On the stability of a partially accessible multi‐station queue with state‐dependent routing

We consider a multi‐station queue with a multi‐class input process when any station is available for the service of only some (not all) customer classes. Upon arrival, any customer may choose one of its accessible stations according to some state‐dependent policy. We obtain simple stability criteria for this model in two particular cases when service rates are either station‐ or class‐independent. Then, we study a two‐station queue under general assumptions on service rates. Our proofs are based on the fluid approximation approach. This revised version was published online in June 2006 with corrections to the Cover Date.     

Phase contribution to dynamic gratings recorded in Er-doped fiber with saturable absorption

Experimental observation of phase (i.e. refractive index) component in the dynamic gratings recorded in erbium-doped optical fiber with saturation of optical absorption is reported. We utilized configuration of transient two-wave mixing with rectangular phase modulation of one of counterpropagating recording waves, where unshifted phase grating resulted in a transient energy exchange. The reported experiments were performed with heavily doped (≈5400 ppm erbium) fibers in a wide spectral range of Er³⁺ fundamental absorption at selected laser wavelengths 1492, 1526, 1549, and 1568 nm. Relative contribution of phase grating was especially large (up to ≈100% of the maximal amplitude component) at the opposite sides of the investigated spectral range and was significantly lower in its central part. The amplitude grating was found especially strong at short wavelength side of the spectrum (i.e. at 1492 nm), where the grating amplitude proved to be only two times lower than the theoretically predicted from consideration of two-level model.     

Transient two-wave mixing in a linear configuration of an adaptive interferometer based on Er-doped fiber with saturable absorption

We report results of transient two-wave mixing (TWM) in Er-doped fibers with saturable absorption in a linear configuration of an adaptive interferometric vibrometer with essentially different powers of recording waves. The TWM signal modulation depth detected in the weak (reflected) wave was shown to be twice as strong as in the symmetric configuration with equal recording powers. In accordance with theoretical predictions, the experimentally observed TWM signal amplitude grew continuously with the fiber optical density in the whole investigated range of alpha(0)L approximately 0.2-4. At the recording wavelength 1492 nm it proved to be quite close to the theoretical limit of approximately alpha(0)L/2 for weakly absorbing fibers, and in 1-m-long fiber of high optical density reached maximal value of approximately 0.8. The TWM response time went down with the recording light power and for P(0) approximately 10 mW was in the submillisecond region.     

Upper bounds in quantum dynamics

We develop a general method to bound the spreading of an entire wavepacket under Schrödinger dynamics from above. This method derives upper bounds on time-averaged moments of the position operator from lower bounds on norms of transfer matrices at complex energies.

This general result is applied to the Fibonacci operator. We find that at sufficiently large coupling, all transport exponents take values strictly between zero and one. This is the first rigorous result on anomalous transport.

For quasi-periodic potentials associated with trigonometric polynomials, we prove that all lower transport exponents and, under a weak assumption on the frequency, all upper transport exponents vanish for all phases if the Lyapunov exponent is uniformly bounded away from zero. By a well-known result of Herman, this assumption always holds at sufficiently large coupling. For the particular case of the almost Mathieu operator, our result applies for coupling greater than two.

     

Evaluation of the adsorption free energy of light guest molecules in nanoporous host structures

We present a simple method for estimation of the adsorption free energy of lightweight featureless molecules in nanoporous structures. The partition function of the system is computed quantum mechanically within the ideal gas approximation, and leads directly to the free adsorption energy. Storage capacities can be estimated by combining the ideal gas results with the real gas equation of state. Two possible implementations of the approach are discussed. The assumptions and potential sources of errors in the calculations are analyzed. The performance of the method is illustrated for graphitic slit pores and solid C60.     

Three-dimensional visualization of the first hyperpolarizability tensor

With polarization dependent second harmonic generation (SHG) microscopy becoming a more popular method for investigating the structure of biological materials, there is a need to develop tools with which to understand and interpret the observed SHG properties. Quantum mechanical calculations of the hyperpolarizability tensor have become a popular method for understanding the SHG properties of biomolecules. Visualization of the full hyperpolarizability tensor, termed the unit sphere representation, has been developed to provide insight and intuition on the relationship between SHG properties and molecules. A single vector representation is also presented, which approximates the SHG properties of molecules for certain cases, where the anisotropy is negligible.     

