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The model is named after the Dutch physicist Hendrik Antoon Lorentz. It is a classical , phenomenological model for materials with characteristic resonance frequencies (or other characteristic energy scales) for optical absorption, e.g. ionic and molecular vibrations , interband transitions (semiconductors), phonons , and collective excitations.
In particular, the Lorenz attractor is a set of chaotic solutions of the Lorenz system. The term " butterfly effect " in popular media may stem from the real-world implications of the Lorenz attractor, namely that tiny changes in initial conditions evolve to completely different trajectories .
The Tauc–Lorentz model is a mathematical formula for the frequency dependence of the complex-valued relative permittivity, sometimes referred to as the dielectric function. The model has been used to fit the complex refractive index of amorphous semiconductor materials at frequencies greater than their optical band gap .
The experimental and theoretical work was honored with the Nobel prize in physics in 1902. Lorentz' name is now associated with the Lorentz–Lorenz equation, the Lorentz force, the Lorentzian distribution, the Lorentz oscillator model and the Lorentz transformation.
The Lorenz attractor arises in the study of the Lorenz oscillator, a dynamical system. In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space, such as in a parametric curve.
Lorenz equations used to generate plots for the y variable. The initial conditions for x and z were kept the same but those for y were changed between 1.001 , 1.0001 and 1.00001 . The values for ρ {\displaystyle \rho } , σ {\displaystyle \sigma } and β {\displaystyle \beta } were 45.91 , 16 and 4 respectively.
1909 – Lorentz develops the classical Lorentz oscillator model to describe the optical response of materials. [53] 1911 – Heike Kamerlingh Onnes and Gilles Holst discover superconductivity in mercury. 1912 – Max von Laue discovers diffraction of X-rays by crystals.
An example would be plotting the , value every time it passes through the = plane where is changing from negative to positive, commonly done when studying the Lorenz attractor. In the case of the Rössler attractor, the x = 0 {\displaystyle x=0} plane is uninteresting, as the map always crosses the x = 0 {\displaystyle x=0} plane at z = 0 ...