Physics: “Optics of lenses and mirrors”. Introduction to the optics of lenses and mirrors. Concave, convex, converging, diverging; real, virtual; upright, inverted, magnified, shrunk. Sign conventions for focal length, image distance, object distance, magnification. The lens/mirror equation; the...
In most sources I come across that try to justify the Einstein Field Equations outside the context of Einstein-Hilbert action, the argument goes mostly as follows: In analogy with the Poisson equation for Newtonian potential, it is tempting to postulate Rab=8πGNTabRab=8πGNTab. However by ...
General conservation equations for multiphase systems:constitutive theory for porous media flow[J]. Adv. Water Res.,1980,3(3):25～40Hassanizadeh SM, Gray WG. General conservation equations for multiphase systems: 3 Constitutive theory for porous media flow. Adv Water Resour 1980;3:25-40....
The initial density profile is modulated in order to test the first phases of the disc evolution, solving the diffusion equation for a single system characterized by an initial wavy (ringed) profile, therefore modelling a set of |$\ell$|co–rotating rings with same characteristics: rotation ...
-product in curved spacetime, which might also be more suitable for quantization of dgr. additionally, one would like to calculate the \(\delta _{\mu \nu }\) correction term in the \(\star \) -einstein equation explicitly and apply the result to cosmology, such as \(\star \) -flrw...
In global geometry, the object of study is not one particular solution (or family of solutions) to Einstein’s equations. Rather, relations that hold true for all geodesics, such as the Raychaudhuri equation, and additional non-specific assumptions about the nature of matter (usually in the ...
aIn this chapter we develop the mathematical basis for a comprehensive general purpose model of fluid flow and heat transfer from the basic principles of conservation of mass, momentum and energy. This leads to the governing equations of fluid flow and a discussion of the necessary auxiliary condit...
Theorem 2: For the general holonomic system (2), if the generators ξ 0 and ξ s of the infinitesimal transfor- mations (5) satisfy the conformal factor (23) or (25), and there exists a gauge function G = G(t, q, ˙ q) satis- fying the following structure equation of Lie ...
It may also be derived by appending a source term to the wave equation (1) and then applying stress–energy conservation using (23); see [30] for a full discussion of the minimally-coupled case, also including extended-body and self-interaction effects. The factor of −2 in the ...
The actual equations that are solved are typically obtained by restating the conservation equation in weak form: the field variables are written in terms of the basis functions, the equation is multiplied by appropriate test functions, and then integrated over an element. Since the FEM solution ...