Ляпунов方法在充液腔体旋转运动稳定问题中的应用

<正> 处理连续系统的运动稳定问题通常有二种办法:一种为简正模方法(Normal mode approuch);另一种为整体法(Global approuch),包括直接方法和能量法。前一方法要和后者等价必须假定本征模是完全的(个别情形能证明)。在最近三十年来,直接方法推广到连续系统已取得很大进展。在文献[3]中,我们应用简正模方法处理了充液腔体整体旋转运动的稳定问题。现有的

Non-modal instabilities of two-dimensional disturbances in plane Couette flow of a power-law fluid

Instabilities of fluid flows have traditionally been investigated by normal mode analysis, i.e. by linearizing the equations of flow and testing for unstable eigenvalues of the linearized problem. However, the results of eigenvalue analysis agree poorly in many cases with experiments, especially for shear flows. In this paper we study the instabilities of two-dimensional Couette flow of a polymeric fluid in the framework of non-modal stability theory rather than normal mode analysis. A power-law model is used to describe the polymeric liquid. We focus on the response to external excitations and initial conditions by examining the pseudospectra structures and the transient energy growths. For both Newtonian and non-Newtonian flows, the results show that there can be a rather large transient growth even though the linear operator of Couette flow has no unstable eigenvalue. The effects of non-Newtonian viscosity on the transient behaviors are examined in this study. The results show that the "shear-thinning/shear-thickening" effect increases/decreases the amplitude of responses to external excitations and initial conditions. (C) 2010 Elsevier B.V. All rights reserved.

Instabilities and transient behaviors of a liquid film flowing down a porous inclined plane

The nonmodal linear stability of a falling film over a porous inclined plane has been investigated. The base flow is driven by gravity. We use Darcy's law to describe the flow in the porous medium. A simplified one-sided model is used to describe the fluid flow. In this model, the influence of the porous layer on the flow in the film can be identified by a parameter beta. The instabilities of a falling film have traditionally been investigated by linearizing the governing equations and testing for unstable eigenvalues of the linearized problem. However, the results of eigenvalue analysis agree poorly in many cases with experiments, especially for shear flows. In the present paper, we have studied the linear stability of three-dimensional disturbances using the nonmodal stability theory. Particular attentions are paid to the transient behavior rather than the long time behavior of eigenmodes predicted by traditional normal mode analysis. The transient behaviors of the response to external excitations and the response to initial conditions are studied by examining the pseudospectral structures and the energy growth function G(t) Before we study the nonmodal stability of the system, we extend the results of long-wave analysis in previous works by examining the linear stabilities for streamwise and spanwise disturbances. Results show that the critical conditions of both the surface mode and the shear mode instabilities are dependent on beta for streamwise disturbances. However, the spanwise disturbances have no unstable eigenvalue. 2010 American Institute of Physics. [doi:10.1063/1.3455503]

Sequential deprotonation of meso-(p-hydroxyphenyl)porphyrins in DMF: From hyperporphyrins to sodium porphyrin complexes

Sequential deprotonations of meso-(p-hydroxyphenyl)porphyrins (p-OHTPPH2) in DMF + H2O (V/V = 1:1) mixture have been verified to result in the appearance of hyperporphyrin spectra. However, when the deprotonations of these p-OHTPPH2 are carried out in DMF, the spectral changes differ considerably from those in the mixture mentioned above. At low [OH-], the optical spectra in the visible region are still considered to have characteristics of hyperporphyrin spectra. Further deprotonation at much higher basicity makes the optical spectra form three-banded spectra similar to those in the acidic solution. To clarify the molecular origins of these changes, UV-vis, resonance Raman (RR), proton nuclear magnetic resonance (H-1 NMR) experiments are carried out. Our data give evidence that p-OHTPPH2 in DMF can be further deprotonated of pyrrolic-H by higher concentrated NaOH, due to an aprotic medium like DMF effectively weakening the basicity of the porphyrin relative to that of the NaOH, and coordinates with two sodium ions (except the sodium ions that interact with the peripherial phenoxide anions) to form the sodium complexes of p-OHTPPH2 (Na2P, to lay a strong emphasis on the sodium ions that coordinate with the central nitrogen atom), which can be regarded as the porphyrin anions being perturbed by the sodium cations due to their highly ionic character.

