Finite Difference Time Domain Analysis of Diffusion Equations with Nonuniform Grids for Time-Resolved Reflectance of an Optical Pulse in Three-Dimensional Scattering Medium

An integral form of diffusion equations and their finite difference time domain (FDTD) analysis have been formulated. The analysis is extended to FDTD analysis with nonuniform grids in three-dimensional (3-D) scattering medium. It has been confirmed that 600 time steps in calculation sequences of the time-resolved reflectance for 3-D medium 80 × 80 × 30 mm³ in volume is completed within 4 seconds by utilizing 2³ and 4³ mm³ nonuniform cubic grids, when a conventional personal computer with 3 GHz CPU clock is used. The conditions for keeping numerical accuracies comparable to those in 2³ mm³ uniform grids are made clear. The proposed analysis greatly reduces time to run and memory space in 3-D scattering medium numerical analysis.     

Pruned optical banyan networks on vertical stacking scheme for faster connection establishment

In this paper, we address the issue of faster connection establishment in a large vertically stacked optical Banyan (VSOB) network. The best known global routing algorithm, which turns an N × N crosstalk-free VSOB network into a rearrangeably non-blocking one, has time complexity O (NlogN). This is quite large compared to O (NlogN) time complexity of a single plane banyan network, which is a self-routing network with very high blocking probability. For a large size of switching network this O (NlogN) time complexity may result unacceptably long delay. Therefore, an optical network with very low blocking probability and O (NlogN) time complexity will be useful. Previously proposed Plane Fixed Routing (PFR) algorithm has O (logN) time complexity but results in higher than 2% blocking probability with zero-crosstalk constraint for a network as large as 4096 × 4096 at full load. In this paper, first we propose the pruning of VSOB networks that reduces the hardware cost by almost 30%. The networks can still use the PFR algorithm and results in the same blocking probability. However, we show that the blocking probability can be reduced dramatically while keeping the optimum time complexity O (logN) by allowing only a small amount of crosstalk. Then, we propose a new kind of switching networks in which extra regular banyan planes have been added with the pruned VBOS (P-VSOB) networks. Necessary routing algorithms, namely, PFR_RS and PFR_LS show that this new switching network can reduce the blocking probability to very low value even with zero-crosstalk constraint while keeping the hardware cost 3almost the same as for P-VSOB networks. Both these algorithms also have time complexity O (NlogN).     

Host–guest and guest–guest interactions in noble gas hydrates

The encapsulation of noble gas atoms, helium, neon, argon and krypton in dodecahedral (DD) and its fused cages is studied using the dispersion corrected density functional theoretical method employing B97-D functional and cc-pVTZ basis set. The influence of an adjacent cage and the presence of a guest atom therein on the host–guest and the guest–guest interactions in noble gas hydrates are investigated. It is revealed that the host–guest interaction increases with an increase in the size of the encapsulated atom. The feasibility of encapsulation of guest species is analysed in terms of change in enthalpy (?H) and Gibbs free energy (?G). The results indicate that Kr@DD is stable at a relatively high temperature and low pressure (260 K, 1 atm), whereas the encapsulation of Ne and Ar at the same temperature requires high pressure (～100 atm). It is also found that the values of ?H and ?G for the encapsulation do not depend on the presence of an adjacent cage or the guest species trapped in the neighbouring cavity.     

Strings fromN=2 gauged Wess-Zumino-Witten models

We present an algebraic approach to string theory. An embedding ofsl(2|1) in a super Lie algebra together with a grading on the Lie algebra determines a nilpotent subalgebra of the super Lie algebra. Chirally gauging this subalgebra in the corresponding Wess-Zumino-Witten model, breaks the affine symmetry of the Wess-Zumino-Witten model to some extension of theN=2 superconformal algebra. The extension is completely determined by thesl(2|1) embedding. The realization of the superconformal algebra is determined by the grading. For a particular choice of grading, one obtains in this way, after twisting, the BRST structure of a string theory. We classify all embeddings ofsl(2|1) into Lie super algebras and give a detailed account of the branching of the adjoint representation. This provides an exhaustive classification and characterization of both all extendedN=2 superconformal algebras and all string theories which can be obtained in this way.     

