桡动脉压力波随生理参数的变化

本文将臂动脉比拟为一根均匀弹性管,以臂动脉与主动脉分叉处的实测压力波形作为臂动脉的输入波形,并用一系列小阶梯波来近似逼近这输入波形。然后在线化条件下,求得桡动脉处瞬态压力的分析表达式。文章详细讨论了心脏搏动周期、臂动脉弹性与臂动脉端点阻力等生理参数对桡动脉压力波波形的影响情况,并逐一将所得结果与实验结果作比较,发现二者相当一致。     

非线性参数激励系统的动力分叉研究

本文针对弹性梁动力曲屈分叉问题,建立了系统的非线性Mathiue方程,较全面地讨论了此类参数激励系统的1/2亚谐分叉特性,指出以往对此类问题的研究得到的只是一种退化情形下的分叉特性,阐述了分叉方程的截断对分叉结果的影响,得到了一些新的结果。文中还介绍了一个模型弹性梁系统分叉响应特性的实测结果,证实了理论分析的可靠性。     

可压缩球膜的膨胀和分叉

利用大变形迭加小变形的一般方法详细考察了可压缩球膜的膨胀和分叉问题.得到了可压缩球膜分叉的控制微分方程组,并通过求解非线性偏微分方程组,给出了不同情形的分叉模式及相应的分叉判据,但为了与Alexancler的实验对比,只认为01模式的分叉解在物理上是可行的.结果表明:可压缩球膜分叉解的控制微分方程组与不可压缩时非常相似,都只有3个独立的弹性系数,但弹性系数的定义是不同的;从理论上证明了可压缩球膜的分叉也是在内压达到极大值之后发生的,且在球膜的膨胀过程中.当内压达到极大值后,球膜的形状不再是标准的球形.而是上半球的厚度变大,下半球厚度变小,此时球膜分叉了,这与实验结果是一致的.     

一类慢变参数振子系统的同宿分叉及其安全盆侵蚀

分析一个具有慢变参数的非线性系统,利用Ｍｅｌｎｋｏｖ方法,分析了系统在参数发生变化时的同宿分叉,同时利用分叉结果,数值讨论了当系统参数发生变化时安全盆的侵蚀及分叉,混沌的联系。     

随机干扰与随机参数激励联合作用下的Hopf分叉

本文研究van der Pol-Duffing型的非线性振子在随机干扰和随机参数联合作用下的Hopf分叉现象。本文所得结果证实了当系统处在于Hopf分叉点附近时,对系统的参数的变化具有敏感性。在研究过程中,我们利用Markov扩散过程逼近系统的随机响应,得到了沿稳定矩的概率1稳定和矩稳定的条件。对于非线性振子,我们得到了振幅过程的稳态概论密度函数。研究发现,确定性系统的Hopf分叉点在随机参数作用下具有漂移现象,这种漂移是由系统的性质所决定的,当分叉点为超临界的,分叉点向前漂移;而当分叉点为亚临界时,这种漂移是向后的。当系统处在外部随机干扰作用下时,系统出现非零响应。另外我们发现,稳态矩的分叉与其阶数无关。     

气相爆轰在T形管中传播新现象的实验研究

对2H2/O2/Ar系统爆轰波在T形管(截面为40mm×40mm)中传播现象进行了实验研究.用烟迹片记录了T形管中爆轰波的胞格结构,用压电传感器记录了分叉口附近指定点压力时间曲线,得到了爆轰波在分叉口附近的平均速度和胞格图案演变.结果表明:初压P0≥2.67kPa,在水平和垂直支管下游区域(距离分叉口约3.5—6倍方管截面边长),分叉口影响消失,爆轰波恢复稳定,且强度基本保持不变.在分叉口绕射过程中,爆轰波在膨胀区中衰减,诱导激波阵面弯曲.两个支管中发生马赫反射,三波点迹线清晰可见.该传播特性是爆轰波的诱导激波和横波共同作用的结果.分叉口附近的胞格结构先消失再恢复,在无胞格和平衡胞格之间的区域存在细密胞格的过渡区,表征了在诱导激波与化学反应阵面分离后的区域中出现二次点火.P0=2.00kPa,水平支管中稳定自持爆轰能重建,垂直支管中爆轰熄灭.P0<2.00kPa,分叉口上游已不能形成稳定爆轰.还对胞格结构中的几个特征参数进行了测量,并初步分析了P0对这些参数的影响.     

