Pyrolysis of homoadamant-3-ene

Pyrolysis of homoadamant-3-ene ($\text{5}$), generated from 1-adamantylcarbene ($\text{7}$), leads to the same three olefins ($\text{2}$, $\text{3}$, and $\text{4}$) that are produced from pyrolysis of 3-homoadamantyl acetate ($\text{1}$).     

Quantum mechanical study of the potential energy surface of the ClO + NO2 reaction

In the study of the reaction pathways of the ClO + NO2 reaction including reliable structures of the reactants, products, intermediates, and transition states as well as energies the MP2/6-311G(d), B3LYP/6-311G(d), and G2(MP2) methods have been employed. Chlorine nitrate, ClONO2, is formed by N-O association without an entrance barrier and is stabilized by 29.8 kcal mol(-1). It can undergo either a direct 1,3 migration of Cl or OCl rotation to yield an indistinguishable isomer. The corresponding barriers are 45.8 and 7.1 kcal mol(-1), respectively. ClONO2 can further decompose into NO3 + Cl with an endothermicity of 46.4 kcal mol(-1). The overall endothermicity of the NO2 + ClO --> NO3 + Cl reaction is calculated to be 16.6 kcal mol(-1). The formation of cis-perp and trans-perp conformer of chlorine preoxynitrite, ClOONO(cp) and ClOONO(tp), are exothermic by 5.4 and 3.8 kcal mol(-1), respectively. Calculations on the possible reaction pathways for the isomerization of ClOONO to ClONO2 showed that the activation barriers are too high to account for appreciable nitrate formation from peroxynitrite isomerization. All quoted relative energies are related to G2(MP2) calculations.     

About a class of nonlinear oscillators with amplitude-independent frequency

This work is concerned with nonlinear oscillators that have a fixed, amplitude-independent frequency. This characteristic, known as isochronicity/isochrony, is achieved by establishing the equivalence between the Lagrangian of the simple harmonic oscillator and the Lagrangian of conservative oscillators with a position-dependent coefficient of the kinetic energy, which can stem from their mass that changes with the displacement or the geometry of motion. Conditions under which such systems have an isochronous center in the origin are discussed. General expressions for the potential energy, equation of motion as well as solutions for a phase trajectory and time response are provided. A few illustrative examples accompanied with numerical verifications are also presented.     

Potential benefits of a non-linear stiffness in an energy harvesting device

The benefits of using a non-linear stiffness in an energy harvesting device comprising a mass–spring–damper system are investigated. Analysis based on the principle of conservation of energy reveals a fundamental limit of the effectiveness of any non-linear device over a tuned linear device for such an application. Two types of non-linear stiffness are considered. The first system has a non-linear bi-stable snap-through mechanism. This mechanism has the effect of steepening the displacement response of the mass as a function of time, resulting in a higher velocity for a given input excitation. Numerical results show that more power is harvested by the mechanism if the excitation frequency is much less than the natural frequency. The other non-linear system studied has a hardening spring, which has the effect of shifting the resonance frequency. Numerical and analytical studies show that the device with a hardening spring has a larger bandwidth over which the power can be harvested due to the shift in the resonance frequency.     

Polymerization of aromatic nuclei. XIX. Polymerization of thiophene by aluminum chloride

Thiophene was polymerized in high yield on exposure to aluminum chloride in solvent under mild conditions. Experimental evidence [IR, NMR, UV, and mass spectra, elemental analyses, reductive desulfurization, and comparison with the literature trimer of thiophene (prepared with phosphoric acid)] suggests the following structure: From gel permeation chromatography an average weight of 1290 was obtained, which corresponded to the presence of 15 rings; the highest-molecular-weight chains contained about 192 rings. Mechanistically, participation of cationic intermediates is proposed. Apparently chain extension can occur by various routes, including participation of neutral oligomer molecules.     

Ethanolysis and base promoted elimination reaction of bridgehead α-amino sulfides : 3-thioethoxy-4-azahomoadamantanes

Solvolysis of N-methyl-3-thioethoxy-4-azahomoadamantane (4c) in ethanolic sodium ethoxide followed first order kinetics. Reaction presumably proceeds via an S_N1 mechanism with resonance stabilization of the bridgehead carbonium ion by the electrons on adjacent nitrogen. Addition of ethoxide to the bridgehead carbonium ion yields N-methyl-3-ethoxy-4-azahomoadamantane (4c). Solvolysis of N-protio compound (4b) under similar conditions was much more rapid, and followed first order kinetics for both substrate and base. The mechanism apparently involves an elimination-addition pathway in which ethoxide promoted elimination of ethyl mercaptan is followed by net addition of ethanol across the bridgehead imine to form ether 4d.     

A study of a nonlinear vibration isolator with a quasi-zero stiffness characteristic

A vibration isolator consisting of a vertical linear spring and two nonlinear pre-stressed oblique springs is considered in this paper. The system has both geometrical and physical nonlinearity. Firstly, a static analysis is carried out. The softening parameter leading to quasi-zero dynamic stiffness at the equilibrium position is obtained as a function of the initial geometry, pre-stress and the stiffness of the springs. The optimal combination of the system parameters is found that maximises the displacement from the equilibrium position when the prescribed stiffness is equal to that of the vertical spring alone. It also satisfies the condition that the dynamic stiffness only changes slightly in the neighbourhood of the static equilibrium position. For these values, a dynamical analysis of the isolator under asymmetric excitation is performed to quantify the undesirable effects of the nonlinearities. It includes considering the possibilities of the appearance of period-doubling bifurcation and its development into chaotic motion. For this purpose, approximate analytical methods and numerical simulations accompanied with qualitative methods including phase plane plots, Poincaré maps and Lyapunov exponents are used. Finally, the frequency at which the first period-doubling bifurcation appears is found and the effect of damping on this frequency determined.     

On the use of two classical series expansion methods to determine the vibration of harmonically excited pure cubic oscillators

An analytical approach to determine the steady-state response of a damped and undamped harmonically excited oscillator with no linear term and with cubic non-linearity is presented. The governing equation is transformed into a form suitable for the application of a classical series expansion technique. The Linstedt–Poincaré method and the method of multiple scales are then used to determine the amplitude-frequency response and approximate solution for the response at the excitation frequency. The results obtained are compared with numerical solutions and analytical solutions found in the literature for the case when there is strong non-linearity.