Existence of Formal Conservation Laws of a Variable-Coefficient Korteweg-de Vries Equation from Fluid Dynamics and Plasma Physics via Symbolic Computation

Employing the method which can be used to demonstrate the infinite conservation laws for the standard Kortewegde Vries （KdV） equation, we prove that the variable-coeFficient KdV equation under the Painlevé test condition also possesses the formal conservation laws.

Infinite Sequence of Conservation Laws and Analytic Solutions for a Generalized Variable-Coefficient Fifth-Order Korteweg-de Vries Equation in Fluids

在这份报纸，为在液体的一个概括可变系数的第五顺序的 Korteweg-de Vries 方程的能量守恒定律的一个无限的序列基于 B 被构造 ? cklund 转变。Hirota 双线性的形式和符号的计算被使用获得三种答案。可变系数能影响典型的线的保存密度，联系流动，和外观。soliton 结构上的波浪数字的效果也被讨论并且 soliton 结构打字，例如，双 periodic soliton，平行 soliton 和 soliton 建筑群，被介绍。

Darboux Transformation and Soliton Solutions for a Variable-Coefficient Modified Kortweg-de Vries Model from Fluid Mechanics, Ocean Dynamics, and Plasma Mechanics

这份报纸是调查可变系数的修改 Kortweg-de Vries (vc-mKdV ) 为力学建模，它从液体力学，海洋动力学，和血浆描述一些状况。由 AblowitzKaupNewellSegur 过程和符号的计算， vc-MKdV 模型的宽松的对被导出。基于上述的宽松的对，然后， Darboux 转变被构造，一个新 one-soliton-like 答案也被获得。one-soliton-like 答案的特征被分析并且图形地讨论了在 solitonlike 繁殖说明可变系数的影响。

Painlevé Analysis,Soliton Solutions and Bcklund Transformation for Extended (2 + 1)-Dimensional Konopelchenko-Dubrovsky Equations in Fluid Mechanics via Symbolic Computation

This paper is to investigate the extended(2+1)-dimensional Konopelchenko-Dubrovsky equations,which can be applied to describing certain phenomena in the stratified shear flow,the internal and shallow-water waves, plasmas and other fields.Painleve analysis is passed through via symbolic computation.Bilinear-form equations are constructed and soliton solutions are derived.Soliton solutions and interactions are illustrated.Bilinear-form Backlund transformation and a type of solutions are obtained.

Dynamic flight stability of a hovering model insect:lateral motion

The lateral dynamic flight stability of a hovering model insect （dronefly） was studied using the method of computational fluid dynamics to compute the stability derivatives and the techniques of eigenvalue and eigenvector analysis for solving the equations of motion. The main results are as following. （i） Three natural modes of motion were identified： one unstable slow divergence mode （mode 1）, one stable slow oscillatory mode （mode 2）, and one stable fast subsidence mode （mode 3）. Modes 1 and 2 mainly consist of a rotation about the horizontal longitudinal axis （x-axis） and a side translation; mode 3 mainly consists of a rotation about the x-axis and a rotation about the vertical axis. （ii） Approximate analytical expressions of the eigenvalues are derived, which give physical insight into the genesis of the natural modes of motion. （iii） For the unstable divergence mode, td, the time for initial disturbances to double, is about 9 times the wingbeat period （the longitudinal motion of the model insect was shown to be also unstable and td of the longitudinal unstable mode is about 14 times the wingbeat period）. Thus, although the flight is not dynamically stable, the instability does not grow very fast and the insect has enough time to control its wing motion to suppress the disturbances.

The effects of corrugation and wing planform on the aerodynamic force production of sweeping model insect wings

The effects of corrugation and wing planform （shape and aspect ratio） on the aerodynamic force production of model insect wings in sweeping （rotating after an initial start） motion at Reynolds number 200 and 3500 at angle of attack 40℃ are investigated, using the method of computational fluid dynamics. A representative wing corrugation is considered. Wing-shape and aspect ratio （AR） of ten representative insect wings are considered; they are the wings of fruit fly, cranefly, dronefly, hoverfly, ladybird, bumblebee, honeybee, lacewing （forewing）, hawkmoth and dragon- fly （forewing）, respectively （AR of these wings varies greatly, from 2.84 to 5.45）. The following facts are shown. （1） The corrugated and flat-plate wings produce approximately the same aerodynamic forces. This is because for a sweeping wing at large angle of attack, the length scale of the corrugation is much smaller than the size of the separated flow region or the size of the leading edge vortex （LEV）. （2） The variation in wing shape can have considerable effects on the aerodynamic force; but it has only minor effects on the force coefficients when the velocity at r2 （the radius of the second ：moment of wing area） is used as the reference velocity; i.e. the force coefficients are almost unaffected by the variation in wing shape. （3） The effects of AR are remarkably small： whenAR increases from 2.8 to 5.5, the force coefficients vary only slightly; flowfield results show that when AR is relatively large, the part of the LEV on the outer part of the wings sheds during the sweeping motion. As AR is increased, on one hand, the force coefficients will be increased due to the reduction of 3-dimensional flow effects; on the other hand, they will be decreased due to the shedding of part of the LEV; these two effects approximately cancel each other, resulting in only minor change of the force coefficients.