多孔介质中热对流的分叉机理研究

本文利用解析分析方法研究了数值模拟发现的多孔介质层中出现的对流分叉机理，指出控制方程中的Ｒａｙｌｅｉｇｈ数，是决定流动的特征参数。当Ｒａｙｌｅｉｇｈ数小于临界数值时，多孔介质内流动处于静止传热状态，并且这种状态是稳定的。如果Ｒａｙｌｅｉｇｈ数大于临界数值，非线性方程出现分叉解，文中指出，存在多个使平凡解失稳而分叉的临界Ｒａｙｌｅｉｇｈ数，当Ｒａｙｌｅｉｇｈ数由小到大经历这些临界数值时，其由平凡解发展起来的分叉解的流态，依次由单回流区转变为双回流区及三回流区。理论分析给出了分叉解和分叉解的振幅方程，阐明了分叉的机理，其结论和数值结果定性一致．     

参数激励与强迫激励联合作用下非线性振动系统的余维2退化分叉

在本文里我们首先研究了具有Z_2-对称性的范式理论和退化向量场的普适开折理论。然后利用上述理论研究了参数激励与强迫激励联合作用下非线性振动系统的余维2退化分叉,从而解决了当解具有两个零特征值时解的稳定性问题。最后利用Melnikov方法求出了参数平面上的同宿分叉曲线,讨论了全局分叉的存在性。     

基于能量释放率的Ⅱ型裂纹分叉研究

裂纹尖端存在奇异应力场,该类奇异应力场所具有的高度应力集中将导致裂纹开裂.本文应用典型的J积分理论来划分裂纹尖端的积分路径,基于能量释放率理论对Ⅱ型裂纹尖端的复杂分叉情况进行研究.通过所建立的断裂模型求解出Ⅱ型裂纹多种分叉形式的能量释放率的解析解;导出了各种分叉构型的能量驱动力;提出了各种分叉构型的K-型开裂准则;给出了裂纹分叉的临界开裂角;确定了裂纹的分叉韧性与断裂韧性之间的关系.通过本文研究方法得出的裂纹分叉形式及裂纹分叉临界开裂角与已有实验结果十分吻合.     

非线性Mathieu方程1／2亚谐分叉解的实验研究

本文对一类Mathieu方程的1/2亚谐分叉特性进行了实验研究,得出了在整个参数平面上具有不同拓朴结构分叉图的实验曲线,研究了确定非线性系统衰减参数的方法。并对各种特定的物理系统,可能出现的不同拓朴结构的分叉图和所具有的不同参数区域进行了讨论。     

Spatial resolved temperature measurement based on absorption spectroscopy using a single tunable diode laser

A novel method based on wavelength-multiplexed line-of-sight absorption and profile fitting for nonuniform flow field measurement is reported. A wavelength scanning combing laser temperature and current modulation WMS scheme is used to implement the wavelength-multi- plexed-profile fitting method. Second harmonic （2f） signal of eight H20 transitions features near 7,170 cm^-1 are measured in one period using a single tunable diode laser. Spatial resolved temperature distribution upon a CH4/air premixed flat flame burner is obtained. The result validates the feasibility of strategy for non-uniform flow field diagnostics by means of WMS-2f TDLAS.     

Solitary waves on inclined films: their characteristics and the effects on wall shear stress

The properties of solitary waves, developing from inlet disturbances of controlled frequency along an inclined film flow, are systematically studied experimentally and computationally. Time-variations of film height and wall shear stress are measured, using respectively a capacitance probe and an electrodiffusion sensor. Computational data are provided from simulations performed by a Galerkin finite element scheme. The height and spacing of solitary humps, their phase velocity and the wavelength of the preceding capillary ripples are reported as functions of the Reynolds number (10<Re<100) and the inlet frequency (0.5 Hz< f<2.5 Hz). The wall shear stress modulation imposed by the passage of solitary waves is studied experimentally and computationally as a function of Re. Distinct nonlinear characteristics are noted, including a steep maximum and a negative minimum, with the effects intensifying at intermediate Re. All computer predictions are found to be in good quantitative agreement with the experimental data.     

