在固体电磁学中推断碎形顺序复杂性的热力学方法
Basanta R Pahari1, William Oates2
1Hawai'i CC Department of Mathematics, University of Hawai'i, Hilo, HI 96720, USA.
Entropy (Basel, Switzerland)
|January 8, 2025
概括
这项研究引入了一个分数级动力学模型来修改麦克斯韦方程. 它使用信息理论对电磁场进行同质化,为分析复杂数据提供了一种新方法.
科学领域:
- 电磁主义 电磁主义
- 信息理论 信息理论
- 碎形动力学是什么意思
背景情况:
- 麦克斯韦方程是经典电磁学的基础.
- 了解复杂的电磁场通常需要先进的建模技术.
- 信息理论方法为分析物理系统提供了新的途径.
研究的目的:
- 开发一个修改的形式的麦克斯韦的依赖时间的电磁方程,使用一个分数顺序动力学模型.
- 为了整合香农的和分数时刻约束,用于电磁场分析.
- 建立一个自我一致的框架来最大化和推断贝叶斯后方密度.
主要方法:
- 开发一个分数顺序的动态模型.
- 应用信息理论方法,包括香农和分数时刻约束.
- 优化成本函数以导出依赖时间的贝叶斯后密度以实现场均化.
- 制订分形导数定义及其与差分运算符 (分歧,卷曲,拉普拉斯式) 的关系.
主要成果:
- 建立了一个新的碎形顺序动态框架.
- 该框架允许推断贝叶斯后密度,用于模拟固体中的均质化电磁场.
- 证明最大,贝叶斯推理和碎形麦克斯韦方程之间的自我一致性.
- 建立分数导数和标准微分演算子之间的关系.
结论:
- 开发的方法提供了一个新的方法来理解电磁数据的复杂性.
- 分数级动力学模型为分析和同质化电磁场提供了一个强大的工具.
- 这项工作将碎形几何学,信息理论和电磁学的概念结合起来,以推进科学理解.
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