Unidirectional solidification of pivalic acid （PVA）-ethanol （Eth） mixture was performed to examine whether an allowable range of primary dendrite spacing definitely exists at a given growth velocity and how the ra...Unidirectional solidification of pivalic acid （PVA）-ethanol （Eth） mixture was performed to examine whether an allowable range of primary dendrite spacing definitely exists at a given growth velocity and how the range is history-dependent. PVA-0.59 wt pct Eth was unidirectionally solidified in the range of growth velocity 0.5-64 μm/s at the temperature gradient of 2.3 K/ram. Sequential change in growth velocity was imposed to determine the upper and lower limits for the allowable range of stable spacing. An allowable range of the steady state primary spacing was observed at a given growth velocity, and the extent of the range seems to be dependent on the degree to which step-increase or step-decrease in growth velocity is accomplished. As the degree of sequential change in growth velocity increases, the history-dependence of the selection for the primary dendrite spacing tends to disappear.展开更多
SINCE 1956, Michael’s continuous selection theory has been applied to functional analysis,topology, approximation theory and other mathematical fields. In this letter, the concept ofthe pseudo-lower semicontinuity is...SINCE 1956, Michael’s continuous selection theory has been applied to functional analysis,topology, approximation theory and other mathematical fields. In this letter, the concept ofthe pseudo-lower semicontinuity is introduced, and a convex structure of metric space is de-fined. A continuous selection theorem for pseudo-lower semicontinuity is given. This展开更多
文摘Unidirectional solidification of pivalic acid （PVA）-ethanol （Eth） mixture was performed to examine whether an allowable range of primary dendrite spacing definitely exists at a given growth velocity and how the range is history-dependent. PVA-0.59 wt pct Eth was unidirectionally solidified in the range of growth velocity 0.5-64 μm/s at the temperature gradient of 2.3 K/ram. Sequential change in growth velocity was imposed to determine the upper and lower limits for the allowable range of stable spacing. An allowable range of the steady state primary spacing was observed at a given growth velocity, and the extent of the range seems to be dependent on the degree to which step-increase or step-decrease in growth velocity is accomplished. As the degree of sequential change in growth velocity increases, the history-dependence of the selection for the primary dendrite spacing tends to disappear.
文摘SINCE 1956, Michael’s continuous selection theory has been applied to functional analysis,topology, approximation theory and other mathematical fields. In this letter, the concept ofthe pseudo-lower semicontinuity is introduced, and a convex structure of metric space is de-fined. A continuous selection theorem for pseudo-lower semicontinuity is given. This
