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A liutex based definition and identification of vortex core center lines

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Journal of Hydrodynamics 2019年第3期31卷 445-454页

作者： Yi-sheng Gao jian-ming liu Yi-fei Yu Chaoqun liu Department of Mathematics University of Texas at Arlington Arlington Texas 76019 USA School of Mathematics and Statistics Jiangsu Normal University Xuzhou 221116 China

Six core issues for vortex definition and identification concern with (1) the absolute strength,(2) the relative strength,(3) the rotational axis,(4) the vortex core center,(5) the vortex core size, and (6) the vortex boundary (liu C. 2019). However, most of the currently popular vortex identification methods, including the Q criterion, the criterion and the Acj criterion etc., are Eulerian local region-type vortex identification criteria and can only approximately identify the vortex boundary by somewhat arbitrary threshold. On the other hand, the existing Eulerian local line-type methods, which seek to extract line-type features such as vortex core line, are not entirely satisfactory since most of these methods are based on vorticity or pressure minimum that will fail in many cases. The key issue is the lack of a reasonable mathematical definition for vortex core center. To address this issue, a liutex (previously named Rortex) based definition of vortex core center is proposed in this paper. The vortex core center, also called vortex rotation axis line here, is defined as a line where the liutex magnitude gradient vector is aligned with the liutex vector, which mathematically implies that the cross product of the liutex magnitude gradient vector and the liutex vector on the line is equal to zero. Based on this definition, a novel three-step method for extracting vortex rotation axis lines is presented. Two test cases, namely the Burgers vortex and hairpin vortices, are examined to justify the proposed method. The results demonstrate that the proposed method can successfully identify vortex rotation axis lines without any user-specified threshold, so that the proposed method is very straightforward, robust and efficient.

关键词： Vortex definition vortex identification flow visualization liutex liutex magnitude gradient vortex core lines

Objective Omega vortex identification method

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Journal of Hydrodynamics 2019年第3期31卷 455-463页

作者： jian-ming liu Yi-sheng Gao Yi-qian Wang Chaoqun liu School of Mathematics and Statistics Jiangsu Normal University Xuzhou 221116 China Department of Mathematics University of Texas at Arlington Arlington 76019 Texas USA School of Aerospace Engineering Tsinghua University Beijing 100084 China

A new vortex identification method (liu et al. 2016) was proposed to represent the rotation relative strength and capture and visualize the vortices in our previous study. The basic idea of the Ω method is that a ratio of the vorticity squared over the summation of the vorticity squared and the deformation squared should be used to measure the relative rotation strength. However, the vorticity tensor norm is not objective. Thus, a moving observer will observe different vortex structures in a moving reference frame, which will make confusions about the real vortex structures. In the present study, by the definitions of the net spin tensor and the net vorticity vector, an objective Ω vortex identification method is presented with examples to verify that the vortex structures retain in a moving reference frame.

关键词： Vortex identification the Ω method objectivity turbulence visualization turbulence

Explicit formula for the liutex vector and physical meaning of vorticity based on the liutex-Shear decomposition

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Journal of Hydrodynamics 2019年第3期31卷 464-474页

作者： Yi-qian Wang Yi-sheng Gao jian-ming liu Chaoqun liu School of Aerospace Engineering Tsinghua University Beijing 100084 China Department of Mathematics University of Texas at Arlington Arlington 76019 Texas USA School of Mathematics and Statistics Jiangsu Normal University Xuzhou 221116 China

In the present study, the physical meaning of vorticity is revisited based on the liutex-Shear (RS) decomposition proposed by liu et al. in the framework of liutex (previously called Rortex), a vortex vector field with information of both rotation axis and swirling strength (liu et al. 2018). It is demonstrated that the vorticity in the direction of rotational axis is twice the spatial mean angular velocity in the small neighborhood around the considered point while the imaginary part of the complex eigenvalue (2c.) of the velocity gradient tensor (if exist) is the pseudo-time average angular velocity of a trajectory moving circularly or spirally around the axis. In addition, an explicit expression of the liutex vector in terms of the eigenvalues and eigenvectors of velocity gradient is obtained for the first time from above understanding, which can further, though mildly, accelerate the calculation and give more physical comprehension of the liutex vector.

