Determining if a System is Heterogeneous: The Analysis of Single Molecule Rotational Correlation Functions and Their Limitations

Single molecule spectroscopy can be utilized to measure distributions of individual molecular properties that may be averaged out in the ensemble measurement. For example, complex dynamics in disordered systems can be investigated by observing single molecule rotations via fluorescence spectroscopy. The rotational time of a single transient can be calculated from the correlation function of the reduced linear dichroism signal which fluctuates over time as the molecule reorients in its surroundings. Distributions of rotational time constants can be used to characterize the heterogeneity of molecular environments in the material. This paper reviews some theoretical studies on (1) the high numerical aperture effects on the final correlation function, and how it can be related to optical anisotropy decays in a bulk measurement; (2) the statistical errors resulting from the finite observation length that will propagate into distributions of rotational times. These lead to the discussions on how to interpret correctly the distribution of properties measured from a set of single molecule data, and to determine if in fact the system is heterogeneous.     

Local modes of silane within the framework of stretching vibrational polyads

We define stretching relative equilibria (RE) of silane and other similar tetrahedral molecules in terms of the dynamical polyad symmetry which assumes the resonance condition 1:1 between the two stretching vibrational modes ν₁ and ν₃ of the molecule. Exploiting symmetry and topology arguments and reducing the dimension of the classical mechanical system, we find these RE. One of them, with local symmetry C_3v and minimal energy within a polyad, corresponds to the local modes. We give the upper energy limit of the local mode localization within a polyad.     

Linear and non-linear stability limits for centrifugal convection in an anisotropic layer

This paper finds stability limits for the onset of convection in a fluid saturated porous layer subject to alternating directions of centrifugal acceleration. The layer is homogeneous but mechanically and thermally anisotropic. The Brinkman equation is assumed to govern the momentum balance of the fluid flow. A linear analysis based on normal mode approach and a non-linear analysis based on energy method are made. The non-linear results are unconditional and their sharp limits are obtained. The numerical solutions predicted using the compound matrix method show that the anisotropy parameters and offset distances of the axis of rotation significantly affect the stability characteristics.     

Mathematical modelling and analysis of bulk waves in rotating generalized thermoelastic media with voids

The present paper deals with the propagation of body waves in a homogenous isotropic, rotating, generalized thermoelastic solid with voids. The complex quartic secular equation has been solved by employing Descartes’ algorithm and perturbation method to obtain phase velocities, attenuations and specific loss factors of four attenuating and dispersive waves, which are possible to exist in such media. These wave characteristics have been computed numerically for magnesium crystal and presented graphically. Statistical analysis has been performed to compare the obtained computer simulated result in order to have estimate on the suitability of the method to compute various characteristics of the waves. This work may find applications in geophysics and gyroscopic sensors.     

Reparameterization of Semiempirical Techniques to Remove Anomalous Energy Minima

Semiempirical molecular orbital calculations have been shown to predict double minima potential surfaces which are not confirmed by further experimental or theoretical evidence.¹ These same techniques predict barriers to internal rotation which are not only in large error but may not even follow the experimental trends.² These discrepancies offer a large decrease in self confidence for the application of these techniques to molecular systems where direct experimental evidence is not available, and these are often the circumstances where one wants a theory to be used. Therefore, our research group is in the process of reparameterizing the procedure INDO³ to yield barriers to internal rotation, bond angles, and bond lengths within reliable confidence limits. During this process of determining new parameters we have observed that some sets of parameters will also remove the anomalous energy minima predicted by the original INDO parameters. To illustrate this we consider in this paper the molecule CO₂.     

Properties of synchronization in the systems of non-identical coupled van der Pol and van der Pol-Duffing oscillators. Broadband synchronization

The particular properties of dynamics are discussed for dissipatively coupled van der Pol oscillators, non-identical in values of parameters controlling the Hopf bifurcation. Possibility of a special synchronization regime in an infinitively long band between oscillator death and quasiperiodic areas is shown for such system. Features of the bifurcation picture are discussed for different values of the control parameters and for the case of additional Duffing-type nonlinearity. Analysis of the slow-flow equations is presented.     

N’-苄基酰腙分子的氮-氮键旋转位阻及分子构象

采用动态核磁共振波谱(DNMR)和密度泛函理论(DFT)对N'-苄基酰腙化合物进行构象研究. 实验和理论计算表明, 1H NMR图谱中三组不同质子的双峰裂分是由N—N键旋转位阻造成的, 而这三个双峰裂分的化学位移差异随温度升高而减小. 通过模拟化学位移差异与温度的关系, 得到了交换速率常数, 采用Eyring方程计算出N—N键旋转位阻. 提出顺式和反式共存的模型来分析酰胺质子信号分裂的原因, 并利用DFT计算得出优化的异构体构象及其最低能量. 端甲基质子和次甲基质子信号裂分也来源于N—N键旋转受阻. N'-苄基酰腙通过缩合反应转变成1,3,4-二唑化合物, 消除了甲基空间取向的差异, 其信号变为单峰.     

Axial dispersion coefficient in high-speed counter-current chromatography

Experimental measurements of axial dispersion coefficients in high-speed counter-current chromatography have been carried out in the single-phase and two-phase modes. Axial dispersion coefficients were calculated from the residence time distribution curve (or the elution profile). The experimental data obtained were used to develop a model involving Peclet number Pe, Reynolds number and the ratio of flow velocity u to linear angular velocity u_θ for predicting the axial dispersion coefficient. Furthermore, the models obtained from the single-phase and two-phase modes were compared, and a counterintuitive phenomenon was found in that the effects of the flow rate and the rotation speed on the axial dispersion coefficients are inconsistent: the axial dispersion coefficient decreases with the rotation speed and increases with the flow rate in the single-phase mode, but increases with rotation speed and decreases slightly with the flow rate in the two-phase mode.     

新型塑料管材加工方法研究进展

塑料管材综合性能优异,广泛应用于城乡建设的各个领域.随着管材行业的发展,对管材性能的要求也越来越高,塑料管材加工方式也在不断发展.本文说明了塑料管材应用领域,介绍了管材的挤出成型生产方法,概括了塑料管材行业现状,探讨了传统管材加工方式存在的不足,阐明了开发新型管材生产工艺的必要性和重要性,从定义、原理、结构、管材性能等...     

Numerical and experimental investigation of ‘water fan’ effect due to electrohydrodynamic force in a microchamber

Electrohydrodynamics is commonly used in microfluidics to control and manipulate the fluid. Though there are studies on the rotation flow in suspended films, the thin film liquid is easily broken and cannot last long hence not applicable in specific applications. Here, we established a three‐dimensional microchamber embedded with two pairs of microelectrodes to investigate the rotational phenomenon of bulk of liquid which we called ‘water fan’ effect based on the electrohydrodynamics force. When proper voltages were applied on these microelectrodes, the tornado‐like rotation would be generated. Both the numerical and experimental results showed that the controllable and continuous rotation could be achieved in the microchamber. In addition, the concentration effect resulting from the rotation flow was also observed. The proposed method offers great promises in providing theoretical and practical guideline in microfluidic devices for mixing, separating, and cooling applications.