Mesh adaptive direct search algorithms for mixed variable optimization

This paper introduces a new derivative-free class of mesh adaptive direct search (MADS) algorithms for solving constrained mixed variable optimization problems, in which the variables may be continuous or categorical. This new class of algorithms, called mixed variable MADS (MV-MADS), generalizes both mixed variable pattern search (MVPS) algorithms for linearly constrained mixed variable problems and MADS algorithms for general constrained problems with only continuous variables. The convergence analysis, which makes use of the Clarke nonsmooth calculus, similarly generalizes the existing theory for both MVPS and MADS algorithms, and reasonable conditions are established for ensuring convergence of a subsequence of iterates to a suitably defined stationary point in the nonsmooth and mixed variable sense.     

多荧光光纤传感器及其在混合溶剂检测中的应用

微纳光纤与其他微纳结构的集成可以拓展荧光光纤传感器检测范围和集成度,是光纤传感领域的研究热点。目前,国际上关于荧光光纤传感器这一领域的研究还处于单一检测物荧光响应的阶段,对多检测物的多通道荧光响应仍存在很大挑战。本文结合微纳光纤的光波导性能以及有机荧光材料的光功能特性,制备了能够同时激发和收集多种荧光的微纳光纤,并将之应用于高性能荧光光纤传感器的制备。通过选用不同荧光波长的有机材料与凝胶掺杂,制备了多荧光发射的光纤涂层材料,可控构筑了多组分荧光检测剂掺杂凝胶涂层。利用荧光光谱结合色度图分析,确定检测物与色坐标的关系,实现了多检测物的多通道荧光响应,为实现多荧光光纤传感器的可控构筑提供了有益的借鉴和指导意义。     

Gemini表面活性剂/C12En混合体系的界面吸附、扩张粘弹与泡沫稳定性

用表面张力法研究了阳离子gemini表面活性剂乙基-1, 2-双(十二烷基二甲基溴化铵)(简写为12-2-12)和非离子表面活性剂十二烷基聚氧乙烯醚(C₁₂E_n,其中n = 4, 10, 23)混合体系在气液界面上的吸附行为;用扩张流变技术研究了吸附膜的扩张粘弹行为,实验数据用Lucassen-van den Tempel (LVT)模型进行拟合并根据模型得到了极限弹性值.最后研究了混合体系的泡沫行为,用泡沫塌陷到初始高度一半所对应的时间(t_1/2)来表征泡沫的稳定性.结果表明,所有的非离子表面活性剂C₁₂E_n均与12-2-12产生了吸引作用.在12-2-12浓度相同的情况下,混合吸附层中吸附分子的最小分子占据面积的顺序为12-2-12/C₁₂E₂₃ > 12-2-12/C₁₂E₁₀ > 12-2-12/C₁₂E₄,而极限弹性的顺序为ε_{0, fit}(12-2-12/C₁₂E₄) > ε_{0, fit}(12-2-12/C₁₂E₁₀) > ε_{0, fit}(12-2-12/C₁₂E₂₃).与单组分12-2-12形成的吸附膜相比,只有12-2-12/C₁₂E₄形成更加紧密的结构.具有较小亲水头基的非离子表面活性剂C₁₂E₄的加入,可增强12-2-12吸附膜的弹性,进而增强了对应体系泡沫的稳定性.     

A Posteriori Error Analysis of a Fully-Mixed Finite Element Method for a Two-Dimensional Fluid-Solid Interaction Problem

In this paper we develop an a posteriori error analysis of a fully-mixed finite element method for a fluid-solid interaction problem in 2D. The media are governed by the elastodynamic and acoustic equations in time-harmonic regime, respectively, the transmission conditions are given by the equilibrium of forces and the equality of the corresponding normal displacements, and the fluid is supposed to occupy an annular region surrounding the solid, so that a Robin boundary condition imitating the behavior of the Sommerfeld condition is imposed on its exterior boundary. Dual-mixed approaches are applied in both domains, and the governing equations are employed to eliminate the displacement u of the solid and the pressure $p$ of the fluid. In addition, since both transmission conditions become essential, they are enforced weakly by means of two suitable Lagrange multipliers. The unknowns of the solid and the fluid are then approximated by a conforming Galerkin scheme defined in terms of PEERS elements in the solid, Raviart-Thomas of lowest order in the fluid, and continuous piecewise linear functions on the boundary. As the main contribution of this work, we derive a reliable and efficient residual-based a posteriori error estimator for the aforedescribed coupled problem. Some numerical results confirming the properties of the estimator are also reported.     

