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.

对抗条件下基于SAC-Lagrangian的UAV智能规划

无人机因其低成本、可消耗、分布部署、敏捷灵活的优势,在多个民用领域大放异彩。但受其智能化程度限制,如何在复杂对抗条件下自主安全完成任务仍存在巨大挑战。针对目前无人机任务规划存在的智能性和安全性问题,提出一种基于安全强化学习算法的无人机智能规划方法(SAC-Lagrangian)。考虑了雷达威胁、禁飞区安全约束和地导对抗条件,将任务规划问题建模为约束马尔可夫决策过程(CMDP),通过拉格朗日乘子法变为对偶问题,采用最大熵柔性行动者-评论家(SAC)算法近似求解最优策略,保证了智能体在遵守安全约束条件下最大化期望回报。仿真结果表明,与其他基线算法相比,所提方法能在保证任务性能的同时确保安全性,适应动态变化的场景,任务完成率达到96%,因此,具有高效、鲁棒和安全的优势。

An Updated Lagrangian Particle Hydrodynamics (ULPH)-NOSBPD Coupling Approach forModeling Fluid-Structure Interaction Problem

A fluid-structure interaction approach is proposed in this paper based onNon-Ordinary State-Based Peridynamics(NOSB-PD)and Updated Lagrangian Particle Hydrodynamics(ULPH)to simulate the fluid-structure interaction problem with large geometric deformation and material failure and solve the fluid-structure interaction problem of Newtonian fluid.In the coupled framework,the NOSB-PD theory describes the deformation and fracture of the solid material structure.ULPH is applied to describe the flow of Newtonian fluids due to its advantages in computational accuracy.The framework utilizes the advantages of NOSB-PD theory for solving discontinuous problems and ULPH theory for solving fluid problems,with good computational stability and robustness.A fluidstructure coupling algorithm using pressure as the transmission medium is established to deal with the fluidstructure interface.The dynamic model of solid structure and the PD-ULPH fluid-structure interaction model involving large deformation are verified by numerical simulations.The results agree with the analytical solution,the available experimental data,and other numerical results.Thus,the accuracy and effectiveness of the proposed method in solving the fluid-structure interaction problem are demonstrated.The fluid-structure interactionmodel based on ULPH and NOSB-PD established in this paper provides a new idea for the numerical solution of fluidstructure interaction and a promising approach for engineering design and experimental prediction.

Updated Lagrangian Particle Hydrodynamics (ULPH)Modeling of Natural Convection Problems

Natural convection is a heat transfer mechanism driven by temperature or density differences,leading to fluid motion without external influence.It occurs in various natural and engineering phenomena,influencing heat transfer,climate,and fluid mixing in industrial processes.This work aims to use the Updated Lagrangian Particle Hydrodynamics(ULPH)theory to address natural convection problems.The Navier-Stokes equation is discretized using second-order nonlocal differential operators,allowing a direct solution of the Laplace operator for temperature in the energy equation.Various numerical simulations,including cases such as natural convection in square cavities and two concentric cylinders,were conducted to validate the reliability of the model.The results demonstrate that the proposed model exhibits excellent accuracy and performance,providing a promising and effective numerical approach for natural convection problems.

An Unconventional Divergence Preserving Finite-Volume Discretization of Lagrangian Ideal MHD

We construct an unconventional divergence preserving discretization of updated Lagrangian ideal magnetohydrodynamics(MHD)over simplicial grids.The cell-centered finite-volume(FV)method employed to discretize the conservation laws of volume,momentum,and total energy is rigorously the same as the one developed to simulate hyperelasticity equations.By construction this moving mesh method ensures the compatibility between the mesh displacement and the approximation of the volume flux by means of the nodal velocity and the attached unit corner normal vector which is nothing but the partial derivative of the cell volume with respect to the node coordinate under consideration.This is precisely the definition of the compatibility with the Geometrical Conservation Law which is the cornerstone of any proper multi-dimensional moving mesh FV discretization.The momentum and the total energy fluxes are approximated utilizing the partition of cell faces into sub-faces and the concept of sub-face force which is the traction force attached to each sub-face impinging at a node.We observe that the time evolution of the magnetic field might be simply expressed in terms of the deformation gradient which characterizes the Lagrange-to-Euler mapping.In this framework,the divergence of the magnetic field is conserved with respect to time thanks to the Piola formula.Therefore,we solve the fully compatible updated Lagrangian discretization of the deformation gradient tensor for updating in a simple manner the cell-centered value of the magnetic field.Finally,the sub-face traction force is expressed in terms of the nodal velocity to ensure a semi-discrete entropy inequality within each cell.The conservation of momentum and total energy is recovered prescribing the balance of all the sub-face forces attached to the sub-faces impinging at a given node.This balance corresponds to a vectorial system satisfied by the nodal velocity.It always admits a unique solution which provides the nodal velocity.The robustness and the accuracy of this unconventional FV scheme have been demonstrated by employing various representative test cases.Finally,it is worth emphasizing that once you have an updated Lagrangian code for solving hyperelasticity you also get an almost free updated Lagrangian code for solving ideal MHD ensuring exactly the compatibility with the involution constraint for the magnetic field at the discrete level.

