Internal resonance in the higher-order modes of a MEMS beam: experiments and global analysis

This work investigates the dynamics of a microbeam-based MEMS device in the neighborhood of a 2:1 internal resonance between the third and fifth vibration modes. The saturation of the third mode and the concurrent activation of the fifth are observed. The main features are analyzed extensively, both experimentally and theoretically. We experimentally observe that the complexity induced by the 2:1 internal resonance covers a wide driving frequency range. Constantly comparing with the experimental data, the response is examined from a global perspective, by analyzing the attractor-basins scenario. This analysis is conducted both in the third-mode and in fifth-mode planes. We show several metamorphoses occurring as proceeding from the principal resonance to the 2:1 internal resonance, up to the final disappearance of the resonant and non-resonant attractors. The shape and wideness of all the basins are examined. Although they are progressively eroded, an appreciable region is detected where the compact cores of the attractors involved in the 2:1 internal resonance remain substantial, which allows effectively operating them under realistic conditions. The dynamical integrity of each resonant branch is discussed, especially as approaching the bifurcation points where the system becomes more vulnerable to the dynamic pull-in instability.

     

The Diels–Alder Reaction of 4,6‐Dinitrobenzofuroxan with 1‐Trimethylsilyloxybuta‐1,3‐diene: A Case Example of a Stepwise Cycloaddition

The reaction of 4,6‐dinitrobenzofuroxan (DNBF) with 1‐trimethylsilyloxybuta‐1,3‐diene ( 8 ) is shown to afford a mixture of [2+4] diastereomeric cycloadducts ( 10 , 11 ) through stepwise addition–cyclization pathways. Zwitterionic intermediate σ‐adduct 9 , which is involved in the processes, has been successfully characterized by ¹H and ¹³C NMR spectroscopy and UV/visible spectrophotometry in acetonitrile. A kinetic study has been carried out in this solvent that revealed that the rate of formation of 9 nicely fits the three‐parameter equation log k=s(E+N) developed by Mayr to describe the feasibility of nucleophile–electrophile combinations. This significantly adds to the NMR spectroscopic evidence that the overall cycloadditions take place through a stepwise mechanism. The reaction has also been studied in dichloromethane and toluene. In these less polar solvents, the stability of 9 is not sufficient to allow direct characterization by spectroscopic methods, but a kinetic investigation supports the view that stepwise processes are still operating. An informative comparison of our reaction with previous interactions firmly identified as prototype stepwise cycloadditions is made on the basis of the global electrophilicity index, ω, defined by Parr within the density functional theory, and highlighted by Domingo et al. as a powerful tool for understanding Diels–Alder reactions.     

The Horizontal Heat Kernel on the Quaternionic Anti-De Sitter Spaces and Related Twistor Spaces

Potential Analysis - The geometry of the quaternionic anti-de Sitter fibration is studied in details. As a consequence, we obtain formulas for the horizontal Laplacian and subelliptic heat kernel...     

A superior method for the reduction of secondary phosphine oxides

[reaction: see text] Diisobutylaluminum hydride (DIBAL-H) and triisobutylaluminum have been found to be outstanding reductants for secondary phosphine oxides (SPOs). All classes of SPOs can be readily reduced, including diaryl, arylalkyl, and dialkyl members. Many SPOs can now be reduced at cryogenic temperatures, and conditions for preservation of reducible functional groups have been found. Even the most electron-rich and sterically hindered phosphine oxides can be reduced in a few hours at 50-70 degrees C. This new reduction has distinct advantages over existing technologies.     

Super-replication under proportional transaction costs: From discrete to continuous-time models

In this paper, we study the problem of finding the minimal initial capital (i.e. super-replication value) needed in order to hedge (without risk) European contingent claims in a Markov setting under proportional transaction costs. The main result is that the cheapest (trivial) buy-and-hold strategy is optimal. Such a negative result has been derived previously in different contexts. First, we focus on discrete-time binomial models. We prove that the continuous-time limit of the super-replication value is the cost of the cheapest buy-and-hold strategy. Then, the result is proved in a multivariate continuous-time model with Brownian filtration. As a direct consequence, we obtain an explicit characterization of the hedging set, i.e. the set of all initial positions in the market assets from which the contingent claim can be hedged through some admissible portfolio strategy.     

