对2D随机点过程和长距离顺序过程的极端值和沃罗诺伊的收
Mark Frenkel1, Irina Legchenkova1,2, Edward Bormashenko1
1Department of Chemical Engineering, Ariel University, P.O.B. 3, Ariel 407000, Israel.
Entropy (Basel, Switzerland)
|January 28, 2026
概括
沃罗诺伊透 (VE) 量化了点模式中的顺序,从有序集合的0到随机集合的1.69. 与Shannon Entropy不同,VE捕捉了长距离的顺序,并与系统相关性相关联.
科学领域:
- 统计物理学的统计物理.
- 计算几何学计算几何学
- 材料科学是一种材料科学.
背景情况:
- 沃罗诺伊 Entropy (VE) 是对二维点过程中的混乱的测量.
- 超均性描述了被抑制的长距离密度波动的点集.
- 了解 VE 和超均性之间的关系对于描述复杂系统至关重要.
研究的目的:
- 调查 VE 随机和超均点过程的非对称最大值和趋同.
- 为了确定 VE 与诸如多边形数量和区域大小等参数之间的关系.
- 为了比较 VE 捕捉远距离秩序的能力与Shannon Entropy.
主要方法:
- 对于二维随机点过程和超均点集的 VE 的计算.
- 基于点设置顺序的VE范围 (0至1.69) 的分析.
- 对沃罗诺伊图构造和VE和度的临界半径 (Limit-1和Limit-2) 的确定.
主要成果:
- 对于n > 100个多边形,VE的范围从0 (有序) 到1.69 (随机).
- 极限-1 (R=2.5) 是沃罗诺伊图构造的最小半径;极限-2 (R=5.5) 表示VE和.
- 在一些种子点模式中,VE超过1.69,并且与超均系统中的长距离相关性相关.
结论:
- VE是2D点图案中顺序和远距离相关性的敏感指标.
- 由于几何约束,VE捕捉了Shannon Entropy错过的远程顺序的方面.
- 该研究提供了 VE 在从有序到随机的系统中的行为,包括超均材料的洞察.
更多相关视频
11:15Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy
Published on: June 27, 2013
34.4K
09:12Optimization of Processing of Tiebangchui with Highland Barley Wine Based on the Box-Behnken Design Combined with the Entropy Method
Published on: May 19, 2023
1.2K
相关概念视频
Absolute and Local Extreme Values
63
The highest and lowest values of a function, relative to a reference axis, are known as extreme values. These include absolute maximum and absolute minimum values, which represent the highest and lowest points the function reaches across its entire domain. Within a restricted portion of the function, the highest and lowest values are referred to as local maximum and local minimum values, respectively.Periodic functions, such as sine and cosine, show extreme values at infinitely many points due...
63
Entropy
35.7K
Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
35.7K
Entropy
3.6K
The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the work done on it. A quantitative formulation of the second law of thermodynamics leads to defining a state function, the entropy.
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...
3.6K
Entropy Change in Reversible Processes
3.2K
In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
3.2K
Standard Entropy Change for a Reaction
24.2K
Entropy is a state function, so the standard entropy change for a chemical reaction (ΔS°rxn) can be calculated from the difference in standard entropy between the products and the reactants.
24.2K
Convergent Evolution
32.8K
Evolution shapes the features of organisms over time, ensuring that they are suited for the environments in which they live. Sometimes, selection pressure leads to the rise of similar but unrelated adaptations in organisms with no recent common ancestors, a process known as convergent evolution.
32.8K
