The objective of this paper is to investigate water supercooling. Supercooling occurs when a liquid does not freeze although its temperature is below its freezing point. In general, supercooling is an unstable conditi...The objective of this paper is to investigate water supercooling. Supercooling occurs when a liquid does not freeze although its temperature is below its freezing point. In general, supercooling is an unstable condition and occurs under special conditions. The parameters that influence supercooling stability and probability of occurrence include freezer temperature and water’s initial temperature. In this paper, it is shown that with a freezer temperature range of -3℃ to -8℃, supercooling is most likely to happen and is independent of the water’s initial temperature. Furthermore, as the freezer temperature decreases, the probability of nucleation increases, causing instant freezing. Finally, it is concluded that the Mpemba effect, in which initially hot water freezes faster than initially cold water, is due to the supercooling instability in initially hot water in which nucleation agents are more active.展开更多
The Teter,Payne,and Allan“preconditioning”function plays a significant role in planewave DFT calculations.This function is often called the TPA preconditioner.We present a detailed study of this“preconditioning”fu...The Teter,Payne,and Allan“preconditioning”function plays a significant role in planewave DFT calculations.This function is often called the TPA preconditioner.We present a detailed study of this“preconditioning”function.We develop a general formula that can readily generate a class of“preconditioning”functions.These functions have higher order approximation accuracy and fulfill the two essential“preconditioning”purposes as required in planewave DFT calculations.Our general class of functions are expected to have applications in other areas.展开更多
文摘The objective of this paper is to investigate water supercooling. Supercooling occurs when a liquid does not freeze although its temperature is below its freezing point. In general, supercooling is an unstable condition and occurs under special conditions. The parameters that influence supercooling stability and probability of occurrence include freezer temperature and water’s initial temperature. In this paper, it is shown that with a freezer temperature range of -3℃ to -8℃, supercooling is most likely to happen and is independent of the water’s initial temperature. Furthermore, as the freezer temperature decreases, the probability of nucleation increases, causing instant freezing. Finally, it is concluded that the Mpemba effect, in which initially hot water freezes faster than initially cold water, is due to the supercooling instability in initially hot water in which nucleation agents are more active.
基金Y.Zhou is supported in part by the NSF under grant DMS-1228271 and by a J.T.Oden fellowship from the University of Texas at Austin.J.R.Chelikowsky acknowledges support provided by the Scientific Discovery through Advanced Computing(SciDAC)program funded by U.S.Department of Energy,Office of Science,Advanced Scientific Computing Research and Basic Energy Sciences under award number DE-SC0008877X.Gao is supported in part by the NSF of China under grant 61300012 and the Defense Industrial Technology Development Program+2 种基金A.Zhou is supported in part by the Funds for Creative Research Groups of China under grant 11321061the National Basic Research Program of China under grant 2011CB309703the National Center for Mathematics and Interdisciplinary Sciences,Chinese Academy of Sciences.
文摘The Teter,Payne,and Allan“preconditioning”function plays a significant role in planewave DFT calculations.This function is often called the TPA preconditioner.We present a detailed study of this“preconditioning”function.We develop a general formula that can readily generate a class of“preconditioning”functions.These functions have higher order approximation accuracy and fulfill the two essential“preconditioning”purposes as required in planewave DFT calculations.Our general class of functions are expected to have applications in other areas.