From 2D hyperbolic forests to 3D Euclidean entangled thickets

A method is developed to construct and analyse a wide class of graphs embedded in Euclidean 3D space, including multiply-connected and entangled examples. The graphs are derived via embeddings of infinite families of trees (forests) in the hyperbolic plane, and subsequent folding into triply periodic minimal surfaces, including the P, D, gyroid and H surfaces. Some of these graphs are natural generalisations of bicontinuous topologies to bi-, tri-, quadra- and octa-continuous forms. Interwoven layer graphs and periodic sets of finite clusters also emerge from the algorithm. Many of the graphs are chiral. The generated graphs are compared with some organo-metallic molecular crystals with multiple frameworks and molecular mesophases found in copolymer melts. Received 10 December 1999     

Organic LED device based on PtOEP phosphor without doping in host material

Electroluminescence (EL) and photoluminescence (PL) have been studied on multi-layer organic light-emitting diode (OLED) devices based on phosphorescent platinum octaethyl porphine (PtOEP) molecule. A multi-layer OLED (called Pt5) which has 100% PtOEP without doping in host as the emitting layer is investigated and compared its EL and PL characteristics with those of the other OLEDs (Pt2 and Pt3) with emitting layer of PtOEP doped in 4,4′-N,N′-dicarbazole-biphenyl (CBP) host material. It is observed that Pt5 shows a lower EL efficiency than Pt2 and Pt3. Three broad EL bands are observed at 500, 527 and 570 nm in the multi-layer device in addition to red sharp EL band due to PtOEP in Pt5, while only the red PtOEP EL is observed in Pt2 and Pt3. The 500, 527 and 570 nm EL peaks arise from absorption of the broad 525 nm Alq₃ emission band by PtOEP layer. The emission from the Alq₃ electron-transport layer is caused by the carrier leakage from the hole-blocking BAlq layer. The intensity of red EL due to PtOEP is much weaker in Pt5 than in Pt2. Taking into account the result of PL, it is suggested that highly efficient energy transfer from CBP host to PtOEP guest occurs in Pt2 and Pt3, giving rise to higher PtOEP luminance, while concentration quenching occurs in PtOEP layer in Pt5.     

Synthesis of novel bis(β‐cyclodextrin)s linked with aromatic diamine and their molecular recognition with model substrates

Novel β‐cyclodextrin (β‐CD) dimers with aromatic diamine linkers, 1,3‐(aminomethyl)‐benzylamine‐bridged bis(6‐amino‐6‐deoxy‐β‐CD) (2) , 4,4′‐diaminodiphenylmethano‐bridged bis(6‐amino‐6‐deoxy‐β‐CD) (3) , and 4,4′‐ ethylenedianiline‐bridged bis(6‐amino‐6‐deoxy‐β‐CD) (4) , were synthesized. The inclusion complexation behaviors of these compounds, together with 4,4′‐aminophenyl ethyl‐bridged bis(6‐amino‐6‐deoxy‐β‐CD) (5) , with substrates such as acridine red (AR), neutral red (NR), ammonium 8‐anilino‐1‐naphthalenesulfonate (ANS), sodium 2‐(p‐toluidinyl) naphthalenesulfonate (TNS), rhodamine B (RhB), and brilliant green (BG), were investigated by ultraviolet, fluorescence, circular dichroism, and 2D NMR spectroscopy. The results indicated that the two linked CD units cooperatively bound to a guest, and the molecular binding affinity toward substrates, especially curved guest ANS and linear guests such as NR and AR, was increased. The linker length between two CD units played a crucial role in the molecular recognition of the hosts with guest dyes. The binding constants of the hosts for AR, TNS, ANS, and RhB decreased with increasing linker length in hosts 2‐4 . Moreover, structurally similar hosts 3 and 5 exhibited very different binding behavior for the guests. Host 5 showed much higher Ks values toward positively charged guests and lower Ks toward negatively charged guests than host 3 . The 2D NMR spectra of hosts 3 and 5 with RhB were acquired to understand the binding difference between 3 and 5 . The molecular binding ability and selectivity of model substrates by these hosts were sufficiently investigated to reveal not only the cooperative contributions of the linker group and CD cavities upon inclusion complexation with dye guest molecules, but also the controlling factors for the molecular selective binding. Copyright © 2008 John Wiley & Sons, Ltd.     

Dirac fermions on a disclinated flexible surface

A self-consisting gauge-theory approach to describe Dirac fermions on flexible surfaces with a disclination is formulated. The elastic surfaces are considered as embeddings into R ³ and a disclination is incorporated through a topologically nontrivial gauge field of the local SO(3) group which generates the metric with conical singularity. A smoothing of the conical singularity on flexible surfaces is naturally accounted for by regarding the upper half of two-sheet hyperboloid as an elasticity-induced embedding. The availability of the zeromode solution to the Dirac equation is analyzed.     

