OSCILLATORY PROPERTIES OF THE SOLUTIONS OF NONLINEAR DELAY HYPERBOLIC DIFFERENTIAL EQUATIONS OF NEUTRAL TYPE

Ｔｈｅｎｅｗｌｙ—ｄｅｖｅｌｏｐｅｄｔｈｅｏｒｙｏｆｎｏｎｌｉｎｅａｒｄｅｌａｙｐａｒｔｉａｌｆｕｎｃｔｉｏｎａｌｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓａｒｅａｐｐｌｉｅｄｉｎｍａｎｙｆｉｅｌｄｓ,ｓｕｃｈａｓｉｎｅｎｇｉｎｅｅｒｉｎｇ ,ｂｉｏｌｏｇｙ,ｍｅｄｉｃｉｎｅ,ｐｈｙｓｉｃｓａｎｄｃｈｅｍｉｓｔｒｙ .Ａｓｅｒｉｅｓｏｆｓｕｆｆｉｃｉｅｎｔｃｏｎｄｉｔｉｏｎｓ,ｎｅｃｅｓｓａｒｙａｎｄｓｕｆｆｉｃｉｅｎｔｃｏｎｄｉｔｉｏｎｓｆｏｒｏｓｃｉｌｌａｔｉｏｎｓｏｆｔｈｅｅｑｕａｔｉｏｎｓｗｅｒ…     

BIFURCATION ANALYSIS OF A MITOTIC MODEL OF FROG EGGS

ＩｎｔｒｏｄｕｃｔｉｏｎＷｉｔｈｔｈｅｒａｐｉｄｄｅｖｅｌｏｐｍｅｎｔｏｆｂｉｏｌｏｇｙｓｃｉｅｎｃｅｓ,ｃｅｌｌｓｉｇｎａｌｔｒａｎｓｄｕｃｔｉｏｎ ,ｃｅｌｌｅｐｏｐｔｏｓｉｓ,ｇｅｎｏｍｅａｎｄｐｏｓｔ＿ｇｅｎｏｍｉｃａｎａｌｙｓｉｓｈａｖｅａｔｔｒａｃｔｅｄｉｎｃｒｅａｓｉｎｇａｔｔｅｎｔｉｏｎ[1- 6 ].Ｔｈｅｃｅｌｌｄｉｖｉｓｉｏｎｃｙｃｌｅｉｓｔｈｅｓｅｑｕｅｎｃｅｏｆｅｖｅｎｔｓｂｙｗｈｉｃｈａｇｒｏｗｉｎｇｃｅｌｌｄｕｐｌｉｃａｔｅｓａｌｌｉｔｓｃｏｍｐｏｎｅｎｔｓａｎｄｔｈｅｎｄｉｖ…     

NUMERICAL SIMULATION OF OIL MIGRATION-ACCUMULATION OF MULTILAYER AND ITS APPLICATION

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｏｉｌｆｏｒｍａｔｉｏｎｉｎｓｅｄｉｍｅｎｔｂａｓｉｎｓ ,ｉｔｓｄｉｓｐｌａｃｅｍｅｎｔ,ｔｒａｎｓｐｏｒｔａｎｄａｃｃｕｍｕｌａｔｉｏｎ ,ａｎｄｔｈｅｆｉｎａｌｆｏｒｍａｔｉｏｎｏｆｏｉｌｄｅｐｏｓｉｔｓｈａｖｅｂｅｅｎｏｎｅｏｆｔｈｅｋｅｙｐｒｏｂｌｅｍｓｉｎｔｈｅｅｘｐｌｏｒａｔｉｏｎｏｆｏｉｌ＿ｇａｓｒｅｓｏｕｒｃｅｓ.Ｈｏｗｈａｓｏｉｌｂｅｅｎａｃｃｕｍｕｌａｔｅｄｉｎｔｈｅｐｒｅｓｅｎｔｌｏｏｐａｃｃｏｒｄｉｎｇｔｏｔｈｅｍｅｃｈａｎｉｃｓｏｆｉｍｍｉｓｃ…     

