Research on Instability Mechanism and Type of Ore Pillar Based on the Fold Catastrophe Theory

The stability of ore pillar in mine is essential for the safe and efficient mining.Based on the energy evolvement rule in ore pillar and roadway roof system,the roadway roof and ore pillar are treated as energy release body and energy dissipation body,respectively.Therefore,the double-block mechanical model is established with energy dissipation body and energy release body,and the energy mechanism of ore pillar instability is obtained,based on the fold catastrophe mathematical theory.The research result indicates that the dynamic instability of ore pillar is a physical instability problem caused by the strain softening property of ore mass,and the instability type of ore pillar is determined by the stiffness parameter of double-block mechanical system.When the systematical stiffness parameter is greater than or equal to 1,the equilibrium position of double-block mechanical system passes through shaft K-1 or the origin,from branch 1 of unstable equilibrium state to branch 2 of stable equilibrium state by smooth transition,and the ore pillar shows quasi-static fracture.When the systematical stiffness parameter is less than 1,the equilibrium position of double-block system mutates from branch 1 of unstable equilibrium state to branch 2 of stable equilibrium state by jumping transition,and the ore pillar shows dynamic instability.The research result could provide theoretical guidance for the prevention measures of ore pillar instability.

基于M-K模型的TA15钛合金高温成形极限

为了探究TA15钛合金高温环境下的成形极限,明确本构方程中参数对成形极限的影响规律,建立了考虑高温软化效应TA15钛合金高温环境下的本构关系,利用高温成形极限试验平台及M-K失稳理论对TA15钛合金板高温环境下的成形极限分别进行了试验测试及理论预测。理论预测结果表明当温度从800℃提升至880℃时,平面应变状态下的极限主应变由0.18提升至0.33。基于M-K失稳理论和建立的高温本构模型,分析了本构方程中的参数对成形极限的影响规律,结果表明提高加工硬化指数、速率敏感因子及减小软化因子,均可以提升应变强化率的大小,进一步延缓沟槽内应变状态趋于平面应变状态,从而提升理论成形极限曲线在应变空间中的位置。此外,理论计算结果表明速率敏感因子对成形极限曲线的左侧影响程度要大于其对右侧部分的影响,该现象主要归因于速率敏感因子对不同应变大小下的应变强化率的影响不同。

Small scale effects on buckling and postbuckling behaviors of axially loaded FGM nanoshells based on nonlocal strain gradient elasticity theory

By means of a comprehensive theory of elasticity, namely, a nonlocal strain gradient continuum theory, size-dependent nonlinear axial instability characteristics of cylindrical nanoshells made of functionally graded material(FGM) are examined. To take small scale effects into consideration in a more accurate way, a nonlocal stress field parameter and an internal length scale parameter are incorporated simultaneously into an exponential shear deformation shell theory. The variation of material properties associated with FGM nanoshells is supposed along the shell thickness, and it is modeled based on the Mori-Tanaka homogenization scheme. With a boundary layer theory of shell buckling and a perturbation-based solving process, the nonlocal strain gradient load-deflection and load-shortening stability paths are derived explicitly. It is observed that the strain gradient size effect causes to the increases of both the critical axial buckling load and the width of snap-through phenomenon related to the postbuckling regime, while the nonlocal size dependency leads to the decreases of them. Moreover, the influence of the nonlocal type of small scale effect on the axial instability characteristics of FGM nanoshells is more than that of the strain gradient one.

Application of Arnoldi method to boundary layer instability

The Arnoldi method is applied to boundary layer instability, and a finite difference method is employed to avoid the limit of the finite element method. This modus operandi is verified by three comparison cases, i.e., comparison with linear stability theory（LST） for two-dimensional（2D） disturbance on one-dimensional（1D） basic flow, comparison with LST for three-dimensional（3D） disturbance on 1D basic flow, and comparison with Floquet theory for 3D disturbance on 2D basic flow. Then it is applied to secondary instability analysis on the streaky boundary layer under spanwise-localized free-stream turbulence（FST）. Three unstable modes are found, i.e., an inner mode at a high-speed center streak, a sinuous type outer mode at a low-speed center streak, and a sinuous type outer mode at low-speed side streaks. All these modes are much more unstable than Tollmien–Schlichting（TS） waves, implying the dominant contribution of secondary instability in bypass transition. The modes at strong center streak are more unstable than those at weak side streaks, so the center streak is ‘dangerous＇ in secondary instability.

