Note on the velocity and related fields of steady irrotational two-dimensional surface gravity waves

The velocity and other fields of steady two-dimensional surface gravity waves in irrotational motion are investigated numerically. Only symmetric waves with one crest per wavelength are considered, i.e. Stokes waves of finite amplitude, but not the highest waves, nor subharmonic and superharmonic bifurcations of Stokes waves. The numerical results are analysed, and several conjectures are made about the velocity and acceleration fields.     

Placement of a non-isosceles-triangle insert in an asymmetrical two-dimensional bin-hopper

This work presents a novel and simplified method for determining placement and size of a non-isosceles-triangle insert that eliminates the quasi-stagnant zone next to the wall in an asymmetrical bin-hopper. A two-dimensional model silo with a rectangular base was created to observe flow patterns, analyze flow regions and support this proposed technique for designing a non-isosceles-triangle insert. Placement of the non-isosceles-triangle insert for different hopper geometries and different insert apex angles was determined and tested. Moreover, a simple method was developed to plot the path lines of black particles that are in the same height at beginning. Accordingly, the area of the quasi-stagnant zone next to the wall of bin-hopper could be calculated properly, and these path lines also supported the discussion of flow regions in this investigation. Experimental results demonstrate that a non-isosceles-triangle insert designed using the proposed method effectively reduces the quasi-stagnant zone next to the wall in an asymmetrical bin-hopper.     

Higher-order extrema in two-dimensional wave fields

Higher-order extrema with topological indices greater than unity are discussed. Explicit constructions are given for their wave functions, and simple geometric rules are presented for analysis of their topological indices. Experimental means for verifying the theory with use of Gaussian laser beams are considered, unusual properties of optical vortices constructed from this new type of critical point are described, and applications to topologically based optical arithmetic are suggested.     

Recovering physical fields with a two-dimensional fiber-optics measurement grid

A tomographic fiber-optics grid can be used to record two-dimensional field patterns. The structure of the grid is described, and a processing algorithm has been tested, which reduces the number of fiber lines required by a factor of 4. An experimental model has been tested successfully in the recovery of the two-dimensional transverse vibration pattern at the surface of a ship's fuel tank. Translated from Izmeritel'naya Tekhnika, No. 3, pp. 24–30, March, 1999.     

二维可展板壳结构展开过程分析

 基于折纸模型的二维可展板壳结构,在折叠体积较小的情况下可以获得较大的展开面积,展开效率较高.从二维折纸模型出发,研究基于此类模型的可展结构的特点,并对模型的展开过程进行分析模拟.利用Moore-Penrose广义逆矩阵的方法,结合板单元理论及相应的约束处理,对展开过程进行了计算、模拟,结合动力学方程还可以计算出展开速度和加速度.     

On steady plane magnetohydrodynamic flows with orthogonal magnetic and velocity fields

Hodograph transformation is employed to obtain a partial differential equation of second order, which is exploited to obtain solutions for plane viscous incompressible flows with orthogonal magnetic and velocity fields. This approach is illustrated through three examples.     

Drift velocity and deflection in non-perpendicular electric and magnetic fields

Accurate tracking in inhomogeneous and arbitrarily oriented magnetic fields requires the velocity and direction of the drifting ionization to be known to high precision. A semi-empirical method of calculating drift velocities and magnetic deflection angles is presented for non-perpendicular electric and magnetic fields. Data obtained using a drift chamber rotated in a B-field verify the calculation. The model is used to restore accuracy in the L3 forward/backward muon detector where non-orthogonal and inhomogeneous electric and magnetic fields are present.     

Critical currents and electric fields of two-dimensional systems

We calculate the critical current of a thin, superconducting film with periodically modulated thickness placed in a perpendicular magnetic field. This problem is shown to be closely connected with the problem of the commensurate-incommensurate phase transition in two dimensions. The main mechanism responsible for the vortex motion appears to be the creation of a soliton in a vortex lattice on the boundary of a sample. The critical current is zero in the incommensurate phase. An analogous phenomenon is the critical longitudinal field for the Wigner crystal of electrons on the surface of liquid helium. The shear modulus for an Abrikosov vortex lattice in a thin film is found for a wide range of parameters.     

Study of velocity fields in vortex dust collectors

Results are given of experimental studies of velocity fields in vortex dust collecting apparatus.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 20, No. 6, June, 1971.     

Moisture penetration patterns in thin films

A technique is described for examining moisture adsorption in narrow band filters; it involves the photographing of the filter in monochromatic light and the analysis of the patterns obtained. The mechanism of moisture penetration and its influence on filter drift is discussed. Changes in the structure of the layers due to heat treatment can be detected by change in the moisture penetration patterns.     

Crack patterns in brittle thin films

The physical system studied is a brittle elastic film bonded to an elastic substrate with different elastic properties; a residual tensile stress is presumed to exist in the film. The focus of the study is the influence of the mismatch in elastic properties on patterns of crack formation in the film. The stress intensity factor and crack driving force for growth of a periodic array of cracks in the direction normal to the interface under two-dimensional conditions are determined for any crack depth and any mismatch in elastic parameters. It is found that, even for a relatively stiff film material, the stress intensity factor of each crack as a function of crack depth exhibits a local maximum. The driving force for crack extension in the direction parallel to the interface is then determined on the basis of these two-dimensional results, and the equilibrium spacing of crack arrays is estimated for given residual stress. The results of the calculations are used as a basis for qualitative arguments to explain the crack patterns which have been observed in GaN films on Si substrates.     

