Among Thurston maps (orientation-preserving, postcritically finite branched coverings of the 2-sphere to itself), those that arise as subdivision maps of a finite subdivision rule form a special family. For such maps,...Among Thurston maps (orientation-preserving, postcritically finite branched coverings of the 2-sphere to itself), those that arise as subdivision maps of a finite subdivision rule form a special family. For such maps, we investigate relationships between various notions of expansion—combinatorial, dynamical, algebraic,and coarse-geometric.展开更多
Earth’s outer core is generally thought to be a well-mixed liquid consisting mostly of iron and a small amount of lighter elements.Recent seismic studies using Sm KS waves show that the top a few hundred kilometers o...Earth’s outer core is generally thought to be a well-mixed liquid consisting mostly of iron and a small amount of lighter elements.Recent seismic studies using Sm KS waves show that the top a few hundred kilometers of the outer core possess a P-wave velocity slightly lower than the PREM model,which cannot be explained by self-compression of a chemically homogeneous outer core.We investigated the Sm KS waveforms of a deep earthquake occurring beneath South America recorded by a large and dense seismic array in China,and measured the differential arrival times of the Sm KS pairs.We found significant waveform distortion of the Sm KS caused by postcritical refraction and reflection at the core-mantle boundary.This waveform distortion can introduce significant bias to the measured differential times,leading to incorrect estimate of P-wave velocity of the outer core.Whether stable stratification is occurring in outer core or not requires further seismic investigations.展开更多
基金supported by Simons Foundation Collaboration Grants for Mathematicians (Grant No. 245269)
文摘Among Thurston maps (orientation-preserving, postcritically finite branched coverings of the 2-sphere to itself), those that arise as subdivision maps of a finite subdivision rule form a special family. For such maps, we investigate relationships between various notions of expansion—combinatorial, dynamical, algebraic,and coarse-geometric.
基金jointly supported by the National Key Research and Development Program of China(2017YFC1500303)the National Natural Science Foundation of China(41630209)
文摘Earth’s outer core is generally thought to be a well-mixed liquid consisting mostly of iron and a small amount of lighter elements.Recent seismic studies using Sm KS waves show that the top a few hundred kilometers of the outer core possess a P-wave velocity slightly lower than the PREM model,which cannot be explained by self-compression of a chemically homogeneous outer core.We investigated the Sm KS waveforms of a deep earthquake occurring beneath South America recorded by a large and dense seismic array in China,and measured the differential arrival times of the Sm KS pairs.We found significant waveform distortion of the Sm KS caused by postcritical refraction and reflection at the core-mantle boundary.This waveform distortion can introduce significant bias to the measured differential times,leading to incorrect estimate of P-wave velocity of the outer core.Whether stable stratification is occurring in outer core or not requires further seismic investigations.