复辛空间■^(2),■^(4)中的完全Lagrangian子空间的分类

讨论复辛空间■^(2),■^(4)中的完全Lagrangian子空间的标准型。通过参数化的方法研究复辛空间■^(2),■^(4)中的完全Lagrangian子空间的表示与分类。

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.

有约束极大极小优化问题的修正Lagrangian算法

对于有不等式约束的极大极小优化问题,本文构造了一个修正的Lagrangian函数并分析了其在一般条件下的性质,建立了与之对应的修正Lagrangian算法.最后对文献中的几个问题给出了数值计算结果验证了算法.

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。

新的Lagrangian松弛法求解CLSP问题

ＣＬＳＰ（ｃａｐａｃｉｔａｔｅｄｓｉｎｇｌｅ－ｌｅｖｅｌｌｏｔ－ｓｉｚｉｎｇｐｒｏｂｌｅｍ）是在受能力约束限制下，确定Ｎ种不同的项目在给定的计划范围Ｔ内的每一个时间段批量，使得在整个计划范围内（ｐｌａｎｎｉｎｇｈｏｒｉｚｏｎ）项目总的调整费用和库存保管费用以及生产费用之和最小．本文基于Ｌａｇｒａｎｇｉａｎ松弛法和新的启发式算法相结合求解ＣＬＳＰ问题，通过测试１０个问题，仿真实验表明，平均对偶误差可达到２％以内．

一种基于Lagrangian松弛法求解化工批处理过程调度的方法

提出一种快速求取化工批处理过程次优调度的方法。通过约束变换、引入操作批量的函数和松弛物料存贮能力约束,将调度问题分解为一个两层次的优化问题。用动态规划求解下层问题,用次梯度法求解上层对偶问题。然后依据对偶问题的解,以启发式方法构作原问题的可行解。数值测试结果证明了读方法的有效性和实用性。

线性空间中集值映射向量优化问题的最优性条件与Lagrangian乘子(英文)

本文在广义次似凸性假设下，利用择一性定理，在线性空间中获得了含等式与不等式约式集值向量最优化问题的 Ｋｕｈｎ－Ｔｕｃｋｅｒ型最优性条件及 Ｌａｇｒａｎｇｉａｎ乘子定理．

二维Lagrangian坐标系下可压气动方程组的间断Petrov-Galerkin方法（英文）

构造矩形网格下求解Lagrangian坐标系下气动方程组的单元中心型格式.空间离散采用控制体积间断Petrov-Galerkin方法,时间离散采用二阶TVD Runge-Kutta方法.利用限制器来抑制非物理震荡并保证RKCV算法的稳定性.构造的算法可以保证物理量的局部守恒.与Runge-Kutta间断Galerkin(RKDG)方法相比较,RKCV方法的计算公式少一项积分项使得计算较简单.给出一些数值算例验证了算法的可靠性及效率.

高温气流内顺/逆流喷雾的Eulerian-Lagrangian数值仿真(英文)

用Eulerian-Lagrangian方法对高温气流内顺/逆流喷雾过程进行了数值仿真。气相方程用Eulerian方法建立,用k-ε模型封闭;液滴相方程用Lagrangian方法建立,采用了随机轨道模型;考虑了气体和液滴间的双向耦合。结果表明,高温气流内喷雾后,气相流场内产生了速度亏损和温度亏损,气体出口压力变化不大,液滴运动决定于气流湍流强度和自身惯性力,液滴在气道内的停留时间决定于液滴运动特性和气流湍流强度;逆流喷雾对气流的影响比顺流喷雾时大。仿真结果与文献结果基本一致。

基于单参数的Lagrangian支持向量回归算法及其应用

支持向量机（Support Vector Machines，SVM）是基于统计学习理论框架下的一种处理非线性分类和非线性回归的有效方法。由于具有完备的理论基础和出色的学习性能，该方法已成为当前国际机器学习界的研究热点，能较好地对解决小样本、高维数、非线性和局部极小点等实际问题。提出了一种基于单参数的Lagrangian支持向量回归算法，并将该算法应用在外贸货物吞吐量预测中。估算结果证明了这种改进的支持向量回归算法在吞吐量预测中的有效性和实用性。

联合更换策略的机会性Lagrangian松弛方法

零部件的联合更换是通过协调不同零部件的更换决策使其尽可能共享资源以节约费用的优化问题.这类随机组合策略优化问题在实际中大量存在,对生产生活的经济性起着重要影响.由于随机因素和组合效应,其有限阶段的策略求解非常困难.本文针对飞机引擎维护中的零部件联合更换问题,利用问题中随机耦合约束的特征,给出了一个可分解的模型及相应的分解协调方法机会性Lagrangian松弛(Opportunistic Lagrangian relaxation,OLR).与现有的两种利用先验最优策略规则的方法相比,OLR方法可在无先验知识的情况下直接得到更佳的协调效果.

S^3到CP^4中的等变弱Lagrangian极小浸入

研究3维球面S3到复射影空间CP4中的非常数截面曲率的等变弱Lagrangian极小浸入。