理查德-克纳的 "路径积分法 "旨在理解自组织物质聚集并将其转化为能量景观动力学范式

IF 1.9 3区 数学 Q1 MATHEMATICS, APPLIED Axioms Pub Date : 2023-12-22 DOI:10.3390/axioms13010008
Gerado G. Naumis
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引用次数: 0

摘要

物质通过生长和自我组装产生复杂的结构,如病毒外壳、碳富勒烯、蛋白质、玻璃等。由于其复杂性,用纸笔计算来解释和描述这种组装非常麻烦。多年前,理查德-克纳提出了一种理解自组织物质的纸笔路径积分法。尽管这种方法成功地解决了许多重要问题,包括富勒烯形成的产率、掺杂瑀玻璃的玻璃化转变温度、B2O3 玻璃中硼氧环的比例、对玻璃窗和派尔克斯玻璃经验配方的首次理论解释,以及对病毒噬菌体自组装的理解,但它仍然不是解决类似问题时的首要选择。原因在于它与基于能量景观范式和非平衡热力学的主流方法存在分歧。在此背景下,我们将对理查德-克纳方法进行批判性评述,证明它实际上是一种识别相关构型的巧妙方法。它的方程是能量景观动力学方程的物理常识简化版。随后,在局部两级能谱模型动力学的背景下,分析了过渡马尔可夫链概率中平衡玻尔兹曼因子的使用。分析表明,当反应坐标态之间的局部能障小于热能时,平衡波尔兹曼因子的使用仍然有效。这一发现将理查德-克纳模型与其他更复杂的方法相提并论,希望能促进人们将其作为描述物质自聚集的初步和有用的选择。
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Richard Kerner’s Path Integral Approach Aims to Understand the Self-Organized Matter Agglomeration and Its Translation into the Energy Landscape Kinetics Paradigm
Matter grows and self-assembles to produce complex structures such as virus capsids, carbon fullerenes, proteins, glasses, etc. Due to its complexity, performing pen-and-paper calculations to explain and describe such assemblies is cumbersome. Many years ago, Richard Kerner presented a pen-and-paper path integral approach to understanding self-organized matter. Although this approach successfully addressed many important problems, including the yield of fullerene formation, the glass transition temperature of doped chalcogenide glasses, the fraction of boroxol rings in B2O3 glasses, the first theoretical explanation for the empirical recipe of window and Pyrex glass and the understanding of virus capsid self-assembly, it still is not the primary choice when tackling similar problems. The reason lies in the fact that it diverges from mainstream approaches based on the energy landscape paradigm and non-equilibrium thermodynamics. In this context, a critical review is presented, demonstrating that the Richard Kerner method is, in fact, a clever way to identify relevant configurations. Its equations are simplified common physical sense versions of those found in the energy landscape kinetic equations. Subsequently, the utilization of equilibrium Boltzmann factors in the transition Markov chain probabilities is analyzed within the context of local two-level energy landscape models kinetics. This analysis demonstrates that their use remains valid when the local energy barrier between reaction coordinate states is small compared to the thermal energy. This finding places the Richard Kerner model on par with other more sophisticated methods and, hopefully, will promote its adoption as an initial and useful choice for describing the self-agglomeration of matter.
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Axioms
Axioms Mathematics-Algebra and Number Theory
自引率
10.00%
发文量
604
审稿时长
11 weeks
期刊介绍: Axiomatic theories in physics and in mathematics (for example, axiomatic theory of thermodynamics, and also either the axiomatic classical set theory or the axiomatic fuzzy set theory) Axiomatization, axiomatic methods, theorems, mathematical proofs Algebraic structures, field theory, group theory, topology, vector spaces Mathematical analysis Mathematical physics Mathematical logic, and non-classical logics, such as fuzzy logic, modal logic, non-monotonic logic. etc. Classical and fuzzy set theories Number theory Systems theory Classical measures, fuzzy measures, representation theory, and probability theory Graph theory Information theory Entropy Symmetry Differential equations and dynamical systems Relativity and quantum theories Mathematical chemistry Automata theory Mathematical problems of artificial intelligence Complex networks from a mathematical viewpoint Reasoning under uncertainty Interdisciplinary applications of mathematical theory.
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