Wing kinematics measurement and aerodynamics of free-flight maneuvers in drone-flies

The time courses of wing and body kinematics of two free-flying drone-flies, as they performed saccades, were measured using 3D high-speed video, and the morpho- logical parameters of the wings and body of the insects were also measured. The measured wing kinematics was used in a Navier-Stokes solver to compute the aerodynamic forces and moments acting on the insects. The main results are as following. （1） The turn is mainly a 90° change of heading. It is made in about 10 wingbeats （about 55 ms）. It is of interest to note that the number of wingbeats taken to make the turn is approximately the same as and the turning time is only a little different from that of fruitflies measured recently by the same approach, even if the weight of the droneflies is more than 100 times larger than that of the fruitflies. The long axis of body is about 40° from the horizontal during the maneuver. （2） Although the body rotation is mainly about a vertical axis, a relatively large moment around the yaw axis （axis perpendicular to the long axis of body）, called as yaw moment, is mainly needed for the turn, because moment of inertial of the body about the yaw axis is much larger than that about the long axis. （3） The yaw moment is mainly pro- duced by changes in wing angles of attack： in a right turn, for example, the dronefly lets its right wing to have a rather large angle of attack in the downstroke （generally larger than 50°） and a small one in the upstroke to start the turn, and lets its left wing to do so to stop the turn, unlike the fruitflies who generate the yaw moment mainly by changes in the stroke plane and stroke amplitude.

Aerodynamic Effects of Corrugation in Flapping Insect Wings in Forward Flight

We have examined the aerodynamic effects of corrugation in model wings that closely mimic the wing movements of a forward flight bumblebee using the method of computational fluid dynamics. Various corrugated wing models were tested （care was taken to ensure that the corrugation introduced zero camber）. Advance ratio ranging from 0 to 0.57 was considered. The results shown that at all flight speeds considered, the time courses of aerodynamic force of the corrugated wing are very close to those of the flat-plate wing. The cornlgation decreases aerodynamic force slightly. The changes in the mean location of center of pressure in the spanwise and chordwise directions resulting from the corrugation are no more than 3% of the wing chord length. The possible reason for the small aerodynamic effects of wing corrugation is that the wing operates at a large angle of attack and the flow is separated： the large angle of incidence dominates the corrugation in determining the flow around the wing, and for separated flow, the flow is much less sensitive to wing shape variation.

Recent progress on the study of asymmetric vortex flow over slender bodies

The investigations of forebody vortex flow and its flow control have great importance in both academic field and engineering application areas. A large number of papers and many review papers have been published. However in this research field of forebody asymmetric vortices, three problems such as tip perturbation effect, Reynolds number effect and flow instability are less studied and thus not understood completely. So many researches are still working on the issues in recent years. The present paper attempts to provide a review of recent research progress on first two problems. The first problem is mainly concerned with how the vortex flow evolves after tip perturbation; how to solve the problem of repeatability and reproducibility of wind tunnel testing data; how to develop a conception of active flow control technique with tip perturbation based on the study of vortex flow response to tip perturbation. For the second problem one is mainly concerned that how the asymmetric vortices are developed with the increase of Reynolds number; how to classify the vortex flow patterns in different Reynolds number regimes; how to develop an appropriate boundary layer transition technique to simulate flows at high Reynolds number in the convention wind tunnels. Finally, some important ques- tions that deserve answers are proposed in the concluding remarks.

