User:Janopus/sandbox

= Sandbox Content= I use my sandbox to test Wikipedia format and text editing features and as a play ground and memory aide (some editing features are not so easy to find).

I also use it in the traditional sense for creating tentative Wikipedia pages.

whale
(I found on site and wondered what it would do) 

=Styled text and divs=

Below is not a table, but is styled text creating a shaded background. It is not clear when it is appropriate to use styled text in a wikipedia article.



What? What's going on?

I've screwed this Example:

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FRACTIONS
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Example: plainlist
one

two

three

etc. Manual_of_Style/Lists

1.6&thinsp;kg

Example
Link to cleanup page


 * See banner examples: Template_messages/Cleanup

Example 2 multiple image
Example template to display two images

Example 3 $whatever$
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Example 4 $something$
polysaccharides $whatever$

$What the heck?$

$What the heck?$

What the heck? what the heck? has the same effect but changes font to serif font

Example Primary source template:
This is a test.

Right to screw up
testing "Boxboxbottom"

colored fonts
Something to say!

=info boxes= Closest example I can find:

=now what=

=How to Make Tables=

This is a Table

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 * rowspan="2" ="middle" | [[Image:700 lab fix.JPG|100px]]
 * style="font-size: x-large; padding: 0; vertical-align: middle; height: 1.1em;" | Your Opinion is More Important than You Think '''
 * style="vertical-align: middle; border-top: 1px solid gray;" | Just Playing with fonts ¤
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One row One col table:
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 * style="font-size: 10pt; padding: 0; vertical-align: middle; height: 1.1em;" | Your Opinion is Less Important than You Think 
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This is a one row, one cell table
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=Notes to myself=

in-line references
https://en.wikipedia.org/wiki/Spin–spin_relaxation needs in-line references

citation templates
another note: https://en.wikipedia.org/wiki/Wikipedia:Citation_templates --->Citation_templates

another note:   ; example of see template

displaytitle
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=math examples How I did NOE article= A series of experiments are carried out with increasing mixing times, and the increase in NOE enhancement is followed. The closest protons will show the most rapid build-up rates of the NOE. While rf irradiation can only induce single-quantum transitions (due to so-called quantum mechanical selection rules) giving rise to observable spectral lines, dipolar relaxation may take place through any of the pathways. The dipolar mechanism is the only common relaxation mechanism that can cause transitions in which more than one spin flips. Specifically, the dipolar relaxation mechanism gives rise to transitions between the αα and ββ states (W2) and between the αβ and the βα states (W0).

Expressed in terms of their bulk NMR magnetizations, the experimentally observed steady-state NOE for nucleus I when the resonance of nucleus S is saturated ($$M_{S} = 0 $$) is defined by the expression:
 * $$\eta_{I}^{S} = \left(\frac{M_{I}^{S}-M_{0I}}{M_{0I}}\right)$$

where $$M_{0I}$$ is the magnetization (resonance intensity) of nucleus $$I$$ at thermal equilibrium. An analytical expression for the NOE can be obtained by considering all the relaxation pathways and applying the Solomon equations to obtain
 * $$\eta_{I}^{S}=\frac{M_{I}^{S}-M_{0I}}{M_{0I}} = \frac{\gamma_S }{\gamma_I }\frac{\sigma_{IS}}{\rho_{I}} = \frac{\gamma_S}{\gamma_I}\left(\frac{W_{2}-W_{0}}{2W_{1}^{I}+W_{0}+W_{2}}\right)$$

where
 * $$\rho_{I} = 2W_{1}^{I}+W_{0}+W_{2}$$ and $$\sigma_{IS} = W_{2} - W_{0}$$.

$$\rho_{I}$$ is the total longitudinal dipolar relaxation rate ($$1/T_{1}$$) of spin I due to the presence of spin s, $$\sigma_{IS}$$ is referred to as the cross-relaxation rate, and $$\gamma_{I}$$ and $$\gamma_{S}$$ are the magnetogyric ratios characteristic of the $$I$$ and $$S$$ nuclei, respectively.

