The result of this behaviour is a highly nonlinear current-voltage characteristic, in which the MOV has a high resistance at low voltages and a low resistance at high voltages.

This is due to the nonlinear behaviour of shock waves.

Small changes in certain parameters of a nonlinear system can cause equilibria to appear or disappear, or to change from attracting to repelling and vice versa, leading to large and sudden changes of the behaviour of the system.

Moreover, many empirical studies illustrate inefficient behaviour arising from nonlinear objective performance measures, or measures over the course of a long period ( e. g., a year ), which create nonlinearities in time due to discounting behaviour.

Nonlinear optics is the branch of optics that describes the behaviour of light in nonlinear media, that is, media in which the polarization P responds nonlinearly to the electric field E of the light.

However, they are based on linear elastic response and hence the applicability decreases with increasing nonlinear behaviour, which is approximated by global force reduction factors.

Approximation schemes of this kind have been particularly used in time series prediction and control of nonlinear systems exhibiting sufficiently simple chaotic behaviour, 3D reconstruction in computer graphics ( for example, hierarchical RBF and Pose Space Deformation ).

Happenings take place anywhere, and are often multi-disciplinary, with a nonlinear narrative and the active participation of the audience.

Thus the optical system may contain no nonlinear materials nor active devices ( except possibly, extremely linear active devices ).

They are implemented by active electronic components ( transistors ) having current-stable nonlinear output characteristic when driven by steady input quantity ( current or voltage ).

Biocomplexity is the study of complex structures and behaviors that arise from nonlinear interactions of active biological agents, which may range in scale from molecules to cells to organisms.

Hill's work thoroughly exploits the capacity of video to offer complex nonlinear narratives that encourage active engagement on the part of the viewer.

Other more complex laws may be needed if the network contains nonlinear or reactive components.

The only drawback to using a nonlinear component rather than a multiplier is that, in addition to the sum and difference frequencies, it produces other unwanted frequency components called harmonics which must be filtered from the output to leave the desired heterodyne frequency.

Examples of nonlinear components that are used as mixers are vacuum tubes and transistors biased near cutoff ( class C ), and diodes.

There are, however, components of electrical circuits which do not obey Ohm's law ; that is, their relationship between current and voltage ( their I – V curve ) is nonlinear ( or non-ohmic ).

In other words, a nonlinear system is any problem where the variable ( s ) to be solved for cannot be written as a linear combination of independent components.

For example, when two unpatterned lights are modulated at slightly different frequencies ( F1 and F2 ) and superimposed, multiple nonlinear cross-modulation components of frequency ( mF1 ± nF2 ) are created in the SSEP, where m and n are integers.

These components allow nonlinear processing in the brain to be investigated.

In these methods, nonlinear optical effects in intracavity components are used to provide a method of selectively amplifying high-intensity light in the cavity, and attenuation of low-intensity light.

From a signal-processing standpoint, an unsharp mask is generally a linear or nonlinear filter that amplifies high-frequency components.

Less technically, a nonlinear system is any problem where the variable ( s ) to be solved for cannot be written as a linear sum of independent components.

This technique is often extended to small-signal nonlinear circuits like tube and transistor circuits, by linearizing the circuit about the DC bias point Q-point, using an AC equivalent circuit made by calculating the equivalent small signal AC resistance of the nonlinear components at the bias point.

In data analysis, GTMs are like a nonlinear version of principal components analysis, which allows high dimensional data to be modelled as resulting from Gaussian noise added to sources in lower-dimensional latent space.

NEi Nastran is a general purpose finite element analysis solver used to analyze linear and nonlinear stress, dynamics, and heat transfer characteristics of structures and mechanical components.

It not only corrects for linear distortion, but also second degree and higher nonlinear components.

In such analyses, it is essential to achieve accurate nonlinear modeling of structural components such as beams, columns, beam-column joints, shear walls etc.

Thus, experimental results play an important role in determining the modeling parameters of individual components, especially those that are subject to significant nonlinear deformations.

