We present an iterative scheme for solving Poisson’s equation in 2D. Using finite differences, we discretize the equation into a Sylvester system, AU +UB = F, involving tridiagonal matrices A and B. The iterations oc...We present an iterative scheme for solving Poisson’s equation in 2D. Using finite differences, we discretize the equation into a Sylvester system, AU +UB = F, involving tridiagonal matrices A and B. The iterations occur on this Sylvester system directly after introducing a deflation-type parameter that enables optimized convergence. Analytical bounds are obtained on the spectral radii of the iteration matrices. Our method is comparable to Successive Over-Relaxation (SOR) and amenable to compact programming via vector/array operations. It can also be implemented within a multigrid framework with considerable improvement in performance as shown herein.展开更多
In this paper we derive LPS＇s criterion for the breakdown of classical solutions to the incompressible nematic liquid crystal flow, a simplified version of Ericksen-Leslie system modeling the hydrodynamic evolution o...In this paper we derive LPS＇s criterion for the breakdown of classical solutions to the incompressible nematic liquid crystal flow, a simplified version of Ericksen-Leslie system modeling the hydrodynamic evolution of nematic liquid crystals in R^3. We show that if 0 〈 T 〈 ＋∞ is the maximal time interval for the unique smooth solution u ∈ C^∞（[0, T）,R^3）,then ｜u｜＋｜△d｜∈L^q（[0,T],L^p（R^3））,where p and q satisfy the Ladyzhenskaya-Prodi-Serrin＇s condition：3/p＋2/q=1 and p∈（3,＋∞].展开更多
With recent advances in numerical modeling, design of underground structures increasingly relies on numerical modeling-based analysis approaches. While modeling tools like the discrete element method(DEM) and the comb...With recent advances in numerical modeling, design of underground structures increasingly relies on numerical modeling-based analysis approaches. While modeling tools like the discrete element method(DEM) and the combined finite-discrete element method(FDEM) are useful for investigating small-scale damage processes, continuum models remain the primary practical tool for most field-scale problems.The results obtained from such models are significantly dependent on the selection of an appropriate yield criterion and dilation angle. Towards improving its capabilities in handling mining-related problems, the authors have previously developed a new yield criterion(called progressive S-shaped criterion). The focus of the current study is to demonstrate its use in modeling rock pillars through a comparative analysis against four other yield criteria. In addition to the progressive S-shaped criterion,only one out of the four other criteria predicted a trend in strength consistent with an empirical pillar strength database compiled from the literature. Given the closely-knit relationship between yield criteria and dilation angle in controlling the overall damage process, a separate comparison was conducted using a mobilized dilation model, a zero degree dilation angle and a constant non-zero dilation angle. This study also investigates the impact of meso-scale heterogeneity in mechanical properties on the overall model response by assigning probability distributions to the input parameters. The comparisons revealed that an isotropic model using a combination of progressive S-shaped criterion and mobilized dilation angle model is sufficient in capturing the behaviors of rock pillars. Subsequently, the pillar model was used to assess the effect of L/W(length/width) ratio on the peak strength.展开更多
The present paper aims at giving some general ideas concerning the micromechanical approach of the strength of a porous material. It is shown that its determination theoretically amounts to solving a nonlinear boundar...The present paper aims at giving some general ideas concerning the micromechanical approach of the strength of a porous material. It is shown that its determination theoretically amounts to solving a nonlinear boundary value problem defined on a representative elementary volume(REV). The principle of nonlinear homogenization is illustrated based on the case of a solid phase having a Green’s strength criterion. An original refinement of the so-called secant method(based on two reference strains) is also provided. The paper also describes the main feature of the Gurson’s model which implements the principle of limit analysis on a conceptual model of hollow sphere. The last part of the paper gives some ideas concerning poromechanical couplings.展开更多
In this paper, we presented a sufficient condition on the frequency domain for the absolutely stable analysis of the Takagi-Sugeno (T-S)fuzzy control system, based on the Popov’s criterion. we use some numerical exam...In this paper, we presented a sufficient condition on the frequency domain for the absolutely stable analysis of the Takagi-Sugeno (T-S)fuzzy control system, based on the Popov’s criterion. we use some numerical examples to illustrate the efficiency of frequency domain-based condition.展开更多
