Ab initio molecular dynamical investigation of the finite temperature behavior of the tetrahedral Au19 and Au20 clusters

Density functional molecular dynamics simulations have been carried out to understand the finite temperature behavior of Au19 and Au20 clusters. Au20 has been reported to be a unique molecule having tetrahedral geometry, a large HOMO-LUMO energy gap, and an atomic packing similar to that of the bulk gold (Li, J.; et al. Science 2003, 299, 864). Our results show that the geometry of Au19 is exactly identical with that of Au20 with one missing corner atom (called a vacancy). Surprisingly, our calculated heat capacities for this nearly identical pair of gold clusters exhibit dramatic differences. Au20 undergoes a clear and distinct solid-like to liquid-like transition with a sharp peak in the heat capacity curve around 770 K. On the other hand, Au19 has a broad and flat heat capacity curve with continuous melting transition. This continuous melting transition turns out to be a consequence of a process involving a series of atomic rearrangements along the surface to fill in the missing corner atom. This results in a restricted diffusive motion of atoms along the surface of Au19 between 650 to 900 K during which the shape of the ground state geometry is retained. In contrast, the tetrahedral structure of Au20 is destroyed around 800 K, and the cluster is clearly in a liquid-like state above 1000 K. Thus, this work clearly demonstrates that (i) the gold clusters exhibit size sensitive variations in the heat capacity curves and (ii) the broad and continuous melting transition in a cluster, a feature that has so far been attributed to the disorder or absence of symmetry in the system, can also be a consequence of a defect (absence of a cap atom) in the structure.     

Ge clusters in Si matrix: structure and dynamics

We have determined by computer simulations, some structural properties of Ge clusters embedded in a Si crystalline host matrix for cluster sizes varying from 0.5 to 1.5 nm. In order to describe inter-atomic forces we have chosen a Valence Force Field (VFF) semi-empirical potential. Next we have calculated the density of vibrational states by diagonalization of the dynamical matrix defined with the same potential. The influence of the volume/interface ratio of Ge on the vibrational properties is discussed. Received 10 December 1998 and Received in final form 7 April 1999     

Existence and asymptotic behaviour of solutions to first- and second-order difference equations with periodic forcing

By using previous results of Djafari Rouhani for non-expansive sequences in Refs (Djafari Rouhani, Ergodic theorems for nonexpansive sequences in Hilbert spaces and related problems, Ph.D. Thesis, Yale University, Part I (1981), pp. 1–76; Djafari Rouhani, J. Math. Anal. Appl. 147 (1990), pp. 465–476; Djafari Rouhani, J. Math. Anal. Appl. 151 (1990), pp. 226–235), we study the existence and asymptotic behaviour of solutions to first-order as well as second-order difference equations of monotone type with periodic forcing. In the first-order case, our result extends to general maximal monotone operators, the discrete analogue of a result of Baillon and Haraux (Rat. Mech. Anal. 67 (1977), 101–109) proved for subdifferential operators. In the second-order case, our results extend among other things, previous results of Apreutesei (J. Math. Anal. Appl. 288 (2003), 833–851) to the non-homogeneous case, and show the asymptotic convergence of every bounded solution to a periodic solution.     

Sonochemical synthesis and characterization of NiMoO4 nanorods

NiMoO₄ nanorods have been successfully synthesized by sonochemical method process by using Ni(CH₃COO)₂·4H₂O and (NH₄)₆Mo₇O₂₄·4H₂O as starting materials. Some parameters including ultrasonic power, ultrasonic irradiation time, stirring effect, solvent effect, and surfactant effect were investigated to reach optimum condition. The as synthesized nanostructures were characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), transmittance electron microscopy (TEM), photoluminescence (PL) spectroscopy, Fourier transform infrared (FT-IR) spectra and energy dispersive X-ray microanalysis (EDX). Facile preparation and separation are important features of this route. This work has provided a general, simple, and effective method to control the composition and morphology of NiMoO₄ in aqueous solution, which will be important for inorganic synthesis methodology.     

