• Back
• Continuity_equation
• Euler_equation
• Poisson's_equation
• Euler_of_state
\begin{equation} \begin{aligned} \vec{a}_{\mathrm{con}} &=\underbrace{(\vec{v} \cdot \vec{\nabla})}_{\text{directional derivative}} \vec{v} \\ &=\left[\left(\begin{array}{c} v_{x} \\ v_{y} \\ v_{z} \end{array}\right) \cdot\left(\begin{array}{c} \frac{\partial}{\partial x} \\ \frac{\partial}{\partial y} \\ \frac{\partial}{\partial z} \end{array}\right)\right] \cdot\left(\begin{array}{c} v_{x} \\ v_{y} \\ v_{z} \end{array}\right) \\ &=\left[v_{x} \frac{\partial}{\partial x}+v_{y} \frac{\partial}{\partial y}+v_{z} \frac{\partial}{\partial z}\right] \cdot\left(\begin{array}{c} v_{x} \\ v_{y} \\ v_{z} \end{array}\right) \\ &=\left(\begin{array}{c} v_{{x}} \frac{\partial v_{{x}}}{\partial x}+v_{{y}} \frac{\partial v_{{x}}}{\partial y}+v_{{z}} \frac{\partial v_{{x}}}{\partial z} \\ v_{{x}} \frac{\partial v_{{y}}}{\partial x}+v_{{y}} \frac{\partial v_{{y}}}{\partial y}+v_{{z}} \frac{\partial v_{{y}}}{\partial z} \\ v_{{x}} \frac{\partial v_{{z}}}{\partial x}+v_{{y}} \frac{\partial v_{{z}}}{\partial y}+v_{{z}} \frac{\partial v_{{z}}}{\partial z} \end{array}\right) \end{aligned} \end{equation} $$E^2 = m^2c^4 + p^2c^2$$ An electromagnetic wave impinging on a charged particle, such as an electron, creates an oscillating motion of the charge. In turn, the oscillating charge generates radiation. This process is known as scattering. If the motion of the charge is nonrelativistic, the process is called Thompson scattering. The relativistic case is called Compton scattering. https://phas.ubc.ca/~hickson/astr530/ASTR530_2015_ch8.pdf http://www.ira.inaf.it/~ddallaca/L05_Scatt.pdf Compton scattering occurs when the energy of the incident photon is suciently great that significant momentum is imparted to the charged particle. As a result, the energy of the photon is changed by the scattering process.