基于平板波导的小型红外光栅光谱仪光学设计

为实现红外光谱仪器的小型化,通过分析现有小型光谱仪,提出了一种基于平板波导的小型红外光栅光谱仪的设计方法。平板波导光谱仪的小型化原理与一般的微小型光谱仪不同。在平板波导光谱仪中,光束被限制在一层薄薄的平板波导介质中传播,看起来像是整个光学系统被压扁了。在垂直于平板波导的方向上光学元件的尺寸可以做到很小,从而显著减小光学系统的尺寸。该系统的设计可分为Czerny-Turner结构设计、波导结构设计。先根据像差理论设计Czerny-Turner结构,目标是保证光谱分辨率及校正像差;然后根据几何光学理论设计波导结构,包括平板波导和两个柱面透镜,目标是压缩光束并校正像散;最后将它们输入Zemax软件中进行综合优化,以获得最优的光学系统。据此方法设计了一个平板波导红外光栅光谱仪,工作波段为8~12 μm,数值孔径为0.22,采用线阵探测器。通过Zemax软件对结果进行分析和评价,表明仪器光学系统的尺寸为130 mm×125 mm×20 mm,工作波段内光谱分辨率达到80 nm,满足设计指标要求。证明了该优化设计方法是可行的,所得系统尺寸小、性能高。     

The effect of total reflection in PLIF imaging of annular thin films

Planar laser-induced fluorescence (PLIF) imaging techniques are increasingly used to study wavy annular flows in vertical and horizontal pipes. We present a ray-tracing study that analyzes the imaging properties of the PLIF technique for uniform and wavy annular films. Part of the emitted fluorescence will hit the water–air interface at angles greater than the critical angle of total reflection. As a consequence, PLIF imaging probes the film twice: From bottom to top and then again from top to bottom. Deflected fluorescence widens PLIF images of uniform films by about 30%. Surface waves further increase the contribution of deflected rays to the overall signal. At the steep slopes of large amplitude axial waves, total reflection might widen PLIF signals by up to a factor of two.     

Planar Hall effect in biosensor with a tilted angle of the cross-junction

A typical planar Hall effect (PHE) sensor junction consists of two Hall bars that the bars appear normal to each other and the junction can have the required four terminals for current and voltage measurements. We are now introducing a tilted angle of the cross-junction and studying the role of the PHE therein. The results show that although there is a tilted angle of the cross-junction, the PHE voltage is remained constant. The result is interpreted by assuming the sensor material with the behavior of a basic single domain structure under the external magnetic field reversals. The calculations of the model are found to be in good concurrence with the experimental results.     

平面光波导器件时域有限差分束传输法分析中边界和初始条件的处理

从慢变包络（SVEA）时域光传输方程出发,对比了综合道格拉斯（GD）和传统的中心差分（CN）两种离散化格式,指出GD法比CN法精度有了很大提高.重点讨论了GD法的TD-BPM边界处理问题,给出了吸收边界和透明边界离散的显式和隐式表达式,分析并确定了交替方向隐式法（ADIM）的边界处理方式;同时,对激励源加入的连接边界进行了仔细讨论.结果表明对于隐式GD-TD-BPM法边界处理应采用隐式,中间激励更能反映光波导反射场的情况.     

An imaging pH optode for cell studies based on covalent attachment of 8-hydroxypyrene-1,3,6-trisulfonate to amino cellulose acetate films

The objective of this study was to create a thin film optode for fast pH measurements that meets the requirements for imaging pH-responses from cells as well as for a future hybrid design for detection of multiple analytes simultaneously. The sensor is based on the covalent attachment of 8-hydroxypyrene-1,3,6-trisulfonate (HPTS) to a film forming cellulose acetate material through a sulfonamide linkage. The synthesis routes of the cellulose material and regio-specific covalent attachment of the dye are described in detail. The sensor was sterilized in two different ways and showed excellent biocompatibility with Chinese hamster ovary cells. Imprints from cells and μm thin cell extensions were visualized when altering pH of the surrounding solution. The sensor was tested together with time-dependent sigmoidal calibrations giving pH determinations with an exceptional precision and accuracy during measurement within pH 6-8. The precision of the optode, calculated as pooled S.D. (n = 8) according to IUPAC recommendations between pH 6.641 and 7.742 was 0.0029. The accuracy was significantly better than the electrode used as reference during the measurements. The response time (0-95%) was 100 s between pH 6.641 and 7.742 and the reverse response (95-0%) was 80 s. The sensor shows great potential for extra-cellular pH determination over time during cell growth and pharmacological exposure.     

