超导体/正常金属/半导体/正常金属/超导体结的研究

在约瑟夫逊效应的理论研究中,大体上有微观和宏观两种方法。采用的是宏观的方法。利用推广的Ja-cobson方法,讨论了超导体/正常金属/半导体/正常金属/超导体结的约瑟夫逊效应,并在小电流假设下,推导出了该结的电流密度与位相之间的关系。     

The Three Gap Theorem and Riemannian geometry

The classical Three Gap Theorem asserts that for a natural number n and a real number p, there are at most three distinct distances between consecutive elements in the subset of [0,1) consisting of the reductions modulo 1 of the first n multiples of p. Regarding it as a statement about rotations of the circle, we find results in a similar spirit pertaining to isometries of compact Riemannian manifolds and the distribution of points along their geodesics.      

管网结点处两相流相分离流动可视化在线检测实验研究

采用在线式可视化图象技术，对管网中的特征结构元件－－等直径水平Ｔ形分叉管（Ｄ＝３５ｍｍ）的空气－水泡状流，弹状流，分层流的相分离现象进行了实验研究，发现并定义了“新型完全相分离现象”，即在特定工况下，入流的气相流体将完全从直管出口流出，另外通过可视化研究对“压力波反馈效应”及“分叉管中气相重组现象”进行了分析和探讨；将入口质量流量、入口干度及支管质量抽走率对两相分离率的影响作了比较和分析。     

A globally convergent descent method for nonsmooth variational inequalities

We propose a descent method via gap functions for solving nonsmooth variational inequalities with a locally Lipschitz operator. Assuming monotone operator (not necessarily strongly monotone) and bounded domain, we show that the method with an Armijo-type line search is globally convergent. Finally, we report some numerical experiments. This work has been supported by the National Research Program PRIN/2005017083 “Innovative Problems and Methods in Nonlinear Optimization”.     

Neurotrophic regulation of synapse development and plasticity

Neurotrophic factors are traditionally thought to be secretory proteins that regulate long-tern survival and differe, ntiation of neurons. Recent studies have revealed a previously unexpected role for these factors in synaptie de velopment ami plasticity in diverse neuronal populations. Here we review experimeuts carried oul in our own laboratory in the last few years.. We have made two important discoveries.First,we were among the first to report that brain-derived. neurotrophie faclor (BDNF) facilitates hippocampal hmg-term potentiation (LTP), a form of synaptic plaslicity believed to be involved in learning and memory. BDNF modulates LTP al CAI synapses by enhaneing synaptic responses to high frequency, tetanic slimulalion. This is achieved primafily by facilitating synaptie vesicle doeking, possibly due to an in crease in the levels of the vesicle prolein synaptobrevin and synaptoplysin in the nerve terminals. Gene knockout study demonstrates thai the effects of BDNF are primarily mediated through presynaptic mechanisms. Second, we demonstrated a form of long-term, neurotrophin-mediated synaptic regulation. We showed that long-term treatment of the neuromuscu lar synapses with neurotrophin-3 (NT3) resulted in an enhancement of both spontaneous and evoked synaptic currcuts, as well as profound changes in thc number of synaptic varicosities and syuaptic vesicle proteins in motoneurons, all of which are indicative of more mature synapses. Our current work addresses the following issues:(i) activity-dependent trafficking of neurotrophin receptors, and its role in synapse-specific modulation; (ii) signal transduction mechanisms medialing the acute enhancement of synaplic transmission by neurotrophins; (iii) acute and long-tenn synaptie actions of the GDNF family; (iv) role of BDNF in late-phase LTP and in the development of hippocampal circuit.     

Stability and instability of nonlinear defect states in the coupled mode equations—Analytical and numerical study