Saturation of the degenerate W1S transitions disturbs the equilibrium populations so that Pαα = Pαβ and Pβα = Pββ. The system's relaxation pathways, however, remain active and act to re-establish an equilibrium, except that the W1S transitions are irrelevant because the population differences across these transitions are fixed by the RF irradiation while the population difference between the WI transitions does not change from their equilibrium values. This means that if only the single quantum transitions were active as relaxation pathways, saturating the $$S$$ resonance would not affect the intensity of the $$I$$ resonance. Therefore to observe an NOE on the resonance intensity of I, the contribution of $$W_{0}$$ and $$W_{2}$$ must be important. These pathways, known as cross-relaxation pathways, only make a significant contribution to the spin-lattice relaxation when the relaxation is dominated by dipole-dipole or scalar coupling interactions, but the scalar interaction is rarely important and is assumed to be negligible. In the homonuclear case where $$\gamma_{I} = \gamma_{S}$$, if $$W_{2}$$ is the dominant relaxation pathway, then saturating $$S$$ increases the intensity of the $$I$$ resonance and the NOE is positive, whereas if $$W_0$$ is the dominant relaxation pathway, saturating $$S$$ decreases the intensity of the $$I$$ resonance and the NOE is negative.

$$\rightarrow, \leftarrow$$

****

$\overline{vinculum}$

T

=Deuterium NMR=

Deuterium NMR is NMR spectroscopy of deuterium (2H or D), an isotope of hydrogen.

Deuterium is an isotope with spin = 1, unlike hydrogen which is spin = 1/2. Deuterium NMR has a range of chemical shift similar to proton NMR but with poor resolution. It may be used to verify the effectiveness of deuteration: a deuterated compound will show a peak in deuterium NMR but not proton NMR.

Deuterium NMR spectra are especially informative in the solid state because of its relatively small quadrupole moment in comparison with those of bigger quadrupolar nuclei such as chlorine-35, for example. One example is the use of deuterium NMR to study lipid membrane phase behavior.

old lede
In magnetic resonance imaging (MRI) and nuclear magnetic resonance spectroscopy (NMR), the term relaxation describes how signals change with time. In general signals deteriorate with time, becoming weaker and broader. The deterioration reflects the fact that the NMR signal, which results from nuclear magnetization, arises from the over-population of an excited state. Relaxation is the conversion of this non-equilibrium population to a normal population. In other words, relaxation describes how quickly spins "forget" the direction in which they are oriented. The rates of this spin relaxation can be measured in both spectroscopy and imaging applications.

The energy gap between the spin-up and spin-down states in NMR is really quite small by atomic emission standards — at 1.5T it is only about 2 x 10−7 eV (electron-volts). By comparison, visible light photons have energies of about 2 eV, or 10 million times higher. There is thus a considerable "advantage" for a high-energy light photon to be emitted by phosphorescence, but relatively little "motivation" for an already low energy nuclear spin to switch states spontaneously.

Most energy emission in NMR must be induced through a direct interaction of a nucleus with its external environment This interaction may be through the electrical or magnetic fields generated by other nuclei, electrons, or molecules

another lede alteration
In MRI and NMR spectroscopy, nuclear spin polarization (magnetization) forms inside a homogeneous magnetic field where the magnetic moments of the nuclei in the sample precess about the direction of the applied field at a characteristic frequency called the Larmor frequency. At thermal equilibrium, this polarization is not detectable because the phase of the spins is random and does not result in a net polarization orthogonal to the magnetic field. During an intense RF pulse, the spin polarization rotates with the magnetic component of the RF field. Following the pulse, any of the resultant transverse polarization that remains orthogonal to the field can induce a signal in an RF coil or detector, which can be observed when amplified by an RF receiver. The RF pulse causes the population of spin-states to be perturbed from their thermal equilibrium value. The return of the longitudinal component of the magnetization to its equilibrium value is termed spin-lattice relaxation while the loss of phase-coherence of the spins is termed spin-spin relaxation, which is manifest as an observed free induction decay (FID).