Crack patterns in brittle thin films

The physical system studied is a brittle elastic film bonded to an elastic substrate with different elastic properties; a residual tensile stress is presumed to exist in the film. The focus of the study is the influence of the mismatch in elastic properties on patterns of crack formation in the film. The stress intensity factor and crack driving force for growth of a periodic array of cracks in the direction normal to the interface under two-dimensional conditions are determined for any crack depth and any mismatch in elastic parameters. It is found that, even for a relatively stiff film material, the stress intensity factor of each crack as a function of crack depth exhibits a local maximum. The driving force for crack extension in the direction parallel to the interface is then determined on the basis of these two-dimensional results, and the equilibrium spacing of crack arrays is estimated for given residual stress. The results of the calculations are used as a basis for qualitative arguments to explain the crack patterns which have been observed in GaN films on Si substrates.     

基于时滞惯性流形的二维平面壁板非线性气动弹性分析

详细研究了二维平面壁板的非线性气动弹性现象。采用平板的Von Karman几何大变形理论以及气动力的一阶活塞理论,推导出系统的非线性偏微分控制方程。然后,运用基于时滞惯性流形的非线性Galerkin方法求解方程,将高阶屈曲模态用低阶模态来表示并引入时间滞后,这样既保留计算精度又大幅度地节约计算时间。最后,详细数值分析了其中的气动弹性行为,分别以无量纲动压和无量纲压缩内力为分岔参数,无量纲幅值为响应给出了分岔图,发现系统存在阵发性通往混沌的途径,以及混沌区域周期窗口和自相似的特征。进一步,通过对系统的相图、位移的FFT频谱以及Lyapunov指数的分析,发现系统的动力学行为存在稳定、屈曲、谐调和非谐调运动四种典型类型,而非谐调运动又表现出倍周期运动、准周期运动和混沌运动等丰富的非线性响应,所研究结果为识别和进一步控制此类非线性气动弹性现象提供了理论依据。     

Heat and mass transport in random velocity fields with application to dispersion in porous media

The effective equations describing the transport of a Brownian passive tracer in a random velocity field are derived, assuming that the lengthscales and timescales on which the transport process takes place are much larger than the scales of variations in the velocity field. The effective equations are obtained by applying the method of homogenization, that is a multiple-scale perturbative analysis in terms of the small ratio between the characteristic micro- and macro-lengthscales. After expanding the dependent variable and both space and time gradients in terms of , equating coefficients of like powers of yields expressions to determine the dependent variable up to any order of approximation. Finally, a Fickian constitutive relation is determined, where the effective transport coefficients are expressed in terms of the ensemble properties of the velocity field. Our results are applied to the transport of passive tracers in the stationary flow field generated in dilute fixed beds of randomly distributed spheroids, finding the effective diffusivity as a function of the spheroid eccentricity. Our result generalizes the expression of Koch and Brady (1985), who considered spherical inclusions, and is readily applied to the cases of random beds of slender fibers and flat disks.     

Solid-phase velocity patterns in free and constrained fluidized beds

A dynamometer system has been used to measure the average and instantaneous velocities of the solid phase in systems of diameters 0.3 and 0.7 m; it is found that these quantities are affected by low-volume packing.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 56, No. 4, pp. 633–641, April, 1979.     

Numerical determination of two-dimensional temperature fields in transpiration cooling

We present a numerical method for solving a wide range of transpiration cooling problems.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 47, No. 6, pp. 984–991, December, 1984.     

Optical measurement of ultrasonic Poynting and velocity vector fields

This report describes a method for estimating several wide bandwidth ultrasonic field parameters from optical measurements of the local, acoustically induced, refractive index perturbation in water. These parameters include Poynting and particle velocity vector fields as well as pressure and density fields at any temporal delay under mild (forward-propagating) assumptions on the angular plane-wave spectrum of the ultrasound field. A sampling theorem is derived stating that two complete measurements of the three-dimensional pressure field separated in time by Δt allow release of the forward-propagating assumption for every acoustic wave number k satisfying k ≠ nπ/(cΔt), where c is the acoustic wave speed in the medium and n an integer greater than zero. The approach provides detailed measurements of very general ultrasound fields. Two optical measurement methods that acquire the Radon transform of the three-dimensional refractive index perturbation are briefly reviewed. It is shown that the Radon transform of the field itself satisfies a two-dimensional wave equation and may be propagated independently forward or backward in time under a source-free model. Conversely, the Radon transform of the ultrasound field measurement at several known time delays provides a means of applying a filter to the data based on known ultrasound propagation models. Each two-dimensional distribution may be propagated to a common time point and the ensemble averaged, thus incorporating the propagation model into the measurement. We support the presented theory with several experiments     

Phase transitions in two-dimensional electron-hole systems in high magnetic fields

We consider phase transitions with an excitonic condensate formation in quasi-two-dimensional semiconductors in high magnetic fields. The phase diagram is constructed and thermodynamic quantities are calculated for all densities. In the Hartree-Fock approximation all thermodynamic potentials prove to be the same as those of the electron-hole (e-h) drop state. Therefore the transition from a tenuous e-h gas to a dense e-h liquid can be treated either as a first-order transition or as two successive second-order transitions. With allowance for the correlation corrections the thermodynamic properties of the excitonic phase become slightly different from those of the drop state.