Size-dependent sinusoidal beam model for dynamic instability of single-walled carbon nanotubes

In this study, a model for dynamic instability of embedded single-walled car- bon nanotubes （SWCNTs） is presented. SWCNTs are modeled by the sinusoidal shear deformation beam theory （SSDBT）. The modified couple stress theory （MCST） is con- sidered in order to capture the size effects. The surrounding elastic medium is described by a visco-Pasternak foundation model, which accounts for normal, transverse shear, and damping loads. The motion equations are derived based on Hamilton＇s principle. The differential quadrature method （DQM） in conjunction with the Bolotin method is used in order to calculate the dynamic instability region （DIR） of SWCNTs. The effects of differ- ent parameters, such as nonlocal parameter, visco-Pasternak foundation, mode numbers, and geometrical parameters, are shown on the dynamic instability of SWCNTs. The re- sults depict that increasing the nonlocal parameter shifts the DIR to right. The results presented in this paper would be helpful in design and manufacturing of nano-electromechanical system （NEMS） and micro-electro-mechanical system （MEMS）.

Scalings for the Alfvén-cyclotron instability in a bi-kappa plasma

The particle velocity distribution in space plasma usually exhibits a non-Maxwellian high-energy tail that can be well modeled by kappa distributions.In this study,we focus on the growth rates of the Alfvén-cyclotron instability driven by ion temperature anisotropy in a kappa plasma.By solving the kinetic linear dispersion equation,we explore the sensitivity of growth rates to the spectral indexκof a bi-kappa distribution under different plasma conditions,including a variety of plasma beta β_(hp) and temperature anisotropy A_(hp) values of hot protons.Furthermore,a concise,analytic scaling formula is derived that relates the dimensionless maximum growth rate to three independent variables:the spectral index and the plasma beta and temperature anisotropy of hot protons.Our results show that as theκ-value increases,the instability bandwidth narrows and the maximum growth rate increases significantly.For higherβ_(hp)and A_(hp)′the maximum instability undergoes a sharp increase as well.When our fits of dimensionless maximum growth rates are compared with solutions to kinetic linear dispersion theory,the results generally exhibit good agreement between them.Especially under the circumstances of largeκ-values and highβ_(hp)and A_(hp)′the scalings of maximum growth rates primarily accurately model the numerical solutions.Our analytic expressions can readily be used in large-scale models of the Earth’s magnetosphere to understand wave generation due to the Alfvén-cyclotron instability.

Study of Diffusion Instability in Some Ternary Gas Mixtures at Various Temperatures

Within the linear theory of stability, the process of isothermal mixing of three-component gas mixtures in a channel of final dimensions in the absence of mass-transfer through its walls is considered. The comparison of experimental data with the results of theoretical calculations for the mixtures He+Ar-N2 and H2+N2-CH4 is shown, that a stable diffusion process as the temperature increased will remain the same and be described by the ordinary diffusion laws, but unstable one lost its intensity and tend to the stable diffusion.

Global instability of Stokes layer for whole wave numbers

The study on the global instability of a Stokes layer, which is a typical unsteady flow, is usually a paradigm for understanding the instability and transition of unsteady flows. Previous studies suggest that the neutral curve of the global instability obtained by the Floquet theory is only mapped out in a limited range of wave numbers （0.2 ≤ a ≤ 0.5）. In this paper, the global instability is investigated with numerical simulations for all wave numbers. It is revealed that the peak of the disturbances displays irregularity rather than the periodic evolution while the wave number is beyond the above range. A ＂neutral point＂ is redefined, and a neutral curve of the global instability is presented for the whole wave numbers with this new definition. This work provides a deeper understanding of the global instability of unsteady flows.

An Obliquely Propagating Electromagnetic Lower-Hybrid-Drift Instability in Plasmas with Negative Ions

In this study, by employing a local fluid theory for warm plasma containing negative ions, an obliquely propagating electromagnetic instability in the lower hybrid frequency range driven by cross-field currents or relative drifts between electrons and ions was investigated. It is found that the growth rate of the lower-hybrid-drift instability （LHDI） can be controlled by appropriate selection of the propagation direction, the wave number and the relative population of the negative ions.

Electromechanical responses and instability of electro-active polymer cylindrical shells

Based on the theories of finite deformation elasticity, electromechanical responses and instability of an incompressible electro-active polymer （EAP） cylindrical shell, which is subjected to an internal pressure and a static electric field, are studied. Deformation curves and distribution of stresses are obtained. It is found that an internal pressure together with an electric field may cause the unstable non-monotonic deforma- tion of the shell. It is also shown that a critical thickness for the shell exists, and the shell may undergo the unstable deformation if its thickness is less than this critical value. In addition, the effects of the electric field, axial stretch, thickness, and internal pressure on the instability of the shell are discussed.

