分段线性电路切换系统的复杂行为及非光滑分岔机理

分析了分段线性电路系统在周期切换下的复杂动力学行为及其产生的机理. 基于平衡点分析, 给出了两子系统Fold分岔和Hopf分岔条件. 考虑了在不同稳定态时两子系统周期切换的分岔特性, 产生了不同的周期振荡, 并揭示了其产生的机理. 在不同的周期振荡中, 切换点的数量随参数变化产生倍化, 导致切换系统由倍周期分岔进入混沌. 关键词： 分段线性电路 切换系统 非光滑分岔     

Theoretical investigation of imidazolium based ionic liquid/alcohol mixture: a molecular dynamic simulation

In this work, molecular dynamic simulation of the mixture of imidazolium based ionic liquids with alcohols is implemented in order to investigate mixing excess properties and some structural and physical properties of the mixture. Excess volumes and enthalpies are evaluated for 11 different mole fractions of ionic liquids at each 0.1, in the range of 0 to 1. Radial distribution function, cohesive energy density, potential of mean force, solvation energy, and diffusion coefficient are reported and analysed. The effects of the cationic alkyl chain length, in comparison with changes of the anions, on these properties are reported. Results reveal that the methanol molecule participates with its hydrophilic characteristics in the mixing process and tends to aggregate around anion part of the ionic liquids, especially in the case of Cl.     

Application of h-adaptive,high order finite element method to solve radial Schrödinger equation

The h-adaptive, high order finite element method is applied to solve a second order one dimension eigenvalue problem. The finite element formulation for the Lobatto basis is given, for which basis functions of arbitrary order can be constructed. The adaptive algorithm is simple, yet very efficient and straightforward to implement. The algorithm is based on the observation that the expansion coefficients of Lobatto basis functions decay rapidly. It allows evaluating the smallest eigenvalues simultaneously with the comparable accuracy for all eigenvalues. The presented algorithm is applied to solve the radial Schrödinger equation with the Coulomb and the Woods–Saxon potentials. For both potentials the convergence rate is presented. After seven adaptive iterations nine-digit accuracy was obtained.     

Structural characterization of pseudo-binary semiconducting alloys using molecular simulations

Monte Carlo simulations with the Keating model have been performed to predict the lattice constant and bond length variations with composition for pseudo-binary semiconducting alloys. In general, it is observed that the deviations of the lattice constants from Vegard's law predictions are larger as the lattice mismatch between the constituent binaries increases. Further, it is noted that these alloys have partial virtual crystal model characteristics and tend to be more towards the flexible (floppy) crystal limit as compared to the rigid crystal limit. The topological rigidity parameters are bond-type dependent. The angular deviations from perfect tetrahedral structure are also measured.     

High resolution dynamic cardiac MRI using partial separability of spatiotemporal signals with a novel sampling scheme

The partial separability (PS) of spatiotemporal signals has been exploited to accelerate dynamic cardiac MRI by sampling two datasets (training and imaging datasets) without breath-holding or ECG triggering. According to the theory of partially separable functions, the wider the range of spatial frequency components covered by the training dataset, the more accurate the temporal constraint imposed by the PS model. Therefore, it is necessary to develop a new sampling scheme for the PS model in order to cover a wider range of spatial frequency components. In this paper, we propose the use of radial sampling trajectories for collecting the training dataset and Cartesian sampling trajectories for collecting the imaging dataset. In vivo high resolution cardiac MRI experiments demonstrate that the proposed data sampling scheme can significantly improve the image quality. The image quality using the PS model with the proposed sampling scheme is comparable to that of a commercial method using retrospective cardiac gating and breath-holding. The success of this study demonstrates great potential for high-quality, high resolution dynamic cardiac MRI without ECG gating or breath-holding through use of the PS model and the novel data sampling scheme.     

