Exact synchronization and asymptotic synchronization for linear ODEs

Science China Mathematics - This paper studies exact synchronization and asymptotic synchronization problems for a controlled linear system of ordinary differential equations. In this paper, we...     

Effect of astrocyte on synchronization of thermosensitive neuron-astrocyte minimum system

Astrocytes have a regulatory function on the central nervous system (CNS), especially in the temperature-sensitive hippocampal region. In order to explore the thermosensitive dynamic mechanism of astrocytes in the CNS, we establish a neuron-astrocyte minimum system to analyze the synchronization change characteristics based on the Hodgkin-Huxley model, in which a pyramidal cell and an interneuron are connected by an astrocyte. The temperature range is set as 0 ℃-40 ℃ to juggle between theoretical calculation and the reality of a brain environment. It is shown that the synchronization of thermosensitive neurons exhibits nonlinear behavior with changes in astrocyte parameters. At a temperature range of 0 ℃-18 ℃, the effects of the astrocyte can provide a tremendous influence on neurons in synchronization. We find the existence of a value for inositol triphosphate (IP₃) production rate and feedback intensities of astrocytes to neurons, which can ensure the weak synchronization of two neurons. In addition, it is revealed that the regulation of astrocytes to pyramidal cells is more sensitive than that to interneurons. Finally, it is shown that the synchronization and phase transition of neurons depend on the change in Ca²⁺ concentration at the temperature of weak synchronization. The results in this paper provide some enlightenment on the mechanism of cognitive dysfunction and neurological disorders with astrocytes.     

A Lie theoretic categorification of the coloured Jones polynomial

We use the machinery of categorified Jones-Wenzl projectors to construct a categorification of a type A Reshetikhin-Turaev invariant of oriented framed tangles where each strand is labelled by an arbitrary finite-dimensional representation. As a special case, we obtain a categorification of the coloured Jones polynomial of links.     

TBOR-shaped electro-optic modulator with dual output based on double-layer graphene

We proposed an electro-optic modulator with two-bus one-ring (TBOR) structure to improve the extinction ratio and reduce insert loss. It has a dual output compared with one-bus one-ring structure. In addition, double-layer graphene makes it possible for the modulation in the visible to mid-infrared wavelength range. It shows that this new electro-optic modulator can present two switching states well with low insertion loss, high absorption and high extinction ratio. At $\lambda =1550\text{ nm}$, when the switching states are based on the chemical potential, ${\mu }_{\mathrm{c}}=0.38\text{ eV}$ and ${\mu }_{\mathrm{c}}=0.4\text{ eV}$, the insertion losses of both output ports are less than 2 dB, the absorption of the output port coupled via a micro-ring reaches 45 dB and the extinction ratio reaches 14 dB. When the refractive index of the dielectric material is 4.2, the applied voltage will be less than 1.2 V, thus can be used in low-voltage CMOS technology.     

TFSI钝化晶体硅表面性质的第一性原理研究

晶体硅表面钝化是高效率晶体硅太阳能电池的核心技术,直接影响晶体硅器件的性能。本文采用第一性原理方法研究了一种超强酸-双三氟甲基磺酰亚胺(TFSI)钝化晶体硅(001)表面。研究发现,TFSI的四氧原子结构能够与Si(001)表面Si原子有效成键,吸附能达到-5.124 eV。电子局域函数研究表明,TFSI的O原子与晶体硅表面的Si的成键类型为金属键。由态密度和电荷差分密度分析可知,Si表面原子的电子向TFSI转移,从而有效降低了Si表面的电子复合中心,有利于提高晶体硅的少子寿命。Bader电荷显示,伴随着TFSI钝化晶体硅表面的Si原子,表面Si原子电荷电量减少,而TFSI中的O原子和S原子电荷电量相应增加,进一步证明了TFSI钝化Si表面后的电子转移。该工作为第一性原理方法预测有机强酸钝化晶体硅表面的钝化效果提供了数据支撑。     

Pentapnictogen heterocyclic monoanions: Structure,stability, and aromaticity

Inorganic planar ring-shape molecules with 4n + 2 π electrons are always the focus of experimental synthesis and theoretical research due to their potential aromaticity and stability. In this work, the whole series of five-membered heterocycle monoanions X _nY_5-n⁻ (X, Y = group 15 elements; n = 1-4) were thoroughly investigated by means of density functional theory calculations. They all have large formation energies and HOMO-LUMO gap energies, suggesting the potential thermodynamic and kinetic stability. Their aromaticities are comparable to that of typical aromatic hydrocarbons. Their thermal stabilities were firmly established by the ab initio molecular dynamics simulations. As most of them are predicted for the first time, their various spectra were simulated for experimental characterization. Furthermore, we demonstrate that these five-membered cyclic anions can be employed as η⁵-ligand to construct novel all-inorganic metallocenes, which may serve as the building blocks of low-dimensional nanomaterials.     

Water‐Soluble Luminescent Hybrid Composites Consisting of Oligosilsesquioxanes and Lanthanide Complexes and their Sensing Ability for Cu2+

Water‐soluble hybrid composites with great potential for selective and sensitive sensing and that are obtained through simple, rapid, and environmentally friendly methods are highly desirable and remain a challenging task. Herein, we present luminescent hybrid composites that were realized by linking Na₃[Ln(dpa)₃] (dpa=2,6‐pyridinedicarboxylic acid) to octa‐amino functionalized polyhedral oligomeric silsesquioxane (POSS‐NH₂) through hydrogen‐bonding interactions between the oxygen atoms of the carboxylate groups of dpa and the hydrogen‐bond‐donor amino groups. The resulting hybrid composites Ln(dpa)₃@POSS‐NH₂ are highly soluble in aqueous solutions and the quantum yield of Eu(dpa)₃@POSS‐NH₂ is as high as 56.5 % or 46.3 % in the solid state and in aqueous solution, respectively, as determined by using the integrating sphere method. The novel water‐soluble luminescent hybrid composites exhibit high thermal and photostability, and the emitted colors of the resulting hybrid composite can be finely tuned by changing the Eu³⁺/Tb³⁺ ratio. Interestingly, Eu(dpa)₃@POSS‐NH₂ hybrid composites exhibited an effective switch‐off fluorescence response to Cu²⁺ over other common metal ions in aqueous media.     

真空中金属丝电爆炸数值模拟研究

利用金属丝电爆炸物理数学模型对电爆炸物理过程开展了数值模拟，研究了不同直径铝丝电爆炸特性，进一步分析了金属丝内沉积能量、电压击穿时刻、电压峰值随金属丝直径的变化规律，并与相关实验数据作了对比。