Altered Lede
In MRI and NMR spectroscopy, an observable nuclear spin polarization (magnetization) is created by an RF pulse or a train of pulses applied to a sample in a homogeneous magnetic field at the resonance (Larmor) frequency of the nuclei. At thermal equilibrium, nuclear spins precess randomly about the direction of the applied field but become abruptly phase coherent when any of the resultant polarization is created orthogonal to the field. This transverse magnetization can induce a signal in an RF coil that can be detected and amplified by an RF receiver. The RF pulses cause the population of spin-states to be perturbed from their thermal equilibrium value. The return of the longitudinal component of the magnetization to its equilibrium value is termed spin-lattice relaxation while the loss of phase-coherence of the spins is termed spin-spin relaxation, which is manifest as an observed free induction decay (FID).

For spin=½ nucleic (such as 1H), the polarization due to spins oriented with the field N- relative to the spins oriented against the field N+ is given by the Boltzmann distribution:
 * $$\frac{N_{+}}{N_{-}} = e^\frac{\Delta E}{kT}$$

where ΔE is the energy level difference between the two populations of spins, k is the Boltzmann constant, and T is the sample temperature. At room temperature, the number of spins in the lower energy level, N−, slightly outnumbers the number in the upper level, N+. The energy gap between the spin-up and spin-down states in NMR is minute by atomic emission standards at magnetic fields conventionally used in MRI and NMR spectroscopy. Energy emission in NMR must be induced through a direct interaction of a nucleus with its external environment rather than by spontaneous emission. This interaction may be through the electrical or magnetic fields generated by other nuclei, electrons, or molecules. Spontaneous emission of energy is a radiative process involving the release of a photon and typified by phenomena such as fluorescence and phosphorescence. As stated by Abragam, the probability per unit time of the nuclear spin-1/2 transition from the + into the - state through spontaneous emission of a photon is a negligible phenomenon. Rather, the return to equilibrium is a much slower thermal process induced by the fluctuating local magnetic fields due to molecular or electron (free radical) rotational motions that return the excess energy in the form of heat to the surroundings.

Rather, relaxation of nuclear spins requires a microscopic mechanism for a nucleus to change orientation with respect to the applied magnetic field and/or interchange energy with the surroundings (the "lattice"). The return to thermal equilibrium is a much slower thermal process than spontaneous emission that is induced by the fluctuating local magnetic fields due to molecular or electron (e.g., free radicals or paramagnetic ions) rotational motions that return the excess energy in the form of heat to the surroundings. Molecular tumbling can then modulate various orientation-dependent spin-interactions called "relaxation mechanisms".

old mechanism text: blue font example
Relaxation of nuclear spins requires a microscopic mechanism for a nucleus to change orientation with respect to the applied magnetic field and/or interchange energy with the surroundings (called the lattice). The most common mechanism is the magnetic dipole-dipole interaction between the magnetic moment of a nucleus and the magnetic moment of another nucleus or other entity (electron, atom, ion, molecule). This interaction depends on the distance between the pair of dipoles (spins) but also on their orientation relative to the external magnetic field. Several other relaxation mechanisms also exist. The chemical shift anisotropy (CSA) relaxation mechanism arises whenever the electronic environment around the nucleus is non spherical, the magnitude of the electronic shielding of the nucleus will then be dependent on the molecular orientation relative to the (fixed) external magnetic field. The spin rotation (SR) relaxation mechanism arises from an interaction between the nuclear spin and a coupling to the overall molecular rotational angular momentum. Nuclei with spin I ≥ 1 will have not only a nuclear dipole but a quadrupole. The nuclear quadrupole has an interaction with the electric field gradient at the nucleus which is again orientation dependent as with the other mechanisms described above, leading to the so-called quadrupolar relaxation mechanism. Molecular reorientation or tumbling can then modulate these orientation-dependent spin interaction energies. According to quantum mechanics, time-dependent interaction energies cause transitions between the nuclear spin states which result in nuclear spin relaxation. The application of time-dependent perturbation theory in quantum mechanics shows that the relaxation rates (and times) depend on spectral density functions that are the Fourier transforms of the autocorrelation function of the fluctuating magnetic dipole interactions. The form of the spectral density functions depend on the physical system, but a simple approximation called the BPP theory is widely used. Another relaxation mechanism is the electrostatic interaction between a nucleus with an electric quadrupole moment and the electric field gradient that exists at the nuclear site due to surrounding charges. Thermal motion of a nucleus can result in fluctuating electrostatic interaction energies. These fluctuations produce transitions between the nuclear spin states in a similar manner to the magnetic dipole-dipole interaction.