The individual components are then assembled to create a full nonlinear model of the structure.

Models for functional data and methods for their analysis may resemble those for conventional multivariate data, including linear and nonlinear regression models, principal components analysis, and many others.

This tensor equation is a complicated set of nonlinear partial differential equations for the metric components.

Some electronic components develop lower resistances or lower triggering voltages ( for nonlinear resistances ) as their internal temperature increases.

Because of their high amplitude to wavelength ratio, ultrasonic waves commonly display nonlinear propagation.

Thus, a nonlinear system is one whose behavior can't be expressed as a sum of the behaviors of its parts ( or of their multiples ).

The nonlinear stretching process leaves objects in the center of the screen with approximately their original aspect ratio ; objects at the left and right edges are distorted.

But as the waves reach more rarefied air at higher altitudes, their amplitude increases, and nonlinear effects cause the waves to break, transferring their momentum to the mean flow.

Founded by a marketing manager from Apollo Computer, Inc., Bill Warner, a prototype of their first digital nonlinear editing system ( the Avid / 1 ) was shown in a private suite at the National Association of Broadcasters ( NAB ) convention in April 1988.

This interweaving and nonlinear structure makes any true synopsis of the novel difficult, especially since the narrators are all unreliable in their own way, making their accounts not necessarily trustworthy at all times.

The T52 had ten pinwheels, which were stepped in a complex nonlinear way, based in later models on their positions from various delays in the past, but in such a way that they could never stall.

The nonlinear elements, in particular the sheaths, provide harmonics in the discharge current and excite the plasma and the sheath at their series resonance characterized by the so-called geometric resonance frequency.

Shenmue was a major step forward for 3D open world, nonlinear gameplay, touted as offering an unparalleled level of player freedom, giving them full reign to explore an expansive sandbox city with its own day-night cycles, changing weather, and fully voiced non-player characters going about their daily routines.

As an aside, it may be noted that real-world departures from this linear two-pole model occur due to two major complications: first, real amplifiers have more than two poles, as well as zeros ; and second, real amplifiers are nonlinear, so their step response changes with signal amplitude.

The photorefractive effect is a nonlinear optical effect seen in certain crystals and other materials that respond to light by altering their refractive index

However most optical materials have a relatively weak nonlinear response, meaning that their properties only change by a small amount for large changes in the intensity of the electromagnetic field.

" In awarding the 2006 Steele Prize to Gardner, Greene, Kruskal, and Miura, the American Mathematical Society stated that before their work " there was no general theory for the exact solution of any important class of nonlinear differential equations.

" The AMS added, " In applications of mathematics, solitons and their descendants ( kinks, anti-kinks, instantons, and breathers ) have entered and changed such diverse fields as nonlinear optics, plasma physics, and ocean, atmospheric, and planetary sciences.

Two generally true circumstances underlie the theory of thoughtful, therapeutic polypharmacy: ( 1 ) Drugs given for a single somatic locale act on biochemical mechanisms present throughout the body such that their nonlinear interactions can produce an ( unknown except empirically ) global physiological state of health ;( 2 ) The more independent variables, " handles ", to manipulate, the greater the likelihood of finding and stabilizing a small available parametric space of healthy function while minimizing unwanted effects.

In addition to pre-and post-processing capabilities, several Nastran vendors have integrated more advanced nonlinear capabilities into their Nastran products.

Among other contributions, he suggested that nonlinear phenomena and the fundamental laws defining their behavior were essential in order to understand biology and its evolutionary paths.

Usually, the absorption of waves does not depend on their intensity ( linear absorption ), although in certain conditions ( usually, in optics ), the medium changes its transparency dependently on the intensity of waves going through, and the saturable absorption ( or nonlinear absorption ) occurs.

Even the fundamental questions of existence, uniqueness, and extendability of solutions for nonlinear differential equations, and well-posedness of initial and boundary value problems for nonlinear PDEs are hard problems and their resolution in special cases is considered to be a significant advance in the mathematical theory ( cf.