A Contribution to the Second Neighborhood Problem

Seymour’s Second Neighborhood Conjecture asserts that every oriented graph (without digons) has a vertex whose first out-neighborhood is at most as large as its second out-neighborhood. It is proved for tournaments, tournaments missing a matching and tournaments missing a generalized star. We prove this conjecture for classes of oriented graphs whose missing graph is a comb, a complete graph minus two independent edges, or a cycle of length 5.     

Adaptive control of uncertain nonlinear systems using mixed backstepping and Lyapunov redesign techniques

In this paper, a robust adaptive control law for a class of uncertain nonlinear systems is proposed. The proposed controller guarantees asymptotic output tracking of systems in the strict-feedback form with unknown static parameters, and matched and unmatched dynamic uncertainties. This controller takes advantages of a robust stability property of the Lyapunov redesign method and a systematic design procedure of the backstepping technique. In fact, the backstepping technique is employed to enrich the Lyapunov redesign method to compensate for not only matched - but also unmatched-uncertainties. On the other hand, using the Lyapunov redesign method in each step of the conventional backstepping technique makes backstepping robust. The suggested controller is designed through repeatedly utilizing the Lyapunov redesign method in each step of the backstepping technique. Simulation results reveal the efficiency of the Lyapunov redesign-based backstepping controller.     

Atomic-scale determination of DNA conformational response to strained furanose: a static mode approach

An original approach of macromolecular ‘induced-fit’ flexibility, namely the static modes, is applied to shed light on some fundamental mechanisms impacting DNA conformations. We first investigate a constrained nucleic acid of the D-CNA family, in which some backbone torsional angles are conformationally restricted by a dioxaphosphorinane ring structure. We take a special interest in α,β-D-CNA, in which α and β angles are restricted to the canonical conformation. We used the static mode method to evaluate the impact of the insertion of modified nucleotides on the stability of DNA/DNA and DNA/RNA duplexes. Although our approach authorizes the design of complex excitation modes on a specific molecule, we here establish with an atomic precision how a DNA south to north transition can be optimally operated through C5′ and O5′ single excitations.     

Preparation of Silica Nanoparticles from Organic Laboratory Waste of Silica Gel HF254 and Their Use as a Highly Efficient Catalyst for the One‐Pot Synthesis of 2,3‐Dihydro‐1H‐isoindolone Derivatives

Reaction of an isocyanide with an iminium ion intermediate, formed by reaction between 6‐formyl‐2,3‐dimethoxybenzoic acid and secondary amines (dibenzyl‐ or benzyl(isopropyl)amine) in the presence of silica nanoparticles (silica NPs, ca. 70 nm) proceeds smoothly at room temperature to afford 2,3‐dihydro‐1H‐isoindolone derivatives in high yields.     

Improvement of size-based particle separation throughput in slanted spiral microchannel by modifying outlet geometry

The inertial microfluidic technique, as a powerful new tool for accurate cell/particle separation based on the hydrodynamic phenomenon, has drawn considerable interest in recent years. Despite numerous microfluidic techniques of particle separation, there are few articles in the literature on separation techniques addressing external outlet geometry to increase the throughput efficiency and purity. In this work, we report on a spiral inertial microfluidic device with high efficiency (>98%). Herein, we demonstrate how changing the outlet geometry can improve the particle separation throughput. We present a complete separation of 4 and 6 μm from 10 μm particles potentially applicable to separate microalgae (Tetraselmis suecica from Phaeodactylum tricornutum). Two spiral microchannels with the same cross section dimension but different outlet geometry were considered and tested to investigate the particle focusing behavior and separation efficiency. As compared with particle focusing observed in channels with a simple outlet, the particle focusing in a modified outlet geometry appears in a more successful focusing manner with complete separation. This simple approach of particle separation makes it attractive for lab-on-a-chip devices for continuous extraction and filtration of a wide range of cell/particle sizes.