It was possible, however, to decompose the compliance into a sum of a frequency-independent component and two viscoelastic mechanisms, each compatible with the Boltzmann superposition principle and with a consistent set of time-temperature equivalence factors.

Diffraction arises because of the way in which waves propagate ; this is described by the Huygens – Fresnel principle and the principle of superposition of waves.

The analysis of linear systems is possible because they satisfy a superposition principle: if u ( t ) and w ( t ) satisfy the differential equation for the vector field ( but not necessarily the initial condition ), then so will u ( t ) + w ( t ).

The solution to this system can be found by using the superposition principle ( linearity ).

Multiplying the impulse response shifted in time according to the arrival of each of these delta functions by the amplitude of each delta function, and summing these responses together ( according to the superposition principle, applicable to all linear systems ) yields the output waveform.

The law of summation is in accord with the principle of superposition --- every diagram contributes a factor to the total amplitude for the process.

Nicolas Steno ( 1638 – 1686 ) is credited with the law of superposition, the principle of original horizontality, and the principle of lateral continuity: three defining principles of stratigraphy.

The principle of superposition states that a sedimentary rock layer in a tectonically undisturbed sequence is younger than the one beneath it and older than the one above it.

Because deeper rock is often older, as noted by the principle of superposition, this can result in older rocks moving on top of younger ones.

By the superposition principle, the wavepacket at any time t is:

Using Huygens ' theory and the principle of superposition of waves, the complex amplitude at a further point P is found by summing the contributions from each point on the sphere of radius r < sub > 0 </ sub >.

In nonlinear optics, the superposition principle no longer holds.

This was derived empirically by Fresnel in 1815, based on Huygen's hypothesis that each point on a wavefront generates a secondary spherical wavefront, which Fresnel combined with the principle of superposition of waves.

In the absence of nonlinear effects, the superposition principle can be used to predict the shape of interacting waveforms through the simple addition of the disturbances.

To further illustrate, Schrödinger describes how one could, in principle, transpose the superposition of an atom to large-scale systems.

In particular, many media are linear, or nearly so, so the calculation of arbitrary wave behavior can be found by adding up responses to individual sinusoidal waves using the superposition principle to find the solution for a general waveform.

This equation is linear, as the sum of any two solutions is again a solution: in physics this property is called the superposition principle.

The basic wave equation is a linear differential equation and so it will adhere to the superposition principle.

This property, called the principle of superposition, is very useful, e. g., solutions to complex problems can be constructed by summing simple solutions.

Fermat's principle is the main principle of quantum electrodynamics where it states that any particle ( e. g. a photon or an electron ) propagates over all available ( unobstructed ) paths and the interference ( sum, or superposition ) of its wavefunction over all those paths ( at the point of observer or detector ) gives the correct probability of detection of this particle ( at this point ).

The behavior of nonlinear systems is not subject to the principle of superposition while that of linear systems is subject to superposition.

At the speed of sound the way that lift is generated changes dramatically, from being dominated by Bernoulli's principle to forces generated by shock waves.

File: Christiaan Huygens-painting. jpeg | Christiaan Huygens ( 1629-1695 ): studied the rings of Saturn and discovered its moon Titan, invented the pendulum clock, studied optics and centrifugal force, theorized that light consists of waves ( Huygens – Fresnel principle ) which became instrumental in the understanding of wave-particle duality.

In the classic mechanics of waves, Fermat's principle follows from the extremum principle of mechanics ( see variational principle ).

The core principle of spread spectrum is the use of noise-like carrier waves, and, as the name implies, bandwidths much wider than that required for simple point-to-point communication at the same data rate.

The total voltage on the transmission line is given by the superposition principle, which is just a matter of adding the two waves:

Huygens achieved note for his argument that light consists of waves, now known as the Huygens – Fresnel principle, which two centuries later became instrumental in the understanding of wave-particle duality.