PROPER APPLICATION OF A KIND OF MATRIX CON-STRUCTION METHOD IN PHYSICAL PARAMETER IDENTIFICATION OF DYNAMIC MODEL

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｐｈｙｓｉｃｓｐａｒａｍｅｔｅｒｉｄｅｎｔｉｆｉｃａｔｉｏｎｐｒｏｂｌｅｍｓａｒｅｆｒｅｑｕｅｎｔｌｙｅｎｃｏｕｎｔｅｒｅｄｉｎｔｈｅｆｉｅｌｄｓｏｆａｖｉａｔｉｏｎ,ｓｐａｃｅ,ｍｅｃｈａｎｉｓｍａｎｄｃｉｖｉｌｅｎｇｉｎｅｅｒｉｎｇ .Ｆｏｒｅｘａｍｐｌｅ ,ｄｕｅｔｏｔｈｅｃｏｍｐｌｅｘｉｔｙｏｆｍａｔｅｒｉａｌｐｒｏｐｅｒｔｉｅｓｉｎｃｉｖｉｌｅｎｇｉｎｅｅｒｉｎｇ ,ｔｈｅｐｈｙｓｉｃｓｐａｒａｍｅｔｅｒｓｕｓｕａｌｌｙａｒｅｉｄｅｎｔｉｆｉｅｄｂｙｔｅｓｔｄａｔ…     

NUMERICAL ANALYSIS OF THE LARGE DEFLECTION OF AN ELASTIC-PLASTIC BEAM

ＩｎｔｒｏｄｕｃｔｉｏｎＷｉｔｈｔｈｅｄｅｖｅｌｏｐｍｅｎｔｏｆｎａｔｕｒａｌｓｃｉｅｎｃｅａｎｄｔｈｅｉｎｃｒｅａｓｉｎｇｒｅｑｕｉｒｅｍｅｎｔｉｎｔｅｃｈｎｏｌｏｇｙ,ｔｈｅｌａｒｇｅｄｅｆｌｅｃｔｉｏｎｎｏｎｌｉｎｅａｒｐｒｏｂｌｅｍｏｆｂａｒｓｉｓａｌｗａｙｓａｎｉｍｐｏｒｔａｎｔｒｅｓｅａｒｃｈｉｎｅｎｇｉｎｅｅｒｉｎｇａｐｐｌｉｃａｔｉｏｎｆｉｅｌｄ.Ｉｎｔｈｅ1960ｓ,ｔｈｅｒｅｓｅａｒｃｈｓｃｏｐｅｗａｓｏｎｌｙｌｉｍｉｔｅｄｔｏＥｕｌｅｒ’ｓＥｌａｓｔｉｃａｔｈｅｏｒｙ,ｗｈｉｃｈｗ…     

THE PROPERTIES OF A KIND OF RANDOM SYMPLECTIC MATRICES

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｒｅｗａｓａｎＱＲ＿ｌｉｋｅａｌｇｏｒｉｔｈｍ[1,2 ]ｆｏｒｔｈｅｓｏｌｕｔｉｏｎｏｆｒｅａｌａｌｇｅｂｒａｉｃＲｉｃｃａｔｉｅｑｕａｔｉｏｎｏｒｃｏｍｐｕｔｉｎｇｔｈｅｒｅａｌｉｎｖａｒｉａｎｔｓｕｂｓｐａｃｅａｓｓｏｃｉａｔｅｄｗｉｔｈｔｈｅｎｅｉｇｅｎｖａｌｕｅｓｗｉｔｈｎｅｇａｔｉｖｅｒｅａｌｐａｒｔｏｆｔｈｅｃｏｒｒｅｓｐｏｎｄｉｎｇｒｅａｌＨａｍｉｌｔｏｎｉａｎｍａｔｒｉｘ .ＩｎｔｈｅＱＲ＿ｌｉｋｅａｌｇｏｒｉｔｈｍ ,ｔｏｐｒｅｓｅｒｖｅｔｈｅＨａｍｉｌｔ…     

