Kinetics and mechanism of trichloroisocyanuric acid/NaNO2-triggered nitration of aromatic compounds under acid-free and Vilsmeier-Haack conditions

Kinetics and mechanism of nitration of aromatic compounds using trichloroisocyanuric acid (TCCA)/NaNO₂, TCCA-N,N-dimethyl formamide (TCCA-DMF)/NaNO₂, and TCCA-N,N-dimethyl acetamide (TCCA-DMA)/NaNO₂ under acid-free and Vilsmeier-Haack conditions. Reactions followed second-order kinetics with a first-order dependence on [Phenol] and [Nitrating agent] ([TCCA], [(TCCA-DMF)], or [(TCCA-DMA)] >> [NaNO₂]). Reaction rates accelerated with the introduction of electron-donating groups and retarded with electron-withdrawing groups, but did not fit well into the Hammett's theory of linear free energy relationship or its modified forms like Brown-Okamoto or Yukawa-Tsuno equations. Rate data were analyzed by Charton's multiple linear regression analysis. Isokinetic temperature (β) values, obtained from Exner's theory for different protocols, are 403.7 K (TCCA-NaNO₂), 365.8 K (TCCA-DMF)/NaNO₂, and 358 K (TCCA-DMA)/NaNO₂. These values are far above the experimental temperature range (303-323 K), indicating that the enthalpy factors are probably more important in controlling the reaction.     

The Riemann–Hilbert analysis to the Pollaczek–Jacobi type orthogonal polynomials

In this paper, we study polynomials orthogonal with respect to a Pollaczek–Jacobi type weight The uniform asymptotic expansions for the monic orthogonal polynomials on the interval (0,1) and outside this interval are obtained. Moreover, near , the uniform asymptotic expansion involves Airy function as , and Bessel function of order α as in the neighborhood of , the uniform asymptotic expansion is associated with Bessel function of order β as . The recurrence coefficients and leading coefficient of the orthogonal polynomials are expressed in terms of a particular Painlevé III transcendent. We also obtain the limit of the kernel in the bulk of the spectrum. The double scaled logarithmic derivative of the Hankel determinant satisfies a σ‐form Painlevé III equation. The asymptotic analysis is based on the Deift and Zhou's steepest descent method.     

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.     

Relationship of nanostructure and thermo-chemical response/thermal ablation of carbon aerogels

In this work, the interfacial mass balance relations combined with the non-parametric kinetic (NPK) analysis results were used for evaluating the thermo-chemical ablation process and oxidation mechanism of carbon aerogels with various porous structure. It was found that the two-parameter model of Nomen–Sempereis was able to describe the kinetics of the oxidation reaction and to reveal the structure-dependent contribution of two main processes with chemical and physical nature. The porosity of the carbon aerogel, rather than the other microstructural features, was realized more effective on the rate of ablation.     

基于有限体积虚拟区域方法的两相流动直接模拟

为提高计算效率，提出有限体积法离散下的虚拟区域颗粒两相流动直接模拟方法.在控制方程中加入相应的虚拟区域源项，保证了颗粒内部的刚体运动特性.该源项中含有颗粒信息部分及流体信息部分.在每次迭代后，对源项中的流体信息部分进行更新，从而更好地保证颗粒内速度的刚体分布.计算静止颗粒圆柱绕流及单个颗粒的沉降过程，验证了算法的准确性.     