Vibronic transitions and site substitution of Eu2+ and codoped ions in KMgF3 : Eu-X (X=Ce, Cr, Gd, Cu) system

The high-resolution emission spectra of KMgF3 : Eu and KMgF3 : Eu-X(X = Ce, Cr, Gd, Cu) single crystals were measured at 300 and 77 K. The vibronic side bands of Eu2+ were characterized and an assignment of the normal mode frequencies to particular vibrations has been made. The correlation between the vibronic frequencies of Eu2+ and the site substitution of other co-dopcd ions was first found. The relationship between vibronic intensity of Eu2+ and other doped ions concentration showed that Cr3+, Gd3+ ions competed K+ sites with Eu2+ ions. Ce3+ and Eu3+ occurred the electron transference. The introduction of Cu+ made for Eu2+ substuting for K+ sites.

Effect of low-frequency Rossby wave on thermal structure of the upper southwestern tropical Indian Ocean

We investigate the influence of low-frequency Rossby waves on the thermal structure of the upper southwestern tropical Indian Ocean (SWTIO) using Argo profiles, satellite altimetric data, sea surface temperature, wind field data and the theory of linear vertical normal mode decomposition. Our results show that the SWTIO is generally dominated by the first baroclinic mode motion. As strong downwelling Rossby waves reach the SWTIO, the contribution of the second baroclinic mode motion in this region can be increased mainly because of the reduction in the vertical stratification of the upper layer above thermocline, and the enhancement in the vertical stratification of the lower layer under thermocline also contributes to it. The vertical displacement of each isothermal is enlarged and the thermal structure of the upper level is modulated, which is indicative of strong vertical mixing. However, the cold Rossby waves increase the vertical stratification of the upper level, restricting the variability related to the second baroclinic mode. On the other hand, during decaying phase of warm Rossby waves, Ekman upwelling and advection processes associated with the surface cyclonic wind circulation can restrain the downwelling processes, carrying the relatively colder water to the near-surface, which results in an out-of-phase phenomenon between sea surface temperature anomaly (SSTA) and sea surface height anomaly (SSHA) in the SWTIO.

Novel method for design of surface relief guided-mode resonant gratings at normal incidence

We demonstrate that the surface relief guided-mode resonant gratings with specified central wavelength and FWHM in the visible wavelength range can be designed by analyzing the complex poles of Reflectance and transmission coefficient matrix algorithm (RTCM), a variant of S-matrix propagation algorithm proposed for calculation of multilayer gratings. In addition, FWHM is computed with couple-mode (CM) theory of resonant gratings which is firstly extended by Norton et al. in calculation of waveguide grating. Furthermore, the side band reflections of the filter can be reduced to less than 5% in the visible wavelength with the antireflection (AR) design technique widely used in the thin-film field. (C) 2008 Elsevier B.V. All rights reserved.

Viscosity-induced mode splitting and potential energy criterion for mode stability

This paper points out that viscosity can induce mode splitting in a uniform infinite cylinder of an incompressible fluid with self-gravitation, and that the potential energy criterion cannot be appropriate to all normal modes obtained, i.e., there will be stable modes with negative potential energy (<0). Therefore the condition >0 is not necessary, although sufficient, for the stability of a mode in an incompressible static fluid or magnetohydrodynamics (MHD) system, which is a correction of both Hare's [Philos. Mag. 8, 1305 (1959)] and Chandrasekhar's [Hydrodynamic and Hydromagnetic Stability (Oxford U.P., Oxford, 1961), p. 604] stability criterion for a mode. These results can also be extended to compressible systems with a polytropic exponent.

Mode properties of off-axis one-sided hybrid resonator for novel high average power dual-slab laser

A novel dual-slab laser with off-axis one-sided hybrid resonator is presented. The mode properties of the hybrid resonator are calculated using a fast Fourier transform method (FFT). The influence of wavefront distoration on the output beam quality is considered. Results indicate that the novel dual-slab laser is better than the normal dual-slab laser with off-axis one-sided hybrid resonator.