The law follows from Fermat's principle of least time, which in turn follows from the propagation of light as waves.

This technique works by superposing ( interfering ) the signal waves from the different telescopes on the principle that waves that coincide with the same phase will add to each other while two waves that have opposite phases will cancel each other out.

In the second part of his 1924 thesis, de Broglie used the equivalence of the mechanical principle of least action with Fermat's optical principle: " Fermat's principle applied to phase waves is identical to Maupertuis ' principle applied to the moving body ; the possible dynamic trajectories of the moving body are identical to the possible rays of the wave.

In 1961 the first important legislative victory of the Kennedy Administration came when the principle of national responsibility for local economic distress won out over a `` state's-responsibility '' proposal -- provision was made for payment for unemployment relief by nation-wide taxation rather than by a levy only on those states afflicted with manpower surplus.

For better or for worse, we all now live in welfare states, the organizing principle of which is collective responsibility for individual well-being.

The greatest impact of the matching-fund principle has been in initially encouraging the poorest states and school districts to spend enough to obtain their full allocation of outside funds.

To prevent this unphysical situation from happening, Dirac proposed that a " sea " of negative-energy electrons fills the universe, already occupying all of the lower-energy states so that, due to the Pauli exclusion principle, no other electron could fall into them.

The most important of these was the principle that came to be called Ampère ’ s law, which states that the mutual action of two lengths of current-carrying wire is proportional to their lengths and to the intensities of their currents.

This provision has been dormant since Queen Victoria ascended the throne, because she did not inherit Hanover under the Salic Laws of the German states, but in principle it could again become relevant in the future.

The strong anthropic principle ( SAP ) as explained by Barrow and Tipler ( see variants ) states that this is all the case because the Universe is compelled, in some sense, for conscious life to eventually emerge.

Critics of the SAP argue in favor of a weak anthropic principle ( WAP ) similar to the one defined by Brandon Carter, which states that the universe's ostensible fine tuning is the result of selection bias: i. e., only in a universe capable of eventually supporting life will there be living beings capable of observing any such fine tuning, while a universe less compatible with life will go unbeheld.

The anthropic principle states that this is a necessity, because if life were impossible, no one would know it.

The cosmological principle states that on large scales the Universe is homogeneous and isotropic.

If the large-scale Universe appears isotropic as viewed from Earth, the cosmological principle can be derived from the simpler Copernican principle, which states that there is no preferred ( or special ) observer or vantage point.

According to some versions of functionalism, even non-human systems, such as other animal species, alien life forms, or advanced computers can, in principle, have mental states.

Fred Dretske has objected to the transitivity principle on the basis that we often experience mental states that are consciously different without being aware of the conscious different.

In physical cosmology, the Copernican principle, named after Nicolaus Copernicus, states that the Earth is not in a central, specially favored position.

An underlying principle in Taoism states that within every independent entity lies a part of its opposite.

The Huygens – Fresnel principle is one such model ; it states that each point on a wavefront generates a secondary spherical wavelet, and that the disturbance at any subsequent point can be found by summing the contributions of the individual wavelets at that point.

The guiding principle for the qualification of Dublin Core elements, colloquially known as the Dumb-Down Principle, states that an application that does not understand a specific element refinement term should be able to ignore the qualifier and treat the metadata value as if it were an unqualified ( broader ) element.

The report to the European Parliament of 2001 states: " If UKUSA states operate listening stations in the relevant regions of the earth, in principle they can intercept all telephone, fax and data traffic transmitted via such satellites.

This argument is embodied in the Copernican principle, which states that the Earth does not occupy a unique position in the Universe, and the mediocrity principle, which holds that there is nothing special about life on Earth.

The competitive exclusion principle states that two species cannot coexist indefinitely by living off the same limiting resource ; one will always outcompete the other.

The first principle of skilled memory, the meaningful encoding principle, states that experts exploit prior knowledge to durably encode information needed to perform a familiar task successfully.