Unidirectional optical Bloch oscillations in asymmetric waveguide arrays

We present an analytical proof of the existence of unidirectional optical Bloch oscillations in a waveguide array system. It is shown that the presence of nonreciprocity in the system allows for a complete normal-mode dephasing in one of the propagation directions, resulting in a unidirectional breakdown in Bloch oscillations. A model system consisting of an array of transversely magnetized asymmetric Si/SiO2 waveguides with a magneto-optic cover layer is presented. Large index contrasts between film and cover are critical for practical realizations.     

Time reversal for obstacle location in elastodynamics from acoustic recording

The Note is concerned with a feasibility study of time reversal in a non-homogeneous elastic medium, from data recorded in an acoustic medium. Our aim here is to determine the presence and some physical properties of elastic “inclusions” (unknown, not observable solid objects, characterized by their elastic properties) from partial observations of acoustic waves scattered by these inclusions. A finite element numerical method, based on a variational acousto-elastodynamics formulation, is derived and used to solve the forward, and then, the time-reversed problem. A criterion, derived from the reverse time migration framework, is introduced, to help construct images of the inclusions to be determined. Numerical illustrations on configurations that mimic the breast cancer configuration are proposed, and show that one can differentiate between two inclusions, even with different properties.     

Determination of Economic Packaging Set-up Frequency of Jointly Replenished Items

This paper deals with the problem of determining the economic operating policy for inventory items which are manufactured jointly but packaged individually. The proposed new approach is very simple and efficient. An extensive simulation study is presented so that the results of several heuristics (based on a wide range of data, measuring the number of optimal solutions, average error and maximum error) can be compared.     

The isomorphism problem for some universal operator algebras

This paper addresses the isomorphism problem for the universal (non-self-adjoint) operator algebras generated by a row contraction subject to homogeneous polynomial relations. We find that two such algebras are isometrically isomorphic if and only if the defining polynomial relations are the same up to a unitary change of variables, and that this happens if and only if the associated subproduct systems are isomorphic. The proof makes use of the complex analytic structure of the character space, together with some recent results on subproduct systems. Restricting attention to commutative operator algebras defined by a radical ideal of relations yields strong resemblances with classical algebraic geometry. These commutative operator algebras turn out to be algebras of analytic functions on algebraic varieties. We prove a projective Nullstellensatz connecting closed ideals and their zero sets. Under some technical assumptions, we find that two such algebras are isomorphic as algebras if and only if they are similar, and we obtain a clear geometrical picture of when this happens. This result is obtained with tools from algebraic geometry, reproducing kernel Hilbert spaces, and some new complex-geometric rigidity results of independent interest. The C^?-envelopes of these algebras are also determined. The Banach-algebraic and the algebraic classification results are shown to hold for the wot-closures of these algebras as well.     

Linear response in the strong field domain

We show that, while it is well-known that first-order perturbation theory leads to linear response (of, e.g., a material system to an external field), the reverse is not true: linear response does not necessarily imply the validity of first-order perturbation theory, nor does it follow from it that the external perturbation is weak. We do so by analyzing the intensity dependence in the photoexcitation followed by dissociation or isomerization of a bound molecular system by a shaped broadband laser pulse. We show that, in certain cases where strong field effects are definitely present, the observed photoexcitation yield as a function of intensity may exhibit linear dependence over a wide range of intensities. The behavior is shown to coexist with a rather extensive range of coherent control over the branching ratios, an effect that was shown in the past to be impossible in the single precursor state (e.g., in the first-order perturbation theory) domain. For example, we demonstrate computationally that when (flat continuum-mediated) Raman transitions are present, appropriate pulse shaping can lead to a linear yield with intensity over a wide range of intensities, while coherent control over the branching ratio is significant. Thus, it is not necessary to invoke external bath effects (as is currently being done) to explain present-day experiments where coherent control is observed in the linear response regime.     