Stoichiometry,Association Constant,and Solvation Model of Chiral Hydroxyfuranones in the Presence of Pirkle's Alcohols

ABSTRACT

(S)-(+)-Dihydro-3-hydroxy-4,4-dimethyl-2(3H)-furanone, (R)-(-)-dihydro-3-hydroxy-4,4-dimethyl-2(3H)-furanone, (S)-(-)-dihydro-4-hydroxy-2(3H)-furanone, and (S)-(-)-5-hydroxymethyl-2(5H)-furanone in the presence of pure enantiomers of 2,2,2-trifluoro-1-(9-anthryl)ethanol were studied by ¹H NMR in deuterated chloroform solutions. Experimental Job's plots suggest that the resulting solvates are formed with one molecule of solute and one of the chiral solvating agent. From the magnitude of the association constant determined for (S)-(+)-dihydro-3-hydroxy-4,4-dimethyl-2(3H)-furanone in the presence of (R)-(-)-2,2,2-trifluoro-1-(9-anthryl)ethanol (1.26 ± 0.09 M^?1), it is inferred that the solvate is weak and cannot be isolated at 298 K. The correlation between the magnitude of induced chemical shifts, NOESY maps, and the known configuration of solutes and chiral solvating agents suggests that intermolecular hydroxyl-hydroxyl interaction is the primary interaction. Accordingly, the secondary interaction might occur between benzylic-hydrogen of the chiral solvating agent and the carbonyl- or furan ring-oxygen atoms of the solute.     

Hydrophobic Bimetallic Catalysts for H/D Exchange Reaction between Hydrogen and Water

Hydrophobic bimetallic catalysts of Pt-M on styrenedivinylbenzene were prepared, where M represents successively: Ir, Rh, Pd, Cu and Ag. The total metal loading was 0.5 wt% and the weight fractions of the metal M were: 0.0,0.05,0.1,0.25,0.5,0.75 and 1.0. For each sample, the catalytic activity for H/D exchange between hydrogen and water vapor was measured. In case of monometallic catalysts, no activity was detected for M = Cu and M = Ag, and the order of the activity values for the other metals was: Pt < Ir < Rh < Pd. For each bimetallic catalyst, the activity measurements indicated a clear interaction between the platinum and the second metal, thus the activity was significantly increased for M = Ir, increased for M = Rh, decreased for M = Pd, drastically decreased for M = Cu and M = Ag.     

Radiation Effects on Optical Properties of Ethylene Vinyl Acetate Copolymer Films

The optical properties of ethylene vinyl acetate (EVA) film have been studied. The effects of gamma irradiations on the optical spectrum of EVA films have been investigated using spectrophotometric measurements of reflectance and transmittance in the wavelength range 200–1100 nm. The absorption spectra were recorded in the UV–vis region for the unirradiated and irradiated films (from 0 to 50 kGy). Optical constants such as refractive index (n), extinction coefficient (K), and complex dielectric constant have been determined, as well as the optical dispersion parameters and high frequency dielectric constants. A large dependence of the fundamental optical constants on the irradiation dose was noticed. On irradiation, a higher refractive index was obtained as compared with that for unirradiated film. The dispersion parameters, such as E ₀ (single‐oscillator energy), E _d (dispersive energy), and M _?1 and M _?3 (moments), are discussed in terms of the single‐oscillator Wemple–DiDomenico model.     

On gradient field theories: gradient magnetostatics and gradient elasticity

In this work, the fundamentals of gradient field theories are presented and reviewed. In particular, the theories of gradient magnetostatics and gradient elasticity are investigated and compared. For gradient magnetostatics, non-singular expressions for the magnetic vector gauge potential, the Biot–Savart law, the Lorentz force and the mutual interaction energy of two electric current loops are derived and discussed. For gradient elasticity, non-singular forms of all dislocation key formulas (Burgers equation, Mura equation, Peach–Koehler stress equation, Peach–Koehler force equation, and mutual interaction energy of two dislocation loops) are presented. In addition, similarities between an electric current loop and a dislocation loop are pointed out. The obtained fields for both gradient theories are non-singular due to a straightforward and self-consistent regularization.     

Nonequilibrium fluctuations in μ space

The properties of fluctuations in space in or outside thermal equilibrium are obtained by solving hierarchies of equations derived either from the Liouville or the Master equation. In particular we study the one-, two-, etc., time correlation functions that describe the spatial and temporal behavior of the fluctuations in space. Explicit solutions are obtained for a dilute gas. The Langevin approach is briefly discussed. Our results are compared with those obtained in the extensive literature, which is reviewed in some detail.