Lower-Hybrid Drift Instability in Modified Harris Current Sheet

Lower-hybrid drift instability （LHDI） in a Harris current sheet including a uniform background distribution is investigated in linear local kinetic theory. It is found that the introduction of a uniform background distribution reduces the growth rate and real frequency of LHDI at all wavelengths. Some physical explanations about the effects of the background distribution are provided.

Convective Instability and Appearance of Structured Flows for Diffusion in Multicomponent Gas Mixtures

The main objective of this article is to investigate the behavior of gaseous systems with two and more independent gradients or thermodynamic forces exhibiting complicated behavior,when the convective flows occur.The existence of structural formations in these systems is shown by the schlieren method and the fast-response transducers.The linear analysis of stability can explain reasons of the appearance of convective instability in multicomponent gas mixtures.

Mode-Coupling Analysis of Parametric Decay Instability in Magnetized Plasmas

In this paper, derived from Maxwell and fluid equations of plasmas, unified nonlinear wave equations are used to describe the parametric decay instability （PDI） in magnetized plasmas, and in view of mode-coupling, we can obtain all the possible PDI channels. By solving the nonlinear equations with a mode-coupling method, we obtain the growth rate of the PDI, of which all of the three waves are ordinary mode （O-mode） or extraordinary mode （X-mode） wave. Under the dipole approximation, an explicit formula of the growth rate of the X-mode and the condition of the equilibrium density scale are obtained. According to the existence conditions of three X-mode waves, this kind of instability might exist in ECRH with the second harmonic X-mode wave.

Nonlinear density fluctuation field theory for large scale structure

We develop an effective field theory of density fluctuations for a Newtonian self-gravitating N-body system in quasi-equilibrium and apply it to a homogeneous universe with small density fluctuations. Keeping the density fluctuations up to second or- der, we obtain the nonlinear field equation of 2-pt correlation ξ（r）, which contains 3-pt correlation and formal ultra-violet divergences. By the Groth-Peebles hierarchical ansatz and mass renormalization, the equation becomes closed with two new terms beyond the Gaussian approximation, and their coefficients are taken as parameters. The analytic solution is obtained in terms of the hypergeometric functions, which is checked numerically. With one single set of two fixed parameters, the correlation ξ（r） and the corresponding power spectrum P（k） simultaneously match the results from all the major surveys, such as APM, SDSS, 2dfGRS, and REFLEX. The model gives a unifying understanding of several seemingly unrelated features of large scale structure from a field-theoretical perspective. The theory is worth extending to study the evolution effects in an expanding universe.

Instability of OTSG in movable NPP by using multivariable frequency domain method

The instability occurring in OTSG (Once-Through Steam Generator) of movable nuclear power plants is presented by a multivariable frequency domain theory.As concerning coupling interactions of OTSG tubing,it is more efficient for analyzing the instability of OTSG compared the common single variable method.A mathematical model for the system is derived from the fundamental equations by using the perturbation,Laplace-transform and the nodalization techniques.The stable boundary and parameters which influence the stability of the system are evaluated through computer simulation.Numerical examples are given in the paper and the predictions of the model agree with the experimental results well.

同忻煤矿8105工作面上覆坚硬岩层失稳破断研究

为研究坚硬岩层破断对回采工作面的影响,以同忻煤矿8105工作面坚硬顶板为工程背景,利用破裂线理论,得到了极限荷载破坏公式;为探究坚硬岩层失稳破断对工作面的影响,借助薄板理论,建立坚硬岩层结构模型,结合坚硬岩层失稳模式,给出了坚硬岩层失稳判据,分别为坚硬岩层初次失稳尺度及周期失稳计算公式;根据8105工作面综合柱状及物理力学参数,通过坚硬岩层协同变形载荷计算公式、坚硬岩层初次失稳计算公式等,确定低、中、高坚硬岩层层位及坚硬岩层破断尺度。结果显示:低、中、高位坚硬岩层初次失稳尺度分别为35.4 m、74.9 m、122.1 m,周期失稳尺度分别为13.5 m、63 m、109.9 m。通过理论计算坚硬岩层破断尺度发现:高位坚硬岩层失稳尺度最大,而低位和中位坚硬岩层失稳尺度接近一致。因此,高位坚硬岩层破断对工作面开采影响最大;8105工作面上覆岩层失稳破断对微震事件具有一定的影响。通过微震数据统计可知:坚硬岩层随着工作面的开采逐步发生失稳破断,不同坚硬岩层之间易发生耦合作用,形成复合矿压。坚硬岩层失稳判据的理论计算与实际硬岩破断尺度对比发现,高位坚硬岩层的预测准确率最高。

