改进的同伦内点方法求解非线性规划问题

最近学者们提出了组合同伦内点法(简记为CHIP方法)去求解一类非线性规划问题.在求解凸规划问题时,与内路径跟踪算法相比,文中在没有要求对数障碍函数是严格凸的以及解集是非空有界的条件下,取得了CHIP方法的全局收敛性结果.文中对CHIP方法进行了改进并利用改进的方法去求解更大一类的非凸规划问题.数值例子表明此改进是有效的.     

一类信号恢复问题的投影迭代硬阈值算法

本文给出了基于L₀模求解该问题的非凸模型,借助于稀疏正则化方法来克服问题的不适定性。该模型利用紧小波框架对信号进行稀疏逼近,并利用L₀模度量稀疏性。提出了求解该模型的投影迭代硬阈值算法,并证明了算法的全局收敛性。该算法每一步都有闭式解,计算过程简洁高效。数值实验表明,方法在重建信号的视觉质量和量化指标方面均优于所对比的pFISTA方法。     

同伦内点方法求解无界域上的非线性规划问题

冯果忱等人提出了同伦内点方法,在可行域有界的条件下求解一类非线性规划问题.并且还猜想此结果能够推广到无界可行域上.本文提出1个无界性条件,在此基础上,部分解决了该猜想.最后给出2个数值例子来进一步验证结果的有效性.     

同伦内点方法求解无界域上的非线性规划问题

冯果忱等人提出了同伦内点方法,在可行域有界的条件下求解一类非线性规划问题,并且还猜想此结果能够推广到无界可行域上。本文提出1个无界性条件,在此基础上,部分解决了该猜想。最后给出2个数值例子来进一步验证结果的有效性。     

随机集值映射的一个不动点定理

随机不动点定理在随机泛函分析中起重要作用。最近,随机集值映射的不动点定理得到了广泛地研究。本文研究具有随机定义域的随机集值映射的一个新的不动点定理,这一定理推广了S.Reich等人的重要结果。     

一类时滞脉冲广义Nicholson果蝇模型的正周期解

研究了一类时滞脉冲广义Nicholson果蝇模型的正周期解问题,利用锥拉伸与锥压缩不动点定理、Laypunov方法及不等式技巧得到了这类模型正周期解存在唯一的充分条件,并通过一个实例和仿真说明了结论的有效性,推广和改进了已有文献的结果。     

随机集值映射的一个不动点定理

随机不动点定理在随机泛函分析中起重要作用。最近，随机集值映射的不动点定理得到了广泛地研究。本文研究具有随机定义域的随机集值映射的一个新的不动点定理，这一定理推广了S.Reich等人的重要结果。     

时滞Hopfield神经网络的概周期解

主要研究一类无限区间上的具有S-分布时滞的Hopfield神经网络模型的概周期解问题。一方面去掉激活函数必须满足全局Lipschitz条件的限制,另一方面扩大时滞的应用范围,利用Banach不动点定理和不等式分析技巧,得到了保证所研究的神经网络的概周期解的存在性与全局吸引性的充分条件,并用一个例子说明了所得结果的有效性与可行性。本文结果在一定程度上改善和推广了已有文献的结论。     

多视角聚类的数值方法研究

针对Zhang等提出的多视角子空间聚类方法,本文给出了一种求解该非凸优化问题的方法并对其提出的算法进行了新的分析和改进。得到的主要结果包括：(1)选择一个好的近似解作为初始点,提高了算法的收敛速度和对全局最优解的收敛概率。(2)用MM思想重新推导出Zhang的方法,由此证明了一个新的收敛性定理;(3)改进了Wen提出的基于流形的正交约束算法并用于求解多视角子空间聚类模型,在算法中加入了初始点,大大提高了运行速度。通过对合成数据和实际数据的实验,验证了算法的有效性。     

带Hardy-Sobolev项的p-Laplace方程解的存在性

本文利用对称性临界点原理,在无界的柱形区域上,得到一类带Hardy-Sobolev项的p-Laplace方程的非平凡解的存在性。所得结果推广补充了已有的结论。     

Vortex dynamics of a fluid near a boundary with a circular cavity

The motion of a point vortex along a rectilinear boundary with a circle cavity, which models the coastline of a bay, and associated fluid particle advection are studied within a model of barotropic inviscid fluid. Using an analytical expression for the complex potential through which the velocity field is determined, we show that fluid particles start moving irregularly when the vortex is passing the cavity due to the nonstationarity of the velocity field generated by the vortex. Some of the fluid particles which were initially inside the vortex atmosphere leave it due to the irregularity and remain within the cavity vicinity. Depending on the initial position of the vortex and a parameter that determines the cavity size, the fraction of these fluid particles can differ significantly from fluid particles initially uniformly distributed within the vortex atmosphere. The escape of fluid particles from the vortex atmosphere is shown to be most efficient in the case of a relatively closed cavity under the condition that the initial vortex atmosphere area should be significantly smaller than the cavity area.     

Long period waves at a mouth of a bay in a basin

By a model bay with a mouth and a narrow, an experiment on long period waves is carried out to discuss the behavior of the tsunamis and storm surges. Emphasis is placed on the analysis of the characteristics of the current velocities associated with the long period waves incoming through the mouth in terms of Ursell's parameter.     

Response of a thin plate resting on a fluid-layer to a moving point load

This paper is concerned with the vibrations of a thin plate resting on a fluid-layer subjected to a moving point force. The frequency is assumed to be low and the fluid is deep. Both the fluid and the point force are always in contact with the plate. Hankel Transform and complex integration techniques are used to calculate the lateral displacements withrespect to a moving coordinate system and a coordinate transformation is used to achieve the results with respect to a fixed point. Numerical results are discussed with respect to the velocity of the moving force, its direction of movement and the fluid depth.     

