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The part of the disturbance outside the forward light cone can usually be safely neglected, but if it is necessary to develop a reasonable speed for the transmission of heat, a hyperbolic problem should be considered instead – like a partial differential equation involving a second-order time derivative. Some models of nonlinear heat ...
The Crank–Nicolson stencil for a 1D problem. The Crank–Nicolson method is based on the trapezoidal rule, giving second-order convergence in time.For linear equations, the trapezoidal rule is equivalent to the implicit midpoint method [citation needed] —the simplest example of a Gauss–Legendre implicit Runge–Kutta method—which also has the property of being a geometric integrator.
Plate tectonics is a theory suggesting that the Earth's lithosphere is essentially composed of plates floating on the mantle. [97] The mantle convection model is fundamental in modeling the plates floating on it, and there are two major approaches to incorporate the plates into this model: rigid-block approach and rheological approach. [2]
Note that this definition of convection is only applicable in Heat transfer and thermodynamic contexts. It should not be confused with the dynamic fluid phenomenon of convection , which is typically referred to as Natural Convection in thermodynamic contexts in order to distinguish the two.
The photon Hamiltonian for the quantized radiation field (second quantization) is [37] [38] = (+) =, († +), where e e and b e are the electric and magnetic fields of the EM radiation, ε o and μ o are the free-space permittivity and permeability, V is the interaction volume, ω ph,α is the photon angular frequency for the α mode and c α ...
In the second type, subducting oceanic plates (which largely constitute the upper thermal boundary layer of the mantle) plunge back into the mantle and move downwards towards the core-mantle boundary. Mantle convection occurs at rates of centimeters per year, and it takes on the order of hundreds of millions of years to complete a cycle of ...
The second case is when natural convection acts in the opposite way of the forced convection. Consider a fan forcing air upward over a cold plate. [5] In this case, the buoyant force of the cold air naturally causes it to fall, but the air being forced upward opposes this natural motion.
In computational physics, the term advection scheme refers to a class of numerical discretization methods for solving hyperbolic partial differential equations.In the so-called upwind schemes typically, the so-called upstream variables are used to calculate the derivatives in a flow field.