Noether symmetry and conserved quantity for dynamical system with non-standard Lagrangians on time scales

This paper focuses on studying the Noether symmetry and the conserved quantity with non-standard Lagrangians,namely exponential Lagrangians and power-law Lagrangians on time scales. Firstly, for each case, the Hamilton principle based on the action with non-standard Lagrangians on time scales is established, with which the corresponding Euler–Lagrange equation is given. Secondly, according to the invariance of the Hamilton action under the infinitesimal transformation, the Noether theorem for the dynamical system with non-standard Lagrangians on time scales is established.The proof of the theorem consists of two steps. First, it is proved under the infinitesimal transformations of a special one-parameter group without transforming time. Second, utilizing the technique of time-re-parameterization, the Noether theorem in a general form is obtained. The Noether-type conserved quantities with non-standard Lagrangians in both classical and discrete cases are given. Finally, an example in Friedmann–Robertson–Walker spacetime and an example about second order Duffing equation are given to illustrate the application of the results.

Lagrangian coherent structure analysis on transport of Acetes chinensis along coast of Lianyungang,China

Spatial heterogeneity or“patchiness”of plankton distributions in the ocean has always been an attractive and challenging scientific issue to oceanographers.We focused on the accumulation and dynamic mechanism of the Acetes chinensis in the Lianyungang nearshore licensed fishing area.The Lagrangian frame approaches including the Lagrangian coherent structures theory,Lagrangian residual current,and Lagrangian particle-tracking model were applied to find the transport pathways and aggregation characteristics of Acetes chinensis.There exist some material transport pathways for Acetes chinensis passing through the licensed fishing area,and Acetes chinensis is easy to accumulate in the licensed fishing area.The main mechanism forming this distribution pattern is the local circulation induced by the nonlinear interaction of topography and tidal flow.Both the Lagrangian coherent structure analysis and the particle trajectory tracking indicate that Acetes chinensis in the licensed fishing area come from the nearshore estuary.This work contributed to the adjustment of licensed fishing area and the efficient utilization of fishery resources.

Canonical Transformations and Poisson Theory for Dynamics with Non-Standard Lagrangians

The canonical transformation and Poisson theory of dynamical systems with exponential,power-law,and logarithmic non-standard Lagrangians are studied,respectively.The criterion equations of canonical transformation are established,and four basic forms of canonical transformations are given.The dynamic equations with non-standard Lagrangians admit Lie algebraic structure.From this,we es-tablish the Poisson theory,which makes it possible to find new conservation laws through known conserved quantities.Some examples are put forward to demonstrate the use of the theory and verify its effectiveness.

Perturbation to Noether Symmetry and Adiabatic Invariants for Dynamical Systems with Nonstandard Lagrangians

The perturbation to Noether symmetry and adiabatic invariants for dynamical systems with nonstandard Lagrangians are studied. Based on two kinds of nonstandard Lagrangians( i. e.exponential Lagrangians and power-law Lagrangians),the exact invariants of Noether type are given. Based on the definition of highorder adiabatic invariants,the relationship between the perturbation of Noether symmetry and the adiabatic invariants of the system under a small disturbance is studied,and then the corresponding theorems of adiabatic invariants are established. Finally, two examples are given to illustrate the methods and results appear in this paper.

Symmetry of Lagrangians of holonomic systems in terms of quasi-coordinates

This paper discusses the symmetry of Lagrangians of holonomic systems in terms of quasi-coordinates.Firstly,the definition and the criterion of the symmetry are given.Secondly,the condition under which there exists a conserved quantity and the form of the conserved quantity are obtained.Finally,an example is shown to illustrate the application of the results.