Comparison between a U-OWC and a conventional OWC

With an additional vertical duct at the wave-beaten side, an OWC is expected to give some much better performances. This is, essentially, due to two reasons. First, an OWC with the additional vertical duct (U-OWC) has an eigenperiod greater than the eigenperiod of a conventional OWC. Second, the amplitude of the pressure fluctuations on the opening of a U-OWC is greater than the amplitude of the pressure fluctuations on the opening of a conventional OWC (the greater the smaller the wave period is). For the first reason, a U-OWC can give performances better than those of a conventional OWC both with swells and large wind waves. For the second reason, a U-OWC can give performances better than those of a conventional OWC also with small wind waves.     

Frictionless Generation of a Tidal Eulerian Residual Flow over a Sill in a Narrow Channel

Using a vertically two-dimensional, two-layer model, we have analytically examined the generation mechanism of a nonzero Eulerian residual flow by strong tide-topography interaction in a narrow channel where the frictional effect is not included. In this case, tidally generated baroclinic disturbances are forced non-uniformly in space and time while being advected by a strong tidal flow over the non-uniform slope of the bottom topography. Consequently, nonzero Eulerian residual flow results when averaged over one tidal period. Although the time average of the velocity field is thus nonzero, the associated Eulerian residual transport in each layer is compensated by a Stokes transport so that no Lagrangian residual transport results in both layers. This warns us that simple time averaging of the velocity data obtained at a fixed mooring station might lead to a spurious material transport. This revised version was published online in August 2006 with corrections to the Cover Date.     

Wave motion over a breakwater system of a horizontal plate and a vertical porous wall

A two-dimensional analytical solution is presented to study the reflection and transmission of linear water waves propagating past a submerged horizontal plate and through a vertical porous wall. The velocity potential in each fluid domain is formulated using three sets of orthogonal eigenfunctions and the unknown coefficients are determined from the matching conditions. Wave elevations and hydrodynamic forces acting on the porous wall are computed. Reflection and transmission coefficients are presented to examine the performance of the breakwater system. The present analytical solutions are found in fairly good agreement with the available laboratory data. The results indicate that the plate length, the porous-effect, the gap between plate and porous wall, and the submerged depth of the plate all show a significant influence on the reflected and transmitted wave fields. It is also interesting to note that the submerged plate plays an important role in reducing the transmitted wave height, especially for long incident waves.     

Run-Up of a Nonlinear Monochromatic Wave on a Plane Beach in Presence of a Tide

Oceanology - Abstract—The nonlinear problem of run-up of a long wave on a plane beach in presence of a tide is solved within nonlinear shallow water theory using the Carrier–Greenspan...     

About a limiting vortical wave on a fluid surface

A non-linear stabilized vortical wave on the surface of an infinitely-deep fluid is considered. The angle between the tangents at the apex of the limiting symmetric wave, similar to the Stokes limiting, is shown to equal 120°.Translated by V. Puchkin.     

Inleakage of a vortex-ring bunch onto a plane screen

A method is suggested for simulating axisymmetric laminar or turbulent flows formed during the motion of a vortex-ring bunch of given geometry and circulation toward a plane screen. Earlier, similar problems were simulated with the numerical solution of the Navier-Stokes equations for laminar flows. Turbulent flows have remained unconsidered until now. When a vortex ring approaches the screen, the secondary nonstationary flow is induced near the screen’s surface and this secondary flow causes the formation of the radial boundary layer (provided that air viscosity is taken into account). First, the medium spreads out from the critical point at the screen’s center with the negative pressure gradient along the radial coordinate and then detaches in the region of the positive pressure gradient. This radial wall flow and the corresponding boundary layer are considered in the quasi-stationary approximation. When the boundary layer detaches at successive instances, the flow is replenished with the radially moving secondary vortex rings whose circulations have the sign opposite to that of the circulation of the primary vortex ring. It is the interaction of the primary and secondary vortices that governs process dynamics, which differs substantially from that in the case when the formation of secondary vortices is disregarded. The suggested method is based on the method of discrete vortices (a perfect liquid) and the boundary-layer (laminar or turbulent) theory. During the development of the flow under investigation, the nonstationary ascending flow in the direction perpendicular to the screen’s plane is formed and then this flow decays and dissipates. Simulations for large Reynolds numbers corresponding to the formation of the turbulent boundary layer show that the velocity of ascending vortices in the plane of the initial vortex bunch is less than one-tenth of the initial velocity of the descending vortex ring. The boundary layer is introduced into calculations with the sole goal of determining the parameters of the secondary vortex rings formed during boundary-layer detachments. The interaction of the primary and secondary vortices is then considered within the framework of a perfect medium. Simulations for large Reynolds numbers corresponding to the formation of the turbulent boundary layer on the screen were correlated with the available data obtained in laboratory experiments for small Reynolds numbers. Qualitative agreement between the simulations and experiments is fairly satisfactory. The simulation for one combination of the circulation and vortex-ring geometry takes at most 10–15 min with the use of an average PC.     

Analysis of a jet-controlled high-lift hydrofoil with a flap

A jet-controlled high-lift hydrofoil with a flap is investigated using both experimental and computational methods. Experiments were carried out in a cavitation tunnel to measure forces and moment acting on the hydrofoil, and surface pressure distribution. The measured data show the feasibility of such a device for marine applications. Computational studies have also been carried out in parallel with the measurements. The computational results are analyzed in terms of global and local quantities using available experimental data. The present computational results compare well with the well-known experimental data for circulation control flows. The results for flow around a hydrofoil with a blown flap further validate the concept behind the proposed device. The results of the study demonstrate the applicability of the technology to the design of practical control surfaces.