Definition of scientific term
- Chinese name:
- Nonlinear
- English name:
- Nonlinearity
- definition:
- The device, network or transmission medium does not conform to the working properties of the superposition principle within the specified working range.
- Subject:
- Communication Technology (a subject); communication principle and basic technology (two subjects)
Non-linear, ie non-linear, refers to the situation where the output input is neither proportional. For example, the universe forms the initial chaotic state. There is no linear relationship between the independent variable and the variable, and the curve or parabola relationship may not be quantitative. This relationship is called a nonlinear relationship.
The difference between linear and nonlinear "linear" and "nonlinear" is often used to distinguish the dependence of the function y = f (x) on the independent variable x. A linear function is a linear function whose image is a straight line. Other functions are nonlinear functions whose images are not straight lines.
Detailed definition of linearity, the proportional and linear relationship between quantity and quantity, representing regular and smooth motion in space and time; and non-linear, non-proportional, non-linear relationship, representing irregular motion and mutation. For example: How many times the visual acuity of two eyes is one eye? It's easy to think twice, but it's actually 6-10 times! This is nonlinear: 1+1 is not equal to 2.
Although the common nonlinear relationship is ever-changing, it still has some commonalities different from linear relations. Linear relations are independent relationships that are independent of each other, while nonlinearity is an interaction, and it is this interaction that makes the whole no longer simply equal to the sum of parts, but may have a gain different from "linear superposition" or Loss. The generation of the laser is nonlinear! When the applied voltage is small, the laser is like an ordinary electric light, and the light is scattered in all directions. When the applied voltage reaches a certain value, a new phenomenon suddenly appears: the excited atom seems to hear the "right-to-right" command, and emits Monochromatic light with the same phase and direction is the laser. So far, there is no clear and complete understanding of the concept of nonlinearity and the nature of nonlinearity, and its philosophical significance has not been fully explored.
Defining linearity: It is defined from two perspectives of mutual correlation. One is that the superposition principle is established; the other is that the functional relationship between physical variables is a straight line, and the rate of change between variables is constant. After clarifying the meaning of linearity, the corresponding nonlinear concept is easy to define: - "Defining the nonlinear operator N(φ) for some a, b or φ, ψ not satisfying L(aφ+bψ)=aL The operator of (φ)+bL(ψ), that is, the superposition principle does not hold, which means that there is a coupling between φ and ψ, and the pair of (aφ+bψ) is equal to φ and ψ*, respectively. Add the intersection of φ and ψ (coupling term), or φ, ψ is discontinuous (with mutation or fracture), not microscopic (with vertices). Second, as an equivalent expression, we can understand nonlinearity from another angle: in a set of certain physical variables used to describe a system, the change of a system's initial variable zui The corresponding change of this or other variables is disproportionate. In other words, the rate of change between variables is not constant. The slope of the function has no or unequal in its definition domain. In a nutshell, it is between physical variables. The one-level incremental relationship is asymmetrical within the domain of the variable. It can be said that this symmetry breaking is the basic embodiment of the nonlinear relationship and the root of the complexity of the nonlinear system. These two expressions of the nonlinear concept are actually equivalent. The fact that the superposition principle is not established will inevitably lead to the asymmetry of the two physical variables; on the contrary, if the physical variable relationship is asymmetrical, the superposition principle will not hold. The two expressions are used because the two expressions have their own conveniences for different objects in different situations. For example, the former is convenient for examining the relationship between the whole and the part of the system and the nature of the differential equation. The latter would be convenient for examining the relationships between specific variables, including the temporal behavior of the variables.
The characteristics of non-linear characteristics are: cross-cutting various professions and infiltrating various fields, which can almost be said to be: "Everywhere is everywhere." Indeed.
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