Cyclization of Nitrospirobenzopyrans to Bridged Benzoxazepino[3,2-a]indoles

Condensation of 1-substituted 1,2,3,9a-tetrahydro-9H-imidazo[1,2-a]indol-2-ones with 5-nitrosalicylaldehyde afforded 1′-[(N-monosubstituted carbamoyl)methyl]indoline nitrospirobenzopyrans. Treatment of the latter with strong base led to the formation of a mixture of cis/trans-5a,13-methano-1,3-benzoxazepino[3,2-a]indoles. Results of semiempirical calculations gave evidence that such a transformation of nitrospirobenzopyrans to bicyclic indole derivatives could proceed via a single transition state, where the negatively charged carbon atom attacks the vinylic double bond of the spiropyran system.     

Generators and normal forms of Richard Thompson’s group F and the four-color theorem

We use a result of Kauffman to explore the connection between Richard Thompson’s Group F and the four-color theorem.     

Experimental snap-through boundaries for acoustically excited,thermally buckled plates

This paper presents some recent experimental results on the dynamic snap-through behavior of a clamped, rectangular plate subject to thermal loading and intense acoustic excitation. The likelihood of snap-through oscillations is characterized in terms of boundaries separating regions of snap-through and no snap-through in the parameter space. Two scenarios are considered. First, using tonal inputs, the regions of snap-through are mapped in the sound pressure level—input frequency domain ((SPL, ) plane). Second, random acoustic inputs are used, and the effect of varying the overall sound pressure level and frequency bandwidth are investigated ((SPL, ) plane). Several nonlinear characteristics are evident and discussed.     

Hopf-flip bifurcation of high dimensional maps and application to vibro-impact systems

This paper addresses the problem of Hopf-flip bifurcation of high dimensional maps. Using the center manifold theorem, we obtain a three dimensional reduced map through the projection technique. The reduced map is further transformed into its normal form whose coefficients are determined by that of the original system. The dynamics of the map near the Hopf-flip bifurcation point is approximated by a so called ‘‘time-2τ² map’’ of a planar autonomous differential equation. It is shown that high dimensional maps may result in cycles of period two, tori T¹ (Hopf invariant circles), tori 2T¹ and tori 2T² depending both on how the critical eigenvalues pass the unit circle and on the signs of resonant terms’ coefficients. A two-degree-of-freedom vibro-impact system is given as an example to show how the procedure of this paper works. It reveals that through Hopf-flip bifurcations, periodic motions may lead directly to different types of motion, such as subharmonic motions, quasi-periodic motions, motions on high dimensional tori and even to chaotic motions depending both on change in direction of the parameter vector and on the nonlinear terms of the first three orders.The project supported by the National Natural Science Foundation of China (10472096)The English text was polished by Ron Marshall.     

Modular access to heterocycles: methyl 3-aminobenzo[<Emphasis Type="Italic">b</Emphasis>]thiophene-2-carboxylate–thiourea linkage or pyrimidine-4-one-2-thione formation

Abstract  Modular conditions for the formation of thioureas or pyrimidine-4-one-2-thiones connected to the benzo[b]thiophene, benzene and indole structures were performed. A benzo[b]thiophene isothiocyanate derivative was used as a model to study the condensation with simple aromatic amines and amino-l-sorbose derivative. The construction of pyrimidine-4-one-2-thiones using basic conditions afforded efficiently new heterocyclic aromatics, which were further transformed using the alkylated sulfur as a leaving group in palladium-catalyzed cross-coupling reactions. Graphical abstract        

Large oscillations of beams and columns including self-weight

Large-amplitude, in-plane beam vibration is investigated using numerical simulations and a perturbation analysis applied to the dynamic elastica model. The governing non-linear boundary value problem is described in terms of the arclength, and the beam is treated as inextensible. The self-weight of the beam is included in the equations. First, a finite difference numerical method is introduced. The system is discretized along the arclength, and second-order-accurate finite difference formulas are used to generate time series of large-amplitude motion of an upright cantilever. Secondly, a perturbation method (the method of multiple scales) is applied to obtain approximate solutions. An analytical backbone curve is generated, and the results are compared with those in the literature for various boundary conditions where the self-weight of the beam is neglected. The method is also used to characterize large-amplitude first-mode vibration of a cantilever with non-zero self-weight. The perturbation and finite difference results are compared for these cases and are seen to agree for a large range of vibration amplitudes. Finally, large-amplitude motion of a postbuckled, clamped–clamped beam is simulated for varying degrees of buckling and self-weight using the finite difference method, and backbone curves are obtained.     

Principal component analysis calibration method for dual-luminophore oxygen and temperature sensor films: application to luminescence imaging

Oxygen sensor films are frequently used to image air-pressure distributions on surfaces in aerodynamic wind tunnels. In this application, the sensor film is referred to as a pressure-sensitive paint (PSP). A Stern-Volmer calibration is used to relate the emission intensity ratio of a long-lifetime luminescent dye (the pressure-sensitive luminophore, PSL) to surface air pressure. A major problem in PSP measurements arises because the Stern-Volmer calibration of the PSL's emission varies with temperature. To correct for the temperature dependence, a second luminescent dye that has an emission that varies with temperature (the temperature-sensitive luminophore, TSL) is incorporated into the sensor film. With such a dual-luminophore PSP (DL-PSP), it is possible to measure the surface-temperature distribution with the TSL emission, and this information is then used to correct the temperature dependence of the PSL's pressure response. In the present article, we report the application of a DL-PSP to obtain high-resolution air-pressure distributions on a surface that is subjected to a 20 degrees C temperature gradient. Two different calibration methods are used to generate surface-temperature and air-pressure distributions from the luminescence imaging data, and a quantitative comparison of the results obtained from the two methods is provided. The first method is based on an intensity-ratio calibration that uses luminescence images collected at two wavelengths, one corresponding to the TSL emission and the second corresponding to the PSL emission. The second method is based on principal component analysis (PCA) of luminescence images obtained at four wavelengths throughout the spectral region of the TSL and PSL emission (hyperspectral imaging, 550-750 nm). The results demonstrate that the PCA method allows the measurement of surface air pressure with higher accuracy and precision compared to those of the intensity-ratio method. The improvement is especially significant at pressures near 1 atm, where the temperature interference is most pronounced. Surface-pressure distributions are measured with comparable accuracy and precision with the two methods.     

Buckling of elastic columns with second-mode imperfections

Meccanica - The pin-ended, slender, Euler strut has been used as the archetypal buckling problem for many years (Euler in Additamentum I de curvis elasticis, methodus inveniendi lineas curvas...