在河西走廊中部,采用挖掘法挖取红砂和白刺根系,应用拓扑学与分形理论分析了根系构型的特征.结果表明:2种荒漠植物根系的拓扑指数均较小,根系分支模式均近似为叉状分支结构.红砂和白刺根系具有较好的分形特征,其分形维数分别为(1.18...在河西走廊中部,采用挖掘法挖取红砂和白刺根系,应用拓扑学与分形理论分析了根系构型的特征.结果表明:2种荒漠植物根系的拓扑指数均较小,根系分支模式均近似为叉状分支结构.红砂和白刺根系具有较好的分形特征,其分形维数分别为(1.18±0.04)和(1.36±0.06);分形维数、分形丰度与根系平均连接长度均呈显著正相关.2种荒漠植物根系的平均连接长度均较大,以扩大植物的有效营养空间,从而适应干旱贫瘠的土壤环境.2种荒漠植物根系分支前的横截面积等于根系分支后的横截面积之和,验证了Leonardo da Vinci法则.对17个根系构型参数进行主成分分析,根系拓扑指数、根系连接数量、逐步分支率和根系直径4个根系构型参数能很好地表示2种荒漠植物根系构型特征.展开更多
Higher-order topological phases(HOTPs) are systems with topologically protected in-gap boundary states localized at their ed à nT-dimensional boundaries, with d the system dimension and n the order of the topolog...Higher-order topological phases(HOTPs) are systems with topologically protected in-gap boundary states localized at their ed à nT-dimensional boundaries, with d the system dimension and n the order of the topology. This work proposes a dynamics-based characterization of one large class of Z-type HOTPs without specifically relying on any crystalline symmetry considerations. The key element of our innovative approach is to connect quantum quench dynamics with nested configurations of the socalled band inversion surfaces(BISs) of momentum-space Hamiltonians as a sum of operators from the Clifford algebra(a condition that can be partially relaxed), thereby making it possible to dynamically detect each and every order of topology on an equal footing. Given that experiments on synthetic topological matter can directly measure the winding of certain pseudospin texture to determine topological features of BISs, the topological invariants defined through nested BISs are all within reach of ongoing experiments. Further, the necessity of having nested BISs in defining higher-order topology offers a unique perspective to investigate and engineer higher-order topological phase transitions.展开更多
文摘在河西走廊中部,采用挖掘法挖取红砂和白刺根系,应用拓扑学与分形理论分析了根系构型的特征.结果表明:2种荒漠植物根系的拓扑指数均较小,根系分支模式均近似为叉状分支结构.红砂和白刺根系具有较好的分形特征,其分形维数分别为(1.18±0.04)和(1.36±0.06);分形维数、分形丰度与根系平均连接长度均呈显著正相关.2种荒漠植物根系的平均连接长度均较大,以扩大植物的有效营养空间,从而适应干旱贫瘠的土壤环境.2种荒漠植物根系分支前的横截面积等于根系分支后的横截面积之和,验证了Leonardo da Vinci法则.对17个根系构型参数进行主成分分析,根系拓扑指数、根系连接数量、逐步分支率和根系直径4个根系构型参数能很好地表示2种荒漠植物根系构型特征.
基金the Singapore Ministry of Education Academic Research Fund Tier-3 Grant No.MOE2017T3-1-001(WBS.No.R-144-000-425-592)the Singapore National Research Foundation Grant No.NRF-NRFI2017-04(WBS No.R-144-000-378-281)。
文摘Higher-order topological phases(HOTPs) are systems with topologically protected in-gap boundary states localized at their ed à nT-dimensional boundaries, with d the system dimension and n the order of the topology. This work proposes a dynamics-based characterization of one large class of Z-type HOTPs without specifically relying on any crystalline symmetry considerations. The key element of our innovative approach is to connect quantum quench dynamics with nested configurations of the socalled band inversion surfaces(BISs) of momentum-space Hamiltonians as a sum of operators from the Clifford algebra(a condition that can be partially relaxed), thereby making it possible to dynamically detect each and every order of topology on an equal footing. Given that experiments on synthetic topological matter can directly measure the winding of certain pseudospin texture to determine topological features of BISs, the topological invariants defined through nested BISs are all within reach of ongoing experiments. Further, the necessity of having nested BISs in defining higher-order topology offers a unique perspective to investigate and engineer higher-order topological phase transitions.