Finite Element Approximations of Symmetric Tensors on Simplicial Grids in $\mathbb{R}^n$: The Higher Order Case

The design of mixed finite element methods in linear elasticity with symmetric stress approximations has been a longstanding open problem until Arnold and Winther designed the first family of mixed finite elements where the discrete stress space is the space of $H(div, Ω\;\mathbb{S}) — P_{k+1}$ tensors whose divergence is a $P_{k-1}$ polynomial on each triangle for $k$ ≥ 2. Such a two dimensional family was extended, by Arnold, Awanou and Winther, to a three dimensional family of mixed elements where the discrete stress space is the space of $H(div, Ω\;\mathbb{S}) — P_{k+2}$ tensors, whose divergence is a $P_{k-1}$ polynomial on each tetrahedron for $k$ ≥ 2. In this paper, we are able to construct, in a unified fashion, mixed finite element methods with symmetric stress approximations on an arbitrary simplex in $\mathbb{R}^n$ for any space dimension. On the contrary, the discrete stress space here is the space of $H(div, Ω\;\mathbb{S}) — P_k$ tensors, and the discrete displacement space here is the space of $L²(Ω ; \mathbb{R}^n) — P_{k-1}$ vectors for $k ≥ n$+1. These finite element spaces are defined with respect to an arbitrary simplicial triangulation of the domain, and can be regarded as extensions to any dimension of those in two and three dimensions by Hu and Zhang.     

Weak Convergence Theorems for Mixed Type Asymptotically Nonexpansive Mappings

The purpose of this paper is to prove some weak convergence theorems for mixed type asymptotically nonexpansive mappings with mean errors in uniformly convex Banach spaces. The results presented in this paper extend the corresponding results in the references.     

水体高光谱反演混合光谱空间信息分解模型研究

水体高光谱中的混合效应问题是水体定量遥感中的难点。已有研究表明,仅依赖标量光谱信息难以解决复杂的水体混合光谱问题。广域水体污染物除光谱信息之外,还具有明显的空间分布特性。充分利用其空间维信息,可以作为遥感光谱维信息的有益补充,有利于水体复杂光谱的解混。以巢湖为例,HJ-1A HSI高光谱数据为数据源,辅以水面光谱测量数据,在空间地统计学和遗传算法理论基础上,利用地统计学中的变异函数模拟相邻空间两像元的分布差异,将邻域像元空间变异函数作为遗传算法目标函数的约束条件,建立基于协同克里格遗传算法的湖泊水体高光谱反演混合光谱空间信息分解模型,并对悬浮物浓度反演结果进行检验。结果显示,与常规混合光谱分解模型相比,混合光谱空间信息分解模型对悬浮物浓度的预测值与实测值相关系数为0.82,均方根误差9.25 mg·L-1,相关系数提高了8.9%,均方根误差下降了2.78 mg·L-1,表明该模型对悬浮物浓度具有较强的预测能力。该方法将水体的空间信息与光谱信息有效结合,可以避免水色参数光谱信号弱导致反演结果失真,同时由于高光谱波段多、信息量大,带来信息提取计算量大而复杂等问题,也为复杂水体混合光谱模型的求解和模型反演精度的提高提供了有效途径。     

纤维素菌体残留物提取类腐殖质的红外光谱研究

微生物驱动下,纤维素分解及转化在腐殖质形成中具有重要作用。采用红外光谱辅以元素分析的技术手段对单一真菌(木霉、青霉和黑曲霉)及复合菌液体摇瓶培养70 d后菌体残留物的类腐殖质(类胡敏酸HLA和类胡敏素)结构进行了分析对比。结果表明：(1)两技术手段的结合有助于菌体残留物HLA分子结构的阐明,然而在表征残留物类Hu结构方面,尚需进一步探讨;(2)木霉有利于其所形成菌体残留物HLA分子的缩聚作用,而青霉则更有利于该组分的降解;(3)青霉和复合菌对残留物HLA分子表现为氧化降解作用;(4)复合菌和黑曲霉均有助于培养液无机氮化合物向残留物HLA和类Hu组分中有机氮成分的转移,促使其氨基C含量增加,为腐殖化进程提供氮源。     

混合菁染料J-聚集体的光谱性能研究

对2种混合菁染料吸附在溴化银颗粒表面形成的J-聚集体的反射光谱及感光性能与对应菁染料单独吸附在溴化银颗粒表面进行了对比研究。用紫外-可见分光光计测定了菁染料吸附在溴化银颗粒表面形成J-聚集体的反射光谱。结果表明:2种混合菁染料吸附在溴化银颗粒表面形成的J-聚集体的反射光谱分别具有2个最大峰值波长,并且与对应菁染料单独使用时的峰值波长相一致。2种混和菁染料的感光性能比对应菁染料单独使用时有较大提高。