单脉冲飞秒激光烧蚀炸药过程的热效应研究

飞秒激光能够在极短时间内烧蚀炸药产生高温高压等离子体。可以利用飞秒激光对含能材料或含能元器件进行精密加工。深入认识飞秒激光烧蚀炸药过程中,炸药内部的热效应是发展飞秒激光加工炸药技术的基础。建立了单脉冲飞秒激光烧蚀炸药过程的流固耦合计算模型,考虑了在高温高压等离子体和炸药自热反应的共同作用下,炸药内部的热效应。对飞秒激光烧蚀TNT炸药过程进行了流体力学数值模拟。计算结果表明：TNT炸药中未烧蚀区域产生了热效应,峰值温度高于TNT炸药的点火温度,但由于炸药内热效应区域极小,高温持续时间极短,因此炸药内温度迅速下降,没有发生点火现象。     

The signatures of the congruence subgroups G 0(τ) of the hecke groups G 4 and G 6

We determine the signatures of the congruence subgroups of the Hecke groups G ₄ and G ₆.     

Optimal L~2 Extension and Siu's Lemma

In this paper, we discuss our most recent results on the optimal L~2 extension problem and Siu's lemma as applications of the strong openness property of multiplier ideal sheaves obtained by Guan and Zhou.     

Computational existence proofs for spherical <Emphasis Type=Italic>t</Emphasis>-designs

Spherical t-designs provide quadrature rules for the sphere which are exact for polynomials up to degree t. In this paper, we propose a computational algorithm based on interval arithmetic which, for given t, upon successful completion will have proved the existence of a t-design with (t + 1)² nodes on the unit sphere S² ì mathbbR³{S^2 subset mathbb{R}^3} and will have computed narrow interval enclosures which are known to contain these nodes with mathematical certainty. Since there is no theoretical result which proves the existence of a t-design with (t + 1)² nodes for arbitrary t, our method contributes to the theory because it was tested successfully for t = 1, 2, . . . , 100. The t-design is usually not unique; our method aims at finding a well-conditioned one. The method relies on computing an interval enclosure for the zero of a highly nonlinear system of dimension (t + 1)². We therefore develop several special approaches which allow us to use interval arithmetic efficiently in this particular situation. The computations were all done using the MATLAB toolbox INTLAB.     

A metaheuristic approach to the urban transit routing problem

The urban transit routing problem (UTRP) is NP-Hard and involves devising routes for public transport systems. It is a highly complex multi-constrained problem and the evaluation of candidate route sets can prove both time consuming and challenging, with many potential solutions rejected on the grounds of infeasibility. Due to the problem difficulty, metaheuristic algorithms are highly suitable, yet the success of such methods depend heavily on: (1) the quality of the chosen representation, (2) the effectiveness of the initialization procedures and (3) the suitability of the chosen neighbourhood moves. Our paper focuses on these three issues, and presents a framework which can be used as a starting point for solving this problem. We devise a simple model of the UTRP to evaluate candidate route sets. Finally, our approach is validated using simple hill-climbing and simulated annealing algorithms. Our simple method improves upon published results for Mandl’s benchmark problems. In addition, the potential for solving larger problem instances has been explored.     

An Enhanced Quartic B-spline Method for a Class of Non-linear Fifth-Order Boundary Value Problems

Mediterranean Journal of Mathematics - In this paper, we apply quartic B-splines properly to study a new approximation method for numerical solutions and numerical derivatives for a class of...     

Representation of Integers by Ternary Quadric Forms

In this paper we give a formula for the number of representations of some square-free integers by certain ternary quadratic forms and estimate the lower bound of the 2-power appearing in this number. Supported by NSFC and RFDP.     

基于银纳米链的马赫-曾德干涉仪结构的生物传感器

优化了一种基于表面等离激元银纳米链的马赫-曾德干涉式传感结构.该结构由参考臂、传感臂及纳米线波导构成.纳米线波导由银纳米线包裹一定厚度的硅来构成.引入两条银纳米链分别作为马赫-曾德干涉仪的参考臂和传感臂,并研究所设计结构的传输特性,通过降低传输损耗以提高所设计结构的精确度与灵敏度.相比于两条完全相同的银纳米线作为参考臂和传感臂的情况,在参考臂和传感臂改为银纳米链后,传输特性有明显提高,单位长度损耗明显降低.这是由于银纳米链中的单元结构之间的长程/库仑相互作用增强了结构中的电磁场,进而降低了传输损耗.将两条银纳米链的晶格常数设置为不同的情况,研究发现,在特定的银包硅纳米线的宽度与某些占空比下,含有非对称的银纳米链结构的单位传输损耗小于含有对称的银纳米链结构.由此可以知道,具有小损耗的银纳米颗粒链可以弥补大损耗的银纳米颗粒链的传输损失.利用这个特点,进一步优化设计结构,将一侧银纳米链改为纳米线.改变另一侧银纳米链的晶格常数与占空比,可以发现大多数情况下,这类结构传输特性优于含有两条银纳米链以及含有两条银纳米线的结构.本文的设计结构可以大幅减小传统的马赫-曾德干涉仪的传输损耗,且在结构的制备...