The impact of nonlinear stability and instability on the validity of tangent linear model (TLM) is investigated by comparing its results with those produced by the nonlinear model (NLM) with the identical initial pert...The impact of nonlinear stability and instability on the validity of tangent linear model (TLM) is investigated by comparing its results with those produced by the nonlinear model (NLM) with the identical initial perturbations. The evolutions of different initial perturbations superposed on the nonlinearly stable and unstable basic flows are examined using the two-dimensional quasi-geostrophic models of double periodic-boundary condition and rigid boundary condition. The results indicate that the valid time period of TLM, during which TLM can be utilized to approximate NLM with given accuracy, varies with the magnitudes of the perturbations and the nonlinear stability and instability of the basic flows. The larger the magnitude of the perturbation is, the shorter the valid time period. The more nonlinearly unstable the basic flow is, the shorter the valid time period of TLM. With the double—periodic condition the valid period of the TLM is shorter than that with the rigid—boundary condition. Key words Nonlinear stability and instability - Tangent linear model (TLM) - Validity This work was supported by the National Key Basic Research Project “Research on the Formation Mechanism and Prediction Theory of Severe Synoptic Disasters in China” (No.G1998040910) and the National Natural Science Foundation of China (No.49775262 and No.49823002).展开更多
Fine control of the dynamics of a quantum system is the key element to perform quantum information processing and coherent manipulations for atomic and molecular systems. We propose a control protocol using a tangentp...Fine control of the dynamics of a quantum system is the key element to perform quantum information processing and coherent manipulations for atomic and molecular systems. We propose a control protocol using a tangentpulse driven model and demonstrate that it indicates a desirable design, i.e., of being both fast and accurate for population transfer. As opposed to other existing strategies, a remarkable character of the present scheme is that high velocity of the nonadiabatic evolution itself not only will not lead to unwanted transitions but also can suppress the error caused by the truncation of the driving pulse.展开更多
The anisotropic continuum stored energy density (ACSED) functional is applied for accurate constitutive modeling of biological tissues and finite element implementation without the isochoric—volumetric split, the ani...The anisotropic continuum stored energy density (ACSED) functional is applied for accurate constitutive modeling of biological tissues and finite element implementation without the isochoric—volumetric split, the anisotropic—isotropic split, or the anisotropic invariant split. Related stress and elasticity tensors in the reference and current configurations are worked out. A new kinematic model is derived based on the tangent Poisson’s ratio as a cubic polynomial function of stretch. The ACSED model, along with the kinematic model, accurately fits uniaxial extension test data for compressible human skin, bovine articular cartilage, and human aorta samples.展开更多
以日本房总半岛2011年、2013~2014年、2018年3次慢滑移事件(slow slip event, SSE)为例,利用自主研发的GPS坐标时序分析(GPS coordinate time series analysis, GTSA)软件批量处理该半岛多个GPS站点2009~2019年共10 a的坐标时序数据,构...以日本房总半岛2011年、2013~2014年、2018年3次慢滑移事件(slow slip event, SSE)为例,利用自主研发的GPS坐标时序分析(GPS coordinate time series analysis, GTSA)软件批量处理该半岛多个GPS站点2009~2019年共10 a的坐标时序数据,构建包含周期性SSE的坐标时序模型。结果表明:1)双曲正切函数的数学特性与SSE的运动规律十分吻合,表现为缓慢加速-快速滑动-缓慢减速,最后恢复至稳态;2)函数对SSE的精准建模可有效确定SSE发生时间的中心、持续时长和地表位移;3)2011年SSE持续时间最长可达50 d, 2013~2014年和2018年的SSE持续时间最长为25 d;4)3次SSE的水平位移均朝东南方向,高程位移量均表现为下沉,2018年SSE最大水平位移达5.2 cm, 2013~2014年最大高程位移达3.8 cm。展开更多
文摘The impact of nonlinear stability and instability on the validity of tangent linear model (TLM) is investigated by comparing its results with those produced by the nonlinear model (NLM) with the identical initial perturbations. The evolutions of different initial perturbations superposed on the nonlinearly stable and unstable basic flows are examined using the two-dimensional quasi-geostrophic models of double periodic-boundary condition and rigid boundary condition. The results indicate that the valid time period of TLM, during which TLM can be utilized to approximate NLM with given accuracy, varies with the magnitudes of the perturbations and the nonlinear stability and instability of the basic flows. The larger the magnitude of the perturbation is, the shorter the valid time period. The more nonlinearly unstable the basic flow is, the shorter the valid time period of TLM. With the double—periodic condition the valid period of the TLM is shorter than that with the rigid—boundary condition. Key words Nonlinear stability and instability - Tangent linear model (TLM) - Validity This work was supported by the National Key Basic Research Project “Research on the Formation Mechanism and Prediction Theory of Severe Synoptic Disasters in China” (No.G1998040910) and the National Natural Science Foundation of China (No.49775262 and No.49823002).
文摘Fine control of the dynamics of a quantum system is the key element to perform quantum information processing and coherent manipulations for atomic and molecular systems. We propose a control protocol using a tangentpulse driven model and demonstrate that it indicates a desirable design, i.e., of being both fast and accurate for population transfer. As opposed to other existing strategies, a remarkable character of the present scheme is that high velocity of the nonadiabatic evolution itself not only will not lead to unwanted transitions but also can suppress the error caused by the truncation of the driving pulse.
文摘The anisotropic continuum stored energy density (ACSED) functional is applied for accurate constitutive modeling of biological tissues and finite element implementation without the isochoric—volumetric split, the anisotropic—isotropic split, or the anisotropic invariant split. Related stress and elasticity tensors in the reference and current configurations are worked out. A new kinematic model is derived based on the tangent Poisson’s ratio as a cubic polynomial function of stretch. The ACSED model, along with the kinematic model, accurately fits uniaxial extension test data for compressible human skin, bovine articular cartilage, and human aorta samples.