关键词： Vorticity liutex liutex-Shear(RS)decomposition explicit formula of liutex

An Analogue of Beurling's Theorem for the Jacobi Transform

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Acta Mathematica Sinica,English Series 2009年第1期25卷 85-94页

作者： Ji Zheng HUANG He Ping liu jian ming liu LMAM School of Mathematical Sciences Peking University Beijing lO0871 P. R. China

In this paper, we prove Beurling＇s theorem for the Jacobi transform, from which we derive some other versions of uncertainty principles.

关键词： Jacobi transform uncertainty principle Beurling's theorem Abel transform

Effect of the microstructure of Al 7050-T7451 on anodic oxide formation in sulfuric acid

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International Journal of Minerals,Metallurgy and Materials 2009年第4期16卷 432-438页

作者： jian-hua liu ming Li Song-mei Li Min Huang School of Materials Science and Engineering Beihang University Beijing 100083 China

The effect of the microstructure of an Al 7050-T7451 substrate on the anodic oxide formation in sulfuric acid was studied in this article. The microstructure of the substrate was assessed by optical microscope （OM） and transmission electron microscope （TEM）. The surface and cross-section morphologies of the oxide films were examined by scanning electron microscope （SEM）. The chemical composition of intermetallic particles in the alloys and films was investigated using energy dispersive spectroscope （EDS）. The roles of intermetallic phases and grain or subgrain boundaries on the oxide film formation were researched using the potentiodynamic and potentiostatic polarization technique in sulfuric acid solution. The results show that the transition of coarse intermetallic particles or grain （subgrain） boundaries at the surface of Al alloys can be characterized by potentiodynamic polarization curves. The surface and cross-section micrographs of the anodic layer seem to preserve the microstructure of the substrate. Large cavities in the anodic films are caused by the preferential dissolution of coarse AItCuMg particles and the entrance of Cu-rich remnants into the electrolyte during anodizing. The Al7Cu2Fe particles tend to be occluded in the oxide layer or lose from the oxide surface because of peripheral trenching. Small pores in the films are induced by the dissolution of precipitates in grain or subgrain boundaries. The film surface of recrystallized grain bodies is smooth and homogeneous.

关键词： aluminum alloys anodic oxide intermetallic particles grain boundaries

Mathematical foundation of turbulence generation-From symmetric to asymmetric liutex

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Journal of Hydrodynamics 2019年第3期31卷 632-636页

作者： jian-ming liu Yue Deng Yi-sheng Gao Sita Charkrit Chaoqun liu School of Mathematics and Statistics Jiangsu Normal University Xuzhou 221116 China Department of Mathematics University of Texas at Arlington Arlington 76019 Texas USA Department of Physics University of Texas at Arlington Arlington 76019 Texas USA

Vortices have been regarded as the building blocks and muscles of turbulence for a long time. To better describe and analyze vortices or vortical structures, recently a new physical quantity called liutex (previously named Rortex) is introduced to present the rigid rotation part of fluid motion (liu et al. 2018). Since turbulence is closely related to the vortex, it can be postulated that there exists no turbulence without liutex. According to direct numerical simulations (DNS) and experiments, forest of hairpin vortices has been found in transitional and low Reynolds number turbulent flows, while one-leg vortices are predominant in full developed turbulent flows. This paper demonstrates that the hairpin vortex is unstable. The hairpin vortex will be weakened or lose one leg by the shear and liutex interaction, based on the liutex definition and mathematical analysis without any physical assumptions. The asymmetry of the vortex is caused by the interaction of symmetric shear and symmetric liutex since the smaller element of a pair of vorticity elements determines the rotational strength. For a 2-D fluid rotation, if a disturbance shear effects the larger element, the rotation strength will not be changed, but if the disturbance shear effects the smaller element, the rotation strength will be immediately changed due to the definition of the liutex strength. For a rigid rotation, if the shearing part of the vorticity and liutex present the same directions, e.g., clockwise, the liutex strength will not be changed. If the shearing part of the vorticity and liutex present different directions, e.g., one clockwise and another counterclockwise, the liutex strength will be ***, the hairpin vortex could lose the symmetry and even deform to a one-leg vortex. The one-leg vortex cannot keep balance, and the chaotic motion and flow fluctuation are doomed. This is considered as the mathematical foundation of turbulence formation. The DNS results of boundary laye

