Exploration of non-trivial relations for the non-steady state nucleation rate: usefulness of the elliptic theta functions for its experimental estimations
Exploration of non-trivial relations for the non-steady state nucleation rate: usefulness of the elliptic theta functions for its experimental estimations
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非稳态成核率的非平凡关系的探索：椭圆 theta 函数在实验估计中的有用性
DOI：
10.1007/s42452-022-05189-4
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发表时间：
2022
影响因子：
2.6
通讯作者：
Shota Shigetomi and Mizuki Nishiwaki (co-first author)
中科院分区：
文献类型：
--
作者：
T. Shimizu;K. Tadakuma;M. Watanabe;K. Abe;M. Konyo and S. Tadokoro;Shota Shigetomi and Mizuki Nishiwaki (co-first author)
已知非稳态成核速率可以表示为稳态成核速率与椭圆函数的乘积。然而，利用椭圆函数丰富的数学性质来分析非稳态成核过程的研究还很少。在本文中，我们利用这些性质达到了两个目的。第一个是利用椭圆函数丰富的数学性质，推导非稳态成核速率的非平凡关系，这在传统的经典成核理论中由于其复杂性而无法发现。二是通过求解非稳态成核速率的差分方程来求解两个问题：(1)在某些特殊条件下估计非稳态成核速率的时间演化需要大量的精力和成本；(2)在某些特殊情况下不可能测量非稳态成核速率。结果表明，我们的结果有助于降低非稳态成核速率的估计成本，并使非稳态成核速率的机械估计从过去到未来成为可能。从椭圆函数的数学性质出发，得到了非稳态成核速率的非平凡关系。结果表明，我们的结果有助于降低非稳态成核速率的估计成本。结果表明，我们的结果使得从过去到未来的非稳态成核速率的力学估计成为可能。
It is known that the non-steady state nucleation rate can be expressed as the product of the steady state nucleation rate and an elliptic theta function. However, there has been no research where rich mathematical properties of the elliptic theta functions were utilized to analyze the non-steady state nucleation processes. In this paper, we achieved two objectives by using the properties. The first one is to derive non-trivial relations for the non-steady state nucleation rate by using the rich mathematical properties of the elliptic theta functions, which could not be discovered in the conventional classical nucleation theory because of its complexities. The second one is to find solutions to two problems by solving a difference equation for the non-steady state nucleation rate: (i) it requires a large amount of effort and cost to estimate the time evolution of the non-steady state nucleation rate under some special conditions, and (ii) it is impossible to measure the non-steady state nucleation rate under some special cases. It is shown that our result help reduce the estimation cost of the non-steady state nucleation rate and makes mechanical estimation of the non-steady state nucleation rate possible from the past to the future.Article highlightsNon-trivial relations for the non-steady state nucleation rate are found from the mathematical properties of the elliptic theta functions.It is shown that our result help reduce the estimation cost of the non-steady state nucleation rate.It is shown that our result makes mechanical estimation of the non-steady state nucleation rate possible from the past to the future.
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影响因子：
3.5
作者：
KALININA, AM;FILIPOVICH, VN;FOKIN, VM
通讯作者：
FOKIN, VM
DOI：
--
发表时间：
2019
期刊：
arXiv: Soft Condensed Matter
影响因子：
--
作者：
D. Cassar;A. Serra;O. Peitl;A. M. Rodrigues;Edgar Dutra Zanotto
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影响因子：
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作者：
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S. Kharchev;A. Zabrodin
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影响因子：
3.5
作者：
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通讯作者：
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影响因子：
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作者：
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通讯作者：
V. Shneidman