强度解调型光纤光栅温度传感实验

光纤光栅在工程上应用广泛,但由于存在解调系统复杂、成本高,尤其是需要使用光纤光谱仪等波长解调仪器,使得光纤光栅很难走入本科教学的实验课堂.本文提出了一种基于窄线宽DFB激光器的强度解调方案,极大地简化了光纤光栅传感器的解调系统,完全满足较高分辨率和实时检测的系统要求.合理安排的温度传感实验可以非常直观地展示光纤光栅的线性传感性能,使得工程化的光纤光栅传感技术轻松走进本科教学课堂,具有极高的推广和应用潜力.     

基于化学学科认知障碍突破的中考复习教学实践* ——以“二氧化碳的性质”为例

分析学生对二氧化碳的3个典型学科认知障碍,以“二氧化碳的捕捉”为情境,通过“尝试捕捉二氧化碳”“谁在捕捉二氧化碳”“捕捉背后的原理”等3个主要环节,实现对学科认知障碍的突破,展示了一种新的中考复习教学思路。     

Spectral estimates for saddle point matrices arising in weak constraint four‐dimensional variational data assimilation

We consider the large sparse symmetric linear systems of equations that arise in the solution of weak constraint four‐dimensional variational data assimilation, a method of high interest for numerical weather prediction. These systems can be written as saddle point systems with a 3 × 3 block structure but block eliminations can be performed to reduce them to saddle point systems with a 2 × 2 block structure, or further to symmetric positive definite systems. In this article, we analyse how sensitive the spectra of these matrices are to the number of observations of the underlying dynamical system. We also obtain bounds on the eigenvalues of the matrices. Numerical experiments are used to confirm the theoretical analysis and bounds.     

Convergence of solutions for the fractional Cahn–Hilliard system

This paper deals with the Cauchy–Dirichlet problem for the fractional Cahn–Hilliard equation. The main results consist of global (in time) existence of weak solutions, characterization of parabolic smoothing effects (implying under proper condition eventual boundedness of trajectories), and convergence of each solution to a (single) equilibrium. In particular, to prove the convergence result, a variant of the so-called ?ojasiewicz–Simon inequality is provided for the fractional Dirichlet Laplacian and (possibly) non-analytic (but $C^1$) nonlinearities.     

Potts models with magnetic field: Arithmetic,geometry, and computation

We give a sheaf theoretic interpretation of Potts models with external magnetic field, in terms of constructible sheaves and their Euler characteristics. We show that the polynomial countability question for the hypersurfaces defined by the vanishing of the partition function is affected by changes in the magnetic field: elementary examples suffice to see non-polynomially countable cases that become polynomially countable after a perturbation of the magnetic field. The same recursive formula for the Grothendieck classes, under edge-doubling operations, holds as in the case without magnetic field, but the closed formulae for specific examples like banana graphs differ in the presence of magnetic field. We give examples of computation of the Euler characteristic with compact support, for the set of real zeros, and find a similar exponential growth with the size of the graph. This can be viewed as a measure of topological and algorithmic complexity. We also consider the computational complexity question for evaluations of the polynomial, and show both tractable and NP-hard examples, using dynamic programming.     

The effects of resource limitation and consensual incentives on cooperation

Exploring the evolution of cooperation has been one of the most challenging topics and attracted increasing attention in various realms. Hereby, we institute an analytic model where the relationship between the common benefits and contributions is the typical saturation nonlinearity. We investigate the evolutionary dynamics of cooperation with and without consensual incentives respectively. The population always evolves to full defection when the incentives are absent. Cooperation, however, can be promoted by consensual incentives when the degree of cooperators' preferences for incentives is great. There exists an intermediate amount of resources at which the positive effect of consensual incentives on cooperation is minimized. Furthermore, there is a U-shape relationship between the degree of cooperators' preference for an incentive and the evolution of cooperation. A greater basin of full cooperation can be induced when the cooperators' preference for reward is more pronounced than that for punishment.     

Norbornene derivatives from a metal‐free,strain‐promoted cycloaddition reaction: New building blocks for ring‐opening metathesis polymerization reactions

The preparation of new ring opening metathesis polymerization (ROMP) monomers using a 1,3‐dipolar cycloaddition between aryl azides and norbornadiene is described. Various norbornenetriazolines, obtained through a solvent‐and catalyst‐free reaction, can subsequently be incorporated into polymer backbones through ROMP reactions. Furthermore, thermal decomposition of the triazoline moiety can allow for further polymer functionalization. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 2357–2362