Single particle versus ensemble average: from power-law intermittency of a single quantum dot to quasistretched exponential fluorescence decay of an ensemble

Light-induced diffusion-controlled electron transfer is proposed as an underlying mechanism for the intermittency (power law and breakdown) of a single quantum dot and ensemble-averaged fluorescence decay. The intensity decay can be approximated to a stretched exponential expression. The physical links to the free energy gap, reorganization energy, electronic coupling, and diffusion correlation times are discussed. A procedure is described for extracting these molecular-based parameters from experiments and is demonstrated with examples using existing data.     

Synthesis and Characterization of (βDiketonate)(7-norbornadienyl acetate)Copper(l) Complexes,Single-Crystal Structure of (hfac)Cu(7-AcO-NBD)

Copper(I) complexes of general formula (β-diketonate)Cu(7-AcO-NBD), where 7-AcO-NBD = 7-norbornadienyl acetate and β-diketonate = 1,1,1,5,5,5-hexafluoro-2,4-pentanedionate (1), 1,1,1-trifluoro-2,4-pentanedionate (2), 2,4-pentanedionate (3), 4,4,4-trifluoro-1-(2-thienyl)-1,3-butanedionate (4), 4,4,4-trifluoro-1-phenyl-1,3-butanedionate (5), were prepared from reactions of CuCl with Na(β-diketonate) in the presence of 7-AcO-NBD. AH compounds were characterized by elemental analyses, ¹H, ¹³C, ¹⁹F NMR and IR spectra. Single-crystal strucutre of compound 1 was determined by X-ray diffraction analysis that showed a mononuclear copper species with coordination of a chelating β-diketonate ligand through two oxygen atoms and the 7-AcO-NBD through its C? C double bond and an oxygen atom in the solid state. For compound 1, the crystal data are: triclinic, space group $ {\rm P}\bar 1 $, a= 5.4519(14) Å, b= 11.852(3) Å, c= 13.304(3) Å, α = 74.721(20)° β = 80.220(20)°, γ= 76.848(19)°, Z = 2, R_F = 0.060 and R_w = 0.064. Hot-wall chemical vapor deposition experiments revealed that compound 1 is suitable as a precursor for deposition of copper films in the temperature range 170–260 °C.     

Intrinsic impurities in glass alkali-vapor cells

We report NMR measurements of metallic (133)Cs in glass cells. The solid-liquid phase transition was studied by observing the NMR peaks arising from these two phases; surprisingly, many cells yielded two additional NMR peaks below the melting point. We attribute these signals to two distinct impurities which can dissolve in the liquid alkali metal and affect its chemical shift. Intentional contamination of cesium cells with O(2) confirms this hypothesis for one peak. The other contaminant remains unknown but can appear in evacuated cells. Similar effects have been seen in (87)Rb cells.     

Circuits of Each Length in Tournaments

A tournament is a directed graph whose underlying graph is a complete graph. A circuit is an alternating sequence of vertices and arcs of the form v ₁, a ₁, v ₂, a ₂, v ₃, . . . , v _n-1, a _n-1, v _n in which vertex v _n  = v ₁, arc a _i  = v _i v _i+1 for i = 1, 2, . . . , n?1, and \({a_i \neq a_j}\) if \({i \neq j}\) . In this paper, we shall show that every tournament T _n in a subclass of tournaments has a circuit of each length k for \({3 \leqslant k \leqslant \theta(T_n)}\) , where \({\theta(T_n) = \frac{n(n-1)}{2}-3}\) if n is odd and \({\theta(T_n) = \frac{n(n-1)}{2}-\frac{n}{2}}\) otherwise. Note that a graph having θ(G) > n can be used as a host graph on embedding cycles with lengths larger than n to it if congestions are allowed only on vertices.     

On a coupled system of reaction–diffusion-transport equations arising from catalytic converter

This paper is concerned with two mathematical models which describe the transient behavior of a catalytic converter in automobile engineering. The first model consists of a coupled system of a heat-conduction equation and two integral equations while the second model involves only one integral equation. It is shown that for any nonnegative initial and boundary functions the three-equation model has a unique bounded global solution while the solution of the two-equation model blows up in finite time. The proof for the global existence and finite-time blow-up property of the solution is by the method of upper and lower solutions and its associated monotone iteration. This method can be used to develop computational algorithms for numerical solutions of the coupled systems.     

Direct contact versus solvent-shared ion pairs in NiCl2 electrolytes monitored by multiplet effects at Ni(II) L edge X-ray absorption

We investigate the local electronic structure in aqueous NiCl2 electrolytes by Ni L edge X-ray absorption spectroscopy. The experimental findings are interpreted in conjunction with multiplet calculations of the electronic structure and the resulting spectral shape. In contrast to the situation in the solid, the electronic structure in the electrolyte reflects the absence of direct contact Ni-Cl ion pairs. We observe a systematic change of the intensity ratio of singlet- and triplet-related spectral features as a function of electrolyte concentration. These changes can be described theoretically by a change in the weight of transition matrix contributions with different symmetries. We interpret these findings as being due to progressive distortions of the local symmetry induced by solvent-shared ion pairs.     

Fluorescence intermittency of silicon nanocrystals and other quantum dots: a unified two-dimensional diffusion-controlled reaction model

We present a unified model involving two-dimensional diffusion-controlled reactions of both slow and fast reaction coordinates to elucidate the dynamic origin of fluorescence intermittency observed not just in quantum dots but also in organic chromphores and biomolecules. This improved model also solves the puzzling behavior of Si nanocrystals which display an unusually large m (exceeding 2) for the power-law decay of t(-m) and provides remedies for the deficiencies in existing models.     

Optically controllable bistable reflective liquid crystal display

This Letter demonstrates a photo-addressable, bistable reflective liquid crystal display that is based on a dye-doped liquid crystal (DDLC). Bistable bright and dark states can be attained using the 45 deg twisted nematic (TN) and photo-induced isotropic states (PHI) of the DDLC, respectively. Both the 45 deg TN and PHI states can exist stably for tens of hours, and each can be rapidly switched to the other by the isomerization effect using UV and green light. A bistable reflective liquid crystal display is simply fabricated, easily operated, and rapidly switched. It therefore has the potential to be used in portable information systems.     

Two thresholds of a batch arrival queueing system under modified T vacation policy with startup and closedown

This paper studies the operating characteristics of the variant of an M^[x]/G/1 vacation queue with startup and closedown times. After all the customers are served in the system exhaustively, the server shuts down (deactivates) by a closedown time, and then takes at most J vacations of constant time length T repeatedly until at least one customer is found waiting in the queue upon returning from a vacation. If at least one customer is present in the system when the server returns from a vacation, then the server reactivates and requires a startup time before providing the service. On the other hand, if no customers arrive by the end of the J th vacation, the server remains dormant in the system until at least one customer arrives. We will call the vacation policy modified T vacation policy. We derive the steady‐state probability distribution of the system size and the queue waiting time. Other system characteristics are also investigated. The long‐run average cost function per unit time is developed to determine the suitable thresholds of T and J that yield a minimum cost. Copyright © 2007 John Wiley & Sons, Ltd.