ANALYSIS OF FINANCIAL DERIVATIVES BY MECHANICAL METHOD (Ⅰ)—BASIC EQUATION OF PRICE OF INDEX FUTURES

1　ＭｅａｎｉｎｇａｎｄＭｅｔｈｏｄｓｏｆＳｔｕｄｙｉｎｇｏｆＦｉｎａｎｃｉａｌＤｅｒｉｖａｔｉｖｅｓＦｉｎａｎｃｉａｌｄｅｒｉｖａｔｉｖｅｓａｒｅｔｈｏｓｅｆｉｎａｎｃｉａｌｐｒｏｄｕｃｔｓｗｈｉｃｈａｒｅｄｅｒｉｖｅｄｆｒｏｍｂａｓｉｃａｓｓｅｒｔｓ (ｏｒｕｎｄｅｒｌｙｉｎｇｉｎｓｔｒｕｃｍｅｎｔｓ) (ｅ .ｇ .ｓｔｏｃｋ ,ｂｏｎｄ ,ｃｕｒｒｅｎｃｙ ,ｉｎｔｅｒｅｓｔｒａｔｅ,ｅｔｃ.)ｏｆｔｒａｄｉｔｉｏｎａｌｍａｒｋｅｔｓ(ｅ.ｇ .ｓｔｏｃｋｍａｒｋｅｔ,ｂｏｎｄ’ｓｍａｒｋｅｔ,ｃｕｒｒｅｎｃｙ…     

SINGULAR ANALYSIS OF BIFURCATION OF NONLINEAR NORMAL MODES FOR A CLASS OF SYSTEMS WITH DUAL INTERNAL RESONANCES

ＩｎｔｒｏｄｕｃｔｉｏｎＡｎｉｎｔｅｒｅｓｔｉｎｇｆｅａｔｕｒｅｉｎｔｈｅｆｒｅｅｖｉｂｒａｔｉｏｎｏｆａｎｏｎｌｉｎｅａｒｓｙｓｔｅｍｉｓｔｈｅｆａｃｔｔｈａｔｔｈｅｎｕｍｂｅｒｏｆｅｘｉｓｔｉｎｇｎｏｒｍａｌｍｏｄｅｓｍａｙｅｘｃｅｅｄｔｈｅｎｕｍｂｅｒｏｆｄｅｇｒｅｅｓｏｆｆｒｅｅｄｏｍ ,ａｐｈｅｎｏｍｅｎｏｎｎｏｔｅｎｃｏｕｎｔｅｒｅｄｉｎａｌｉｎｅａｒｓｙｓｔｅｍａｎｄｃａｕｓｅｄｂｙｍｏｄｅｂｉｆｕｒｃａｔｉｏｎ .Ｔｈｅｒｅｆｏｒｅｍｕｃｈｗｏｒｋｈａｓｂｅｅｎｄｏｎｅｏｎｔｈｅｓｔ…     

DOUBLE METHOD OF CHARACTERISTICS TO ANALYZE HYDRAULIC-THERMAL TRANSIENTS OF PIPELINE FLOW

ＩｎｔｒｏｄｕｃｔｉｏｎＭｅｔｈｏｄｏｆｃｈａｒａｃｔｅｒｉｓｔｉｃｓ (ＭＯＣ)ｈａｓｓｔｉｌｌｂｅｅｎｔｈｅｐｏｗｅｒｆｕｌｔｏｏｌｔｏａｎａｌｙｚｅｈｙｄｒａｕｌｉｃｔｒａｎｓｉｅｎｔｏｆｐｉｐｅｌｉｎｅｆｌｏｗｓｉｎｃｅｔｈｅ 1 960ｓ.Ｓｅｌｄｏｍｈａｓｔｈｅｔｈｅｒｍａｌｔｒａｎｓｉｅｎｔｂｅｅｎｔａｋｅｎｉｎｔｏａｃｃｏｕｎｔ.Ｈｅａｔｄｕｅｔｏｆｒｉｃｔｉｏｎｖａｒｉｅｓｗｈｅｎｆｌｏｗｒａｔｅｃｈａｎｇｅｄｂｅｃａｕｓｅｏｆｖａｒｉｏｕｓｋｉｎｄｓｏｆｒｅａｓｏｎｓ,ｗｈｉｃｈｃａｕｓ…     

