Optimized transfer trajectories in the earth--moon system

Investigations of low energy transfer trajectories are important for both celestial mechanics and astronautics. Methodologies using the theories from dynamical systems are developed in recent years. This paper investigates the dynamics of the earth--moon system. Low energy transfer trajectories are solved numerically by employing a hybrid strategy: first, a genetic hide and seek method performs a search in large domain to confine the global minimum $f({\eta})$ (objective function) region; then, a deterministic Nelder--Mead method is utilized to refine the minimum quickly. Some transfer trajectories of the spacecraft in the earth--moon system are successfully simulated which verify the desired efficiency and robustness of the method of this paper.     

Passive control of aeroelastic instability in a long span bridge model prone to coupled flutter using targeted energy transfer

In this paper we study a problem of passive nonlinear targeted energy transfer between a two degrees of freedom long span bridge model prone to coupled flutter and a single degree of freedom nonlinear energy sink (NES). This study is mainly analytical and use complexification methods, multiple scales expansions and exploits also the concept of limiting phase trajectories (LPTs). The system is studied under 1:1:1 nonlinear resonance involved in targeted energy transfer mechanisms. Several behaviors that suppress aeroelastic instability are identified. We show that analytical calculations permit to design a NES able to efficiently control the aeroelastic instability of the bridge. Numerical simulations are performed and good agreement with analytical predictions is observed. It results that the concept of limiting phase trajectories (LPT) allows formulating adequately the problem of intensive energy transfer from a bridge to a nonlinear energy sink.     

基于最小相位法的屏蔽电缆瞬态响应分析方法

为了分析屏蔽电缆在电磁脉冲作用下的时域响应,对基于最小相位法的频域等效方法进行了研究。首先,通过建立转移阻抗测试系统的电路模型,推导系统的频域传递函数,并验证其为最小相位系统与全通系统的级联;其次,采用最小相位法,对测得的幅频曲线进行相位重构,根据推导的传递函数的零、极点分布,对重构的最小相位传递函数进行相位补偿;最后,将补偿后的传递函数与瞬态干扰信号在频域相乘后变换到时域,得到了屏蔽电缆的时域响应。仿真及实验结果验证了该方法的有效性。     

积与积减原理

文章分析了重力势能、引力势能、电荷势能、化学势能、热量势能、质量积、动量积等多种势能,发现它们均可表达为一种守恒广延量和对应的强度量的乘积,因此可将其统一定义为"积".基于积这一概念,文章得到了孤立系统内守恒广延量传递过程的积减原理,即孤立系统内进行的守恒广延量传递过程中系统的积总是减小的.进一步,文章还基于积的概念发展了孤立系统和封闭系统的势平衡判据,发现孤立系统达到势平衡状态时,系统的积达到最小值(最小积原理);当封闭系统达到势平衡状态时,系统的准自由积达到最小值(最小准自由积原理).上述结论应用于传热学中即可得到热量传递过程的(火积)减原理及相应的热平衡判据.与热力学中的核心概念熵相对应,由于物理量(火积)可以描述传热过程的不可逆性,作为传热过程的优化准则,度量系统的无序度,并给出系统的热平衡判据,因此(火积)是传热学中的核心概念. 关键词： 势能 积 积减原理 平衡判据     

“Step-up” versus “step-down” scattering asymmetry in the neutralization of H on free-electron vicinal metal surfaces

The charge transfer between H⁻ and a free-electron vicinal metallic surface is studied using a wave-packet propagation method. We apply a statistical Thomas-Fermi-von Weizsäcker model with a local density approximation for the exchange-correlation energy to compute the ground-state electronic structure of the substrate. The long-range image charge effects in the electron transfer are included on a phenomenological level. We obtain the ion-survival probability from a rate equation for a set of realistic scattering trajectories of projectiles that are incident with a kinetic energy of 50 eV. Our calculations reveal a pronounced substrate orientation dependence of the charge transfer dynamics expressed in a “left-right” (or “step-up-step-down”) scattering asymmetry in the final ion-survival probability, which is caused by an enhancement of electron loss on the outgoing part of those ion trajectories which approach steps from below.     

Escorted free energy simulations: improving convergence by reducing dissipation

Nonequilibrium, "fast switching" estimates of equilibrium free energy differences DeltaF are often plagued by poor convergence due to dissipation. We propose a method to improve these estimates by generating trajectories with reduced dissipation. Introducing an artificial flow field that couples the system coordinates to the external parameter driving the simulation, we derive an identity for DeltaF in terms of the resulting trajectories. When the flow field effectively escorts the system along a near-equilibrium path, the free energy estimate converges efficiently and accurately. We illustrate our method on a model system and discuss the general applicability of our approach.     