Edge-choosability of planar graphs without adjacent triangles or without 7-cycles

A graph G is edge-L-colorable, if for a given edge assignment L={L(e):e∈E(G)}, there exists a proper edge-coloring ? of G such that ?(e)∈L(e) for all e∈E(G). If G is edge-L-colorable for every edge assignment L with |L(e)|≥k for e∈E(G), then G is said to be edge-k-choosable. In this paper, we prove that if G is a planar graph with maximum degree Δ(G)≠5 and without adjacent 3-cycles, or with maximum degree Δ(G)≠5,6 and without 7-cycles, then G is edge-(Δ(G)+1)-choosable.     

Equitable list coloring of planar graphs without 4- and 6-cycles

A graph G is equitably k-choosable if for any k-uniform list assignment L, there exists an L-colorable of G such that each color appears on at most vertices. Kostochka, Pelsmajer and West introduced this notion and conjectured that G is equitably k-choosable for k>Δ(G). We prove this for planar graphs with Δ(G)≥6 and no 4- or 6-cycles.     

Polychromatic Colorings of Plane Graphs

We show that the vertices of any plane graph in which every face is incident to at least g vertices can be colored by ⌊(3g−5)/4⌋ colors so that every color appears in every face. This is nearly tight, as there are plane graphs where all faces are incident to at least g vertices and that admit no vertex coloring of this type with more than ⌊(3g+1)/4⌋ colors. We further show that the problem of determining whether a plane graph admits a vertex coloring by k colors in which all colors appear in every face is in ℘ for k=2 and is -complete for k=3,4. We refine this result for polychromatic 3-colorings restricted to 2-connected graphs which have face sizes from a prescribed (possibly infinite) set of integers. Thereby we find an almost complete characterization of these sets of integers (face sizes) for which the corresponding decision problem is in ℘, and for the others it is -complete. Research of N. Alon was supported in part by the Israel Science Foundation, by a USA–Israeli BSF grant, and by the Hermann Minkowski Minerva Center for Geometry at Tel Aviv University. Research of R. Berke was supported in part by JSPS Global COE program “Computationism as a Foundation for the Sciences.” Research of K. Buchin and M. Buchin was supported by the Netherlands’ Organisation for Scientific Research (NWO) under BRICKS/FOCUS project no. 642.065.503. Research of P. Csorba was supported by DIAMANT, an NWO mathematics cluster. Research of B. Speckmann was supported by the Netherlands’ Organisation for Scientific Research (NWO) under project no. 639.022.707.     

Weighted coloring on planar, bipartite and split graphs: Complexity and approximation

We study complexity and approximation of min weighted node coloring in planar, bipartite and split graphs. We show that this problem is NP-hard in planar graphs, even if they are triangle-free and their maximum degree is bounded above by 4. Then, we prove that min weighted node coloring is NP-hard in P₈-free bipartite graphs, but polynomial for P₅-free bipartite graphs. We next focus on approximability in general bipartite graphs and improve earlier approximation results by giving approximation ratios matching inapproximability bounds. We next deal with min weighted edge coloring in bipartite graphs. We show that this problem remains strongly NP-hard, even in the case where the input graph is both cubic and planar. Furthermore, we provide an inapproximability bound of 7/6−ε, for any ε>0 and we give an approximation algorithm with the same ratio. Finally, we show that min weighted node coloring in split graphs can be solved by a polynomial time approximation scheme.     

Planar graphs with maximum degree 8 and without adjacent triangles are 9-totally-colorable

The Total Coloring Conjecture, in short, TCC, says that every simple graph is (Δ+2)-totally-colorable where Δ is the maximum degree of the graph. Even for planar graphs this conjecture has not been completely settled yet. However, every planar graph with Δ≥9 has been proved to be (Δ+1)-totally-colorable. In this paper, we prove that planar graphs with maximum degree 8 and without adjacent triangles are 9-totally-colorable.