N粒子分支布朗运动前速度的负大偏差 布朗运动
Baruch Meerson1, Pavel V Sasorov2
1Hebrew University of Jerusalem, Racah Institute of Physics, Jerusalem 91904, Israel.
Physical review. E
|February 7, 2025
概括
这项研究研究了分支布朗运动系统中的负正面速度. 我们发现,这些负速度的速率函数表现出普遍的行为和关键的过渡点.
科学领域:
- 统计物理 统计物理
- 随机过程 随机过程
- 数学生物学 数学生物学
背景情况:
- 分支布朗运动 (BBM) 模型对于理解人口动态和前部传播至关重要.
- 确定性理论预测了前极速度的限制,但偏差,特别是负速度,不太了解.
- 宏观波动理论 (MFT) 提供了一个研究这种系统中罕见事件和大偏差的框架.
研究的目的:
- 分析经验前速的负大偏差在单面的N粒子分支布朗运动 (N-BBM) 系统中.
- 为了确定系统的最佳路径,条件是特定的负正面速度.
- 为了研究负速度的速率函数s(c) 的行为,并识别任何相位过渡.
主要方法:
- 宏观波动理论 (MFT) 的应用来研究N-BBM系统.
- 为条件前速计算最佳路径的计算.
- 对速率函数的临界值c*的数值确定.
主要成果:
- 对于接近确定性极限 (c0-c≪c0) 的速度,速率函数s(c) 与来自费舍尔-科尔莫戈罗夫-彼得罗夫斯基-皮斯库诺夫 (FKPP) 普遍性类的普遍函数保持一致.
- 对于较大的负速度,s(c) 接近由抑制分支衍生的边界.
- 确定了一个关键值c* (<0),在此下,s(c) 等于被抑制的分支边界,表明在c*处的第二阶段动态相位过渡.
结论:
- 在N-BBM中,负前速率的速率函数在确定性极限附近表现出普遍的行为,在较大的负值时表现出明显的行为.
- 在c*观察到一个关键现象,标志着最佳路径动态的变化和速率函数的第二阶段过渡.
- 该研究提供了对罕见事件统计和分支和扩散系统中的相位过渡的见解.
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