Electric field enhancement in guided-mode resonance filters

Electric fields inside guided-mode resonance filters (GMRFs) may be intensified by resonance effects. The electric field enhancement is investigated in two GMRFs: one is resonant at normal incidence, the other at oblique incidence. It is shown that the two GMRFs exhibit different behaviors in their electric enhancement. Differences between the electric field distributions of the two GMRFs arise because coupling between counter-propagating modes occurs in the first case. It is also shown that the order of the electric field of maximum amplitude can be controlled by modulation of the dielectric constant of the grating. (c) 2006 Optical Society of America.

Nonpolarizing guided-mode resonance filter

A normal-incidence nonpolarizing guided-mode resonance filter is designed. There are two waveguide layers and one grating layer in the filter. By adjusting the distance between the two waveguide layers, the same resonance wavelength for both TE and TM polarization can be achieved. An antireflection design method is also used to decrease the sideband reflection of the filter. The results show that the filter has high reflection, more than 99.9% at 500 nm, and the FW-HMs of TE- and TM-polarized light are 2.16 and 0.15 nm, respectively. (C) 2009 Optical Society of America

Reproduction mode of an artificial allotetraploid carp (Pisces; Cyprinidae)

Mature eggs of allotetraploid carp were activated by inactive sperm or crossed with normal sperms of common carp (Cyprinus carpio), crucian carp (Carassius auratus), Chinese blunt snout bream (Megalobrama amblycephala), Hemiculter leucisculus and Pseudorasbora parva. Chromosome counts showed that all offspring of these crosses presented a mode number of 200 chromosomes (4n = 200), and their morphological traits are much like maternal. Microsatelite marker and RAPD patterns between allotetraploid maternal and its offspring, reproduced from different paternal species, were identical. Cytological, morphological and molecular evidences suggested that allotetraploid carp female nucleus would not fuse with any male nucleus and its reproduction mode might be gynogenesis and therefore their offspring are retaining their tetraploidy and give origin to clonal individuals.

Harmonic mode-locked ytterbium-doped fibre ring laser

We demonstrate a harmonic mode-locked ytterbium-doped fibre ring laser, which consists of a polarization-sensitive isolator, two polarization controllers, two 976 nm laser diodes as the pump source and a two-segment ytterbium-doped fibre. Utilizing an additive pulse mode-locked technique based on nonlinear polarization evolution, the ytterbium-doped fibre laser can operate in mode-locked state by adjusting the position of polarization controllers. The cavity fundamental repetition rate is 23.78 MHz. We also observe the second- and third-harmonic mode locking in the normal dispersion region, and their repetition rates are 47.66 MHz and 71.56 MHz, respectively. Over-driving of the saturable absorber in the harmonic mode-locking pulse is analysed and discussed in detail.

Efficient Mode-locked and Q-switched Nd∶YVO_4 Laser with Semiconductor Saturable Absorber Mirror

We reported an efficient diode pumped Nd ! YVO, 1 064 nm laser passively mode-locked and Q-switched by a semiconductor saturable absorber mirror(SESAM). At the incident pump power of 7. 5 W, 2. 81 W average output power was obtained during stable CW mode locking with a repetition rate of 111 MHz. The optical conversion efficiency was 37. 5% , and the slope efficiency was 39%. So far as we know, this is the highest optical-optical conversion efficiency with a SESAM at home.

Manipulation, dissection, and lithography using modified tapping mode atomic force microscope

A modified tapping mode of the atomic force microscope (AFM) was introduced for manipulation, dissection, and lithography. By sufficiently decreasing the amplitude of AFM tip in the normal tapping mode and adjusting the setpoint, the tip-sample interaction can be efficiently controlled. This modified tapping mode has some characteristics of the AFM contact mode and can be used to manipulate nanoparticles, dissect biomolecules, and make lithographs on various surfaces. This method did not need any additional equipment and it can be applied to any AFM system.