new mechanism text
Relaxation of nuclear spin polarization requires a microscopic mechanism for nuclei to interchange energy with their surroundings. In principle, any fluctuating magnetic field that has frequency components at the Larmor or resonance frequency of the polarized spins can induce spin transitions that will return the system to thermal equilibrium. Such fluctuating fields are provided by the weak magnetic fields induced by the tumbling or translational motions of other nearby dipolar nuclei, paramagnetic ions, or free radicals.

Relaxation Mechanisms

 * {| class="wikitable"

! Mechanism !! bloc !! Correlation Time !! Comments
 * + Nucelar Spin Relaxation Mechanisms
 * Dipole-Dipole, nuclear-nuclear     || R1C2      || reorientation/translational    || r1c4
 * Dipole-Dipole, electron-nuclear     || R1C2      || reorientation/translational    || r1c4
 * Spin Rotation     || R2C2      || angular momentum     || e1c4
 * Chemical Shift Anisotropy     || R2C2      || reorientation    || e1c4
 * Scalar Coupling    || R2C2      || R2C3     || e1c4
 * Quadrupolar     || R2C2      || reorientation    || e1c4
 * }
 * Chemical Shift Anisotropy     || R2C2      || reorientation    || e1c4
 * Scalar Coupling    || R2C2      || R2C3     || e1c4
 * Quadrupolar     || R2C2      || reorientation    || e1c4
 * }
 * Quadrupolar     || R2C2      || reorientation    || e1c4
 * }

Spin rotation
Relaxation of nuclear spins requires a microscopic mechanism for a nucleus to change orientation with respect to the applied magnetic field and/or interchange energy with the surroundings (called the lattice). Molecular reorientation or tumbling can then modulate these orientation-dependent spin interaction energies. The most commonly encountered mechanism is the magnetic dipole-dipole interaction between the magnetic moment of a nucleus and the magnetic moment of another nucleus or other entity (electron, atom, ion, molecule). This interaction depends on the distance between the pair of dipoles (spins) but also on their orientation relative to the external magnetic field. Several other relaxation mechanisms also exist. The chemical shift anisotropy (CSA) relaxation mechanism arises whenever the electronic environment around the nucleus is non spherical, the magnitude of the electronic shielding of the nucleus will then be dependent on the molecular orientation relative to the (fixed) external magnetic field. The spin rotation (SR) relaxation mechanism arises from an interaction between the nuclear spin and a coupling to the overall molecular rotational angular momentum. Nuclei with spin I ≥ 1 will have not only a nuclear dipole but a quadrupole. The nuclear quadrupole has an interaction with the electric field gradient at the nucleus which is again orientation dependent as with the other mechanisms described above, leading to the so-called quadrupolar relaxation mechanism.

Molecular reorientation or tumbling can then modulate these orientation-dependent spin interaction energies. According to quantum mechanics, time-dependent interaction energies cause transitions between the nuclear spin states which result in nuclear spin relaxation. The application of time-dependent perturbation theory in quantum mechanics shows that the relaxation rates (and times) depend on spectral density functions that are the Fourier transforms of the autocorrelation function of the fluctuating magnetic dipole interactions. The form of the spectral density functions depend on the physical system, but a simple approximation called the BPP theory is widely used.

Another relaxation mechanism is the electrostatic interaction between a nucleus with an electric quadrupole moment and the electric field gradient that exists at the nuclear site due to surrounding charges. Thermal motion of a nucleus can result in fluctuating electrostatic interaction energies. These fluctuations produce transitions between the nuclear spin states in a similar manner to the magnetic dipole-dipole interaction.

=Ends and Odds=

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NOE Ref
Kulhman et al.

=how to make a quote box=

=A couple of wiki tests=

Where the Fireworks Are