一种非结构/结构多层混合网格方法及其应用

对于粘性绕流的数值模拟,在自适应直角网格基础上,结合三角形非结构网格和结构化网格,利用其各自的优势和特点,提出一种生成混合杂交网格的思路和方法.在物面附近生成适合粘性流计算的大长宽比结构化网格,在远场分布自适应直角网格,快速离散计算空间.对于复杂的多体问题,采用三角形网格来连接各体网格,并运用网格合并的方法,保证各网格之间的光滑过渡与连接,提高网格质量.针对一些二维、三维外形的绕流问题,在上述网格基础上,采用B-L代数湍流模型和中心有限体积法,完成Navier-Stokes和Euler方程数值模拟的对比计算,结果表明网格生成和流场计算是正确的.     

The synthesis of generalised Mach–Zehnder optical switches based on multimode interference (MMI) couplers

The space-division switching properties of a generalised Mach–Zehnder photonic switch are examined in this paper. It is shown for the first time that such an N × N switch can only produce N independent point-to-point switching states. A method that unambiguously identifies these states and thereby provides a synthesis technique for the design of these switches is presented.     

Deformations of the embedding of the SU(2) monopole solution in SU (3)

This paper is concerned with static Yang-Mills-Higgs fields, in the Prasad-Sommerfield limit of no Higgs self-interaction. One can obtain SU (3) multipole solutions from SU(2) solutions by embedding, in several different ways. In some of these cases, the embedding belongs to a family of SU(3) solutions that are not all embeddings; in other words, some embeddings can be deformed into non-embeddings. The simplest case, an embedding of the SU(2) spherically symmetric monopole, is studied with the aid of the twistor construction procedure. The family of axially symmetric SU(3) solutions to which it belongs is described.     

The Yamada polynomial of spacial graphs and knit algebras

The Yamada polynomial for embeddings of graphs is widely generalized by using knit semigroups and polytangles. To construct and investigate them, we use a diagrammatic method combined with the theory of algebrasH _N,M(a,q), which are quotients of knit semigroups and are generalizations of Iwahori-Hecke algebrasH _n(q). Our invariants are versions of Turaev-Reshetikhin's invariants for ribbon graphs, but our construction is more specific and computable.This research was supported in part by NSF grant DMS-9100383     

On coordination and continuous hawk-dove games on small-world networks

It is argued that small-world networks are more suitable than ordinary graphs in modelling the diffusion of a concept (e.g. a technology, a disease, a tradition, ...). The coordination game with two strategies is studied on small-world networks, and it is shown that the time needed for a concept to dominate almost all of the network is of order , where N is the number of vertices. This result is different from regular graphs and from a result obtained by Young. The reason for the difference is explained. Continuous hawk-dove game is defined and a corresponding dynamical system is derived. Its steady state and stability are studied. Replicator dynamics for continuous hawk-dove game is derived without the concept of population. The resulting finite difference equation is studied. Finally continuous hawk-dove is simulated on small-world networks using Nash updating rule. The system is 2-cyclic for all the studied range. Received 8 July 2000 and Received in final form 23 July 2000     

Algebraic isometric embeddings of charged spherically symmetric space-times

Recent results concerning isometric embeddings of charged spherically symmetric space-times as algebraic 4-surfaces of a pseudo-Euclidean ⁿ are given. Several problems arising in algebraic isometric embeddings of space-times with horizons are analyzed by studying the Reissner-Nordström solution. The connection between the images of radial null geodesics and the possibility of extending the algebraic isometric embedding through a horizon is studied in detail.     

Spectroscopic and thermal studies on the inclusion of trans‐cinnamic acid and a number of its hydroxyl‐derivatives with α, β and γ‐cyclodextrins molecules

The inclusion compounds of α‐, β‐ and γ‐cyclodextrins (α‐CD, β‐CD and γ‐CD) with trans‐cinnamic acid (t‐CIA), 3‐hydroxy‐trans‐cinnamic acid (t‐3OHCIA), 4‐hydroxy‐trans‐cinnamic acid (t‐4OHCIA) and 3,4‐dihydroxy‐trans‐cinnamic acid (t‐3,4OHCIA) were prepared and characterized, in the solid state, by means of thermogravimetry and Raman spectroscopy. The effects of the inclusion process on the guest molecules and on the hydrogen bond interactions of the guest were studied by monitoring sensitive vibrational modes, such as CO, CC and ring C H stretching modes. By combining Raman and TG data with ab initio calculations and information from CSD database on similar compounds, inclusion geometries for the different compounds are proposed. The size of the host cavity and the maximization of host/guest hydrogen‐bonding contacts appear to be the main factors determining the inclusion geometries. Copyright © 2009 John Wiley & Sons, Ltd.     

