Optimal Groomings with Grooming Ratios Six and Seven

Grooming uniform all‐to‐all traffic in optical (SONET) rings with grooming ratio C requires the determination of a decomposition of the complete graph into subgraphs each having at most C edges. The drop cost of such a grooming is the total number of vertices of nonzero degree in these subgraphs, and the grooming is optimal when the drop cost is minimum. The determination of optimal C‐groomings has been considered for , and completely solved for . For , it has been shown that the lower bound for the drop cost of an optimal C‐grooming can be attained for almost all orders with 5 exceptions and 308 possible exceptions. For , there are infinitely many unsettled orders; especially the case is far from complete. In this paper, we show that the lower bound for the drop cost of a 6‐grooming can be attained for almost all orders by reducing the 308 possible exceptions to 3, and that the lower bound for the drop cost of a 7‐grooming can be attained for almost all orders with seven exceptions and 16 possible exceptions. Moreover, for the unsettled orders, we give upper bounds for the minimum drop costs.     

Forwarding and optical indices of 4-regular circulant networks

An all-to-all routing in a graph G is a set of oriented paths of G, with exactly one path for each ordered pair of vertices. The load of an edge under an all-to-all routing R is the number of times it is used (in either direction) by paths of R, and the maximum load of an edge is denoted by $\pi (G,R)$. The edge-forwarding index $\pi (G)$ is the minimum of $\pi (G,R)$ over all possible all-to-all routings R, and the arc-forwarding index $\overrightarrow{\pi }(G)$ is defined similarly by taking direction into consideration, where an arc is an ordered pair of adjacent vertices. Denote by $w(G,R)$ the minimum number of colours required to colour the paths of R such that any two paths having an edge in common receive distinct colours. The optical index $w(G)$ is defined to be the minimum of $w(G,R)$ over all possible R, and the directed optical index $\overrightarrow{w}(G)$ is defined similarly by requiring that any two paths having an arc in common receive distinct colours. In this paper we obtain lower and upper bounds on these four invariants for 4-regular circulant graphs with connection set $\{\pm 1,\pm s\}$, $1<s<n/2$. We give approximation algorithms with performance ratio a small constant for the corresponding forwarding index and routing and wavelength assignment problems for some families of 4-regular circulant graphs.     

New Entangled Coordination Networks Based on Charge‐Tunable Keggin‐Type Polyoxometalates

Investigation into a hydrothermal reaction system with transition‐metal (TM) ions, 1,4‐bis(1,2,4‐triazol‐1‐lmethyl)benzene (BBTZ) and various charge‐tunable Keggin‐type polyoxometalates (POMs) led to the preparation of four new entangled coordination networks, [Co^II(HBBTZ)(BBTZ)_2.5][PMo₁₂O₄₀] ( 1 ), [Cu^I(BBTZ)]₅[BW₁₂O₄₀] ? H₂O ( 2 ), [Cu^II(BBTZ)]₃[AsW^V₃W^VI₉O₄₀] ? 10 H₂O ( 3 ), and [Cu^II₅(BBTZ)₇(H₂O)₆][P₂W₂₂Cu₂O₇₇(OH)₂] ? 6 H₂O ( 4 ). All compounds were characterized by using elemental analysis, IR spectroscopy, thermogravimetric analysis, powder X‐ray diffraction, and single‐crystal X‐ray diffraction. The mixed valence of W centers in compound 3 was further confirmed by using XPS spectroscopy and bond‐valence sum calculations. In the structural analysis, the entangled networks of 1 – 4 demonstrate zipper‐closing packing, 3D polythreading, 3D polycatenation, and 3D self‐penetration, respectively. Moreover, with the enhancement of POM negative charges and the use of different TM types, the number of nodes in the coordination networks of 1 – 4 increased and the basic metal–organic building motifs changed from a 1D zipper‐type chain (in 1 ) to a 2D pseudorotaxane layer (in 2 ) to a 3D diamond‐like framework (in 3 ) and finally to a 3D self‐penetrating framework (in 4 ). The photocatalytic properties of compounds 1 – 4 for the degradation of methylene blue under UV light were also investigated; all compounds showed good catalytic activity and the photocatalytic activity order of Keggin‐type species was initially found to be {XMo₁₂O₄₀}>{XW₁₂O₄₀}>{XW_12?nTM_nO₄₀}.     