Dynamical tunneling of bound systems through a potential barrier: Complex way to the top

A semiclassical method of complex trajectories for the calculation of the tunneling exponent n systems with many degrees of freedom is further developed. It is supplemented with an easily implemented technique that enables one to single out the physically relevant trajectory from the whole set of complex classical trajectories. The method is applied to semiclassical transitions of a bound system through a potential barrier. We find that the properties of physically relevant complex trajectories are qualitatively different in the cases of potential tunneling at low energy and dynamical tunneling at energies exceeding the barrier height. Namely, in the case of high energies, the physically relevant complex trajectories describe tunneling via creation of a state close to the top of the barrier. The method is checked against exact solutions of the Schrödinger equation in a quantum-mechanical system of two degrees of freedom.     

Regge trajectories in the quark model

We prove that the large angular momentum behaviour of the leading Regge trajectory of a meson (q \(\bar q\) ) or a baryon (qqq) can be obtained by minimizing the classical energy of the system for given angular momentum. A two-body quark-antiquark linear potential plus relativistic kinematics produces asymptotically linear Regge trajectories for mesons. For baryons we take either a sum of two-body potentials with half strength or a string of minimum length connecting the quarks, and find in both cases that the favoured configuration is a quark-diquark system and that the baryon and meson trajectories have the same slope. Short-distance singularities of the potential are shown to be unimportant.     

Hindered Coulomb explosion of embedded Na clusters — stopping,shape dynamics and energy transport

We investigate the dynamical evolution of a Na₈ cluster embedded in Ar matrices of various sizes from N=30 to 1048. The system is excited by an intense short laser pulse leading to high ionization stages.We analyze the subsequent highly non-linear motion of cluster and Ar environment in terms of trajectories, shapes, and energy flow. The most prominent effects are: temporary stabilization of high charge states for several ps, sudden stopping of the Coulomb explosion of the embedded Na₈ clusters associated with an extremely fast energy transfer to the Ar matrix, fast distribution of energy throughout the Ar layers by a sound wave. Other ionic-atomic transfer and relaxation processes proceed at slower scale of few ps. The electron cloud is almost thermally decoupled from ions and thermalizes far beyond the ps scale.     

Finite element method for radiation heat transfer in multi-dimensional graded index medium

In graded index medium, ray goes along a curved path determined by Fermat principle, and curved ray-tracing is very difficult and complex. To avoid the complicated and time-consuming computation of curved ray trajectories, a finite element method based on discrete ordinate equation is developed to solve the radiative transfer problem in a multi-dimensional semitransparent graded index medium. Two particular test problems of radiative transfer are taken as examples to verify this finite element method. The predicted dimensionless net radiative heat fluxes are determined by the proposed method and compared with the results obtained by finite volume method. The results show that the finite element method presented in this paper has a good accuracy in solving the multi-dimensional radiative transfer problem in semitransparent graded index medium.     

Small amplitude approximation and stabilities for dislocation motion in a superlattice

Starting from the traveling wave solution, in small amplitude approximation, the Sine-Gordon equation can be re- duced to a generalized Duffing equation to describe the dislocation motion in a superlattice, and the phase plane properties of the system phase plane are described in the absence of an applied field. The stabilities are also discussed in the presence of an applied field. It is pointed out that the separatrix orbit describing the dislocation motion as the kink wave may transfer the energy along the dislocation line, keep its form unchanged, and reveal the soliton wave properties of the dislocation motion. It is stressed that the dislocation motion process is the energy transfer and release process, and the system is stable when its energy is minimum.     

Paul阱中共线三离子体系的经典动力学

研究了在Paul阱囚禁场赝势作用下共线构形的三离子体系经典动力学特性.尽管这是一个非线性体系，但不存在混沌，即体系在任何能量下运动都是规则的，而相空间则由两个轨迹为对称和反对称周期(或准周期)轨道的KAM不变环面构成.体系的两条最简单的周期轨道S和A的周期随能量E的下降而增大，并在E趋于体系的最小值E_min=3.0时分别为反对称和对称谐振动. 关键词：     

基于新型MRTD模型研究扫描型红外热像仪的视距

 基于人眼视觉系统可感知的阈值信噪比,提出预测红外热像仪最小可分辨温差（MRTD）方法。该方法根据频谱理论和红外热成像系统的二维调制传递函数,并结合匹配滤波器的概念,描述4条带标准靶的空间频谱函数。利用此空间频谱函数研究了4条带标准靶经过红外热成像系统的调制传递之后人眼视觉系统的感知信噪比。基于人眼视觉系统可感知的阈值信噪比,建立一个新的MRTD模型。依据此MRTD模型和视距模型,实现红外热像仪视距的预测。仿真结果表明,该方法预测的视距与实验数据有很好的一致性。     

强激光场中CO分子经典轨迹的辛算法

采用辛算法计算CO异核双原子分子系统在强激光场作用下的经典轨迹,与Runge-Kutta方法进行比较,分析了CO双原子分子在激光场作用下的振动轨迹、相平面轨道与总能量随时间的变化及CO分子的解离.     