关键词： Turbulence generation mathematical principle liutex/Rortex asymmetry

Dynamic cache resources allocation for energy efficiency

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The Journal of China Universities of Posts and Telecommunications 2009年第1期16卷 121-126页

作者： CHEN Li-ming ZOU Xue-cheng LEI jian-ming liu Zheng-lin Department of Electronics Science and Technology Huazhong University of Science and Technology Wuhan 430074 China

This article proposes a mechanism of low overhead and less runtime, termed dynamic cache resources allocation （DCRA）, which allocates each application with required cache resources. The mechanism collects cache hit-miss information at runtime and then analyzes the information and decides how many cache resources should be allocated to the current executing application. The amount of cache resources varies dynamically to reduce the total number of misses and energy consumption. The study of several applications from SPEC2000 shows that significant energy saving is achieved for the application based on the DCRA with an average of 39% savings.

关键词： cache energy consumption microprocessor

Energy-efficient collaborative target tracking algorithm using cost-reference particle filtering in wireless acoustic sensor networks

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The Journal of China Universities of Posts and Telecommunications 2009年第1期16卷 9-15,43页

作者： YU Zhi-jun WEI jian-ming liu Hai-tao Wireless Sensor Network Research and Development Center Shanghai Institute of Microsystem and Information Technology Shanghai 200050 China

Target tracking is one of the most important applications of wireless sensor networks. Optimized computation and energy dissipation are critical requirements to save the limited resource of sensor nodes. A new robust and energy-efficient collaborative target tracking framework is proposed in this article. After a target is detected, only one active cluster is responsible for the tracking task at each time step. The tracking algorithm is distributed by passing the sensing and computation operations from one cluster to another. An event-driven cluster reforming scheme is also proposed for balancing energy consumption among nodes. Observations from three cluster members are chosen and a new class of particle filter termed cost-reference particle filter （CRPF） is introduced to estimate the target motion at the cluster head. This CRPF method is quite robust for wireless sensor network tracking applications because it drops the strong assumptions of knowing the probability distributions of the system process and observation noises. In simulation experiments, the performance of the proposed collaborative target tracking algorithm is evaluated by the metrics of tracking precision and network energy consumption.

关键词： target tracking cost-reference particle filtering energy-efficient wireless sensor networks (WSNs)

Corrosion behaviour of NiCrFeAl-hBN seal coatings in oxidation environments at a high temperature

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Rare Metals 2021年第1期40卷 212-218页

作者： Su-Yuan Yang Dan Guo Xing-Wang Cheng jian-ming liu Yue-Guang Yu School of Materials Science and Engineering Beijing Institute of TechnologyBeijing 100081.China National Key Laboratory of Science and Technol Beijing General Research

The purpose of this investigation was to evaluate the microstructure,high-temperature oxidation behaviour,and hardness of a seal coating under controlled exposures at 750℃with different exposure *** results reveal that the main phases in the coating are Ni,FeNi3,and hexagonal BN,withα-Al_(2)O_(3)peaks appearing after 2-h *** the exposure time increases,the diffraction peak intensity ofα-Al_(2)O_(3)begins to decrease and Cr_(2)O_(3)peaks appear after 200 *** 1000 h,Cr_(2)O_(3)becomes dominant with only small amounts ofα-Al_(2)O_(3)*** high-temperature oxidation process of the coating includes three stages:the fast stage,transition stage,and slow *** oxidation rate is constant in each stage,and in the fast stage and slow stages with values of7.9×10^(-4)and 8.37×10^(-5)mg^(2)·cm^(-4)·s^(-1),***,α-Al_(2)O_(3)forms near the pores in the coating,followed by the formation of Cr_(2)O_(3).As the exposure time increases,oxidation penetrates into the interior of the coating along phase boundaries to form island-shaped inner oxide layers with high concentrations of Cr,Ni,and ***,hardness increases with increasing oxide percentage.

关键词： NiCrFeAl-hBN Seal coating Oxidation Microstructure High temperature