Analyticity of resonances and eigenvalues and spectral properties of the massless Spin–Boson model

We extend the method of Pizzo multiscale analysis for resonances introduced in [5] in order to infer analytic properties of resonances and eigenvalues (and their eigenprojections) as well as estimates for the localization of the spectrum of dilated Hamiltonians and norm-bounds for the corresponding resolvent operators, in neighborhoods of resonances and eigenvalues. We apply our method to the massless Spin–Boson model assuming a slight infrared regularization. We prove that the resonance and the ground-state eigenvalue (and their eigenprojections) are analytic with respect to the dilation parameter and the coupling constant. Moreover, we prove that the spectrum of the dilated Spin–Boson Hamiltonian in the neighborhood of the resonance and the ground-state eigenvalue is localized in two cones in the complex plane with vertices at the location of the resonance and the ground-state eigenvalue, respectively. Additionally, we provide norm-estimates for the resolvent of the dilated Spin–Boson Hamiltonian near the resonance and the ground-state eigenvalue. The topic of analyticity of eigenvalues and resonances has let to several studies and advances in the past. However, to the best of our knowledge, this is the first time that it is addressed from the perspective of Pizzo multiscale analysis. Once the multiscale analysis is set up our method gives easy access to analyticity: Essentially, it amounts to proving it for isolated eigenvalues only and use that uniform limits of analytic functions are analytic. The type of spectral and resolvent estimates that we prove are needed to control the time evolution including the scattering regime. The latter will be demonstrated in a forthcoming publication. The introduced multiscale method to study spectral and resolvent estimates follows its own inductive scheme and is independent (and different) from the method we apply to construct resonances.     

Hydrothermal synthesis,thermal decomposition and optical properties of Fe2F5(H2O)(Htaz)(taz)(Hdma)

Crystal structure of Fe₂F₅(H₂O)(Htaz)(taz)(Hdma) which crystallizes in the triclinic system space group $\text{P}\overline{1}$ with unit cell parameters a = 8.8392(5) Å, b = 9.1948(5) Å, c = 9.5877(5) Å, α = 82.070(3)°, β = 63.699(3)°, γ = 89.202(3)°, Z = 2, and V = 690.91(7) ų, was synthesized under hydrothermal conditions at 393 K for 72 h, by a mixture of FeF₂/FeF₃, 1,2,4-triazole molecule (Htaz), and hydrofluoric acid solution (HF 4%) in dimethylformamide solvent (DMF). The main feature of this material is the coexistence of two oxidation states for iron atoms (Fe²⁺, Fe³⁺) in the unit cell, which associate by opposite fluorine corners of FeF₅N and FeF₂N₄ octahedra, and/or triazole molecule which originates the 2D produces material. The structure determination, performed from single crystal X-ray diffraction data, lead to the R₁/_WR₂ reliability factors 0.031/0.087. Thermal stability studies (TG/DTG/DTA) show that the decomposition provides in the temperature range 473–773 K and no mass loss was detected before 473 K. Mass spectrometry (MS) has been used. The optical absorption of the solid was measured at the corresponding λ_max using UV–vis diffuse-reflectance spectrum.     

Kinetics of carbon steel dissolution in ammonium chloride solution containing sodium thiosulfate

The dissolution behavior of carbon steel in ammonium chloride (NH₄Cl) solution containing sodium thiosulfate (Na₂S₂O₃) of various concentrations (0.01 and 0.1 M) was investigated using electrochemical impedance spectroscopy (EIS) and other nonelectrochemical techniques. The weight loss and polarization measurements indicate a significant increase in the NH₄Cl corrosion rate of carbon steel on addition of Na₂S₂O_3. The EIS measurements exhibited two capacitive loops at multiple direct current (dc) potentials for both the concentrations. Electrical equivalent circuit (EEC) and reaction mechanism analysis (RMA) were employed to analyze the impedance data. A four-step mechanism with two intermediate adsorbate species of same charge was proposed to explain the dissolution behavior of carbon steel in the given system. The surface coverage values enumerated that the surface was entirely covered with adsorbed species unlike in the pure NH₄Cl system. Charge transfer resistance and polarization resistance values estimated from RMA parameters indicate the increase in a dissolution rate with dc potential. The surface morphology was inspected via field emission scanning electron microscopy, and the corrosion products including surface state of carbon steel electrode were analyzed using energy dispersive X-ray spectroscopy and X-ray photoelectron spectroscopy.