Lorenz system - Wikipedia
WEBThe Lorenz system is a system of ordinary differential equations first studied by mathematician and meteorologist Edward Lorenz. It is notable for having chaotic solutions for certain parameter values and initial conditions. In particular, the Lorenz attractor is a set of chaotic solutions of the Lorenz system.
Lorenz-Attraktor – Wikipedia
WEBDer Lorenz-Attraktor ist der seltsame Attraktor eines Systems von drei gekoppelten, nichtlinearen gewöhnlichen Differentialgleichungen: Formuliert wurde das System um 1963 von dem Meteorologen Edward N. Lorenz (1917–2008) [1], der es als Idealisierung eines hydrodynamischen Systems entwickelte.
WEB6. The Lorenz (1963) Equations The Lorenz equations were originally derived by Saltzman (1962) as a ‘minimalist’ model of thermal convection in a box x_ = ˙(y x) (1) y_ = rx y xz (2) z_ = xy bz (3) where ˙ (\Prandtl number"), r (\Rayleigh number") and b are parameters(> 0). These equations also arise in studies of convection
Lorentz-Lorenz equation - Oxford Reference
WEBThe Lorentz-Lorenz equation can be written in the form α=(3/4πN) [(n 2–1/(n 2+2)], where N is the number of molecules per unit volume. The equation provides a link between a microscopic quantity (the polarizability) and a macroscopic quantity (the refractive index).
Lorentz transformation - Wikipedia
WEBThe relations between the primed and unprimed spacetime coordinates are the Lorentz transformations, each coordinate in one frame is a linear function of all the coordinates in the other frame, and the inverse functions are the inverse transformation.
Lorenz equations - Encyclopedia of Mathematics
WEBJun 22, 2022 · Lorenz equations. Lorenz system. The system of equations. $$ \begin {eqnarray*} \dot x &=& -\sigma x+\sigma y, \\ \dot y &=& rx-y-xz, \\ \dot z &=& -bz+xy. \end {eqnarray*} $$. It arises as the $3$-mode truncation of the two-dimensional convection equations for parallel horizontal walls at constant, but different, temperatures.
Lorenz Equation - an overview | ScienceDirect Topics
WEBThe Lorenz equations are a simplified model of the two-dimensional convective motion within a fluid layer due to a temperature difference ΔT between the upper and lower surfaces. From: Orbital Mechanics for Engineering Students (Fourth Edition), 2021
WEBTHE2 JACOBEAN. The Lorenz di erential equations x_ = F(x) has the Jacobean DF(x;y;z) = 4 ˙ ˙ 0 r z 1 x y x b 3 5. THE ORIGIN. At the equilibrium point (0;0;0), the Jacobean DF(0;0;0) is block diagonal. The eigenvalues are b; 1 s p (1 s)2+4rs p 2. For r < 1, where (1 s)2 +4rs < (1 + s), all three eigenvalues are negative. For r > 1, we
WEB11 Lorenz equations. In this lecture we derive the Lorenz equations, and study their behavior. The equations were first derived by writing a severe, low-order truncation of the equations of R-B convection.
Lorenz System -- from Wolfram MathWorld
WEBAug 22, 2024 · TOPICS. Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics Foundations of Mathematics Geometry History and Terminology Number Theory Probability and Statistics Recreational Mathematics Topology Alphabetical Index New in MathWorld
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