Structured eigenvalue condition numbers and linearizations for matrix polynomials

This work is concerned with eigenvalue problems for structured matrix polynomials, including complex symmetric, Hermitian, even, odd, palindromic, and anti-palindromic matrix polynomials. Most numerical approaches to solving such eigenvalue problems proceed by linearizing the matrix polynomial into a matrix pencil of larger size. Recently, linearizations have been classified for which the pencil reflects the structure of the original polynomial. A question of practical importance is whether this process of linearization significantly increases the eigenvalue sensitivity with respect to structured perturbations. For all structures under consideration, we show that this cannot happen if the matrix polynomial is well scaled: there is always a structured linearization for which the structured eigenvalue condition number does not differ much. This implies, for example, that a structure-preserving algorithm applied to the linearization fully benefits from a potentially low structured eigenvalue condition number of the original matrix polynomial.     

Molecular deformation mechanisms of isotactic polypropylene in α‐ and β‐crystal forms by FTIR spectroscopy

The orientation behavior of isotactic polypropylene (iPP) in α‐ and β‐crystal form was investigated by rheo‐optical Fourier transformed infrared (FTIR) spectroscopy. This method enabled quantification of the degree of orientation as a feature of structural changes during uniaxial elongation in not only the crystalline phase but also the amorphous one. Molecular orientation mechanisms can be successfully derived from experimental results. Generally, three mechanisms were detected for iPP: (1) interlamellar separation in the amorphous phase, (2) interlamellar slip and lamellar twisting at small elongations, and (3) intralamellar slip at high elongations. The third mechanism was favored by α‐PP, whereas β‐PP favored the second mechanism, which, in fact, was responsible for the different mechanical properties of both materials at the macroscopic level. On the other hand, crystallization conditions may have significantly affected the amorphous orientation. Nevertheless, for both iPP types the chains in the amorphous phase always oriented less than did those in the crystalline phase. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 4478–4488, 2004     

Quantum dynamics of inelastic scattering with a moving grid

The time‐dependent discrete variable representation (TDDVR) of a wave function with grid points defined by the Hermite part of the Gauss–Hermite (G‐H) basis set introduces quantum corrections to classical mechanics. The grid points in this method follow classical trajectory and the approach converges to the exact quantum formulation with sufficient trajectories (TDDVR points) but just with a single grid point; only classical mechanics performs the dynamics. This newly formulated approach (developed for handling time‐dependent molecular quantum dynamics) has been explored to calculate vibrational transitions in the inelastic scattering processes. Traditional quantum mechanical results exhibit an excellent agreement with TDDVR profiles during the entire propagation when enough grid points are included in the quantum‐classical dynamics. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Selective control of HOD photodissociation using low quanta O–D excitation and field optimized initial state (FOIST) based combination of states and colors

Selective Control of HOD photodissociation has been investigated using simple field profiles. Initial results indicate that preferential dissociation of O–H bond may be achieved from the ground vibrational state and that the O–D bond can be selectively dissociated using only the fundamental excitation in this mode. Dissociation from 2 quanta of excitation in the O–D mode produces 82.8% products with O–D bond dissociation. Preferential maximization of O–D dissociation vis-à-vis O–H bond may also be achieved from the ground vibrational state using a combination of two lasers with carrier frequencies 54920 cm⁻¹ and 52203 cm⁻¹. The use of Field Optimized Initial STate (FOIST) based scheme to enhance selective control of HOD photodissociation provides additional 6 − 8% H–O + D products compared to those obtained without FOIST.     

New family of aminophenalenyl-based neutral radical molecular conductors: synthesis, structure, and solid state properties

We report the preparation, crystallization, and solid-state characterization of the first members of a new family of spiro-bis-(1,9-diamino-substituted-phenalenyl)boron neutral radicals. The crystal structures show that the three radicals are monomeric and without close contacts in the crystal lattice. In all cases magnetic susceptibility measurements confirm the presence of free radicals with one unpaired spin per molecule. Two of the new radical compounds are among the most highly conducting neutral organic solids, with room-temperature conductivities reaching sigma(RT) = 4 x 10(-2) S/cm. The measured conductivities correlate with the closest intermolecular contacts in the solid state and with the calculated band dispersions, even though the bandwidths are much smaller than those found in other organic conductors.     

