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Applied to a fluid with a given equation of state, the Friedmann equations yield the time evolution and geometry of the universe as a function of the fluid density. Some cosmologists call the second of these two equations the Friedmann acceleration equation and reserve the term Friedmann equation for only the first equation.
The great majority of ordinary matter in the universe is unseen, since visible stars and gas inside galaxies and clusters account for less than 10 % of the ordinary matter contribution to the mass–energy density of the universe. [13] The model includes a single originating event, the "Big Bang", which was not an explosion but the abrupt ...
The nonlinear Schrödinger equation (NLSE) is a fundamental equation in quantum mechanics and other various fields of physics, describing the evolution of complex wave functions. In Quantum Physics, normalization means that the total probability of finding a quantum particle anywhere in the universe is unity. [1]
In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. [1] [2] Nonlinear problems are of interest to engineers, biologists, [3] [4] [5] physicists, [6] [7] mathematicians, and many other scientists since most systems are inherently nonlinear in nature. [8]
An inhomogeneous cosmology is a physical cosmological theory (an astronomical model of the physical universe's origin and evolution) which, unlike the currently widely accepted cosmological concordance model, assumes that inhomogeneities in the distribution of matter across the universe affect local gravitational forces (i.e., at the galactic level) enough to skew our view of the Universe. [3]
This reduces the model equations to a set of three coupled, nonlinear ordinary differential equations. A detailed derivation may be found, for example, in nonlinear dynamics texts from Hilborn (2000) , Appendix C; Bergé, Pomeau & Vidal (1984) , Appendix D; or Shen (2016), [ 32 ] Supplementary Materials.
The free field model can be solved exactly, and then the solutions to the full model can be expressed as perturbations of the free field solutions, for example using the Dyson series. It should be observed that the decomposition into free fields and interactions is in principle arbitrary.
An example of a nonlinear delay differential equation; applications in number theory, distribution of primes, and control theory [5] [6] [7] Chrystal's equation: 1 + + + = Generalization of Clairaut's equation with a singular solution [8] Clairaut's equation: 1