To see why the evolution equation defining the Ricci flow is indeed a kind of nonlinear diffusion equation, we can consider the special case of ( real ) two-manifolds in more detail.

The nonlinear evolution of the instabilities was investigated by means of direct simulations of the time-dependent system of nonlinear equations.

Kruskal received the National Medal of Science in 1993 " for his influence as a leader in nonlinear science for more than two decades as the principal architect of the theory of soliton solutions of nonlinear equations of evolution.

HD is a completely integrable nonlinear evolution equation that may be solved by means of the inverse scattering transform.

Jean-Luc Godard's work since 1959 was also important in the evolution of nonlinear film.

However, dispersion also has an effect in many other circumstances: for example, GVD causes pulses to spread in optical fibers, degrading signals over long distances ; also, a cancellation between group-velocity dispersion and nonlinear effects leads to soliton waves.

They are characterized by a high peak intensity ( or more correctly, irradiance ) that usually leads to nonlinear interactions in various materials, including air.

The intense angle strain leads to nonlinear orbital overlap of its sp < sup > 3 </ sup > orbitals.

The college contains the Research School of Physics and Engineering, a body which focuses primarily on research into materials science and engineering ; lasers, nonlinear optics and photonics ; nanotechnology and mesoscopic physics ; physics of atoms, molecules and the nucleus ; plasma physics and surface science ; physics and the environment.

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.

He made fundamental contributions in many areas of mathematics and science, ranging from plasma physics to general relativity and from nonlinear analysis to asymptotic analysis.

" 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.

A nonlinear reaction in the plasma combines the two oscillations in such a way that, on average, a steady

It was also used for depth of anasthesia assesement and widely in plasma physics ( nonlinear energy transfer ) and also for detection of gravitation waves.

The school's primary research areas are: materials science and engineering ; lasers, nonlinear optics and photonics ; nanotechnology and mesoscopic physics ; physics of atoms, molecules and the nucleus ; plasma physics and surface science ; physics and the environment.

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

Lamps including arc-discharge lamps, incandescent lamps, fluorescent lamps and mercury vapor lamps have two terminals and display nonlinear current – voltage characteristics.

A nonlinear component is one in which the output current or voltage is a nonlinear function of its input.

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 ).

Second, because the magnetic field B and force are nonlinear functions of the current, depending on the nonlinear relation between B and H for the particular core material used.

These perturbations are then run through the full nonlinear model to generate an ensemble forecast, giving a handle on some of the uncertainty that should be allowed for around the current central prediction.

A varistor is an electronic component with a " diode-like " nonlinear current – voltage characteristic.

In the case of a nonlinear device, such as a transistor, the term " output impedance " usually refers to the effect upon a small-amplitude signal, and will vary with the bias point of the transistor, that is, with the direct current ( DC ) and voltage applied to the device.

) The current delivered to a load with nonzero voltage ( drop ) across its terminals ( a linear or nonlinear resistor with a finite resistance, a charged capacitor, an uncharged inductor, a voltage source, etc.

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

The various shapes of electric arc are emergent properties of nonlinear patterns of current and electric field.

Soner ’ s current research interests are nonlinear partial differential equations ; asymptotic analysis of Ginzburg-Landau type systems, viscosity solutions, and mathematical finance.

At any given time step, each non-input unit computes its current activation as a nonlinear function of the weighted sum of the activations of all units from which it receives connections.

He has also provided insights for possibly solving the P vs. NP problem and published works on H-infinity control of nonlinear systems and computational fluid dynamics, while his current research is in cognitive emergence theory.

In an electric circuit, a nonlinear element or nonlinear device is an electrical element which does not have a linear relationship between current and voltage.

Other examples of nonlinear elements are transistors and other semiconductor devices, vacuum tubes, and iron core inductors and transformers when operated above their saturation current.

* Nonlinear element, or nonlinear device, is an electrical element which does not have a linear relationship between current and voltage, e. g., a diode

In chaos theory, the butterfly effect is the sensitive dependence on initial conditions, where a small change at one place in a deterministic nonlinear system can result in large differences to a later state.

This condition provides a link between an experimentalist's and a theoretician's viewpoint on constitutive equations ( linear and nonlinear elastic / inelastic or coupled fields ) as well as a way of spatial and statistical averaging of the microstructure.

In using the Koopman approach of considering the action of the flow on an observable function, the finite-dimensional nonlinear problem involving Φ < sup > t </ sup > gets mapped into an infinite-dimensional linear problem involving U.

Skyrme's original example involved fields which take values on a three-dimensional sphere, the original nonlinear sigma model which describes the large distance behavior of pions.

Other applications rely on the peak pulse power ( rather than the energy in the pulse ), especially in order to obtain nonlinear optical effects.

For instance, laser microscopy focused on biological applications uses ultrashort pulse lasers, or femtosecond lasers, in a number of techniques labeled as nonlinear microscopy, saturation microscopy, and multiphoton fluorescence microscopy.

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

Other input / output RGB devices may also have nonlinear responses, depending on the technology employed.

BBC news http :// www. bbc. co. uk / news / science-environment-12811197 reported on a study that attempted to use mathematical modelling (' nonlinear dynamics ') to predict future religious orientations of populations.

Using a less strict definition of the electro-optic effect allowing also electric fields oscillating at optical frequencies, one could also include nonlinear absorption ( absorption depends on the light intensity ) to category a ) and the optical Kerr effect ( refractive index depends on the light intensity ) to category b ).

Depending on the type and orientation of the nonlinear crystal, and on the direction of the applied electric field, the phase delay can depend on the polarization direction.

The concept of intercept point is based on the assumption of a weakly nonlinear system, meaning that higher-order nonlinear terms are small enough to be negligible.

The ratio V / I for some point along the nonlinear curve is sometimes called the static, or chordal, or DC, resistance, but as seen in the figure the value of total V over total I varies depending on the particular point along the nonlinear curve which is chosen.

In a nonlinear medium, the permittivity can depend on the strength of the electric field.

In the most basic type of block cipher, a substitution-permutation network, analysis is concentrated primarily on the S-boxes, the only nonlinear part of the cipher ( i. e. the operation of an S-box cannot be encoded in a linear equation ).

The nonlinear interaction of the optical patterns of lines creates a real and visible pattern of roughly parallel dark and light bands, the moiré pattern, superimposed on the lines.

The term " nonlinear editing " or " non-linear editing " was formalized in 1991 with the publication of Michael Rubin's Nonlinear: A Guide to Digital Film and Video Editing ( Triad, 1991 ) -- which popularized this terminology over other language common at the time, including " real time " editing, " random-access " or " RA " editing, " virtual " editing, " electronic film " editing, and so on.

TNT HD is criticized for its practice of airing a significant amount of 4: 3 standard definition content stretched to 16: 9 through a nonlinear process similar to the " panorama " setting on many HDTVs that some viewers have nicknamed Stretch-o-Vision ; though other simulcasted HD cable channels have also fallen into this practice, TNT is usually cited since it was one of the first channels with an HD simulcast.

Based on this data, astronomers desired to determine the location of Ceres after it emerged from behind the sun without solving the complicated Kepler's nonlinear equations of planetary motion.