nonlinear


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nonlinear

adjective Not linear, random

nonlinear

(non″lin′ē-ăr)
Not linear; not obeying a linear relationship. In mathematics, a linear equation may be given in the form y = mx + b, where x is the independent variable, and y is the dependent variable. A nonlinear relationship cannot be represented by such an equation.
References in periodicals archive ?
The variability in the literature may be ascribed to differentness in breed, gender, birth type, dam age, managerial conditions, rearing systems, and nonlinear functions or alternative statistical approaches (MARS etc.) used.
HPM was presented by He [33] in 1999, and is considered as a strong and efficient technique in finding an exact or an approximate analytical solutions to nonlinear equations.
To demonstrate the idea of Homotopy Perturbation Method, we consider the general form nonlinear differential equation with initial conditions of the form [3]:
It shows that the nonlinear fit method agrees with experimental data of the I-V curve and previous work.
Comparison manual and nonlinear fit method on the I-V curve of an organic solar cell, ITO/CuPc/PTCBI/Ag [22], is shown in Figure 5.
We consider nonlinear ultrasonic technique where the received signal is not at the frequency of the exciting current, and metallic material is treated as weakly nonlinear elastic because the amplitude of the signal received at higher harmonics is very small relative to the excitation, then harmonics can be generated notably at twice the excitation frequency.
The system also was simulated at different values of nonlinear coefficient of PCF, and it was found that as the input power to PCF was maintained at 32dBm, only one order was created when nonlinear coefficient (C) is between 6 and 12 [W.sup.-1] [km.sup.-1], and two orders were created when C [greater than or equal to] 14 [W.sup.-1] [km.sup.-1].
If the ultrasonic has fixed driving frequency, wave number, and propagation distance, the ultrasonic nonlinear coefficient is proportional to [A.sub.2]/[A.sup.2.sub.1].
where -[[omega].sup.2.sub.0] denotes the linear stiffness constant of the system, D is linear damping coefficient, [gamma] is the nonlinear damping coefficient, [beta] is the nonlinear stiffness constant, and F and [omega] are the external amplitude and driving frequency, respectively.
In view of the fact that the dynamical behaviors of plates with nonlinear elastic restraints are very different from those with simple boundary conditions, in this work, the attention is paid to the treatment of nonlinear elastic restraints.
The quantity [[chi].sup.(3)] stands for the third-order nonlinear optical susceptibility, which is related to the nonlinear refractive index [n.sub.2] through the following expression: [[chi].sup.(3)] where c is the speed of light.
Nonlinear systems and their control can be found in many areas, for example using nonlinear model predictive control in automotive industry [6], receding horizon control of vehicle formation [16], stochastic nonlinear model predictive control in film deposition [2], nonlinear PI control of wind turbine [14], neural network for model predictive control of continuous reactor [23], nonlinear model predictive control of robot manipulator [18], steam valve control of multi-machine power systems [1], or controlling galloping vibrations [4], nonlinear control of boost converter [19], adaptive control of nonlinear finance system [5], to name some.