Two-dimensional bifurcations of stokes waves

Bifurcation techniques are used to obtain a new class of small amplitude water waves of permanent form. This calculation illustrates an approach which can be applied to nonlinear waves of various types to generate new steady solutions from old.Stokes waves are used as a starting point, and the critical value of steepness at which bifurcation can occur is computed for various choices of modulation wavelength and angular orientation. It is found that, for two-dimensional surfaces, bifurcation can occur at small values of wave steepness.Second-order corrections to the wave amplitude, modulation, frequency, and speed, which apply when one moves off the bifurcation point onto a new branch of solutions, are also computed. Two types of new solutions are found, one symmetric with respect to the carrier wave propagation direction, and one asymmetric.The nonlinear Schrödinger equation is used to model water waves, and thus the calculation can be applied rather directly to other systems governed by the nonlinear Schrödinger equation.     

核磁共振陀螺仪泵浦光频率波动抑制

核磁共振陀螺仪利用原子核自旋磁矩在静磁场中进动频率的不变性敏感载体转动信息。针对泵浦激光频率漂移影响核磁共振陀螺仪性能的问题,研究了泵浦激光频率漂移影响核磁共振陀螺仪性能机理和抑制方法。通过分析核磁共振陀螺仪理论输出的数学模型和自旋光泵极化~(129)Xe核子的过程,阐明了泵浦激光频率波动对陀螺仪性能影响的机理。分析表明,为了获得更高的碱金属极化率和稳定性,从而得到更好的陀螺仪零偏稳定性,需要将泵浦光的频率稳定在~(87)Rb的原子的共振跃迁频率处。采用波长调制法实现了泵浦光频率的稳定控制。通过实验对比发现:稳频使得陀螺仪的零偏稳定性从389.68(°)/h(1σ)降低至40.74(°)/h(1σ),降低了89.5%。因而得出结论:抑制泵浦激光频率的漂移可以有效提高核磁共振陀螺仪的性能,主要体现在陀螺仪的零偏稳定性上。     

The effect of vertical vibrations on the onset of convection in a planar rotating layer

The effect of vertical vibrations on the convection in a rotating planar fluid layer heated from below was studied. In this case a modulation parameter, the acceleration due to gravity, appears in the problem. The modulation of the parameter may have a significant effect on the onset of convective instability. Parameter modulation in nonrotating layers has been investigated in earlier work [1–3]. The presence of rotation significantly increases the complexity of the mathematical problem, introducing an additional dependence of the solution on the Taylor number Ta and the Prandtl number Pr. Furthermore, an oscillatory convection regime can occur at the stability limit in rotating fluids with Pr < 1. Parameter modulation in the rotating fluid may not only lead to a change in the stability limit and critical wavelength but also to a change in the eigenfrequency of the oscillatory convection. Rauscher and Kelly [4] examined the effect of parameter modulation on the convective stability of a rotating fluid only for the particular case of a sinusoidal variation in the temperature gradient with a small amplitude for Pr = 1, i.e., the effect of modulation was studied on only a steady convection regime.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 12–22, July–August, 1984.     

Dynamic homogenisation of Maxwell’s equations with applications to photonic crystals and localised waveforms on gratings

A two-scale asymptotic theory is developed to generate continuum equations that model the macroscopic behaviour of electromagnetic waves in periodic photonic structures when the wavelength is not necessarily long relative to the periodic cell dimensions; potentially highly-oscillatory short-scale detail is encapsulated through integrated quantities. The resulting equations include tensors that represent effective refractive indices near band edge frequencies along all principal axes directions, and these govern scalar functions providing long-scale modulation of short-scale Bloch eigenstates, which can be used to predict the propagation of waves at frequencies outside of the long wavelength regime; these results are outside of the remit of typical homogenisation schemes.The theory we develop is applied to two topical examples, the first being the case of aligned dielectric cylinders, which has great importance in modelling photonic crystal fibres. Results of the asymptotic theory are verified against numerical simulations by comparing photonic band diagrams and evanescent decay rates for guided modes. The second example is the propagation of electromagnetic waves localised within a planar array of dielectric spheres; at certain frequencies strongly directional propagation is observed, commonly described as dynamic anisotropy. Computationally this is a challenging three-dimensional calculation, which we perform, and then demonstrate that the asymptotic theory captures the effect, giving highly accurate qualitative and quantitative comparisons as well as providing interpretation for the underlying change from elliptic to hyperbolic behaviour.     