Further study on a class of augmented Lagrangians of Di Pillo and Grippo in nonlinear programming

在这份报纸， Di Pillo 和 Grippo (DGAL ) 的扩充 Lagrangians 的一个类被考虑，为解决经由非强迫的最小化技术的抑制平等的问题。关系进一步在问题的产品空格在 DGAL 的非强迫的 minimizers 之间被讨论变量和 multipliers，和抑制问题的解决方案和 Lagrange multipliers 的相应的值。产生性质更精确显示 DGAL 的这个类更多样地是准确的惩罚功能。因此，抑制平等的问题的一个解决方案和 Lagrange multipliers 的相应的值能被在问题变量和 multipliers 的产品空格执行 DGAL 的单个非强迫的最小化发现。关键词非线性的编程 - 抑制优化 - 扩充 Lagrangians - Di Pillo 和 Grippo 2000 数学题目分类 90C30 的扩充

Symmetry of Lagrangians of nonholonomic systems of non-Chetaev's type

This paper studies the symmetry of Lagrangians of nonholonomic systems of non-Chetaev's type.First,the definition and the criterion of the symmetry of the system are given.Secondly,it obtains the condition under which there exists a conserved quantity and the form of the conserved quantity.Finally,an example is shown to illustrate the application of the result.

Approximate Noether-Type Symmetries and Conservation Laws via Partial Lagrangians for Nonlinear Wave Equation with Damping

以我们部分 Lagrangian 和近似 Euler-Lagrange-type 方程的新准确定义，我们与经由与部分 Lagrangians 联系的近似 Noether 类型对称操作员抑制调查非线性的波浪方程并且在一般形式构造它的近似能量守恒定律。

Symmetry of Lagrangians of a holonomic variable mass system

The symmetry of Lagrangians of a holonomic variable mass system is studied.Firstly,the differential equations of motion of the system are established.Secondly,the definition and the criterion of the symmetry of the system are presented.Thirdly,the conditions under which there exists a conserved quantity deduced by the symmetry are obtained.The form of the conserved quantity is the same as that of the constant mass Lagrange system.Finally,an example is shown to illustrate the application of the result.

Electromagnetic Gauges and Maxwell Lagrangians Applied to the Determination of Curvature in the Space-Time and their Applications

If we consider the finite actions of electromagnetic fields in Hamiltonian regime and use vector bundles of geodesic in movement of the charges with a shape operator (connection) that measures the curvature of a geometrical space on these geodesic (using the light caused from these points (charges) acting with the infinite null of gravitational field (background)) we can establish a model of the curvature through gauges inside the electromagnetic context. In partular this point of view is useful when it is about to go on in a quantized version from the curvature where the space is distorted by the interactions between particles. This demonstrates that curvature and torsion effect in the space-time are caused in the quantum dimension as back-reaction effects in photon propagation. Also this permits the observational verification and encodes of the gravity through of light fields deformations. The much theoretical information obtained using the observable effects like distortions is used to establish inside this Lagrangian context a classification of useful spaces of electro-dynamic configuration for the description of different interactions of field in the Universe related with gravity. We propose and design one detector of curvature using a cosmic censor of the space-time developed through distortional 3-dimensional sphere. Some technological applications of the used methods are exhibited.

Symmetry of the Lagrangians of holonomic nonconservative system in event space

This paper analyzes the symmetry of Lagrangians and the conserved quantity for the holonomic non-conservative system in the event space. The criterion and the definition of the symmetry are proposed first, then a quantity caused by the symmetry and its existence condition are given. An example is shown to illustrate the application of the result at the end.

A drift-kinetic perturbed Lagrangian for low-frequency nonideal MHD applications

We find that the perturbed Lagrangian derived from the drift-kinetic equation in[Porcelli F et al 1994 Phys.Plasmas 1470]is inconsistent with the ordering for the low-frequency large-scale magnetohydrodynamic(MHD).Here,we rederive the expression for the perturbed Lagrangian within the framework of nonideal MHD using the ordering system for the low-frequency largescale MHD in a low-beta plasma.The obtained perturbed Lagrangian is consistent with Chen's gyrokinetic theory[Chen L and Zonca F 2016 Rev.Mod.Phys.88015008],where the terms related to the field curvature and gradient are small quantities of higher order and thus negligible.As the perturbed Lagrangian has been widely used in the literature to calculate the plasma nonadiabatic response in low-frequency MHD applications,this finding may have a significant impact on the understanding of the kinetic driving and dissipative mechanisms of MHD instabilities and the plasma response to electromagnetic perturbations in fusion plasmas.

