language. This dominance is modeled by the introduction of time-dependent connectivity and infectivity among English speakers into an adapted epidemiological model. Extrapolations up to 2050 are made, this being the announced date of a Welsh Assembly language-planning target of one million Welsh speakers.     

平面波输入下海水-海床-结构动力相互作用分析

海洋工程结构的地震反应分析是保证海洋工程结构地震安全的重要环节.由于其所处的复杂环境, 该问题涉及到流固耦合和土-结相互作用.本文基于海水、饱和海床、基岩流固耦合统一计算框架,采用Davidenkov模型和修正的Masing准则考虑饱和海床的非线性,在脉冲SV波垂直入射下, 进行了海域场地和海洋工程结构的动力响应分析. 首先,对比分析了线性自由场和非线性自由场输入情形的海域场地非线性反应,结果表明线性自由场输入时反应不合理,自由场分析和场地分析应该采用相一致的本构模型. 然后,对比分析了海床分别为线性和非线性情形时,海域场地以及海水-海床-结构体系的反应特征. 与线性海床情形相比,非线性对海床反应的影响主要由如下两方面因素控制: 一方面,非线性导致饱和海床模量减小, 饱和海床与基岩间的波阻抗比减小,由基岩到饱和海床间的反射系数和透射系数增加, 导致反应增大; 另一方面,非线性导致阻尼加大, 使海床反应减小. 对于本文算例而言,阻尼对非线性海床结果的影响占主导作用.