Three-dimensional waves on the surface of a viscous fluid

The study of the effect of viscosity on the propagation of surface waves has traditionally been confined to the consideration of plane (two-dimensional) waves [1, 2]. So far the effect associated with taking the transverse modulation of the wave profile into account have not been studied. In what follows, a solution is constructed and analyzed for linear three-dimensional periodic waves in an infinitely deep fluid. Their distinguishing property is the presence of a vorticity in the direction of propagation. An expression for the average (over the wavelength) velocity of horizontal particle drift is found in the quadratic approximation in the small wave steepness.     

Transient two‐layer thin‐film flow

The transient two‐layer thin‐film planar flow is investigated theoretically in this study. The interplay among inertia, viscous and surface/interfacial tension is emphasized. It is found that the film and interface profiles, as well as the flow field, are strongly influenced by the viscosity ratio, velocity and film thickness ratios at inception, and the surface‐to‐interfacial tension ratio. The nonlinear stability of the steady state reveals the formation of a solitary wave after flow inception, which propagates in the form of a convective instability, with the steady state recovered only in the tail (upstream) region of the wave. In the presence of surface/interfacial tension, surface modulation appears, which grows in wavelength and amplitude with position. The flow is found to be particularly stable for higher viscosity of the lower film layer. Copyright © 2010 John Wiley & Sons, Ltd.     

Far field scattering from bodies of revolution

Summary By use of approximations based on physical reasoning radar cross-section results for bodies of revolution are found. In the Rayleigh region (wavelength large with respect to object dimensions) approximate solutions are found. Examples given include a finite cone, a lens, an elliptic ogive, a spindle and a finite cylinder. In the physical optics region (wavelength very small with respect to all radii of curvature) Kirchhoff theory and also geometric optics can be used. When the body dimensions are only moderately large with respect to the wavelength, Fock or Franz theory can be applied, and examples of the circular and elliptic cylinder are presented. In the region where some dimensions of the body are large with respect to the wavelength and other dimensions are small with respect to the wavelength, special techniques are used. One example, the finite cone, is solved by appropriate use of the wedgelike fields locally at the base. Another example is the use of traveling wave theory for obtaining approximate solutions for the prolate spheroid and the ogive. Other results are obtained for cones the base perimeter of which is of the order of a wavelength by using known results for rings of the same perimeter.This paper with minor revision is as the author presented it at the URSI XIIth General Assembly in Boulder, Colorado August 22–September 5, 1957.     

Convection currents in a vertical layer with a space-modulated temperature distribution on the boundaries

Steady convective motions in a plane vertical fluid layer are investigated. The temperature along the boundaries of the layer varies harmonically and has different average values on each of the boundaries. Thus space-period modulation of the temperature of the walls is assigned along with average lateral heating of the layer. The form of the plane steady motions and regions of existence of through currents and currents of cellular structure are found for various values of the parameters of the problem by the finite difference grid-point method. The dependence of the main characteristics of fluid motion on the Grashof number is determined. The results presented in the article pertain to the case when the period of modulation of the temperature of the boundaries coincides with the wavelength of the critical mode of a plane-parallel current. A numerical investigation of supercritical motions in a vertical layer with plane isothermal boundaries heated to a different temperature was carried out in [1–3]. The effect of a space-periodic inhomogeneity due to curvature of walls on the form and stability of convective motions in a vertical layer with lateral heating was examined in [4].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 20–25, September–October, 1978.The author thanks E. M. Zhukhovitskii for formulating the problem and supervising the work and G. Z. Gershuni for discussions and useful comments.