New lower bounds on the radius of spatial analyticity for the KdV equation

The radius of spatial analyticity for solutions of the KdV equation is studied. It is shown that the analyticity radius does not decay faster than $t^{?1/4}$ as time t goes to infinity. This improves the works of Selberg and da Silva (2017) [30] and Tesfahun (2017) [34]. Our strategy mainly relies on a higher order almost conservation law in Gevrey spaces, which is inspired by the I-method.     

Crystal structures of silicon-rich lithium silicides at high pressure

Silicon (Si) is one of the most essential elements, as it is indispensable for modern electronic technology. The standard Si structure at ambient conditions is the cubic diamond structure, and it has an indirect band gap, which prevents it from being considered as a next-generation platform for semiconductor technologies. Therefore, the search for new allotropes of silicon has attracted great attention. Herein, first principles swarm-intelligence structure searches coupled with density-functional theory were performed to explore the stable high-pressure phases of silicon-rich lithium containing compounds, LiSi_x ($x=4\text{–}8$). The LiSi₄ stoichiometry was predicted to be stable, and it was found to assume one of the following space groups, P4/mnc, Cmmm, and C2/m within the pressure range of 0 to 50 GPa. By removing the Li atoms from these compounds, three silicon allotropes were obtained that were metastable at ambient pressures. Our work illustrates how novel silicon allotropes can be predicted using the CALYPSO method.     

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.     

旋涂法制备WO3薄膜电致变色性能

"智能窗"大规模推广顺应可持续发展潮流,三氧化钨(WO_3)是生产"智能窗"的一种重要电致变色材料,但调控WO_3薄膜电致变色性能机制仍待进一步研究。采用旋涂法制备WO_3薄膜,重点研究了溶液浓度和旋涂次数对调控WO_3薄膜电致变色性能的影响。通过表面轮廓仪测量薄膜厚度,X射线衍射(XRD)测量薄膜结晶情况,原子力显微镜(AFM)和扫描电子显微镜(SEM)分析薄膜表面形貌,光谱仪测量薄膜初始态、着色态和褪色态的透射率。实验结果表明,随着溶液浓度增加(0. 2～1. 0 mol/L),薄膜厚度从9. 7 nm增加到33. 3 nm,透射率调制能力从0%提升到37. 0%;多次旋涂薄膜厚度线性增长,线性拟合优度(R~2)达0. 98,5次旋涂后透射率调制能力达51. 3%。改变溶液浓度和旋涂次数都是调控薄膜透射率调制能力的有效手段,精准调控薄膜透射率调制能力对设计不同应用场景的电致变色器件具有重大意义。     

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.     

Attaching tweezers like ionophore to a proton crane: theoretical design of new tautomeric sensors

ABSTRACT

The tautomeric optical sensors based on 4-(phenyldiazenyl)naphthalen-1-ol exist in their pure enol tautomeric form as free ligands, while the addition of metal ion fully shifts the equilibrium towards the keto tautomer allowing a red shift in the measured absorbance. This effect is achieved when a side ionophore group is connected to a tautomeric backbone by a spacer in a way that stabilizes the enol form via hydrogen boding. When the ionophore captures the metal ion the keto form is stabilized due to C─O tautomeric group participation in the complex. In the current study, we model theoretically the effect of symmetric tweezer like ionophores (RCOXCOR, where X, being CH or N, is the linker to the tautomeric backbone) on the tautomeric state and complexation ability of 4-(phenyldiazenyl)naphthalen-1-ol containing ligands. It was found that enol form stabilisation is achieved when R?=?NMe₂, independing on the linker. Both ligands are unsuitable for capturing alkali metal ions. The calculations predict that the complexation with alkali earth metal ions could lead to a full shift of the tautomeric equilibrium towards keto tautomer.     

Natural convection heat transfer at reduced pressures

This paper experimentally studies the natural convection heat transfer characteristics on horizontal and vertical plates at pressures lower than atmospheric value. Eight different pressures ranging from 10Pa to 101.325kPa, and three heating loads were used in the experiments. It is found that natural convection heat transfer characteristics at reduced pressures are independent of the plate arrangements and present different behaviors in two pressure ranges, 10Pa < p < 1000Pa and p > 1000Pa. The experimental heat transfer results are correlated into a non-dimensional equation to help the thermal design of stratosphere aircrafts and airborne equipment.     

A Theoretical study on the charge and discharge states of Na-ion battery cathode material,Na1+xFePO4F

Na₂FePO₄F is a promising cathode material for a Na-ion battery because of its high electronic capacity and good cycle performance. In this work, first principle calculations combined with cluster expansion and the Monte Carlo method have been applied to analyze the charge and discharge processes of Na₂FePO₄F by examining the voltage curve and the phase diagram. As a result of the density functional theory calculation and experimental verification with structural analysis, we found that the most stable structure of Na_1.5FePO₄F has the P2₁/b11 space group, which has not been reported to date. The estimated voltage curve has two clear plateaus caused by the two-phase structure composed of P2₁/b11 Na_1.5FePO₄F and Pbcn Na₂FePO₄F or Na₁FePO₄F and separated along the c-axis direction. The phase diagram shows the stability of the phase-separated structure. Considering that Na₂FePO₄F has diffusion paths in the a- and c-axis directions, Na₂FePO₄F has both innerphase and interphase diffusion paths. We suggest that the stable two-phase structure and the diffusion paths to both the innerphase and interphases are a key for the very clear plateau. We challenge to simulate a nonequilibrium state at high rate discharge with high temperature by introducing a coordinate-dependent chemical potential. The simulation shows agreement with the experimental discharge curve on the disappearance of the two plateaus. © 2018 Wiley Periodicals, Inc.