The Earth is the only body in the solar system for which significant observational constraints are accessible to such a degree that they can be used to discriminate between competing models of Earth's tectonic evo...The Earth is the only body in the solar system for which significant observational constraints are accessible to such a degree that they can be used to discriminate between competing models of Earth's tectonic evolution.It is a natural tendency to use observations of the Earth to inform more general models of planetary evolution.However,our understating of Earth's evolution is far from complete.In recent years,there has been growing geodynamic and geochemical evidence that suggests that plate tectonics may not have operated on the early Earth,with both the timing of its onset and the length of its activity far from certain.Recently,the potential of tectonic bi-stability(multiple stable,energetically allowed solutions)has been shown to be dynamically viable,both from analytical analysis and through numeric experiments in two and three dimensions.This indicates that multiple tectonic modes may operate on a single planetary body at different times within its temporal evolution.It also allows for the potential that feedback mechanisms between the internal dynamics and surface processes(e.g.,surface temperature changes driven by long term climate evolution),acting at different thermal evolution times,can cause terrestrial worlds to alternate between multiple tectonic states over giga-year timescales.The implication within this framework is that terrestrial planets have the potential to migrate through tectonic regimes at similar‘thermal evolution times'(e.g.,points were they have a similar bulk mantle temperature and energies),but at very different'temporal times'(time since planetary formation).It can be further shown that identical planets at similar stages of their evolution may exhibit different tectonic regimes due to random variations.Here,we will discuss constraints on the tectonic evolution of the Earth and present a novel framework of planetary evolution that moves toward probabilistic arguments based on general physical principals,as opposed to particular rheologies,and incorporates the potential of tectonic regime transitions and multiple tectonics states being viable at equivalent physical and chemical conditions.展开更多
针对预测-校正内点法(predictor-corrector primal-dualinterior point method,PCPDIPM)加权最小绝对值状态估计(weighted least absolute squares,WLAV)可能发生校正方向指向错误方向的不足,提出一种基于多预测-校正内点法(multiple PC...针对预测-校正内点法(predictor-corrector primal-dualinterior point method,PCPDIPM)加权最小绝对值状态估计(weighted least absolute squares,WLAV)可能发生校正方向指向错误方向的不足,提出一种基于多预测-校正内点法(multiple PCPDIPM,MPCPDIPM)的WLAV抗差状态估计算法。该算法在PCPDIPM的基础上,通过多次校正,对中心参数动态估计,并采用2阶段线性搜索法确定校正方向在总的牛顿方向中的最优比重,从而保证迭代点向中心轨迹靠拢。最后,通过IEEE算例仿真和我国某省网的测试结果验证了所提方法的有效性。与含不良数据辨识功能的加权最小二乘状态估计相比较,所提方法的收敛速度及抗差能力具有明显的优势。展开更多
基金supported in part by the Cyberinfrastructure for Computational Research funded by NSF under Grant CNS-0821727the Data Analysis and Visualization Cyberinfrastructure funded by NSF under grant OCI-0959097Rice University
文摘The Earth is the only body in the solar system for which significant observational constraints are accessible to such a degree that they can be used to discriminate between competing models of Earth's tectonic evolution.It is a natural tendency to use observations of the Earth to inform more general models of planetary evolution.However,our understating of Earth's evolution is far from complete.In recent years,there has been growing geodynamic and geochemical evidence that suggests that plate tectonics may not have operated on the early Earth,with both the timing of its onset and the length of its activity far from certain.Recently,the potential of tectonic bi-stability(multiple stable,energetically allowed solutions)has been shown to be dynamically viable,both from analytical analysis and through numeric experiments in two and three dimensions.This indicates that multiple tectonic modes may operate on a single planetary body at different times within its temporal evolution.It also allows for the potential that feedback mechanisms between the internal dynamics and surface processes(e.g.,surface temperature changes driven by long term climate evolution),acting at different thermal evolution times,can cause terrestrial worlds to alternate between multiple tectonic states over giga-year timescales.The implication within this framework is that terrestrial planets have the potential to migrate through tectonic regimes at similar‘thermal evolution times'(e.g.,points were they have a similar bulk mantle temperature and energies),but at very different'temporal times'(time since planetary formation).It can be further shown that identical planets at similar stages of their evolution may exhibit different tectonic regimes due to random variations.Here,we will discuss constraints on the tectonic evolution of the Earth and present a novel framework of planetary evolution that moves toward probabilistic arguments based on general physical principals,as opposed to particular rheologies,and incorporates the potential of tectonic regime transitions and multiple tectonics states being viable at equivalent physical and chemical conditions.
文摘针对预测-校正内点法(predictor-corrector primal-dualinterior point method,PCPDIPM)加权最小绝对值状态估计(weighted least absolute squares,WLAV)可能发生校正方向指向错误方向的不足,提出一种基于多预测-校正内点法(multiple PCPDIPM,MPCPDIPM)的WLAV抗差状态估计算法。该算法在PCPDIPM的基础上,通过多次校正,对中心参数动态估计,并采用2阶段线性搜索法确定校正方向在总的牛顿方向中的最优比重,从而保证迭代点向中心轨迹靠拢。最后,通过IEEE算例仿真和我国某省网的测试结果验证了所提方法的有效性。与含不良数据辨识功能的加权最小二乘状态估计相比较,所提方法的收敛速度及抗差能力具有明显的优势。
