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An example of an order parameter for crystallization is "bond orientational order" describing the development of preferred directions (the crystallographic axes) in space. For many systems, phases with more structural (e.g. crystalline) order exhibit less entropy than fluid phases under the same thermodynamic conditions.
Chaos theory can be applied outside of the natural sciences, but historically nearly all such studies have suffered from lack of reproducibility; poor external validity; and/or inattention to cross-validation, resulting in poor predictive accuracy (if out-of-sample prediction has even been attempted).
By creating their own novel model in order to calculate findings similar to what is already known about collective motion, the scientists hope they can encourage future work using this or other ...
Entropy is often loosely associated with the amount of order or disorder, or of chaos, in a thermodynamic system. The traditional qualitative description of entropy is that it refers to changes in the state of the system and is a measure of "molecular disorder" and the amount of wasted energy in a dynamical energy transformation from one state ...
The strictest form of order in a solid is lattice periodicity: a certain pattern (the arrangement of atoms in a unit cell) is repeated again and again to form a translationally invariant tiling of space. This is the defining property of a crystal. Possible symmetries have been classified in 14 Bravais lattices and 230 space groups.
Self-organization, also called spontaneous order in the social sciences, is a process where some form of overall order arises from local interactions between parts of an initially disordered system. The process can be spontaneous when sufficient energy is available, not needing control by any external agent.
A plot of Lorenz' strange attractor for values ρ=28, σ = 10, β = 8/3. The butterfly effect or sensitive dependence on initial conditions is the property of a dynamical system that, starting from any of various arbitrarily close alternative initial conditions on the attractor, the iterated points will become arbitrarily spread out from each other.
The signal, screen, and television electronics in this analogy represent the implicate order, while the image produced represents the explicate order. He also uses an example in which an ink droplet can be introduced into a highly viscous substance (such as glycerine), and the substance rotated very slowly, such that there is negligible ...
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