石墨烯能带中的重叠矩阵效应:Tight-Binding方法在模拟中的研究

采用紧束缚方法计算了石墨烯的价带(π)和导带(π*),考虑了非正交基矢下重叠矩阵效应,重叠积分参量s越小,导带越靠近费米面,而价带越远离费米面.在重叠积分参量s≤0.1时,基本保持了原子在实际空间中重叠所引起的能带的改变,太大(s=0.4)则会导致物理上失效.计算了石墨烯的能态密度,在费米面ε=0处(对应Dirac点)的能态密度为零,并且在Dirac点附近呈线性变化.     

任意维l态Woods-Saxon势的精确解

在D维空间下使用完全量子化规则计算了具有离心项的Woods-Saxon势,根据动量积分 (其中 )和Pekeris近似化条件,得到了系统的任意l波Schrödinger方程的解和能谱方程．讨论了束缚态能谱的有关性质．     

空间关联白噪声影响下小世界神经元网络系统的同步动力学

以电耦合的Terman-Wang小世界神经元网络系统为研究对象, 研究了空间关联白噪声影响下神经元网络系统的同步动力学. 首先将动力学平均场近似理论扩展到受空间关联白噪声影响下的小世界网络系统中, 将描述网络系统动力学演化的2N维随机微分方程简化为11个确定性的矩微分方程. 其次, 基于动力学平均场近似理论所推导的矩方程, 讨论了空间关联噪声、网络结构参数对神经元网络系统同步动力学的关键影响, 发现较大的噪声空间关联系数、耦合强度及节点平均度均对神经元网络系统同步放电具有积极作用. 进一步地, 利用计算机仿真数值模拟原神经元网络系统的同步动力学, 并与基于动力学平均场近似理论所得到的结果进行比较, 发现二者具有较好的一致性.     

Nonlocal Interaction Equations in Environments with Heterogeneities and Boundaries

We study well-posedness of a class of nonlocal interaction equations with spatially dependent mobility. We also allow for the presence of boundaries and external potentials. Such systems lead to the study of nonlocal interaction equations on subsets ? of ? ^d endowed with a Riemannian metric g. We obtain conditions, relating the interaction potential and the geometry, which imply existence, uniqueness and stability of solutions. We study the equations in the setting of gradient flows in the space of probability measures on ? endowed with Riemannian 2-Wasserstein metric.     

An efficient meshfree point collocation moving least squares method to solve the interface problems with nonhomogeneous jump conditions

We are going to study a simple and effective method for the numerical solution of the closed interface boundary value problem with both discontinuities in the solution and its derivatives. It uses a strong‐form meshfree method based on the moving least squares (MLS) approximation. In this method, for the solution of elliptic equation, the second‐order derivatives of the shape functions are needed in constructing the global stiffness matrix. It is well‐known that the calculation of full derivatives of the MLS approximation, especially in high dimensions, is quite costly. In the current work, we apply the diffuse derivatives using an efficient technique. In this technique, we calculate the higher‐order derivatives using the approximation of lower‐order derivatives, instead of calculating directly derivatives. This technique can improve the accuracy of meshfree point collocation method for interface problems with nonhomogeneous jump conditions and can efficiently estimate diffuse derivatives of second‐ and higher‐orders using only linear basis functions. To introduce the appropriate discontinuous shape functions in the vicinity of interface, we choose the visibility criterion method that modifies the support of weight function in MLS approximation and leads to an efficient computational procedure for the solution of closed interface problems. The proposed method is applied for elliptic and biharmonic interface problems. For the biharmonic equation, we use a mixed scheme, which replaces this equation by a coupled elliptic system. Also the application of the present method to elasticity equation with discontinuities in the coefficients across a closed interface has been provided. Representative numerical examples demonstrate the accuracy and robustness of the proposed methodology for the closed interface problems. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1031–1053, 2015     

Numerical solution of one‐dimensional Burgers' equation

In this article, an iterative method for the approximate solution of a class of Burgers' equation is obtained in reproducing kernel space . It is proved the approximation converges uniformly to the exact solution u(x, t) for any initial function under trivial conditions, the derivatives of are also convergent to the derivatives of u(x, t), and the approximate solution is the best approximation under the system © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1251–1264, 2015     

Weak Euler Approximation for Itô Diffusion and Jump Processes

This article studies the rate of convergence of the weak Euler approximation for Itô diffusion and jump processes with Hölder-continuous generators. It covers a number of stochastic processes including the nondegenerate diffusion processes and a class of stochastic differential equations driven by stable processes. To estimate the rate of convergence, the existence of a unique solution to the corresponding backward Kolmogorov equation in Hölder space is first proved. It then shows that the Euler scheme yields positive weak order of convergence.     

