We take up the challenge to explain the correlation between the Jeans instability topic towards star formation within the accelerated expansion of universe and the role of torsional shear-like Alfven waves in triggering the formation of network patterns, by proposing new mathematical models for self-gravitating interstellar non ideal MHD plasmas. The diffusion of the gravitational field is included via a parabolic Einstein’s equation with the cosmological constant, whereas anomalous resistive features are described through non ideal Ohm’s laws incorporating inertia terms, to account of relaxation and retardation magnetic responses. We perform a spectral analysis to test the stability properties of the novel constitutive settings where dissipative and elastic devices act together, by emphasizing the differences with previous models. As a main result, we highlight the definition of a lower critical threshold, here called the Jeans-Einstein wavenumber, against collapse formation towards the formation of longitudinal gravito-magneto-sonic waves and transverse non gravitational Alfven waves exhibiting larger effective wavespeeds, due to the hyperbolic-parabolic diffusion of the magnetic field. Consequently shorter collisional times are allowable so, beyond the plasma-beta, another interesting key point is the definition of the Ohm number to revisit the timescale topic, towards reviewed Reynolds and Lundquist numbers able to better capture the microphysical phenomena of Magnetic Reconnection in narrow diffusion regimes.

中文翻译：

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粘弹性型磁效应和自重力对 MHD 波传播的影响

我们接受了挑战，通过提出新的自引力数学模型，解释 Jeans 不稳定性主题与宇宙加速膨胀中恒星形成的相关性与类似扭转剪切的 Alfven 波在触发网络模式形成中的作用之间的相关性星际非理想 MHD 等离子体。引力场的扩散通过具有宇宙常数的抛物线爱因斯坦方程包括在内，而异常电阻特征则通过结合惯性项的非理想欧姆定律来描述，以说明弛豫和磁滞反应。我们通过强调与先前模型的差异来进行光谱分析，以测试耗散和弹性装置共同作用的新型本构设置的稳定性属性。作为主要结果，我们强调了较低临界阈值的定义，这里称为 Jeans-Einstein 波数，以防止坍缩形成，形成纵向引力磁声波和横向非引力阿尔文波，表现出更大的有效波速，由于磁场的双曲线-抛物线扩散。因此，更短的碰撞时间是允许的，因此，除了等离子-β 之外，另一个有趣的关键点是定义欧姆数以重新审视时间尺度主题，以重新审视雷诺数和伦德奎斯特数，以便能够更好地捕捉窄扩散中磁重联的微物理现象制度。由于磁场的双曲抛物线扩散，形成纵向引力磁声波和横向非引力阿尔文波，表现出更大的有效波速。因此，更短的碰撞时间是允许的，因此，除了等离子-β 之外，另一个有趣的关键点是定义欧姆数以重新审视时间尺度主题，以重新审视雷诺数和伦德奎斯特数，以便能够更好地捕捉窄扩散中磁重联的微物理现象制度。由于磁场的双曲抛物线扩散，形成纵向引力磁声波和横向非引力阿尔文波，表现出更大的有效波速。因此，更短的碰撞时间是允许的，因此，除了等离子-β 之外，另一个有趣的关键点是定义欧姆数以重新审视时间尺度主题，以重新审视雷诺数和伦德奎斯特数，以便能够更好地捕捉窄扩散中磁重联的微物理现象制度。