Forward flight of a model butterfly: Simulation by equations of motion coupled with the Navier-Stokes equations

The forward flight of a model butterfly was stud- ied by simulation using the equations of motion coupled with the Navier-Stokes equations. The model butterfly moved under the action of aerodynamic and gravitational forces, where the aerodynamic forces were generated by flapping wings which moved with the body, allowing the body os- cillations of the model butterfly to be simulated. The main results are as follows： （1） The aerodynamic force produced by the wings is approximately perpendicular to the long-axis of body and is much larger in the downstroke than in the up- stroke. In the downstroke the body pitch angle is small and the large aerodynamic force points up and slightly backward, giving the weight-supporting vertical force and a small neg- ative horizontal force, whilst in the upstroke, the body an- gle is large and the relatively small aerodynamic force points forward and slightly downward, giving a positive horizon- tal force which overcomes the body drag and the negative horizontal force generated in the downstroke. （2） Pitching oscillation of the butterfly body plays an equivalent role of the wing-rotation of many other insects. （3） The body-mass- specific power of the model butterfly is 33.3 W/kg, not very different from that of many other insects, e.g., fruitflies and dragonflies.

Effects of tip perturbation and wing locations on rolling oscillation induced by forebody vortices

The wing rock motion is frequently suffered by a wing-body configuration with low swept wing at high angle of attack. It is found from our experimental study that the tip perturbation and wing longitudinal locations affect significantly the wing rock motion of a wing-body. The natural tip perturbation would make the wing rock motion of a nondeterministic nature and an artificial mini-tip perturbation would make the wing rock motion deterministic. The artificial tip perturbation would, as its circumferential location is varied, generate three different types of motion patterns： （1） limit cycle oscillation, （2） irregular oscillation, （3） equilibrium state with tiny oscillation. The amplitude of rolling oscillation corresponding to the limit cycle oscillatory motion pattern is decreased with the wing location shifting downstream along the body axis.

Wing/body kinematics measurement and force and moment analyses of the takeoff flight of fruitflies

In the paper, we present a detailed analysis of the takeoff mechanics of fruitflies which perform voluntary takeoff flights. Wing and body kinematics of the insects during takeoff were measured using Based on the measured data, high-speed video techniques. inertia force acting on the insect was computed and aerodynamic force and moment of the wings were calculated by the method of computational fluid dynamics. Subtracting the aerodynamic force and the weight from the inertia force gave the leg force. The following has been shown. In its voluntary takeoff, a fruitfly jumps during the first wingbeat and becomes airborne at the end of the first wingbeat. When it is in the air, the fly has a relatively large ＂initial＂ pitch-up rotational velocity （more than 5 000~/s） resulting from the jumping, but in about 5 wingbeats, the pitch-up rotation is stopped and the fly goes into a quasi-hovering flight. The fly mainly uses the force of jumping legs to lift itself into the air （the force from the flapping wings during the jumping is only about 5%-10% of the leg force）. The main role played by the flapping wings in the takeoff is to produce a pitch-down moment to nullify the large ＂initial＂ pitch-up rotational velocity （otherwise, the fly would have kept pitching-up and quickly fallen down）.

Exact Analytic N-Soliton-Like Solution in Wronskian Form for a Generalized Variable-Coefficient Korteweg-de Vries Model from Plasmas and Fluid Dynamics

Applicable in fluid dynamics and plasmas, a generalized variable-coefficient Korteweg-de Vries （vcKdV） model is investigated. The bilinear form and analytic N-soliton-like solution for such a model are derived by the Hirota method and Wronskian technique. Additionally, the bilinear auto-Bǎcklund transformation between （N-1）- soliton-like and N-soliton-like solutions is verified.

Multiple Soliton-Like Solutions and Similarity Reductions of a Spherical Kadomtsev-Petviashvili Equation from Plasma Physics

<正> A spherical Kadomtsev-Petviashvili (SKP) equation for dust acoustic or ion-acoustic waves is studied.Sim-ilarity reductions of the SKP equation are obtained with the one-parameter (ε) Lie group of infinitesimal transformationsand Clarkson-Kruskal direct method.The SKP equation is also solved with a generalized tanh function method.

Dynamic flight stability of hovering model insects:theory versus simulation using equations of motion coupled with Navier-Stokes equations

In the present paper, the longitudinal dynamic flight stability properties of two model insects are predicted by an approximate theory and computed by numerical sim- ulation. The theory is based on the averaged model （which assumes that the frequency of wingbeat is sufficiently higher than that of the body motion, so that the flapping wings＇ degrees of freedom relative to the body can be dropped and the wings can be replaced by wingbeat-cycle-average forces and moments）; the simulation solves the complete equations of motion coupled with the Navier-Stokes equations. Comparison between the theory and the simulation provides a test to the validity of the assumptions in the theory. One of the insects is a model dronefly which has relatively high wingbeat frequency （164 Hz） and the other is a model hawkmoth which has relatively low wingbeat frequency （26 Hz）. The results show that the averaged model is valid for the hawkmoth as well as for the dronefly. Since the wingbeat frequency of the hawkmoth is relatively low （the characteristic times of the natural modes of motion of the body divided by wingbeat period are relatively large） compared with many other insects, that the theory based on the averaged model is valid for the hawkmoth means that it could be valid for many insects.