Designing quantitative structure activity relationships to predict specific toxic endpoints for polybrominated diphenyl ethers in mammalian cells

Polybrominated diphenyl ethers (PBDEs) are known as effective flame retardants and have vast industrial application in products like plastics, building materials and textiles. They are found to be structurally similar to thyroid hormones that are responsible for regulating metabolism in the body. Structural similarity with the hormones poses a threat to human health because, once in the system, PBDEs have the potential to affect thyroid hormone transport and metabolism. This study was aimed at designing quantitative structure–activity relationship (QSAR) models for predicting toxic endpoints, namely cell viability and apoptosis, elicited by PBDEs in mammalian cells. Cell viability was evaluated quantitatively using a general cytotoxicity bioassay using Janus Green dye and apoptosis was evaluated using a caspase assay. This study has thus modelled the overall cytotoxic influence of PBDEs at an early and a late endpoint by the Genetic Function Approximation method. This research was a twofold process including running in vitro bioassays to collect data on the toxic endpoints and modeling the evaluated endpoints using QSARs. Cell viability and apoptosis responses for Hep G2 cells exposed to PBDEs were successfully modelled with an r² of 0.97 and 0.94, respectively.     

Mono- and Di-Fucosylated Glycans of the Parasitic Worm S. mansoni are Recognized Differently by the Innate Immune Receptor DC-SIGN

The parasitic worm, Schistosoma mansoni, expresses unusual fucosylated glycans in a stage-dependent manner that can be recognized by the human innate immune receptor DC-SIGN, thereby shaping host immune responses. We have developed a synthetic approach for mono- and bis-fucosylated LacdiNAc (LDN-F and LDN-DF, respectively), which are epitopes expressed on glycolipids and glycoproteins of S. mansoni. It is based on the use of monosaccharide building blocks having carefully selected amino-protecting groups, facilitating high yielding and stereoselective glycosylations. The molecular interaction between the synthetic glycans and DC-SIGN was studied by NMR and molecular modeling, which demonstrated that the α1,3-fucoside of LDN-F can coordinate with the Ca²⁺-ion of the canonical binding site of DC-SIGN allowing for additional interactions with the underlying LDN backbone. The 1,2-fucoside of LDN-DF can be complexed in a similar manner, however, in this binding mode GlcNAc and GalNAc of the LDN backbone are placed away from the protein surface resulting in a substantially lower binding affinity. Glycan microarray binding studies showed that the avidity and selectivity of binding is greatly enhanced when the glycans are presented multivalently, and in this format Le^x and LDN-F gave strong responsiveness, whereas no binding was detected for LDN-DF. The data indicates that S. mansoni has developed a strategy to avoid detection by DC-SIGN in a stage-dependent manner by the addition of a fucoside to a number of its ligands.     

Investigating aroma diversity combining purge‐and‐trap,comprehensive two‐dimensional gas chromatography,and mass spectrometry

Headspace gas chromatography is frequently used for aroma profiling thanks to its ability to naturally exploit the volatility of aroma compounds, and also to provide chemical information on sample composition. Its main advantages rely on simplicity, no use of solvent, amenability to automation, and the cleanliness of the extract. In the present contribution, the most effective sampling (dynamic extraction), separation (multidimensional gas chromatography), and detection (mass spectrometry) techniques for untargeted analysis are exploited in combination, showing their potential in unraveling aroma profiles in fruit beers. To complete the overall analytical process, a neat workflow for data analysis is discussed and used for the successful characterization and identification of five different beer flavors (berries, cherry, banana, apple, and peach). From the technical viewpoint, the coupling of purge‐and‐trap, comprehensive two‐dimensional gas chromatography, and mass spectrometry makes the global methodology unique, and it is for the first time discussed. A (low‐)flow modulation approach allowed for the full transfer into the second dimension with mass‐spectrometry compatible flow (< 7 mL/min), avoiding the need of splitting before detection and making the overall method sensitive (1.2–5.2‐fold higher signal to noise ratio compared to unmodulated gas chromatography conditions) and selective.