Intermolecular Charge-Transfer Interactions Facilitate Two-Photon Absorption in Styrylpyridine–Tetracyanobenzene Cocrystals

Cocrystals of 4-styrylpyridine and 1,2,4,5-tetracyanobenzene were successfully prepared by supramolecular self-assembly. Donor–acceptor interactions between the molecular components are the main driving force for self-assembly and contribute to intermolecular charge transfer. The cocrystals possess two-photon absorption properties that are not observed in the individual components; suggesting that two-photon absorption originates from intermolecular charge-transfer interactions in the donor–acceptor system. The origin of two-photon absorption in multichromophore systems remains under-researched; thus, the system offers a rare demonstration of two-photon absorption by cocrystallization. Cocrystal engineering may facilitate further design and development of novel materials for nonlinear optical and optoelectronic applications.     

Analytic approximation of the blow‐up time for nonlinear differential equations by the ADM–Padé technique

We present a new approach to calculate analytic approximations of blow‐up solutions and their critical blow‐up times. Our approach applies the Adomian decomposition–Padé method to quickly and easily compute the critical blow‐up times, which comprises the Adomian decomposition method combined with the Padé approximants technique. We validate our new approach with a variety of numerical examples, including nonlinear ODEs, systems of nonlinear ODEs, and nonlinear PDEs. Furthermore, our new method is shown to be more convenient than prior art that relies on compound discretized algorithms. Copyright © 2013 John Wiley & Sons, Ltd.     

The derivation of the conservation law for defocusing nonlinear Schrödinger equations with non-vanishing initial data at infinity

For nonlinear Schrödinger equations in less than or equal to four dimension, with non-vanishing initial data at infinity, a new approach to derive the conservation law is obtained. Since this approach does not contain approximating procedure, the argument is simplified and some of technical assumption of the nonlinearity to derive the conservation law and time global solutions, is removed.     

参数化连分式拟合方法研究及应用

通过倒差商-连分式算法,提出了一种保端点非线性有理参数化拟合算法,通过选取中间点的参数化,利用连分式插值法,得到的拟合函数具有保端点性,规律性和灵活性.实例表明,算法减少了连分式插值迭代次数,避免插值连分式的不存在性,所得到拟合值具有更好的精度,大大提高了计算效率,拟合的误差更具有平稳性,逼近效果更好,并具有较好的预测等方面的应用.     

The solubility of bosentan in aqueous-2-propanol mixtures at several temperatures,measurement and data correlation

ABSTRACT

The solubilities of bosentan (BST) in binary aqueous mixtures of 2-propanol at temperatures ranging from 293.15 to 313.15 K were determined using a shake-flask method. The produced data were modelled with the Jouyban-Acree-van’t Hoff model and difference between the predicted data and experimental ones were illustrated by percent average relative deviations (%ARD). Moreover, the thermodynamic functions of dissolution for BST in the aqueous 2-propanol solutions were computed which suggest that the dissolution process is endothermic and not spontaneous.     

Bi-Hamiltonian structure of multi-component Novikov equation

In this paper, we present the multi-component Novikov equation and derive it's bi-Hamiltonian structure.     

Time-evolution-proof Scattering Data for the Focusing and Defocusing Zakharov-Shabat Systems

In this article we give sufficient conditions on the scattering data of a defocusing or focusing Zakharov-Shabat system in order that its potential is square integrable. For a dense subset of integrable as well as square integrable potentials, we show that the scattering data actually satisfy these sufficient conditions.     

Nonlinear interaction mechanisms of disturbances in supersonic flat-plate boundary layers

Due to the complexity of compressible flows, nonlinear hydrodynamic stability theories in supersonic boundary layers are not sufficient. In order to reveal the nonlinear interaction mechanisms of the rapidly amplified 3-D disturbances in supersonic boundary layers at high Mach numbers, the nonlinear evolutions of different disturbances in flat-plate boundary layers at Mach number 4.5, 6 and 8 are analyzed by numerical simulations. It can be concluded that the 3-D disturbances are amplified rapidly when the amplitude of the 2-D disturbance reaches a certain level. The most rapidly amplified 3-D disturbances are Klebanoff type (K-type) disturbances which have the same frequency as the 2-D disturbance. Among these K-type 3-D disturbances, the disturbances located at the junction of upper branch and lower branch of the neutral curve are amplified higher. Through analyzing the relationship between the amplification rate and the spanwise wavenumber of the 3-D disturbances at different evolution stages, the mechanism of the spanwise wavenumber selectivity of K-type 3-D disturbances in the presence of a finite amplitude 2-D disturbance is explained.     

Model for spontaneous frequency sweeping of an Alfvén wave in a toroidal plasma

We study the frequency chirping signals arising from spontaneously excited toroidial Alfvén eigenmode (TAE) waves that are being driven by an inverted energetic particle distribution whose free energy is tapped from the generic particle/wave resonance interaction. Initially a wave is excited inside the Alfvén gap with a frequency determined from the linear tip model of Rosenbluth, Berk and Van dam (RBV) [1]. Hole/clumps structures are formed and are observed to chirp towards lower energy states. We find that the chirping signals from clump enter the Alfvén continuum which eventually produce more rapid chirping signals. The accuracy of the adiabatic approximation for the mode evolution is tested and verified by demonstrating that a WKB-like decomposition of the time response for the field phase and amplitude agree with the data. Plots of the phase space structure correlate well with the chirping dependent shape of the separatrix structure. A novel aspect of the simulation is that it performed close to the wave frame of the phase space structure, which enables the numerical time step to remain the same during the simulation, independent of the rest frame frequency.