Real World Applications The Maxey–Riley equation
... All these numerical schemes implicitly assume the existence and uniqueness of solutions of the MR equation. The solutions can indeed be found explicitly for certain simple velocity fields [17,23]. To the best of our knowledge, however, general existence and uniqueness results have not been proven, a ...
... All these numerical schemes implicitly assume the existence and uniqueness of solutions of the MR equation. The solutions can indeed be found explicitly for certain simple velocity fields [17,23]. To the best of our knowledge, however, general existence and uniqueness results have not been proven, a ...
4.6 Isosceles, Equilateral, and Right Triangles
... • Use properties of isosceles and equilateral triangles • Use properties of right triangles ...
... • Use properties of isosceles and equilateral triangles • Use properties of right triangles ...
BKL singularity
A BKL (Belinsky–Khalatnikov–Lifshitz) singularity is a model of the dynamic evolution of the Universe near the initial singularity, described by an anisotropic, homogeneous, chaotic solution to Einstein's field equations of gravitation. According to this model, the Universe is oscillating (expanding and contracting) around a singular point (singularity) in which time and space become equal to zero. This singularity is physically real in the sense that it is a necessary property of the solution, and will appear also in the exact solution of those equations. The singularity is not artificially created by the assumptions and simplifications made by the other well-known special solutions such as the Friedmann–Lemaître–Robertson–Walker, quasi-isotropic, and Kasner solutions.The Mixmaster universe is a solution to general relativity that exhibits properties similar to those discussed by BKL.