RESEARCH OF THE PERIODIC MOTION AND STABILITY OF TWO-DEGREE-OF-FREEDOM NONLINEAR OSCILLATING SYSTEMS

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｅｓｙｓｔｅｍｏｆｎｏｎｌｉｎｅａｒｏｓｃｉｌｌａｔｉｎｇ ,ｐｅｒｉｏｄｉｃｍｏｔｉｏｎｉｓｏｆｐｒｉｍｅｉｍｐｏｒｔａｎｃｅ .Ｂｕｔｅｘｉｓｔｅｎｃｅｏｆｐｅｒｉｏｄｉｃｓｏｌｕｔｉｏｎｓｉｓａｖｅｒｙｄｉｆｆｉｃｕｌｔｑｕｅｓｔｉｏｎ .Ｌｕｃｋｉｌｙｔｈｅｒｅｅｘｉｓｔｓｏｍｅｋｉｎｄｓｏｆｐｅｒｉｏｄｉｃｓｏｌｕｔｉｏｎｉｎａｃｔｕａｌｐｈｙｓｉｃａｌｓｙｓｔｅｍｓ .Ｔｈｅｒｅｆｏｒｅ ,ｗｅｕｓｕａｌｌｙｃｏｎｃｅｎｔｒａｔｅｄｏｕｒａｔｔｅｎｔｉｏｎｏｎｔ…     

混合层中柱状粒子取向分布函数的研究

数值模拟了平面流固混合层中柱状粒子在平面取向的分布函数，提出了描述流场中某点直粒子取向占优程度的参数Dψ的分析，说明在混合层中心区域粒子的取向排列是有序的，在混合层相邻两个大涡之间的区域，是粒子最可几角占优程度最高的地方，而且最可几取向就是沿流场的拉伸方向，说明流场的拉伸作用及方向对粒子的取向排列具有重要影响。与其它模型相比，粒子取向的分布函数模型能定量反映流场大涡对粒子取向控制的强弱程度。     

Numerical simulation of flow kinematics and fiber orientation for multi-disperse suspension

The development of flow kinematics and fiber orientation distribution from the parabolic velocity profile and isotropic orientation at the channel inlet was computed in multi-disperse suspension flow through a parallel plate channel and their predictions were compared with those of mono- and bi-disperse suspensions. A statistical scheme (orientations of a large number of fibers are evaluated from the solution of the Jeffery equation along the streamlines) was confirmed to be very useful and feasible method to analyze accurately the orientation distribution of fibers in multi-disperse fiber suspension flow as well as mono- and bi-dispersions, instead of direct solutions of the orientation distribution function of fibers or the evolution equation of the orientation tensor which involves a closure equation. It was found that the flow kinematics and the fiber orientation depend completely on both the fiber aspect-ratio and the fiber parameter for multi-disperse suspension when the fiber–fiber and fiber-wall interactions are neglected. Furthermore, the addition of large aspect-ratio fibers as well as an increase in the fiber parameter related to the large aspect-ratio fibers could suppress the complex velocity field and stress distributions which are observed in suspensions containing small aspect-ratio fibers. From a practical point of view, therefore, the mechanical and physical properties of fiber composites should be improved with an increase in the volume fraction of large aspect-ratio fibers.     

Anisotropic work hardening of steel sheets under plane stress

This work is a follow-up of the previous report by Kim and Yin [Kim, K.H., Yin, J.J., 1997. Evolution of anisotropy under plane stress. J. Mech. Phys. Solids 45, 841–851] regarding the anisotropic work hardening of cold rolled steel sheets. Tensile prestrain has been applied at angles to the rolling direction and then tensile uniaxial yield stress and R-value distributions are measured. As reported earlier, the orientations of local maxima and minima in the yield stress are altered when the prestrain axis is not in the rolling direction. This led Kim and Yin [Kim and Yin (1997)] to suggest that the orientations of orthotropy axes are altered by the tensile prestrain at angles to the rolling direction. However, R-value distribution is found to be hardly affected by the prestrain. The unchanging R-value distribution shows that the material remembers the rolling direction even after the prestrain. An attempt is made to approximate the observed yield and flow behavior based upon isotropic-kinematic hardening with the quadratic yield function (Hill, 1948). The degree of approximation raises the issues of yield point definition, flexibility of yield function, non-associated flow rules, distortional hardening and others.     