Evidence for the Chain‐Growth Synthesis of Statistical π‐Conjugated Donor–Acceptor Copolymers

The synthesis of a series of dithienosilole–benzotriazole donor–acceptor statistical copolymers with various donor–acceptor ratios is reported, prepared by Kumada catalyst‐transfer polymerization. Statistical copolymer structure is verified by ¹H NMR and optical absorption spectroscopy, and supported by density functional theory (DFT) calculations. The copolymers exhibit a single optical absorption band that lies between dithienosilole and benzotriazole homopolymers, which shifts with varying donor–acceptor content. A chain extension experiment using a partially consumed benzotriazole solution as a macroinitiator followed by addition of dithienosilole leads to the synthesis of a statistical dithienosilole–benzotriazole block copolymer from a pure benzotriazole block, demonstrating that both chain extension and simultaneous monomer incorporation are possible using this methodology.

     

Dual Sulfide–Disulfide Crosslinked Networks with Rapid and Room Temperature Self‐Healability

Polymer‐based crosslinked networks with intrinsic self‐repairing ability have emerged due to their built‐in ability to repair physical damages. Here, novel dual sulfide–disulfide crosslinked networks (s‐ssPxNs) are reported exhibiting rapid and room temperature self‐healability within seconds to minutes, with no extra healing agents and no change under any environmental conditions. The method to synthesize these self‐healable networks utilizes a combination of well‐known crosslinking chemistry: photoinduced thiol‐ene click‐type radical addition, generating lightly sulfide‐crosslinked polysulfide‐based networks with excess thiols, and their oxidation, creating dynamic disulfide crosslinkages to yield the dual s‐ssPxNs. The resulting s‐ssPxN networks show rapid self‐healing within 30 s to 30 min at room temperature, as well as self‐healing elasticity with reversible viscoelastic properties. These results, combined with tunable self‐healing kinetics, demonstrate the versatility of the method as a new means to synthesize smart multifunctional polymeric materials.

     

Topologically protected interface mode in plasmonic waveguide arrays

Recent realization of nontrivial topological phases in photonic systems has provided unprecedented opportunities in steering light flow in novel manners. Based on the Su–Schriffer–Heeger (SSH) model, a topologically protected optical mode was successfully demonstrated in a plasmonic waveguide array with a kinked interface that exhibits a robust nonspreading feature. However, under the same excitation conditions, another antikinked structure seemingly cannot support such a topological interface mode, which appears to be inconsistent with the SSH model. Theoretical calculations are carried out based on the coupled‐mode theory, in which the mode properties, excitation conditions, and the robustness are studied in detail. It is revealed that under the exact eigenstate excitations, both kinked and antikinked structures do support such robust topological interface modes; however, for a realistic single‐waveguide input only the kinked structure does so. It is concluded that the symmetry of interface eigenmodes plays a crucial role, and the odd eigenmode in a kinked structure offers the capacity to excite the nonspreading interface mode in the realistic excitation of a one‐waveguide input. Our finding deepens the understanding of mode excitation and propagation in coupled waveguide systems, and could open a new avenue in optical simulations and photonic designs.

     

Raman spectroscopy measurement of levofloxacin lactate in blood using an optical fiber nano‐probe

Liquid chromatography and mass spectrometry were time‐consuming and expensive as the main methods for the drug analysis at present, and the samples must be pretreated. The Raman spectroscopy measurement methods were fast and simple, so the Raman spectroscopy methods for the drug analysis were explored in this paper. An optical fiber nano‐probe coated with gold nanoparticles was fabricated and used with surface‐enhanced Raman spectroscopy (SERS) to measure levofloxacin lactate. The resulting SERS spectra of levofloxacin lactate in mouse blood that was detected by the optical fiber nano‐probe clearly showed the characteristic wave numbers of levofloxacin lactate, indicating that optical fiber nano‐probes can be used with spectral techniques to analyze drugs in vitro or potentially even in vivo. Copyright © 2015 John Wiley & Sons, Ltd.     

Phase‐preserved macroscopic visible‐light carpet cloaking beyond two dimensions

Transformation optics, a recent geometrical design strategy of light manipulation with both ray trajectories and optical phase controlled simultaneously, promises an invisibility cloaking device that can render a macroscopic object invisible even to a scientific instrument measuring optical phase. Recent “carpet” cloaks have extended their cloaking capability to broadband frequency ranges and macroscopic scales, but they only demonstrated the recovery of ray trajectories after passing through the cloaks, while whether the optical phase would reveal their existence still remains unverified. In this paper, a phase‐preserved macroscopic visible‐light carpet cloak is demonstrated in a geometrical construction beyond two dimensions. As an extension of previous two‐dimensional (2D) macroscopic carpet cloaks, this almost‐three‐dimensional carpet cloak exhibits three‐dimensional (3D) invisibility for illumination near its center (i.e. with a limited field of view), and its ideal wide‐angle invisibility performance is preserved in multiple 2D planes intersecting in the 3D space. Optical path length is measured with a broadband pulsed‐laser interferometer, which provides unique experimental evidence on the geometrical nature of transformation optics.