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Stokes fluorescence is the re-emission of longer wavelength photons ( lower frequency or energy ) by a molecule that has absorbed photons of shorter wavelengths ( higher frequency or energy ).
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Stokes and fluorescence
One of the first to explain it was the Irish scientist Sir George Stokes from the University of Cambridge, who named the phenomenon " fluorescence " after fluorite, a mineral many of whose samples fluoresce strongly due to impurities.
* Stokes shift, in fluorescence
Stokes shift is the difference ( in wavelength or frequency units ) between positions of the band maxima of the absorption and emission spectra ( fluorescence and Raman being two examples ) of the same electronic transition.
However, it should be noted that in molecules which exhibit fluorescence, the Stokes lines may be obscured while the anti-Stokes lines remain unaffected.
In the context of optics, a Stokes line refers to the radiation of particular wavelengths present in the line spectra associated with fluorescence and the Raman scattering.
Stokes lines are of longer wavelength than that of the exciting radiation responsible for the fluorescence or Raman effect.
Stokes and is
George Stokes had shown that the mobility for a spherical particle with radius is, where is the dynamic viscosity of the fluid.
The corresponding form of the fundamental theorem of calculus is Stokes ' theorem, which relates the surface integral of the curl of a vector field to the line integral of the vector field around the boundary curve.
Stokes flow is flow at very low Reynolds numbers, Re << 1, such that inertial forces can be neglected compared to viscous forces.
This phenomenon, known as Stokes shift, is due to energy loss between the time a photon is absorbed and when it is emitted.
in light of the Jordan curve theorem and the generalized Stokes ' theorem, F < sub > γ </ sub >( z ) is independent of the particular choice of path γ, and thus F ( z ) is a well-defined function on U having F ( z < sub > 0 </ sub >)
Shown is a sphere in Stokes flow, at very low Reynolds number.
When the Reynolds number is much less than 1, Creeping motion or Stokes flow occurs.
* 1967 – Carl B. Stokes is elected as Mayor of Cleveland, Ohio, becoming the first African American mayor of a major American city.
In differential geometry, Stokes ' theorem ( also called the generalized Stokes ' theorem ) is a statement about the integration of differential forms on manifolds, which both simplifies and generalizes several theorems from vector calculus.
Stokes ' theorem says that the integral of a differential form ω over the boundary of some orientable manifold Ω is equal to the integral of its exterior derivative dω over the whole of Ω, i. e.
This modern form of Stokes ' theorem is a vast generalization of a classical result first discovered by Lord Kelvin, who communicated it to George Stokes in July 1850.
Stokes ' theorem is a vast generalization of this theorem in the following sense.
** Carl B. Stokes is elected mayor of Cleveland, Ohio, becoming the first African American mayor of a major United States city.
The integrability condition and Stokes ' theorem implies that the value of the line integral connecting two points is independent of the path.
An alternative and mathematically convenient description is given by the Stokes parameters, introduced by George Gabriel Stokes in 1852.
The relationship of the Stokes parameters to intensity and polarization ellipse parameters is shown in the equations and figure below.
In terms of the Stokes parameters, the total intensity is reduced while vectors in the Poincaré sphere are " dragged " towards the direction of the favored mode.
Mathematically, under the treatment of the Stokes parameters as a Minkowski 4-vector, the transformation is a scaled Lorentz boost ( due to the isomorphism of SL ( 2, C ) and the restricted Lorentz group, SO ( 3, 1 )).
Stokes and re-emission
After absorption and re-emission of the energy, many wavelengths may emerge due to Stokes shift and various electron transitions.
Stokes and longer
Other Stokes lines ( at wavelengths longer than the incident line ) are observed for transitions 1 → 3, 2 → 4, 3 → 5, etc.
Stokes Valley was located at the junction of the claimed territory of three major Maori tribes, the Ngāti Awa ( who sold it to European settlers, but are no longer present at Wellington ), Ngāti Toa, and the Ngāti Kahungunu, and for this reason it would have in all likelihood never have been inhabited.
Stokes and wavelength
In his 1852 paper on the " Refrangibility " ( wavelength change ) of light, George Gabriel Stokes described the ability of fluorspar and uranium glass to change invisible light beyond the violet end of the visible spectrum into blue light.
Stokes, however, in a letter published some years after the delivery of this address, stated that he had failed to take one essential step in the argument — not perceiving that emission of light of definite wavelength not merely permitted, but necessitated, absorption of light of the same wavelength.
Stokes and photons
The different possibilities of visual light scattering: Rayleigh scattering ( no exchange of energy so the incident and emitted photons have the same energy ), Stokes scattering ( the atom or molecule absorbs energy and the emitted photon has less energy than the absorbed photon ) and anti-Stokes scattering ( the atom or molecule loses energy and the emitted photon has more energy than the absorbed photon )
Stokes and lower
George Gabriel Stokes became a champion of the entrainment interpretation, developing a model in which the aether might be ( by analogy with pine pitch ) rigid at very high frequencies and fluid at lower speeds.
Stokes and frequency
This shift in frequency is designated as a Stokes shift.
CARS is a third-order nonlinear optical process involving three laser beams: a pump beam of frequency ω < sub > p </ sub >, a Stokes beam of frequency ω < sub > S </ sub > and a probe beam at frequency ω < sub > pr </ sub >.
The latter is resonantly enhanced when the frequency difference between the pump and the Stokes beams ( ω < sub > p </ sub >- ω < sub > S </ sub >) coincides with the frequency of a Raman resonance, which is the basis of the technique's intrinsic vibrational contrast mechanism.
In CARS, this oscillator is not driven by a single optical wave, but by the difference frequency ( ω < sub > p </ sub >- ω < sub > S </ sub >) between the pump and the Stokes beams instead.
Stokes and energy
The derivation of the Navier – Stokes equations begins with an application of Newton's second law: conservation of momentum ( often alongside mass and energy conservation ) being written for an arbitrary portion of the fluid.
A general circulation model ( GCM ) is a mathematical model of the general circulation of a planetary atmosphere or ocean and based on the Navier – Stokes equations on a rotating sphere with thermodynamic terms for various energy sources ( radiation, latent heat ).
The Stokes Institute, originally founded by Cambridge graduate Prof. Mark Davies to work on thermofluids problems, is now a large mechanical engineering research group working not only in fluid mechanics, but also in areas such as reliability physics, microfluidic cancer diognostics and energy management.
The equations represent conservation of mass ( continuity ), momentum, and energy, corresponding to the Navier – Stokes equations with zero viscosity and heat conduction terms.
The scattering is inelastic: the photon may lose energy to create a quasiparticle ( Stokes process ) or gain energy by destroying one ( anti-Stokes process ).
The Stokes and anti-Stokes spectra form a symmetric pattern above and below the absorbed photon energy.
However, experimentally it was shown that if the energy of magnon ħω is comparable or smaller than the thermal energy, the Stokes line becomes more intensive as it is followed from the Bose-Einstein statistics.
When the emitted photon has less energy than the absorbed photon, this energy difference is the Stokes shift.
Since the Stokes lines and anti-Stokes lines gain and lose the same amount of energy, they are symmetric with respect to the peak due to elastic ( Rayleigh ) scattering ().
A red shift can be observed when part of the energy of the photon is transferred to the interacting matter, where it adds to its internal energy in a process called Stokes scattering.
The energy of the scattered radiation is less than the incident radiation for the Stokes line and the energy of the scattered radiation is more than the incident radiation for the anti-Stokes line.
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