The most historically significant nonlinear compositing system was the Cineon, which operated in a logarithmic color space, which more closely mimics the natural light response of film emulsions ( the Cineon system, made by Kodak, is no longer in production ).

Magnetic tape has a nonlinear response at low signal strengths, as measured by its coercivity.

Like the BaTiO < sub > 3 </ sub > thermistor, this device has a highly nonlinear resistance / temperature response and is used for switching, not for proportional temperature measurement.

When a medium is nonlinear, the response to complex waves cannot be determined from a sine-wave decomposition.

Generally a nonlinear optical material ( organic polymers have the fastest response rates, and thus are best for this application ) with an incident static or low frequency optical field will see a modulation of its refractive index.

In optical physics, support is also provided in areas such as the nonlinear response of isolated atoms to intense, ultra-short electromagnetic fields, the atom-cavity interaction at high fields, and quantum properties of the electromagnetic field.

Video sampling tends to work on a completely different scale altogether thanks to the highly nonlinear response both of cathode ray tubes ( for which the vast majority of digital video foundation work was targeted ) and the human eye, using a " gamma curve " to provide an appearance of evenly distributed brightness steps across the display's full dynamic range-hence the need to use RAMDACs in computer video applications with deep enough colour resolution to make engineering a hardcoded value into the DAC for each output level of each channel impractical ( e. g. an Atari ST or Sega Genesis would require 24 such values ; a 24-bit video card would need 768 ...).

In spite of this fact, scientists have not yet been able to derive the equations for nonlinear response theory from the FT.

The sensor response is nonlinear, especially toward edges of the capture area.

In many systems, however, driving with a very short strong pulse may drive the system into a nonlinear regime, so instead the system is driven with a pseudo-random sequence, and the impulse response is computed from the input and output signals.

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 optical Kerr effect is a process which results from the nonlinear response of an optical medium to the electric field of an electromagnetic wave.

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.

This stochastic response of molecules on the applied light corresponds also to a highly nonlinear interaction, leading to subdiffraction resolution.

It may also depend upon the electric field ( nonlinear materials ) and have a time dependent response.

While metals do become slightly more resistant at higher temperatures, this class of ceramics ( often barium titanate and lead titanate composites ) has a highly nonlinear thermal response, so that it becomes extremely resistant above a composition-dependent threshold temperature.

Since the connected molecules have more electrons, collective motions of these electrons yield enhanced nonlinear response.

Another exact fluctuation expression derived by Evans and Morriss is the so-called Kawasaki expression for the nonlinear response:

In spite of this fact, no one has yet been able to derive the equations for nonlinear response theory from the FT.

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.

In general, linear procedures are applicable when the structure is expected to remain nearly elastic for the level of ground motion or when the design results in nearly uniform distribution of nonlinear response throughout the structure.

Since the properties of the seismic response depend on the intensity, or severity, of the seismic shaking, a comprehensive assessment calls for numerous nonlinear dynamic analyses at various levels of intensity to represent different possible earthquake scenarios.

For R = 0, no reflection from the first surface and the resultant nonlinear phase shift is equal to the round-trip phase change () – linear response.

However, as can be seen, when R is increased, the nonlinear phase shift gives the nonlinear response to and shows step-like behavior.

The third-order intercept point relates nonlinear products caused by the third-order nonlinear term to the linearly amplified signal, in contrast to the second-order intercept point that uses second order terms.

The nonlinear products caused by n-th order nonlinearity appear at n times the frequency of the input tone.

Solitons are caused by a cancellation of nonlinear and dispersive effects in the medium.

However, most Mira variables exhibit slight cycle-to-cycle changes in period, probably caused by nonlinear behavior in the stellar envelope including deviations from spherical symmetry.

Even when the statistical model is nonlinear, it can be approximated by a linear model for which an analysis of variance may be appropriate.

Semiconductor diodes ' nonlinear current – voltage characteristic can be tailored by varying the semiconductor materials and introducing impurities into ( doping ) the materials.

Note: Any nonlinear electronic block driven by two signals with frequencies f < sub > 1 </ sub > and f < sub > 2 </ sub > would generate intermodulation ( mixing ) products.

The theory of nonlinear functionals was continued by students of Hadamard, in particular Fréchet and Lévy.

It is a connected Lie group that cannot be faithfully represented by matrices of finite size, i. e., a nonlinear group.

Because linear algebra is such a well-developed theory, nonlinear mathematical models are sometimes approximated by linear ones.

Dynamic programming has been coupled with ANNs ( Neuro dynamic programming ) by Bertsekas and Tsitsiklis and applied to multi-dimensional nonlinear problems such as those involved in vehicle routing or natural resources management because of the ability of ANNs to mitigate losses of accuracy even when reducing the discretization grid density for numerically approximating the solution of the original control problems.

is an interaction in which the quantum state of the nonlinear material is not changed by the interaction with the optical field.

Parametric and lossy ' instantaneous ' ( i. e. electronic ) nonlinear optical phenomena, in which the optical fields are not too large, can be described by a Taylor series expansion of the dielectric Polarization density ( dipole moment per unit volume ) P ( t ) at time t in terms of the electrical field E ( t ):

* Encyclopedia of laser physics and technology, with content on nonlinear optics, by Rüdiger Paschotta

* Perelman's proof of the Poincaré conjecture: a nonlinear PDE perspective by Terence Tao, unpublished arxiv. org preprint ( written for mathematicians ).

This model is described by a quantum nonlinear Schrödinger equation.

In certain circumstances, waves of unchanging shape also can occur in nonlinear media ; for example, the figure shows ocean waves in shallow water that have sharper crests and flatter troughs than those of a sinusoid, typical of a cnoidal wave, a traveling wave so named because it is described by the Jacobi elliptic function of m-th order, usually denoted as.

The hypothesis implies that a massive particle is an intrinsically spatially as well as temporally extended wave phenomenon by a nonlinear law.

Unlike the EDFA and SOA the amplification effect is achieved by a nonlinear interaction between the signal and a pump laser within an optical fiber.

If this susceptibility itself depends upon the electric field, one can obtain a nonlinear optical effect of magneto-optical parametric generation ( somewhat analogous to a Pockels effect whose strength is controlled by the applied magnetic field ).

Away from telecom, an optical switch is the unit that actually switches light between fibers, and a photonic switch is one that does this by exploiting nonlinear material properties to steer light ( i. e., to switch wavelengths or signals within a given fiber ).

* Nonlinear methods ( e. g., ) that vary the diffraction pattern in a medium by taking advantage of the material nonlinear properties to deflect light to the desired receiver ;

It remained mysterious until 1965, when Kruskal and Zabusky showed that, after appropriate mathematical transformations, the system can be described by the Korteweg-de Vries equation, which is the prototype of nonlinear partial differential equations that have soliton solutions.

A third-order nonlinear product will increase by 3 dB in power when the input power is raised by 1 dB.