Convergence Properties of the Regularized Newton Method for the Unconstrained Nonconvex Optimization

The regularized Newton method (RNM) is one of the efficient solution methods for the unconstrained convex optimization. It is well-known that the RNM has good convergence properties as compared to the steepest descent method and the pure Newton’s method. For example, Li, Fukushima, Qi and Yamashita showed that the RNM has a quadratic rate of convergence under the local error bound condition. Recently, Polyak showed that the global complexity bound of the RNM, which is the first iteration k such that ‖∇ f(x _k )‖≤ε, is O(ε ⁻⁴), where f is the objective function and ε is a given positive constant. In this paper, we consider a RNM extended to the unconstrained “nonconvex” optimization. We show that the extended RNM (E-RNM) has the following properties. (a) The E-RNM has a global convergence property under appropriate conditions. (b) The global complexity bound of the E-RNM is O(ε ⁻²) if ∇ ² f is Lipschitz continuous on a certain compact set. (c) The E-RNM has a superlinear rate of convergence under the local error bound condition.     

Competing orders and disorder-induced insulator to metal transition in manganites

Effects of disorder on the two competing phases, i.e., the ferromagnetic metal and the commensurate charge/lattice ordered insulator, are studied by Monte Carlo simulation. The disorder suppresses the charge/lattice ordering more strongly than the ferromagnetic order, driving the commensurate insulator to the ferromagnetic metal near the phase boundary in the pure case. Above the ferromagnetic transition temperature, on the contrary, the disorder makes the system more insulating, which might cause an enhanced colossal magnetoresistance as observed in the half-doped or Cr-substituted manganites. No indication of the percolation or the cluster formation is found, and there remains the charge/lattice fluctuations instead which are enhanced toward the transition temperature.     

Spectral study on the molecular orientation of a tetracationic porphyrin dye on the surface of layered silicates

Tetracationic porphyrin dyes TMPyP and ZnPyP were intercalated into hydrophobized layered silicate films of three smectites. The smectites represented the layered silicate specimens of high (Fluorohectorite, Corning; FHT), medium (Kunipia F montmorillonite; KF) and low layer charge (Laponite, Laporte; LAP). The molecular orientations of the dye cations were studied by means of linearly-polarized ultraviolet-visible (UV-VIS) spectroscopy. The spectral analysis and consequent calculations of tilting angles of the transition moments at the wavelengths of Soret band transitions were in the range of 25°-35°. The determined angles indicated molecular orientation of the dye cations being almost parallel to the surface of the silicates. Slightly higher values (above 35°), determined for a FHT film, indicated either a slightly tilted orientation of the dye cations or the change of molecular comformation after the intercalation of the dye. Presented at 5-th International Conference Solid State Surfaces and Interfaces, November 19–24, 2006, Smolenice Castle, Slovakia     

Influence of intramolecular vibrations in charge redistribution at the pentacene-graphite interface

We have investigated the relation between the intramolecular vibrational modes of pentacene and the charge redistribution at the pentacene-graphite interface by using high-resolution electron-energy-loss-spectroscopy. The three main vibrational peaks shift to lower energies as the pentacene film thickness decreases. In order to discuss this energy shift, we have calculated the vibrational energies of a free pentacene molecule by changing its charge state. We have also calculated the vibrational energies of a pentacene molecule adsorbed on a graphite sheet by changing the pentacene-graphite distance. Taking the experimental and calculation results into account, we conclude that the observed energy shifts result from an intramolecular charge redistribution. The present results indicate that the effect of an intramolecular charge redistribution is essential to discuss the origin of an energy shift observed in a vibrational study of an organic molecule/substrate interface.     

Electric conductance of metal nanowires at mechanically controllable break junctions under electrochemical potential control

We have developed the mechanically controllable break junction setup with an electrochemical cell (EC-MCBJ) to measure the electric conductance of metal nanowires under electrochemical potential control. The electric conductance of Au nanowires was investigated in 0.1 M Na₂SO₄ solution using EC-MCBJ. The conductance of the Au nanowires was quantized in units of G₀ (=2e²/h), showing clear features in the conductance histogram. The atomic contact with a specific conductance value was kept for >5 s, indicating the relatively high stability of the present EC-MCBJ system.     

Nano-crater formation on a Si(1 1 1)-(7 × 7) surface by slow highly charged ion-impact

Using scanning tunneling microscopy (STM) and time of flight secondary ion mass spectrometry (TOF/SIMS), we observed radiation effects on a Si(1 1 1)-(7 × 7) surface in the collision of a single highly charged ion (HCI) with a charge state q up to q = 50. The STM observation with atomic resolution revealed that a nanometer sized crater-like structure was created by a single HCI impact, where the size increased rapidly with q. The secondary ion yields also increased with q in which multiply charged Si ions (Siⁿ⁺) were clearly observed in higher q HCI-collisions. The sputtering mechanism is briefly discussed, based on the so-called Coulomb explosion model.     

