论文标题
mond般的分数拉普拉斯理论
MOND-like Fractional Laplacian Theory
论文作者
论文摘要
我从基于分数泊松方程的牛顿理论的分数版本中，从牛顿理论的分数版本中提供了一些特征效应。我采用分数拉普拉斯式的特性来研究所提出模型的基本解决方案的特征。 MOND与这里介绍的分数理论之间的关键区别在于，后者是一种固有的线性理论，具有特征长度比例$ \ ell $，而前者最终是非线性的，它的特征是加速度尺度$ A_0 $。利用Tully-fisher的关系，随着分数订单$ s $接近$ 3/2 $，我将长度尺度比例$ \ ell $连接起来，从这种对牛顿的重力的修改中出现，而关键加速$ a_0 $ a_0 $。最后，讨论了该模型的可变级版本的星系旋转曲线的影响。
I provide a derivation of some characteristic effects of Milgrom's modified Newtonian dynamics (MOND) from a fractional version of Newton's theory based on the fractional Poisson equation. I employ the properties of the fractional Laplacian to investigate the features of the fundamental solution of the proposed model. The key difference between MOND and the fractional theory introduced here is that the latter is an inherently linear theory, featuring a characteristic length scale $\ell$, whilst the former is ultimately nonlinear in nature and it is characterized by an acceleration scale $a_0$. Taking advantage of the Tully-Fisher relation, as the fractional order $s$ approaches $3/2$, I then connect the length scale $\ell$, emerging from this modification of Newton's gravity, with the critical acceleration $a_0$ of MOND. Finally, implications for galaxy rotation curves of a variable-order version of the model are discussed.