Synthesis,characterization, and polymerization activity of [bis(4,4'-bis(neophyldimethylsilylmethyl)-2,2'-bipyridyl)copper(I)]+CuBr2- and Implications for copper(I) catalyst structures in atom transfer radical polymerization

A series of 4,4'-disilyl-substituted-2,2'-bipyridine ligands were prepared using a metathesis reaction of the dianion of 4,4'-dimethyl-2,2'-bipyridine with several trialkylsilyl chlorides: 4,4'bis(tert-butyldimethylsilylmethyl)-2,2'-bipyridine (dTBDMSbipy), 4,4'-bis(dimethylthexylsilylmethyl)-2,2'-bipyridine (dTHEXbipy), and 4,4'-bis(neophyldimethylsilylmethyl)-2-2'-bipyridine (dNEObipy). It was observed that the side chain length correlated with the ability of the ligand to form hydrocarbon soluble complexes of copper(I) bromide, with dNEObipy forming the most soluble and easily crystallized complexes. The atom transfer radical polymerization (ATRP) of styrene using dNEObipy as the ligand displayed molecular weight control equivalent to other ATRP systems in which solubilizing ligands, such as 4,4'-di-5-nonyl-2,2'-bipyridine or 4,4'-di-n-heptyl-2,2'-bipyridine, were used. The one-to-one complex of dNEObipy with CuBr was prepared and its crystal structure was determined. The resulting complex had the ionic formulation [(dNEObipy)2Cu]+[CuBr2]- and displayed similar activities in styrene ATRP as the standard 2 dNEObipy/CuBr catalyst system. These and other polymerization results in addition to NMR experiments suggest that the predominant copper(I) species formed in ATRP solutions is the 2-to-1 ligand-to-copper(I) cation, [(dNEObipy)2Cu]+, with either a dihalocuprate or halide counteranion, depending upon the conditions.     

Predicting solute adsorption on activated carbon: phenol

Activated carbon (AC), the most widely used adsorbent in water and in wastewater treatment, comprises a high surface area of very small, convoluted and interconnected pores. Despite the wide use of AC, there is little fundamental atomic-level understanding of its adsorption capacity and selectivity as well as its pore structure. The purpose of this work is to suggest the methodology for calculation of equilibrium adsorption capacity of common water organic pollutants and use it for phenol as a model. The effects of various functional groups, pore size, and coverage on thermodynamics of phenol adsorption from the gas phase and from water media are calculated using molecular mechanics (MM) and density functional theory (DFT) approaches.     

The design and synthesis of novel IBiox N-heterocyclic carbene ligands derived from substituted amino-indanols

A synthetic route towards a number of novel IBiox N-heterocyclic carbene (NHC) ligands has been developed. The resulting ligands have restricted flexibility and high steric demand. Preliminary studies have shown these ligands to give high levels of asymmetric induction in the copper-free allylic alkylation of cinnamyl bromide.     

Pi-stacking induced NMR spectrum splitting in enantiomerically enriched Ru(II) complexes: evaluation of enantiomeric excess

Several chiral octahedral complexes of the general formula [Ru(bpy)2 (Lig)][PF6]2 (Lig = a ligand that can participate in pi-stacking interactions such as eilatin, isoeilatin, and tpphz) were synthesized in both the racemic and enantiomerically pure/enriched forms. Nonracemic mixtures of enantiomers of all these complexes exhibit splitting of the 1H NMR spectra (NMR nonequivalence); i.e., each spectrum contains a major and a minor set of peaks. The origin of this phenomenon is attributed to a fast equilibrium between monomers and discrete dimers held together by pi-stacking interactions, and it is observed for a wide range of pi-stacking interaction strengths. The NMR spectrum splitting exhibited by these complexes can be exploited for the evaluation of their enantiomeric excess simply from the integral ratio, without addition of chiral shift reagents.     

Effects of structure on properties of some new aromatic-aliphatic polybenzimidazoles

Polybenzimidazoles were prepared in poly(phosphoric acid) from isophthalic, m- and p-phenylene diacetic, succinic, adipic, suberic, and sebacic acids and 3,3′-diaminobenzidine, 3,3′,4,4′-tetraaminodiphenyl ether and 3,3′,4,4′-tetraaminodiphenylmethane. The thermal, mechanical, and bonding properties were studied. A 3:1 copolymer of isophthalic and m-phenylenediacetic acid with 3,3′-diaminobenzidine showed the best results as far as isothermal oxidation resistance and thermal and processing characteristics.