Sharper uncertainty principles associated with Lp-norm

Motivated by the well-established phase derivative embedded technique, this study devotes to sharper uncertainty principles related to the L^p-norm type of uncertainty product, giving rise to two kinds of uncertainty inequalities that improve the classical result through providing tighter lower bounds. The conditions that truly reach these better estimates are obtained. Examples and simulations are carried out to verify the correctness of the derived results, and finally, possible applications in time-frequency analysis are also given.     

Asymptotic convergence of solutions for Laplace reaction–diffusion equations

We study the initial–boundary value problem for a Laplace reaction–diffusion equation. After constructing local solutions by using the theory of abstract degenerate evolution equations of parabolic type, we show asymptotic convergence of bounded global solutions if they exist under the assumption that the reaction function is analytic in neighborhoods of their $\omega$-limit sets. Reduction of degenerate evolution equation to multivalued evolution equation enables us to use the theory of the infinite-dimensional Łojasiewicz–Simon gradient inequality.     

Pair correlation function and freezing transitions in a two-dimensional system of model ultrasoft colloids

Density functional theory (DFT) of freezing has been used to investigate the freezing transitions in a system of colloidal particles confined to a two-dimensional plane. The particles interact via a model Hertzian type potential of varying softness. The pair-correlation functions (PCFs) needed as input structural information in DFT are calculated by solving hypernetted chain (HNC) integral equation theory. The PCFs thus obtained have been compared with those obtained through experiment and simulations and are found to be in good qualitative agreement. We found that the PCFs are sensitive to the softness of the potential: showing splitting of pair-correlation peak in the harder case and anomalous non-monotonic density dependence in the softer case. Using the common tangent construction method, we have also proposed the fluid-triangular solid phase diagrams in the temperature-density plane. We found that the phase diagram exhibit solid-fluid coexistence region whose thickness decreases with the increasing temperature as well as with increasing softness of the potential. In the temperature and density range of our calculation, DFT fails to produce any reentrance in the phase diagram.     

Heteroborospherene nanoclusters as high-performance nonlinear optical materials

Today, the design of new compounds with giant nonlinear optical responses is attracted to many researchers. Inspired by an interesting finding of a new class of heteroborospherenes which were formed by doping four carbon atoms in the B364- nanocluster (C4B32), we suggest the alkali metal-doped C4B32 (M@C4B32, M=Li, Na, and K) nanoclusters as high-performance nonlinear optical materials. Our results show that the alkali metal atoms have a considerable effect on the structural and electronic properties of the C4B32 nanocluster. We found that the doping alkali metal can remarkably decrease the HOMO-LUMO gap and significantly increases the first hyperpolarizability of the C4B32 nanocluster. Also, our results reveal that the first hyperpolarizability of the M@C4B32 nanoclusters can be progressively enhanced by increasing the atomic number of alkali metals. The effect of external electric fields on the nonlinear optical responses of the M@C4B32 has been systematically explored. We found that the first hyperpolarizability of the M@C4B32 compounds can be gradually increased by increasing the imposed external electric field from zero to the critical external electric field along the charge transfer direction (M→C4B32). Accordingly, this work presents an efficient strategy to improve the nonlinear optical responses of the heteroborospherenes.     

Highly efficient perovskite solar cells by tuning electronic structures of thienothiophene-based as hole transport materials

The atomic substitutions were used to study the hole transport materials (HTM) properties of six thiophenothiophene molecules (HTM1-HTM6) to reveal the relationship between their core structures and photoelectric properties. To better investigate the difference between experimentally original and designed molecules, we calculated the hole mobility and some parameters (such as energy levels, stability, and optical properties, etc). The results showed that the molecular orbital levels of the original and designed molecules have well matched with perovskite and Ag electrode to ensure hole transport and inhibit the electron reflux. Among the designed HTMs, HTM5 has the smallest energy gap that results in the red-shifted absorption spectra. Furthermore, there is an obviously increased charge transfer integral V due to the introduction of the Si atom, which greatly improved the hole mobility. Therefore, atom substitution by introducing Si atoms (HTM5) will improve the energy levels and charge transport ability, and molecular design by means of atom substitution can be a potential way to tunable HTM performance in solar cells.     

Porphyrin-like porous nanomaterials as drug delivery systems for ibuprofen drug

In recent years, nanomaterial-based drug delivery carriers have become some of the most attractive to be studied. The purpose of this study is to investigate the interaction of C60 fullerene, carbon nanotube and graphene having porphyrin-like FeN4 clusters with a non-steroidal anti-inflammatory drug (ibuprofen) by means of the density functional theory. Results showed that the graphene with FeN4 clusters could remarkably increase the tendency of graphene for adsorption of ibuprofen drug. Also, our ultraviolet–visible results show that the electronic spectra of the complexes exhibit a blue shift toward lower wavelengths (higher energies). It was found that Ibp/FeN4-graphene had high chemical reactivity, which was important for binding of the drug onto the target site. In order to go further and gain insight into the binding features of considered systems with ibuprofen drug, the Atoms in Molecules analysis was performed. Our results determine the electrostatic features of the Ibp/FeN4-graphene bonding. Consequently, the results demonstrated that the FeN4-graphene could be used as potential carriers for the delivery of ibuprofen drug.     

3d过渡金属掺杂M_2@Si_(20)(M=Sc-Zn)团簇的密度泛函理论研究

利用密度泛函理论(DFT)研究3d过渡金属掺杂硅团簇的几何结构和稳定性,计算了绝热电子亲和能和垂直电离能,内嵌双金属间距,自旋磁矩等.结果表明内嵌的Sc、Ti、V、Mn金属二聚体和十二面体硅笼构成了稳定的富勒烯结构,随着d电子数目的增加其内嵌的富勒烯构型有部分畸变,总体而言Si_(20)团簇掺杂双金属后稳定性得到了提高.     

Na原子链表面等离激元特性的含时密度泛函研究

本文用含时密度泛函理论研究了线性Na原子链的表面等离激元机理.主要在原子尺度下模拟计算了体系随着原子数增加及原子间距变化的集体激发过程.研究发现线性原子链有一个普遍的特性——存在一个纵模和两个横模.两个横模一般在实验上很难被观测到.纵模随着原子链长度增加,能量红移的同时,该纵模主峰的强度呈线性增长.随着原子个数的增加,端点模式(TE)开始蓝移,能量和偶极强度都逐渐趋向饱和.横模能量被劈裂的原因概括如下:(一)每个位置的电子受到的势不同,在两端的电子受到的势要比在中间的电子受到的势要高,因此两端的电荷积累也比中间多;(二)端点存在悬挂键,所以中间的电子-电子间相互作用与端点的不一样,这两方面又都与原子间距d有关.