Theoretical analysis of spin crossover in iron(II) [2×2] molecular grids

We use quantum-chemical density functional theory calculations to elucidate the origin of spin-crossover pathways in two iron(II) [2×2] molecular grids with carbohydrazide-based bridging ligands. The complexes are characterized energetically and structurally in five available spin states. Special attention is paid to analysis of the structural distortion induced on each iron center by spin transition on any of its neighbors. The evolution of coordination polyhedra is monitored using the Continuous Shape Measures. It is demonstrated that a succession of spin transitions on different centers depends on the character of the induced distortion, either approaching or getting them away from a more regular low-spin geometry. These effects, resulting from the elasticity of bridging ligands, can be modulated by weak perturbations such as a change of the positions of the hydrogen atoms.     

Complexation Studies of Bidentate Heterocyclic N-Donor Ligands with Nd(III) and Am(III)

A new bidentate nitrogen donor complexing agent that combines pyridine and triazole functional groups, 2-((4-phenyl-1H-1,2,3-triazol-1-yl)methyl)pyridine (PTMP), has been synthesized. The strength of its complexes with trivalent americium (Am³⁺) and neodymium (Nd³⁺) in anhydrous methanol has been evaluated using spectrophotometric techniques. The purpose of this investigation is to assess this ligand (as representative of a class of similarly structured species) as a possible model compound for the challenging separation of trivalent actinides from lanthanides. This separation, important in the development of advanced nuclear fuel cycles, is best achieved through the agency of multidentate chelating agents containing some number of nitrogen or sulfur donor groups. To evaluate the relative strength of the bidentate complexes, the derived constants are compared to those of the same metal ions with 2,2′-bipyridyl (bipy), 1,10-phenanthroline (phen), and 2-pyridin-2-yl-1H-benzimidazole (PBIm). At issue is the relative affinity of the triazole moiety for trivalent f element ions. For all ligands, the derived stability constants are higher for Am³⁺ than Nd³⁺. In the case of Am³⁺ complexes with phen and PBIm, the presence of 1:2 (AmL₂) species is indicated. Possible separations are suggested based on the relative stability and stoichiometry of the Am³⁺ and Nd³⁺ complexes. It can be noted that the 1,2,3-triazolyl group imparts a potentially useful selectivity for trivalent actinides (An(III)) over trivalent lanthanides (Ln(III)), though the attainment of higher complex stoichiometries in actinide compared with lanthanide complexes may be an important driver for developing successful separations.     

Long‐Lived Charge Separation in Novel Axial Donor–Porphyrin–Acceptor Triads Based on Tetrathiafulvalene,Aluminum(III) Porphyrin and Naphthalenediimide

Two self‐assembled supramolecular donor–acceptor triads consisting of Al^III porphyrin (AlPor) with axially bound naphthalenediimide (NDI) as an acceptor and tetrathiafulvalene (TTF) as a secondary donor are reported. In the triads, the NDI and TTF units are attached to Al^III on opposite faces of the porphyrin, through covalent and coordination bonds, respectively. Fluorescence studies show that the lowest excited singlet state of the porphyrin is quenched through electron transfer to NDI and hole transfer to TTF. In dichloromethane hole transfer to TTF dominates, whereas in benzonitrile (BN) electron transfer to NDI is the main quenching pathway. In the nematic phase of the liquid crystalline solvent 4‐(n‐pentyl)‐4′‐cyanobiphenyl (5CB), a spin‐polarized transient EPR spectrum that is readily assigned to the weakly coupled radical pair TTF^.+NDI^.? is obtained. The initial polarization pattern indicates that the charge separation occurs through the singlet channel and that singlet–triplet mixing occurs in the primary radical pair. At later time the polarization pattern inverts as a result of depopulation of the states with singlet character by recombination to the ground state. The singlet lifetime of TTF^.+NDI^.? is estimated to be 200–300 ns, whereas the triplet lifetime in the approximately 350 mT magnetic field of the X‐band EPR spectrometer is about 10 μs. In contrast, in dichloromethane and BN the lifetime of the charge separation is <10 ns.     

Effect of Swirling Desolvation Gas Flow in an Atmospheric Pressure Ion Source

A numerical study is performed to examine the effect of introducing a swirling desolvation gas flow on the flow transport characteristics in an electrospray and an atmospheric pressure chemical ionization (APCI) system. An ion source having three coaxial tubes is considered: (1) an inner capillary tube to inject the liquid sample, (2) a center coaxial tube to provide a room temperature gas flow to nebulize the liquid, referred to as the nebulizing gas flow, and (3) an outer coaxial tube having a converging exit to supply a high temperature gas for droplet desolvation, referred to as the desolvation gas flow. The results show that a swirling desolvation gas flow reduces the dispersion of the nebulizing gas and suppresses turbulent diffusion. The effect of swirling desolvation flow on the trajectory of a range of droplet sizes emitted from a source is also considered. Figure

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