Molecular aggregation of rhodamine dyes in dispersions of layered silicates: influence of dye molecular structure and silicate properties

The molecular aggregation of six rhodamine dyes (rhodamine 560, B, 3B, 19, 6G, 123) in layered silicate (saponite and fluorohectorite) dispersions was investigated by using visible (vis) spectroscopy. The dye molecular aggregation was influenced by the properties of both the silicates and the dyes themselves. The layer charge of the silicates enhanced the molecular aggregation of the hydrophilic, cationic dyes. The presence of a carboxyl acid group in the dye molecules inhibited adsorption of the dyes on the surface of fluorohectorite, a silicate with a high charge density. A lower or no adsorption could be observed by vis spectroscopy. Strong association of the dyes to the silicate surface led to remarkable changes in the dye spectra, mainly due to the molecular aggregation. Dye assemblies initially formed after mixing the dye solutions with silicate dispersions were unstable. Decomposition of the dye molecular assemblies, and the formation of new species or molecular aggregate rearrangements, were studied on the bases of time-difference spectra. The reaction pathways were specific, not only for the dyes, depending upon their molecular structure and properties, but also on the silicate substrates.     

New layered rare-earth hydroxides with anion-exchange properties

We report the synthesis of a new series of layered hydroxides based on rare-earth elements with a composition of RE(OH)2.5Cl(0.5).0.8 H2O (RE: Eu, Tb, etc.) through the homogeneous precipitation of RECl3.x H2O with hexamethylenetetramine (HMT). Rietveld analysis combined with direct methods revealed an orthorhombic layered structure comprising a positively charged layer of [RE(OH)2.5-(H2O)0.8]0.5+ and interlayer Cl- ions. The Cl- ions were readily exchangeable for various anions (NO3-, SO4(2-), dodecylsulfonate, etc.) at ambient temperature. Photoluminescence studies showed that the compounds display typical RE3+ emission. With rare-earth-based host layers and tunable interlayer guests, the new compounds may be of interest for optoelectronic, magnetic, catalytic, and biomedical materials.     

Aggregation and decomposition of a pseudoisocyanine dye in dispersions of layered silicates

The optical properties of reaction systems composed from a pseudoisocyanine (PIC) solution and dispersed layered silicates were studied using visible spectroscopy. Two series of reduced-charge montmorillonites were used as the silicate materials. Each series consisted of eight samples with different layer charges, which were prepared from one parent material. Observed trends were verified with another series of dioctahedral and trioctahedral smectites of different layer charges, structure, and origin. The layer charge density of the silicates significantly affected the aggregation of PIC cations. In addition to the formation of J-aggregates, dye spectral bleaching was also observed. Silicates with very low charge densities induced neither significant aggregation nor spectral bleaching of the dye. The highest levels of PIC J-aggregate formation were found in dispersions of the layered silicates with a medium surface charge. However, reversible spectral bleaching was also observed in some cases. PIC dye cations probably change their conformations during the adsorption process, due to the tension resulting from the large size of the cations and the relatively high charge density at the silicate surface. The bleached dye recovers, at least partially, with the rearrangement and redistribution of the dye cations over the time. In contrast, the presence of silicates with very high charge densities (synthetic taeniolite and fluorohectorite) led to the very fast and irreversible decomposition of the PIC. Perhaps, the tension in adsorbed dye cations, induced by the high charge density at the silicate surface, resulted in significant destabilization and a decomposition reaction of the chromophore.     

Two-dimensional separation system of coupling capillary liquid chromatography to capillary electrophoresis for analysis of Escherichia coli metabolites

A two-dimensional (2-D) separation system of coupling chromatography to electrophoresis was developed for profiling Escherichia coli metabolites. Capillary liquid chromatography (LC) with a monolithic silica-octadecyl silica column (500 x 0.2 mm ID) was used as the first dimension, from which the effluent fractions were further analyzed by capillary electrophoresis (CE) acting as the second dimension. Field-enhanced stacking was selectively employed as a concentration strategy to interface the two dimensions, which proved to be beneficial for the detection of metabolites. An artificial sample containing 118 standards, some of which lack chromophores or have weak UV absorbance, was used to optimize the 2-D separation system. Under the optimum conditions, 63 components in the artificial sample having absorbance at 254 nm could be well resolved and detected. The utility of the system was demonstrated by comprehensive analysis of E. coli metabolites. Comparing with the previous 2-D separation system we published in Anal. Chem. 2004, 76, 1419-1428, using a longer monolithic column in the first dimension improved the separation efficiency and offered the possibility of increasing the injection volume without compromising the separation efficiency. In the second dimension, field-enhanced stacking was used to improve the concentration sensitivity of the metabolites, and more metabolites in E. coli cell extract were detected and identified using the developed 2-D separation system. In addition, preliminary investigation for future CE-mass spectrometry coupling was also made in the study by using volatile buffers in the capillary LC and CE techniques.