Inspired by Cardano＇s method for solving cubic scalar equations, the addi- tive decomposition of spherical/deviatoric tensor （DSDT） is revisited from a new view- point. This decomposition simplifies the cubic tenso...Inspired by Cardano＇s method for solving cubic scalar equations, the addi- tive decomposition of spherical/deviatoric tensor （DSDT） is revisited from a new view- point. This decomposition simplifies the cubic tensor equation, decouples the spher- ical/deviatoric strain energy density, and lays the foundation for the von Mises yield criterion. Besides, it is verified that under the precondition of energy decoupling and the simplest form, the DSDT is the only possible form of the additive decomposition with physical meanings.展开更多
A frequency-domain-based sufficient condition is derived to guarantee the globally asymptotic stability of the simplest Takagi-Sugeno （T-S） fuzzy control system by using the circle criterion. The analysis is perform...A frequency-domain-based sufficient condition is derived to guarantee the globally asymptotic stability of the simplest Takagi-Sugeno （T-S） fuzzy control system by using the circle criterion. The analysis is performed in the frequency domain, and hence the condition is of great significance when the frequency-response method, which is widely used in the linear control theory and practice, is employed to synthesize the simplest T-S fuzzy controller. Besides, this sufficient condition is featured by a graphical interpretation, which makes the condition straightforward to be used. Comparisons are drawn between the performance of the simplest T-S fuzzy controller and that of the linear compensator. Two numerical examples are presented to demonstrate how this sufficient condition can be applied to both stable and unstable plants.展开更多
针对线性调频(linear frequency modulated,LFM)信号在低信噪比条件下的信号检测问题,提出将广义S变换(generalized S transform,GST)与Hough变换相结合(generalized S transform based on Hough transform,GSTH)信号检测方法。从理论...针对线性调频(linear frequency modulated,LFM)信号在低信噪比条件下的信号检测问题,提出将广义S变换(generalized S transform,GST)与Hough变换相结合(generalized S transform based on Hough transform,GSTH)信号检测方法。从理论层面推导出LFM信号在进行GST后对应的参数特性,论证Hough变换的可行性,推导出GSTH变换后LFM信号与噪声的概率密度分布函数,给出了基于奈曼-皮尔逊准则进行峰值检测时,检测门限的计算方法与确定流程。利用GST时频聚焦性提供良好的直线线性,有易于Hough变换的直线检测,提升变换后主峰峰值并降低副峰高度。通过与WHT(Wigner-Hough transform)、分数阶傅里叶变换与周期WHT算法的仿真对比,定量评估算法的适用性,并与经典算法对比,定性的描述出算法良好的时频聚焦性,凸显GSTH算法在强噪声背景下具有更好的检测精度与适用范围。展开更多
In the seismic safety evaluation (SSE) for key projects, the probability-consistent spectrum (PCS), usually obtained from probabilistic seismic hazard analysis (PSHA), is not consistent with the design response spectr...In the seismic safety evaluation (SSE) for key projects, the probability-consistent spectrum (PCS), usually obtained from probabilistic seismic hazard analysis (PSHA), is not consistent with the design response spectrum given by Code for Seismic Design of Buildings (GB50011-2001). Sometimes, there may be a remarkable difference be-tween them. If the PCS is lower than the corresponding code design response spectrum (CDS), the seismic fortifi-cation criterion for the key projects would be lower than that for the general industry and civil buildings. In the paper, the relation between PCS and CDS is discussed by using the ideal simple potential seismic source. The re-sults show that in the most areas influenced mainly by the potential sources of the epicentral earthquakes and the regional earthquakes, PCS is generally lower than CDS in the long periods. We point out that the long-period re-sponse spectra of the code should be further studied and combined with the probability method of seismic zoning as much as possible. Because of the uncertainties in SSE, it should be prudent to use the long-period response spectra given by SSE for key projects when they are lower than CDS.展开更多
文摘We present an iterative scheme for solving Poisson’s equation in 2D. Using finite differences, we discretize the equation into a Sylvester system, AU +UB = F, involving tridiagonal matrices A and B. The iterations occur on this Sylvester system directly after introducing a deflation-type parameter that enables optimized convergence. Analytical bounds are obtained on the spectral radii of the iteration matrices. Our method is comparable to Successive Over-Relaxation (SOR) and amenable to compact programming via vector/array operations. It can also be implemented within a multigrid framework with considerable improvement in performance as shown herein.
基金Supported by National Natural Science Foundation of China (10976026, 11271305, 11301439, 11226174)
文摘In this paper we derive LPS＇s criterion for the breakdown of classical solutions to the incompressible nematic liquid crystal flow, a simplified version of Ericksen-Leslie system modeling the hydrodynamic evolution of nematic liquid crystals in R^3. We show that if 0 〈 T 〈 ＋∞ is the maximal time interval for the unique smooth solution u ∈ C^∞（[0, T）,R^3）,then ｜u｜＋｜△d｜∈L^q（[0,T],L^p（R^3））,where p and q satisfy the Ladyzhenskaya-Prodi-Serrin＇s condition：3/p＋2/q=1 and p∈（3,＋∞].
