电磁学与流体力学的四元数统一
A quaternionic unification of electromagnetism and hydrodynamics
摘要：
从四元数牛顿定律出发，导出了与洛伦兹变换相容的能量守恒方程。这个牛顿定律直接导出欧拉方程和其它控制流体运动的方程。在这种形式下，压力对系统动力学的贡献与质量相同。流体动力学方程是从麦克斯韦方程组通过采用电磁流体动力学（EMH）的类比。在这个类比中，水电场与流体的局部加速度有关，洛伦兹规范与不可压缩流体条件有关。提出了一种流体力学中的类洛仑兹规范。我们已经表明，当流体的粒子局部加速度偏离速度方向时，流体的涡度就会发展。我们还证明了电磁场中的洛伦兹力与流体中的欧拉力是对应的。此外，我们还得到了流体力学中的类高斯定律、类法拉第定律和类安培定律.
英文摘要：
We have derived energy conservation equations from the quaternionic Newton's law that is compatible with Lorentz transformation. This Newton's law yields directly the Euler equation and other equations governing the fluid motion. With this formalism, the pressure contributes positively to the dynamics of the system in the same way mass does. Hydrodynamic equations are derived from Maxwell's equations by adopting an electromagnetohydrodynamics (EMH) analogy. In this analogy the hydroelectric field is related to the local acceleration of the fluid and the Lorentz gauge is related to the incompressible fluid condition. An analogous Lorentz gauge in hydrodynamics is proposed. We have shown that the vorticity of the fluid is developed whenever the particle local acceleration of the fluid deviates from the velocity direction. We have also shown that Lorentz force in electromagnetism corresponds to Euler force in fluids. Moreover, we have obtained Gauss's, Faraday's and Ampere's -like laws in Hydrodynamics.
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