Coupled backward and forward wave amplitudes of an electromagnetic field propagating in a periodic and nonlinear medium at Bragg resonance are governed by the nonlinear coupled mode equations (NLCME). This system of PDEs, similar in structure to the Dirac equations, has gap soliton solutions that travel at any speed between 0 and the speed of light. A recently considered strategy for spatial trapping or capture of gap optical soliton light pulses is based on the appropriate design of localized defects in the periodic structure. Localized defects in the periodic structure give rise to defect modes, which persist as nonlinear defect modes as the amplitude is increased. Soliton trapping is the transfer of incoming soliton energy to nonlinear defect modes. To serve as targets for such energy transfer, nonlinear defect modes must be stable. We therefore investigate the stability of nonlinear defect modes. Resonance among discrete localized modes and radiation modes plays a role in the mechanism for stability and instability, in a manner analogous to the nonlinear Schrödinger/Gross-Pitaevskii (NLS/GP) equation. However, the nature of instabilities and how energy is exchanged among modes is considerably more complicated than for NLS/GP due, in part, to a continuous spectrum of radiation modes which is unbounded above and below. In this paper we (a) establish the instability of branches of nonlinear defect states which, for vanishing amplitude, have a linearization with eigenvalues embedded within the continuous spectrum, (b) numerically compute, using Evans function, the linearized spectrum of nonlinear defect states of an interesting multiparameter family of defects, and (c) perform direct time-dependent numerical simulations in which we observe the exchange of energy among discrete and continuum modes.     

Numerical simulations of droplet formation in a cross‐junction microchannel by the lattice Boltzmann method

An immiscible liquid–liquid multiphase flow in a cross‐junction microchannel was numerically studied using the lattice Boltzmann method. An improved, immiscible lattice BGK model was proposed by introducing surface tension force based on the continuum surface force (CSF) method. Recoloring step was replaced by the anti‐diffusion scheme in the mixed region to reduce the side‐effect and control the thickness of the interface. The present method was tested by the simulation of a static bubble. Laplace's law and spurious velocities were examined. The results show that our model is more advantageous for simulations of immiscible fluids than the existing immiscible lattice BGK models. Computational results of multiphase flow in a cross‐junction microchannel were obtained and analyzed based on dimensionless numbers. It is found that the flow pattern is decided mostly by the capillary number at a small inlet flux. However, at the same capillary number, a large inlet flux will lead to much smaller droplet generation. For this case, the flow is determined by both the capillary number and the Weber number. Copyright © 2007 John Wiley & Sons, Ltd.     

Short-Time Decoherence of Solid-State Qubit at Optimal Operation Points

We investigate the short-time decoherence of a solid-state qubit under Ohmic noise at optimal operation points. The decoherence is analyzed by maximum norm of the deviation density operator. It is shown that at the temperature T = 3 mK, the loss of the fidelity due to decoherence is much smaller than the DiVincenzo low decoherence criterion, which means that the mode/may be an optimal candidate of qubit for quantum computation.     

Localized solutions to the nonlinear wave equation for flexural motions of an elastic beam traveling in an air-filled tube

Steady-progressive-wave solutions are sought to the nonlinear wave equation derived previously [J. Fluids Struct. 16 (2002) 597] for flexural motions of an elastic beam traveling in an air-filled tube along its center axis at a subsonic speed. Fluid-structure interactions are taken into account through aerodynamic loading on the lateral surface of the beam subjected to small but finite deflection but end effects and viscous effects are neglected. Linear dispersion characteristics are first examined by exploiting the small ratio of the induced mass to the mass of the beam per unit length. Centered around the traveling speed of the beam, there exists such a narrow range of propagation velocity that the linear steady propagation is prohibited. In this range, it is revealed that some interesting nonlinear solutions exist. The periodic wavetrain is found to exist as the exact solution. Asymptotic analysis is then made by applying the method of multiple scales and the stationary nonlinear Schrödinger equation is derived for a complex amplitude. A monochromatic solution to this equation corresponds to the exact periodic solution. Imposing undisturbed boundary conditions at infinity, it is revealed that the localized solution exists as a result of balance between the linear instability and the nonlinearity. This solution is checked by solving the nonlinear equation numerically. It is further revealed that the amplitude-modulated wavetrain exists not only in the range of the velocity mentioned above but also outside of it.     

Ionic liquid salt bridge based on tributyl(2-methoxyethyl)phosphonium bis(pentafluoroethanesulfonyl)amide for stable liquid junction potentials in highly diluted aqueous electrolyte solutions

A moderately hydrophobic ionic liquid, tributyl(2-methoxyethyl)phosphonium bis(pentafluoroethanesulfonyl)amide ([TBMOEP⁺][C₂C₂N⁻]), shows a very stable liquid junction potential upon contact with an aqueous solution whose ionic strength is as low as 1 μmol dm⁻³. The stability with the maximum excursion of the potential within ±0.5 mV for 30 min is very promising for accurate determination of pH and other single ion activities potentiometrically.