Fiber suspension flow in a tapered channel: The effect of flow/fiber coupling

A numerical model for predicting the flow and orientation state of semi-dilute, rigid fiber suspensions in a tapered channel is presented. The effect of the two-way flow/fiber coupling is investigated for low Reynolds number flow using the constitutive model of Shaqfeh and Fredrickson. An orientation distribution function is used to describe the local orientation state of the suspension and evolves according to a Fokker–Plank type equation. The planar orientation distribution function is determined along streamlines of the flow and is coupled with the fluid momentum equations through a fourth-order orientation tensor. The coupling term accounts for the two-way interaction and momentum exchange between the fluid and fiber phases. The fibers are free to interact through long range hydrodynamic fiber–fiber interactions which are modeled using a rotary diffusion coefficient, an approach outlined by Folgar and Tucker. Numerical predictions are made for two different orientation states at the inlet to the contraction, namely a fully random and a partially aligned fiber orientation state. Results from these numerical predictions show that the streamlines of the flow are altered and that velocity profiles change from Jeffery–Hamel, to something resembling a plug flow when the fiber phase is considered in the fluid momentum equations. This phenomenon was found when the suspension enters the channel in either a pre-aligned, or in a fully random orientation state. When the suspension enters the channel in an aligned orientation state, fiber orientation is shown to be only marginally changed when the two-way coupling is included. However, significant differences between coupled and uncoupled predictions of fiber orientation were found when the suspension enters the channel in a random orientation state. In this case, the suspension was shown to align much more quickly when the mutual coupling was accounted for and profiles of the orientation anisotropy were considerably different both qualitatively and quantitatively.     

纳米多晶NiTi形状记忆合金超弹性的晶粒取向依赖性相场研究

本文基于Ginzburg-Landau理论,建立了一个反映纳米多晶NiTi形状记忆合金取向依赖性的二维多晶相场模型,研究了晶粒取向对其超弹性性能的影响。结果表明,纳米多晶NiTi形状记忆合金的超弹性行为依赖于晶粒取向分布,即：多晶模型中在所研究的参数变化范围内,晶粒取向分布范围越广、晶粒间取向差越大（无明显织构）,超弹性性能越差;而晶粒取向分布范围越窄、晶粒间取向差越小（织构越强）,超弹性性能越好。该晶粒取向依赖性可解释为：由于晶粒取向的不同,马氏体相变过程中相邻晶粒间的变形不匹配程度不同,因此,多晶模型中在所研究的参数变化范围内,晶粒间取向差异越大,晶界处的变形失配越严重,由此而产生的局部内应力将阻碍其附近马氏体相变的扩展,进而导致纳米多晶NiTi形状记忆合金超弹性性能下降。     

Theory of non-isotropic spatial resolution in PIV

The spatial resolution of the PIV interrogation technique is discussed from an analytical standpoint and assessed with Monte Carlo numerical simulation of particle image motion. The PIV measurement error associated with lack of spatial resolution is modelled associating the cross-correlation operator to a moving average filter. The error associated with the "low-pass filtering" effect is investigated by adopting a second-order polynomial expression for the velocity spatial distribution. According to the present error analysis, the measurement error is proportional to the second-order spatial derivative of the velocity field and increases with the square of the window linear size. The strategy for the selection of the window size and properties (aspect ratio and orientation) so as to minimize the error is discussed. The principle is based on nonisotropic interrogation windows of elliptical shape, with a constant area and elongated in the direction of the largest curvature radius. The nonisotropic parameters are defined as eccentricity and orientation, which are based on the local eigenvalues/vectors of the Hessian tensor of the displacement spatial distribution. The technique is implemented in a recursive PIV interrogation method. The performance of nonisotropic interrogation technique is assessed by means of synthetic PIV images, which simulate three situations: first, a one-dimensional sinusoidal shear displacement, which allows comparison of the cross-correlation spatial response with the transfer function of linear filters. Second, the stream-wise exponential velocity decay is simulated, which simulates the particle tracers decelerating downstream of a shock wave and gives an example of a flow with main velocity differences aligned with the velocity direction. The results show that keeping the image density fixed, the error caused by insufficient spatial resolution can be reduced by a factor two when a preferential direction is found in the flow field. Finally, a Lamb–Oseen vortex flow is presented, which shows the complex pattern formed by the interrogation windows in a two-dimensional case. In this case, the improvement in interrogation performance is limited due to the isotropic nature of the velocity spatial fluctuation.     

