We investigate the following inverse problem:starting from the acoustic wave equation,reconstruct a piecewise constant passive acoustic source from a single boundary temporal measurement without knowing the speed of s...We investigate the following inverse problem:starting from the acoustic wave equation,reconstruct a piecewise constant passive acoustic source from a single boundary temporal measurement without knowing the speed of sound.When the amplitudes of the source are known a priori,we prove a unique determination result of the shape and propose a level set algorithm to reconstruct the singularities.When the singularities of the source are known a priori,we show unique determination of the source amplitudes and propose a least-squares fitting algorithm to recover the source amplitudes.The analysis bridges the low-frequency source inversion problem and the inverse problem of gravimetry.The proposed algorithms are validated and quantitatively evaluated with numerical experiments in 2D and 3D.展开更多
Critical properties of metallic materials,such as the yield stress,corrosion resistance and ductility depend on the microstructure and its grain size and size distribution.Solute atoms that favorably segregate to grai...Critical properties of metallic materials,such as the yield stress,corrosion resistance and ductility depend on the microstructure and its grain size and size distribution.Solute atoms that favorably segregate to grain boundaries produce a pinning atmosphere that exerts a drag pressure on the boundary motion,which strongly affects the grain growth behavior during annealing.In the current work,the characteristics of grain growth in an annealed Mg-1 wt.%Mn-1 wt.%Nd magnesium alloy were investigated by advanced experimental and modeling techniques.Systematic quasi in-situ orientation mappings with a scanning electron microscope were performed to track the evolution of local and global microstructural characteristics as a function of annealing time.Solute segregation at targeted grain boundaries was measured using three-dimensional atom probe tomography.Level-set computer simulations were carried with different setups of driving forces to explore their contribution to the microstructure development with and without solute drag.The results showed that the favorable growth advantage for some grains leading to a transient stage of abnormal grain growth is controlled by several drivers with varying importance at different stages of annealing.For longer annealing times,residual dislocation density gradients between large and smaller grains are no longer important,which leads to microstructure stability due to predominant solute drag.Local fluctuations in residual dislocation energy and solute concentration near grain boundaries cause different boundary segments to migrate at different rates,which affects the average growth rate of large grains and their evolved shape.展开更多
基金partially supported by the NSF(Grant Nos.2012046,2152011,and 2309534)partially supported by the NSF(Grant Nos.DMS-1715178,DMS-2006881,and DMS-2237534)+1 种基金NIH(Grant No.R03-EB033521)startup fund from Michigan State University.
文摘We investigate the following inverse problem:starting from the acoustic wave equation,reconstruct a piecewise constant passive acoustic source from a single boundary temporal measurement without knowing the speed of sound.When the amplitudes of the source are known a priori,we prove a unique determination result of the shape and propose a level set algorithm to reconstruct the singularities.When the singularities of the source are known a priori,we show unique determination of the source amplitudes and propose a least-squares fitting algorithm to recover the source amplitudes.The analysis bridges the low-frequency source inversion problem and the inverse problem of gravimetry.The proposed algorithms are validated and quantitatively evaluated with numerical experiments in 2D and 3D.
基金support of the Deutsche Forschungsgemeinschaft(DFG),Grant no.AL 1343/7–1,AL 1343/8–1,Yi 103/3–1。
文摘Critical properties of metallic materials,such as the yield stress,corrosion resistance and ductility depend on the microstructure and its grain size and size distribution.Solute atoms that favorably segregate to grain boundaries produce a pinning atmosphere that exerts a drag pressure on the boundary motion,which strongly affects the grain growth behavior during annealing.In the current work,the characteristics of grain growth in an annealed Mg-1 wt.%Mn-1 wt.%Nd magnesium alloy were investigated by advanced experimental and modeling techniques.Systematic quasi in-situ orientation mappings with a scanning electron microscope were performed to track the evolution of local and global microstructural characteristics as a function of annealing time.Solute segregation at targeted grain boundaries was measured using three-dimensional atom probe tomography.Level-set computer simulations were carried with different setups of driving forces to explore their contribution to the microstructure development with and without solute drag.The results showed that the favorable growth advantage for some grains leading to a transient stage of abnormal grain growth is controlled by several drivers with varying importance at different stages of annealing.For longer annealing times,residual dislocation density gradients between large and smaller grains are no longer important,which leads to microstructure stability due to predominant solute drag.Local fluctuations in residual dislocation energy and solute concentration near grain boundaries cause different boundary segments to migrate at different rates,which affects the average growth rate of large grains and their evolved shape.