Path Integral Quantization of Non-Natural Lagrangian

Path integral technique is discussed using Hamilton Jacobi method. The Hamilton Jacobi function of non-natural Lagrangian is obtained using separation of variables method. This function makes an important role in path integral quantization. The path integral is obtained as integration over the canonical phase space coordinates, which contains the generalized coordinate q and the generalized momentum p. One illustrative example is considered to explain the application of our formalism.

基于多目标优化的跨介质航行体水面滑跳初始运动参数设计

基于耦合欧拉-拉格朗日方法,开展了初始运动参数对带滑板跨介质航行体近水面滑跳过程的影响规律研究。采用参数回归方法分别建立最大浸深、最大过载和俯仰角变化3个变量随航行体初始速度、入水角、滑板倾角变化的关系式,得到了跨介质航行体稳定滑跳的参数包络,在入水角2°~5°、滑板倾角10°~25°、速度60~80 m/s范围之间,且在范围内各参数之间会相互制约。在此基础上,基于多目标优化算法获得了最适宜航行体稳定滑跳的初始参数为入水速度60.1 m/s、滑板倾角18.8°、入水角2°,在此参数范围内,跨介质航行体的水面滑跳过程可以在不超过航行体过载要求的条件下获得相对最小的入水浸深和俯仰角变化。

基于CEL方法的带结构物溃坝流数值模拟

随着全球气温的不断升高,极端天气现象增多,溃坝现象成为水工结构方向需要重点防范的自然灾害。溃坝流的发展会对下游结构物产生巨大的破坏作用,因此深入探究溃坝流现象的水动力学特性以及溃坝流下游结构物所受到的冲击力影响势在必行。本文针对带有结构物的溃坝流动问题现象,采用CEL方法(Coupled Eulerian-Lagrangian analysis,耦合欧拉-拉格朗日方法),对于溃坝流的发展、演化进行了数值模拟。研究结果表明,模拟结果中溃坝流自由表面及流体尖端时程变化与文献试验结果拟合较好,CEL方法可应用在溃坝流现象的模拟,并且具有较好的准确性和精度。结构物材料性能、高度及与结构物与溃坝流间的位置,均会影响溃坝流的运动状态以及结构物的受力变形状态,在不考虑结构物破坏的情况下,提高结构物弹性模量,增加结构物高度,以及减小结构物与溃坝流间的距离均可提高结构物对于溃坝流的阻挡作用。

基于CEL法熔滴冲击基板的TPF/FSI数值模拟

航空发动机和燃气轮机的高温工作环境会对其热端金属部件造成不可逆损伤,热障涂层(thermal barrier coatings,TBCs)能够承受高温和高压的侵蚀性环境,从而保证金属部件使用的安全性及可靠性。以空心Y_(2)O_(3)-ZrO_(2)(yttrium-stabilized zirconia,YSZ)粒子在等离子焰流中的2种形态,即全熔熔滴和空心熔滴为研究对象对其冲击铺展过程进行了模拟。基于ABAQUS/EXPLICIT耦合欧拉-拉格朗日(coupled Eulerian-Lagrangian,CEL)有限元方法,首先针对ABAQUS缺少相变模型,导致使用CEL方法计算熔滴铺展形貌失真的问题,给出了适用的动力黏度随温度变化的经验公式。此外,考虑周围空气对熔滴铺展过程的影响,提出了“两相流(two phase flow,TPF)/流-固耦合(fluid-structure-interaction,FSI)”2.5D模型,对熔滴冲击基板凝固成型及空气卷入的过程进行了模拟,并揭示了2种熔滴铺展形貌存在较大差异的机理,对制备隔热性能更优的热障涂层具有指导意义。