Self-organized domain microstructures in a plate-like particle suspension subjected to rapid simple shear

The evolution of the microstructure and rheological properties of plate-like particle suspensions subjected to rapid simple shear is studied numerically. In response to the shear-induced strain, particles in the suspensions rearrange to form a steady-state microstructure, and the suspension viscosity reaches a steady value. Under this condition, the microstructure is composed of two domains having different particle fractions and particle orientations. In the matrix (particle-poor) and cluster (particle-rich) domains, the particles’ long axes are oriented subparallel to the shear plane and normal to the maximum compressive principal direction, respectively. A higher particle concentration and friction coefficient enhance the development of cluster domains relative to matrix domains leading the intensity of the preferred particle orientation to decrease and the number of contacting particles, the aspect ratio of clusters, the inter-particle force, and the suspension viscosity to increase. The domain microstructure is governed by two factors: (1) geometric relations between the particle orientation and the maximum compressive axes and (2) the magnitude of particle–fluid and particle–particle interactions. The first factor results in the coupling of the particle orientation and the local fraction of particles, which is an important character of the domain microstructure. The second factor controls the relative development of the cluster and matrix domains through the change in the particles’ rotational behavior. Our results suggest that the microstructure of plate-like suspensions subjected to rapid shear is predictable in terms of the cluster stability, which has important implications for the kinematics of flow-related microstructures in nature and manufacturing.     

Grid Orientation Revisited: Near-well, Early-time Effects and Solution Coupling Methods

The grid orientation effect is a phenomenon which leads to the computation of fundamentally different solutions on grids oriented diagonal and parallel to the principal flow direction. Grid orientation remains an important consideration for many practical simulation studies, and renewed interest in gas injection processes motivates the revisiting of this classical problem. In this article, we show that there are aspects of the grid orientation effect that can be traced back directly to the treatment of early-time, near-well flow and therefore have a major impact on adverse mobility ratio displacements such as miscible or immiscible gas injection. The details of this effect mean that any uncertainty quantification study should account for the interaction of the near-well heterogeneity and the grid orientation effect. We also show how two possible methods—a well-sponge method and a local embedding technique—are able to produce a solution largely independent of grid orientation for single phase two-component miscible flow. Both methods are versatile in that they can be implemented on general grid topologies. They are illustrated on Cartesian grids for both the standard quarter five spot problem with two different grid orientations, and a problem with a single injection well and two producing wells at different angles to the grid lines. Our results show that it is possible to reduce grid-orientation effects for challenging adverse mobility ratio miscible displacements with only local treatments around the injection wells.     

Structure of supersonic inviscid nonsymmetric conical flow around a V-wing

The shock wave structure of flow around a V-wing and its properties determining the conical flow topology are numerically investigated within the framework of the inviscid gas model on a wide range of the angles of attack and yaw when in the disturbed supersonic flow either nonsymmetric Mach interaction between the shocks attached to the leading edges of the wing or a shockless flow in the compressed layer on the windward cantilever is realized. The subranges of the angles of attack and yaw with the disturbed flow properties characteristic of the wing of the given geometry are determined. It is found that at high angles of attack, when the branching point of the bow shock beneath the leeward cantilever generates an intense contact discontinuity, the structure of the conical flow in the shock layer on the windward cantilever involves a singularity of a new type which can be characterized as a “vortical” Ferri singularity. It is located above the point of convergence of the streamlines proceeding from the leading edges of the wing, at the vertex of the corresponding contact discontinuity. Flow patterns with the point of convergence of the streamlines proceeding from the leading edges located in the elliptical flow region, which is placed at a local maximum of the pressure distribution over the surface are also found. The range of the angles of attack and yaw on which this new property of supersonic conical flows is realized in the presence of a branched shock system is determined.     

Bonded half planes containing an arbitrarily oriented crack

The plane elastostatic problem for two bonded half planes containing an arbitrarily oriented crack in the neighborhood of the interface is considered. Using Mellin Transforms the problem is formulated as a system of singular integral equations. The equations are solved for various crack orientations, material combinations, and external loads. The numerical results given in the paper include the stress intensity factors, the strain energy release rates, and the probable cleavage angles giving the direction of crack propagation.