Energetics of Cd-based binary liquid alloys

The thermodynamic properties such as, free energy of mixing (G_M), heat of mixing (H_M), entropy of mixing (S_M) and microscopic properties such as, concentration fluctuation in long wavelength limit (S_CC(0)), Warren–Cowely short range ordering parameter (α₁), ratio of mutual and intrinsic diffusion coefficients (D_M/D_id) of two Cd-based liquid alloys have been studied by using two different models. The properties of Cd–Hg liquid alloy at 600 K have been studied on the basis of regular solution model, and the properties of Cd–Na liquid alloy at 673 K have been studied on the basis of quasi-chemical expression for weakly interacting system.     

Adduct formation between alkali metal ions and anionic LV(V)O(2)(-) (L(2-) = tridentate ONS ligands) species: syntheses, structural investigation, and photochemical studies

Syntheses of alkali metal adducts [LVO(2)M(H(2)O)(n)] (1-7) (M = Na(+), K(+), Rb(+), and Cs(+); L = L(1)(-)L(3)) of anionic cis-dioxovanadium(V) species (LVO(2)(-)) of tridentate dithiocarbazate-based Schiff base ligands H(2)L (S-methyl-3-((5-(R-2-hydroxyphenyl))methyl)dithiocarbazate, R = H, L = L(1); R = NO(2), L = L(2); R = Br, L = L(3)) have been reported. The LVO(2)(-) moieties here behave like an analogue of carboxylate group and have displayed interesting variations in their binding pattern with the change in size of the alkali metal ions as revealed in the solid state from the X-ray crystallographic analysis of 1, 3, 6, and 7. The compounds have extended chain structures, forming ion channels, and are stabilized by strong Coulombic and hydrogen-bonded interactions. The number of coordinated water molecules in [LVO(2)M(H(2)O)(n)] decreases as the charge density on the alkali metal ion decreases (n = 3.5 for Na(+) and 1 for K(+) and Rb(+), while, for Cs(+), no coordinated water molecule is present). In solution, compounds 1-7 are stable in water and methanol, while in aprotic solvents of higher donor strengths, viz. CH(3)CN, DMF and DMSO, they undergo photoinduced reduction when exposed to visible light, yielding green solutions from their initial yellow color. The putative product is a mixed-oxidation (mu-oxo)divanadium(IV/V) species as revealed from EPR, electronic spectroscopy, dynamic (1)H NMR, and redox studies.     

Short-peptide-based hydrogel: a template for the in situ synthesis of fluorescent silver nanoclusters by using sunlight

N-terminally Fmoc-protected dipeptide, Fmoc-Val-Asp-OH, forms a transparent, stable hydrogel with a minimum gelation concentration of 0.2% w/v. The gelation property of the hydrogel was investigated by using methods such as transmission electron microscopy, field-emission scanning electron microscopy, atomic force microscopy and Fourier transform infrared spectroscopy. The silver-ion-encapsulating hydrogel can efficiently and spontaneously produce fluorescent silver nanoclusters under sunlight at physiological pH (7.46) by using a green chemistry approach. Interestingly, in the absence of any conventional reducing agent but in the presence of sunlight, silver ions were reduced by the carboxylate group of a gelator peptide that contains an aspartic acid residue. These clusters were investigated by using UV/Vis spectroscopy, photoluminescence spectroscopy, high-resolution transmission electron microscopy (HR-TEM), atomic force microscopy (AFM) and X-ray diffraction (XRD) studies. Mass spectrometric analysis shows the presence of a few atoms in nanoclusters containing only Ag(2). The reported fluorescent Ag nanoclusters show excellent optical properties, including a very narrow emission profile and large Stokes shift (>100 nm). The reported fluorescent Ag nanoclusters within hydrogel are very stable even after 6 months storage in the dark at 4 °C. The as-prepared hydrogel-nanocluster conjugate could have applications in antibacterial preparations, bioimaging and other purposes.