تقرير
Non-Equilibrium Noise in V-Shape Linear Well Profiles
| العنوان: | Non-Equilibrium Noise in V-Shape Linear Well Profiles |
|---|---|
| المؤلفون: | MacKay, Noah M. |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics Condensed Matter Mathematical Physics Nonlinear Sciences |
| مصطلحات موضوعية: | Condensed Matter - Statistical Mechanics, Mathematical Physics, Nonlinear Sciences - Adaptation and Self-Organizing Systems, 35Q62, 35Q84, 60G50, 60G51, G.3, I.6.6, J.2, J.3, J.4 |
| الوصف: | Non-equilibrium noise is characterized as noise realizations where external agitations disrupt the harmonic equilibrium of Brownian motion. Excitations in a particle's random walk into a so-called L\'evy flight changes the distribution of the noise from Gaussian to the fat-tailed L\'evy distribution. Generalization between Gaussian and L\'evy distributions is the $\alpha$-stability distribution, where $1<\alpha\leq2$. In this study, the $\alpha$-stability distributed noise is subjugated into the Langevin and fractional Fokker--Planck equations that correspond to a V-shaped linear potential well $V(x)=F|x|$. From these equations, an Euler scheme for computational simulation via iterations is presented, and a probability density function that is normalizable under any $\alpha\in(1,2]$ is obtained. This study is focused more on the theoretical framework of non-equilibrium noise in V-shaped linear well profiles, which is intended to be applied to systems known to exhibit self-organized criticality. Comment: 6 pages, 4 figures; Associated Euler scheme on a Mathematica .nb file with adjustable input parameters can be supplied upon request |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2406.16117 |
| رقم الأكسشن: | edsarx.2406.16117 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |