1
Vector Calculus Foundation
▶
1.1
Basic Types
1.2
Partial Derivatives
1.3
Vector Calculus Operators
1.4
Smoothness Predicates
1.5
Fundamental Lemma and Vector Identities
1.6
Curl Linearity
2
Electromagnetic Waves
▶
2.1
Medium Parameters
2.2
Maxwell’s Equations
2.3
Wave Equation Derivation
3
Plasma Physics
▶
3.1
Vector Algebra
3.2
Fluid Operators
3.3
Lorentz Force
3.4
Two-Fluid Model
3.5
Ideal MHD
3.6
MHD Equilibrium
3.7
Cylindrical Coordinates
3.8
Grad-Shafranov Equation
3.9
Resistive MHD
3.10
FRC Equilibrium
4
Incompressible Navier-Stokes
▶
4.1
Equations of Motion
4.2
Euler Equations
4.3
Vorticity
4.4
Pressure Poisson Equation
Dependency graph
Formal PDE Models for Electromagnetism, Plasma, and Fluids
Ali Bekheet
1
Vector Calculus Foundation
1.1
Basic Types
1.2
Partial Derivatives
1.3
Vector Calculus Operators
1.4
Smoothness Predicates
1.5
Fundamental Lemma and Vector Identities
1.6
Curl Linearity
2
Electromagnetic Waves
2.1
Medium Parameters
2.2
Maxwell’s Equations
2.3
Wave Equation Derivation
3
Plasma Physics
3.1
Vector Algebra
3.2
Fluid Operators
3.3
Lorentz Force
3.4
Two-Fluid Model
3.5
Ideal MHD
3.6
MHD Equilibrium
3.7
Cylindrical Coordinates
3.8
Grad-Shafranov Equation
3.9
Resistive MHD
3.10
FRC Equilibrium
4
Incompressible Navier-Stokes
4.1
Equations of Motion
4.2
Euler Equations
4.3
Vorticity
4.4
Pressure Poisson Equation