基于突变理论的隔水岩体失稳分析及安全厚度计算

为了保障岩溶突水隧道施工和运营安全,基于弹性梁模型,应用突变理论建立岩溶突水顶板在动力扰动下失稳的双尖点突变模型;综合考虑围岩性质、静水压力、动力扰动等因素,分析岩溶突水隧道顶板的失稳机制和破坏条件,建立其失稳突变的判别方程,并采用Matlab软件编程,求解顶板的最小安全厚度;同时,为了避免当静水压力过大时,突变理论公式的不合理性,单独计算仅在静水压力的情况下的最小安全厚度,并取两者计算值中的更大值。结果表明:隔水岩体是否保持稳定是由岩体内外因素共同决定的;岩体跨度越长,岩体最小安全厚度越大;岩体弹性模量越大,岩体最小安全厚度越小。在振动频率一定时,爆破荷载越大,岩体最小安全厚度越大;在爆破荷载的大小一定时,爆破振动的频率越大,岩体最小安全厚度越小;静水压力越大,岩体最小安全厚度越大。该岩溶突水隧道顶板安全厚度计算方法具有可行性与较高的准确性。

从五体理论探讨慢性踝关节不稳

慢性踝关节不稳即陈旧性踝关节扭伤,属于“筋伤病”的范畴,多由急性踝关节扭伤疾病失治、误治所致,该病及其所致的并发症通常导致踝关节运动功能严重受限,生活质量大幅下降。五体层次结构是《内经》人体结构理论躯体部分的主体框架,与人体运动机能密切相关,踝关节不稳的发病过程和临床表现涉及中医五体病机的演变,故笔者试从五体理论出发,探讨和阐述慢性踝关节不稳的发病机制、治疗进展,发现在五体理论指导下,无论是传统中医疗法,或是将其与西医治疗手段相结合,均可对CAI产生良好疗效。

深度学习在边界层流动稳定性分析中的应用

基于线性稳定性理论(linear stability theory,LST)的e^(N)方法是边界层转捩预测中比较可靠的方法之一。为了将传统LST特征值问题的求解过程大幅度简化和自动化,使用卷积神经网络(convolutional neural network,CNN)在边界层相似性解的LST分析样本集上进行训练,针对流向和横流不稳定性,分别在自然层流翼型和无限展长后掠翼上预测扰动的当地增长率、N因子和转捩位置,结果与标准LST一致性良好;验证了CNN可以将边界层剖面速度型导数信息编码为满足伽利略不变性的标量特征,在翼型边界层中起到了表征压力梯度的作用,在后掠翼边界层中起到了表征横流强度的作用;在CNN对LST特征值预测的基础上,以LST控制方程、边界条件和平凡解惩罚项构造总损失函数来训练内嵌物理信息神经网络(physics-informed neural network,PINN),实现了在不依赖样本的情况下对LST特征函数的准确预测,结果表明PINN可以为LST的特征函数问题提供有效的建模方法。

初始大扰动条件下双流系统的粒子相空间振荡

双流系统产生的不稳定性过程是近地空间中常见的等离子体不稳定性现象.地球磁尾、等离子体片边界层、地球弓激波、太阳风、极隙区和极光加速区观测到的静电孤立波被认为是由双流不稳定性产生.地球空间环境并非均匀稳态,因此对双流系统演化过程的研究往往需要考虑初始的扰动.利用所建立的动理论粒子云模型方法,我们研究了初始大扰动下双流系统的不稳定性现象,发现初始大扰动条件下粒子相空间产生振荡现象,且振荡频率与初始扰动的空间波数有关,电场与电场能量也存在该频率成分.通过线性理论,求解出了粒子相空间振荡频率.它与粒子云模拟得到的频率一致.该频率为朗缪尔振荡频率的基础之上叠加一个与初始扰动的空间波数有关的频率偏移量.我们改变等离子体频率,进一步验证了上述结论.该研究结果表明初始扰动能够对双流系统的不稳定性现象产生重要影响,对于加深理解地球磁层中双流系统的演化过程有重要参考意义.