Painleve Analysis and Determinant Solutions of a (3+1)-Dimensional Variable-Coefficient Kadomtsev-Petviashvili Equation in Wronskian and Grammian Form

在这篇论文，调查集中于一(3+1 ) 维的可变系数的 Kadomtsev Petviashvili (vcKP ) 方程，它能在三种空间尺寸在液体动力学和血浆描述现实主义的非线性的现象。以便学习如此的一个方程的 integrability 性质， Painlev é分析在它上被执行。然后基于截断的 Painlev é扩大，双线性的形式(3+1 ) 维的 vcKP 方程被 Wronskian 技术的优点在某些系数限制下面获得，并且它在 Wronskian 决定因素形式的答案被构造并且验证。除 Wronskian 决定因素答案以外，这被显示出(3+1 ) 维的 vcKP 方程也拥有在 Grammian 决定因素形式的一个答案。

The influence of the wake of a flapping wing on the production of aerodynamic forces

The effect of the wake of previous strokes on the aerodynamic forces of a flapping model insect wing is studied using the method of computational fluid dynamics. The wake effect is isolated by comparing the forces and flows of the starting stroke （when the wake has not developed） with those of a later stroke （when the wake has developed）. The following has been shown. （1） The wake effect may increase or decrease the lift and drag at the beginning of a half-stroke （downstroke or upstroke）, depending on the wing kinematics at stroke reversal. The reason for this is that at the beginning of the half-stroke, the wing “impinges” on the spanwise vorticity generated by the wing during stroke reversal and the distribution of the vorticity is sensitive to the wing kinematics at stroke reversal. （2） The wake effect decreases the lift and increases the drag in the rest part of the half-stroke. This is because the wing moves in a downwash field induced by previous half-stroke＇s starting vortex, tip vortices and attached leading edge vortex （these vortices form a downwash producing vortex ring）. （3） The wake effect decreases the mean lift by 6%-18% （depending on wing kinematics at stroke reversal） and slightly increases the mean drag. Therefore, it is detrimental to the aerodynamic performance of the flapping wing.

Effects of T-S wave amplitude on the control of boundary layer transition by streaks

The effects of streaks on boundary layer transition depend on the initial amplitude of T-S waves introduced to excite the transition. This problem was studied in a flat-plate boundary layer in water tunnel by using hydrogen bubble method. Three T-S wave initial amplitudes were tested. The results show that both narrow and wide-spacing streaks depress the transition excited by T-S waves with lower initial amplitude. However, when transition is excited by T-S waves of higher initial amplitude, the narrow-spacing streaks depress the transition, while the wide-spacing streaks promote the transition. Futrther the underlying mechanisms were also analyzed.

Experimental Investigation of Wake-Induced Bypass Transition Control by Surface Roughness

Surface roughness is experimentally used to control the flat-plate boundary layer bypass transition induced by an upstream convected two-dimensional(2D)circular cylinder wake.It is shown that the later stage of this bypass transition is successfully postponed,at the price of accelerating the earlier transition stage.A regularisation process of the hairpin vortices,which are the dominant coherent structures to promote the transition process,are observed under the influence of roughness elements.Significant scale reduction and localisation of these hairpins are achieved,which enhances the possibility of a hairpin self-annihilation process.Therefore,the cascade to large-scale structures in the later transition stage might be impeded/weakened.

Stabilization control of a hovering model insect:lateral motion

Our previous study shows that the lateral disturbance motion of a model drone fly does not have inherent stability （passive stability）,because of the existence of an unstable divergence mode.But drone flies are observed to fly stably.Constantly active control must be applied to stabilize the flight.In this study,we investigate the lateral stabilization control of the model drone fly.The method of computational fluid dynamics is used to compute the lateral control derivatives and the techniques of eigenvalue and eigenvector analysis and modal decomposition are used for solving the equations of motion.Controllability analysis shows that although inherently unstable,the lateral disturbance motion is controllable.By feeding back the state variables （i.e.lateral translation velocity,yaw rate,roll rate and roll angle,which can be measured by the sensory system of the insect） to produce anti-symmetrical changes in stroke amplitude and/or in angle of attack between the left and right wings,the motion can be stabilized,explaining why the drone flies can fly stably even if the flight is passively unstable.