基金funded by The National Institute for Occupational Safety and Health,USA(NIOSH)(Grant No.200-2016-90154)
文摘With recent advances in numerical modeling, design of underground structures increasingly relies on numerical modeling-based analysis approaches. While modeling tools like the discrete element method(DEM) and the combined finite-discrete element method(FDEM) are useful for investigating small-scale damage processes, continuum models remain the primary practical tool for most field-scale problems.The results obtained from such models are significantly dependent on the selection of an appropriate yield criterion and dilation angle. Towards improving its capabilities in handling mining-related problems, the authors have previously developed a new yield criterion(called progressive S-shaped criterion). The focus of the current study is to demonstrate its use in modeling rock pillars through a comparative analysis against four other yield criteria. In addition to the progressive S-shaped criterion,only one out of the four other criteria predicted a trend in strength consistent with an empirical pillar strength database compiled from the literature. Given the closely-knit relationship between yield criteria and dilation angle in controlling the overall damage process, a separate comparison was conducted using a mobilized dilation model, a zero degree dilation angle and a constant non-zero dilation angle. This study also investigates the impact of meso-scale heterogeneity in mechanical properties on the overall model response by assigning probability distributions to the input parameters. The comparisons revealed that an isotropic model using a combination of progressive S-shaped criterion and mobilized dilation angle model is sufficient in capturing the behaviors of rock pillars. Subsequently, the pillar model was used to assess the effect of L/W(length/width) ratio on the peak strength.
文摘The present paper aims at giving some general ideas concerning the micromechanical approach of the strength of a porous material. It is shown that its determination theoretically amounts to solving a nonlinear boundary value problem defined on a representative elementary volume(REV). The principle of nonlinear homogenization is illustrated based on the case of a solid phase having a Green’s strength criterion. An original refinement of the so-called secant method(based on two reference strains) is also provided. The paper also describes the main feature of the Gurson’s model which implements the principle of limit analysis on a conceptual model of hollow sphere. The last part of the paper gives some ideas concerning poromechanical couplings.
文摘In this paper, we presented a sufficient condition on the frequency domain for the absolutely stable analysis of the Takagi-Sugeno (T-S)fuzzy control system, based on the Popov’s criterion. we use some numerical examples to illustrate the efficiency of frequency domain-based condition.
基金supported by the National Natural Science Foundation of China(Nos.11072125 and11272175)the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20130002110044)the China Postdoctoral Science Foundation(No.2015M570035)
文摘Inspired by Cardano＇s method for solving cubic scalar equations, the addi- tive decomposition of spherical/deviatoric tensor （DSDT） is revisited from a new view- point. This decomposition simplifies the cubic tensor equation, decouples the spher- ical/deviatoric strain energy density, and lays the foundation for the von Mises yield criterion. Besides, it is verified that under the precondition of energy decoupling and the simplest form, the DSDT is the only possible form of the additive decomposition with physical meanings.
文摘A frequency-domain-based sufficient condition is derived to guarantee the globally asymptotic stability of the simplest Takagi-Sugeno （T-S） fuzzy control system by using the circle criterion. The analysis is performed in the frequency domain, and hence the condition is of great significance when the frequency-response method, which is widely used in the linear control theory and practice, is employed to synthesize the simplest T-S fuzzy controller. Besides, this sufficient condition is featured by a graphical interpretation, which makes the condition straightforward to be used. Comparisons are drawn between the performance of the simplest T-S fuzzy controller and that of the linear compensator. Two numerical examples are presented to demonstrate how this sufficient condition can be applied to both stable and unstable plants.
文摘针对线性调频(linear frequency modulated,LFM)信号在低信噪比条件下的信号检测问题,提出将广义S变换(generalized S transform,GST)与Hough变换相结合(generalized S transform based on Hough transform,GSTH)信号检测方法。从理论层面推导出LFM信号在进行GST后对应的参数特性,论证Hough变换的可行性,推导出GSTH变换后LFM信号与噪声的概率密度分布函数,给出了基于奈曼-皮尔逊准则进行峰值检测时,检测门限的计算方法与确定流程。利用GST时频聚焦性提供良好的直线线性,有易于Hough变换的直线检测,提升变换后主峰峰值并降低副峰高度。通过与WHT(Wigner-Hough transform)、分数阶傅里叶变换与周期WHT算法的仿真对比,定量评估算法的适用性,并与经典算法对比,定性的描述出算法良好的时频聚焦性,凸显GSTH算法在强噪声背景下具有更好的检测精度与适用范围。
基金Shanghai Science & Technology Development Foundation (022512065) and Shanghai Construction Technology Development Foundation (A0206101).
文摘In the seismic safety evaluation (SSE) for key projects, the probability-consistent spectrum (PCS), usually obtained from probabilistic seismic hazard analysis (PSHA), is not consistent with the design response spectrum given by Code for Seismic Design of Buildings (GB50011-2001). Sometimes, there may be a remarkable difference be-tween them. If the PCS is lower than the corresponding code design response spectrum (CDS), the seismic fortifi-cation criterion for the key projects would be lower than that for the general industry and civil buildings. In the paper, the relation between PCS and CDS is discussed by using the ideal simple potential seismic source. The re-sults show that in the most areas influenced mainly by the potential sources of the epicentral earthquakes and the regional earthquakes, PCS is generally lower than CDS in the long periods. We point out that the long-period re-sponse spectra of the code should be further studied and combined with the probability method of seismic zoning as much as possible. Because of the uncertainties in SSE, it should be prudent to use the long-period response spectra given by SSE for key projects when they are lower than CDS.