Incremental routing strategy on scale-free networks

The most important function of a network is for transporting traffic. Due to the low traffic capacity of network systems under the global shortest path routing, plenty of heuristic routing strategies are emerging. In this paper, we propose a heuristic routing strategy called the incremental routing algorithm to improve the traffic capacity of complex networks. We divide the routing process into N$N$(the network size) steps and, at each step, we heuristically calculate all the routes for one source node considering both the dynamic efficient betweenness centrality and node degree information. We do extensive simulations on scale-free networks to confirm the effectiveness of the proposed incremental routing strategy. The simulation results show that the traffic capacity has been enhanced by a substantial factor at the expense of a slight lengthening in the average path.     

Duality of Orthogonal and Symplectic Matrix Integrals and Quaternionic Feynman Graphs

We present an asymptotic expansion for quaternionic self-adjoint matrix integrals. The Feynman diagrams appearing in the expansion are ordinary ribbon graphs and their non-orientable counterparts. We show that the 2N×2N Gaussian Orthogonal Ensemble (GOE) and N×N Gaussian Symplectic Ensemble (GSE) have exactly the same expansion term by term, except that the contributions from graphs on a non-orientable surface with odd Euler characteristic carry the opposite sign. As an application, we give a new topological proof of the known duality for correlations of characteristic polynomials, demonstrating that this duality is equivalent to Poincaré duality of graphs drawn on a compact surface. Another consequence of our graphical expansion formula is a simple and simultaneous (re)derivation of the Central Limit Theorem for GOE, GUE (Gaussian Unitary Ensemble) and GSE: The three cases have exactly the same graphical limiting formula except for an overall constant that represents the type of the ensemble.Research supported by NSF Grant DMS-9971371 and the University of California, Davis.Research supported by the University of California, Davis.     

Energy transfer dynamics between Alq3 and CdTeS/ZnS core shell nanocrystals

The photoluminescence (PL) properties of the guest-host films, using CdTeS/ZnS core shell quantum dots (QDs) as the guest and organic small-molecule material Alq₃ as the host, are studied by steady-state and time-resolved PL spectroscopy. Both the relative intensity and the PL lifetime are intensively dependent on the weight ratio of Alq₃ and CdTeS/ZnS QDs. The detailed analysis provides clear evidence for a Förster energy transfer from Alq₃ host to QDs guest, based on the nonradiative resonant transfer mechanism. The results are relevant to the application of hybrid organic/inorganic systems to OLEDs.     

(2+1)-D SU(3)0++ Glueball Wavefunction

Adopting connected graphs as independent graphs, the(2+1)-D SU(3) 0⁺⁺ glueball wavefunction is calculated using scheme of truncating eigenvalue equations.     

Theoretical insights into the host–guest interactions between [6]cycloparaphenyleneacetylene and its anthracene‐containing derivative and fullerene C70

The host–guest complexes formed with [6]cycloparaphenyleneacetylene ([6]CPPA) and its anthracene‐containing derivative ([6]CPPAs) hosts and fullerene C₇₀ guest were explored by density functional calculations. Besides two previously reported configurations in which C₇₀ guest is standing or lying in the cavity of the host, we found a new kind of configuration in which C₇₀ guest is half‐lying in the cavity of the host. More interestingly, the calculated results revealed that the fine‐tuning deformations occur readily during the formations of the complexes, suggesting that both [6]CPPA and [6]CPPAs are highly elastic host molecules. The large host–guest binding energies indicate that both two host molecules, [6]CPPA and [6]CPPAs, have excellent encapsulation ability for C₇₀ guest, and the [6]CPPAs even has much better encapsulation ability for C₇₀ than [6]CPPA. Furthermore, the host–guest interactions regions were detected and visualized in real space based on the electron density and reduced density gradient. Additionally, ¹H NMR spectra of those three different kinds of configurations mentioned earlier have been calculated with gage‐independent atomic orbital method, which may be helpful for further experimental characterizations in future. Copyright © 2014 John Wiley & Sons, Ltd.