Thermodynamics and topology of disordered systems: Statistics of the random knot diagrams on finite lattices

The statistical properties of random lattice knots, the topology of which is determined by the algebraic topological Jones-Kauffman invariants, was studied by analytical and numerical methods. The Kauffman polynomial invariant of a random knot diagram was represented by a partition function of the Potts model with a random configuration of ferro-and antiferromagnetic bonds, which allowed the probability distribution of the random dense knots on a flat square lattice over topological classes to be studied. A topological class is characterized by the highest power of the Kauffman polynomial invariant and interpreted as the free energy of a q-component Potts spin system for q→∞. It is shown that the highest power of the Kauffman invariant correlates with the minimum energy of the corresponding Potts spin system. The probability of the lattice knot distribution over topological classes was studied by the method of transfer matrices, depending on the type of local junctions and the size of the flat knot diagram. The results obtained are compared to the probability distribution of the minimum energy of a Potts system with random ferro-and antiferromagnetic bonds.     

基于拉格朗日跟踪法的波纹流道流体特性研究

采用正交实验方法考察了具有不同结构参数的三维周期波纹流道中的流体性能,并采用Webb评价方法对其进行性能评价。比较了不同波纹宽度的波纹流道的阻力因子e_f、传热因子e_Nu和能效因子η的值,结果表明三者都随Re的增大而增大,波纹宽度最小时能效因子η最大。流体在波纹流道中垂直于主流方向的横截面上产生二次流,随着Re增大,二次流增强,阻力增大,温度边界层减薄,温度等值线分布变得不均匀,传热增强。采用拉格朗日粒子跟踪技术分析了不同Re下,流体粒子在波纹流道内的运动轨迹,绘制了不同周期出口流体粒子的庞加莱截面图,结果表明流体粒子在波纹流道中被反复拉伸和折叠,增加了流体粒子的接触面积,提高混合效率,强化了传热。     

La Vitesse Initiale D'un Engin Spatial

Résumé L'hodographe est construit pour déterminer des changements d'impulsion de vitesse réalisant le transfert de l'engin spatial entre deux orbites. Le problème est surtout clair dans le cas des orbites complanaires. Avec le point de départ prescrit et le plan de vol des orbites de transfert forment un système de deux paramètres variables. Pour la demande d'osculation de l'orbite de transfert et d'arrivée le problème se réduit au système d'un paramètre variable: la vitesse de départ (1) est la function de l'angle de départ. On obtient l'angle menant à la vitesse minimum du départ (2) et l'angle, auquel correspond le minimum module du changement de vitesse (3). Le résultat obtenu contient comme cas particulier le transfer de Hohmann parmi les points d'apside.

---

Starting velocity of artifical cosmic bodies

The change of the velocity transferring the known path of departure to the transfer orbit is made clear by an orbital hodograph. The problem is very simple in the case of a pair of complanar rocket trajectories. When the trajectory plane and the in-space launching point is given, the transfer orbits form a twoo-parametric system. Requiring the osculation of the transfer orbit with the trajectory of arrival, the problem is reduced to the solution of an one-parametric system: The initial velocity is a function of the tangential angle in the starting point. The angle corresponding to the minimum of starting velocity and the angle corresponding to the minimum modulus of the change of the velocity are given. The result obtained contains the special case of the Hohmann transfer between the apsidal points.

     

双稳系统的随机能量共振和作功效率

分析了处于双稳系统中的布朗粒子与外界的周期性外力和热随机力的功、热交互作用,建立了基于Langevin方程的随机能量平衡方程.围绕着受周期力、随机力和阻尼力共同作用的Langevin方程,采用动力学和非平衡热力学相结合的方法,从以"力"为立足点转到以"能量"为研究核心,深入分析了布朗粒子沿单一轨线运动时系统与环境之间的能量交换和作功效率,揭示了双稳系统的随机能量共振现象. 关键词： 双稳系统 随机能量共振 作功效率     

Peculiarities of light propagation in chiral liquid crystal cells in an external electric field

We investigate the propagation of the extraordinary ray in a cell with a chiral liquid crystal at oblique incidence. For a 180° twist cell, we study the dependence of the minimum incidence angle at which the light does not yet pass through the cell on the applied voltage. The orientational structure of a liquid crystal in an external electric field has been calculated by directly minimizing the free energy. This has allowed the ray trajectories and the limiting refraction angles to be determined. The results of our calculations are consistent with the experiment. We show that allowance for the electric field nonuniformity in a chiral system is important for agreement between theory and experiment.