In situ observations of unusual drop deformation and wobbling in simple shear flow

Deformation and wobbling of a liquid drop immersed in a liquid matrix were studied under mild shear conditions for various viscosity ratios. In situ visualization experiments were conducted on a homemade transparent Couette cell incorporated to the Paar Physica MCR500 shear rheometer. The effect of drop or matrix elasticity was examined and was found to play a major role in both deformation and wobbling processes. Experimental results were compared to Jackson and Tucker (J Rheol 47:659–682, 2003), Maffettone and Minale (J Non-Newton Fluid Mech 78:227–241, 1998) and Yu and Bousmina (J Rheol 47:1011–1039, 2003) ellipsoidal models. It was found that the agreement between the Newtonian models and the experimental results required an increase in the drop viscosity. Such increment in viscosity was found to scale with the first normal stress difference.     

Photochromism of dihydroindolizines Part XIX. Efficient one‐pot solid‐state synthesis,kinetic, and computational studies based on dihydroindolizine photochromes

For the first time, one‐pot solid‐state synthesis of 12 photochromic materials based on photochromic dihydroindolizine system substituted in both fluorene part (region A) and the heterocyclic part (region C) has been established. This method has immense advantages, which are short‐time reaction, high‐yield and low‐yield by‐products, and easily purification and separation processes. In addition, this method will help in getting over the tremendously purification and low‐yield problems faced since the worth‐finding of this family of photochromic materials. The absorption maxima (λ_max) and the half‐lives (t_1/2) of the colored betaines were detected in all cases using multichannel UV/Vis spectrophotometric measurements. The rate constants of the thermal back reaction of the betaines were determined at constant temperature by measuring the decrease in the maximum absorption intensity (λ_max) with time. The half‐lives (t_1/2) and rate constants (k) of betaines under examination were calculated by plotting lnA against time (t). The kinetic measurements could be detected by both spectra scan and time‐dependent decay measurements. Examination of the Arrhenius parameters reveals an underlying compensation between E_a and log A, whereby an increase in E_a is opposed by an increase in log A. The compensation appears in the corresponding Eyring parameters, ΔH^≠ and ΔS^≠; betaine structural changes that lead to lower, more favorable enthalpies of activation engender opposing entropic changes. At the isokinetic temperature T_iso = β, structural changes do not affect the rate constant of a reaction series because the changes of ΔH^≠ are counterbalanced by changes of ΔS^≠. The existence of an isokinetic relationship indicates a common structure of the transition state of all thermal back reaction of betaine under investigation. The computational results suggest that the decoloration reaction is a two‐step mechanism. The first step corresponds to the transoid–cisoid isomerization with an activation barrier of 10.3 kJ mol^?1, and the second step is the ring closure from the cisoid intermediate with a barrier 71.3 kJ mol^?1, which represent the rate determining step for thermal decoloration. The photochemical ring opening of DHIs to betaines is a disrotatory 1,5‐electrocyclic reaction, whereas the thermal ring‐closing occurs in the conrotatory mode. Copyright © 2016 John Wiley & Sons, Ltd.     

Chemical compounds from Phoenician juniper berries (Juniperus phoenicea)

Natural chemical compounds are a widely researched topic worldwide because of their potential activity against cerebrovascular diseases. Chemicals from Juniperus phoenicea berries are reported in this study. Lipids (11%) from seeds are mainly unsaturated (86%). Minerals are also quantified like Na (63.8?mg per 100?g?DW) or K (373.9?mg per 100?g?DW). Total reduced sugars are ca 192.6?mg?g(-1)?DW. Polyphenols and flavonoids from berries are highly present with an average of 1764?±?174.3?mg gallic acid per 100?g?DW and 890?±?47.6?mg rutin per 100?g?DW, respectively. Mean free radical scavenging activities, determined by DPPH and ABTS, are 1337?±?126.2?mM TEAC per 100?g?DW and 1105.7?±?95.9?mM TEAC per 100?g?DW, respectively. All findings improve the possible presence of biologically active fractions in phytocomplex that could be used as such and/or extracted for the formulation of supplements and/or ingredients for the pharmaceutical industry.     

Flow-based integer linear programs to solve the weekly log-truck scheduling problem

Annals of Operations Research - In this paper we present the solution to a weekly log-truck scheduling problem (LTSP) integrating the routing and scheduling of trucks where all goods are...