考虑出行成本不确定性的路网交通疏散策略

为提高应急管理水平,考虑突发事件影响下的交通出行成本不确定性,对城市交通疏散问题进行研究。首先,根据交通疏散问题的时空特性创建时空耦合网络图,并且结合行程时间成本和冲突风险成本,提出了城市交通路网出行成本的量化方法。进一步考虑路段资源权重上限的影响,通过增加边际约束,构建基于预算不确定集的先验疏散策略的鲁棒优化模型,以最小化路网疏散过程的总交通出行成本。然后运用模型重构技术,将搭建的鲁棒模型转化为混合整数线性规划模型,并设计改进的拉格朗日松弛方法进行解耦求解。最后以SiouxFalls网络进行算例分析,数值结果表明,随着不确定集和模型规模的增大,行程时间成本和冲突风险成本的增速分别提高约29.13%和236.46%,模型预算参数控制在一定的区间,能够较好地权衡解的鲁棒性与最优性。通过南京部分区域路网案例测试验证所述方法在更大规模网络算例的适用性,研究结果表明:相比于传统拉格朗日松弛方法,所提出的改良方法可以在较少的迭代次数内得到高质量的可行解。研究结果可以为应急指挥部门制定可靠的交通疏散策略提供思路。

用Lagrangian松弛法解化工批处理调度问题

研究基于Ｌａｇｒａｎｇｉａｎ松弛法的化工批处理过程的调度方法．建立了化工批处理过程调度问题的一种混合整数规划（ＭＩＬＰ）模型，并通过松弛离散变量和连续变量共存的约束，将问题分解为一个两层次的优化问题，其中上层是原问题的对偶问题，下层由两个子问题构成：一个与产品批量有关，另一个确定操作时间表，分别用线性规划和动态规划方法解这两个子问题．然后从对偶问题的解构作原问题的可行解．数值试验结果证明了该方法的有效性．

基于mixed Lagrangian/Eulerian方法的轮轨滚动接触特性分析

为了缩短有限元方法显式计算轮轨滚动接触的时间,采用mixed Lagrangian/Eulerian方法建立了轮轨滚动接触有限元模型.应用该模型对轮轨接触区的单元进行细化,计算了列车在启动、运行和制动工况下轮轨的接触特性.计算结果表明:不同工况下,轮轨滚动接触区最大Mises应力、最大接触应力和接触斑面积等法向特性变化幅度均在2%以内,但接触区纵向截面中Mises应力分布及纵向剪切应力分布有较大变化;启动和制动工况下,最大Mises应力和最大纵向剪切应力位置均比自由滚动时更接近于轮轨表面;不同工况下,摩擦力大小和方向发生变化,在列车牵引和制动工况中,摩擦力达到极限时轮轨间出现完全滑动,摩擦力方向与滑动方向相反,且不同速度等级下的纵向摩擦力变化幅度也在2%以内.

基于ε-约束方法的增广Lagrangian多目标协同进化算法

介绍了一种利用协同进化算法求解多目标优化问题的算法。这种算法首先采用ε- 约束方法对多目标优化问题进行处理 ,使其转化为一个单目标带约束的优化问题 ;然后 ,采用增广Lagrangian方法把这个单目标约束优化问题转化成一个存在鞍点的二人零和博弈问题 ;最后 ,利用协同进化的思想 ,用两个种群分别表示目标函数和约束这两个局中人 ,对这个二人零和博弈问题求解。进化过程中的选择、重组和变异算子均采用简单遗传算法(SGA)的机制。通过对两个实验测试问题的研究可以看出 ,这种算法比其它同类进化算法所得的结果要精确、稳定。