Interval arithmetic: Difference between revisions

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[[Image:CDF Top Event.jpg|thumb|right|240px|[[Top quark]] and anti top quark pair decaying into jets, visible as collimated collections of particle tracks, and other [[fermion]]s in the [[Collider Detector at Fermilab|CDF]] detector at [[Tevatron]].]]
It is very common to have a dental emergency -- a fractured tooth, an abscess, or severe pain when chewing. Over-the-counter pain medication is just masking the problem. Seeing an emergency dentist is critical to getting the source of the problem diagnosed and corrected as soon as possible.<br><br><br><br>Here are some common dental emergencies:<br>Toothache: The most common dental emergency. This generally means a badly decayed tooth. As the pain affects the tooth's nerve, treatment involves gently removing any debris lodged in the cavity being careful not to poke deep as this will cause severe pain if the nerve is touched. Next rinse vigorously with warm water. Then soak a small piece of cotton in oil of cloves and insert it in the cavity. This will give temporary relief until a dentist can be reached.<br><br>At times the pain may have a more obscure location such as decay under an old filling. As this can be only corrected by a dentist there are two things you can do to help the pain. Administer a pain pill (aspirin or some other analgesic) internally or dissolve a tablet in a half glass (4 oz) of warm water holding it in the mouth for several minutes before spitting it out. DO NOT PLACE A WHOLE TABLET OR ANY PART OF IT IN THE TOOTH OR AGAINST THE SOFT GUM TISSUE AS IT WILL RESULT IN A NASTY BURN.<br><br>Swollen Jaw: This may be caused by several conditions the most probable being an abscessed tooth. In any case the treatment should be to reduce pain and swelling. An ice pack held on the outside of the jaw, (ten minutes on and ten minutes off) will take care of both. If this does not control the pain, an analgesic tablet can be given every four hours.<br><br>Other Oral Injuries: Broken teeth, cut lips, bitten tongue or lips if severe means a trip to a dentist as soon as possible. In the mean time rinse the mouth with warm water and place cold compression the face opposite the injury. If there is a lot of bleeding, apply direct pressure to the bleeding area. If bleeding does not stop get patient to the emergency room of a hospital as stitches may be necessary.<br><br>Prolonged Bleeding Following Extraction: Place a gauze pad or better still a moistened tea bag over the socket and have the patient bite down gently on it for 30 to 45 minutes. The tannic acid in the tea seeps into the tissues and often helps stop the bleeding. If bleeding continues after two hours, call the dentist or take patient to the emergency room of the nearest hospital.<br><br>Broken Jaw: If you suspect the patient's jaw is broken, bring the upper and lower teeth together. Put a necktie, handkerchief or towel under the chin, tying it over the head to immobilize the jaw until you can get the patient to a dentist or the emergency room of a hospital.<br><br>Painful Erupting Tooth: In young children teething pain can come from a loose baby tooth or from an erupting permanent tooth. Some relief can be given by crushing a little ice and wrapping it in gauze or a clean piece of cloth and putting it directly on the tooth or gum tissue where it hurts. The numbing effect of the cold, along with an appropriate dose of aspirin, usually provides temporary relief.<br><br>In young adults, an erupting 3rd molar (Wisdom tooth), especially if it is impacted, can cause the jaw to swell and be quite painful. Often the gum around the tooth will show signs of infection. Temporary relief can be had by giving aspirin or some other painkiller and by dissolving an aspirin in half a glass of warm water and holding this solution in the mouth over the sore gum. AGAIN DO NOT PLACE A TABLET DIRECTLY OVER THE GUM OR CHEEK OR USE THE ASPIRIN SOLUTION ANY STRONGER THAN RECOMMENDED TO PREVENT BURNING THE TISSUE. The swelling of the jaw can be reduced by using an ice pack on the outside of the face at intervals of ten minutes on and ten minutes off.<br><br>When you loved this article and you would love to receive details with regards to [http://www.youtube.com/watch?v=90z1mmiwNS8 dentist DC] generously visit our web-page.
 
A '''jet''' is a narrow cone of [[hadrons]] and other particles produced by the [[hadronization]] of a [[quark]] or [[gluon]] in a [[particle physics]] or heavy [[ion]] experiment.  Because of [[Quantum chromodynamics| QCD]] [[colour confinement|confinement]], particles carrying a color charge, such as quarks, cannot exist in free form. Therefore they fragment into hadrons before they can be directly detected, becoming jets. These jets must be measured in a [[particle detector]] and studied in order to determine the properties of the original quark.
 
In relativistic heavy ion physics, jets are important because the originating hard scattering is a natural probe for the QCD matter created in the collision, and indicate its phase. When the QCD matter undergoes a phase crossover into [[quark gluon plasma]], the energy loss in the medium grows significantly, effectively quenching the outgoing jet.
 
Example of jet analysis techniques are:
 
* jet [[Event reconstruction|reconstruction]] (e.g., ''k''<sub>T</sub> algorithm, cone algorithm)
* jet correlation
* flavor tagging (e.g., [[b-tagging]]).
 
The [[Lund string model]] is an example of a jet fragmentation model.
 
==Jet production==
 
Jets are produced in QCD hard scattering processes, creating high transverse momentum quarks or gluons, or collectively called [[Parton (particle physics)|parton]]s in the partonic picture.
 
The probability of creating a certain set of jets is described by the jet production cross section, which is an average of elementary perturbative QCD quark, antiquark, and gluon processes, weighted by the parton distribution functions. For the most frequent jet pair production process, the two particle scattering, the jet production cross section in a hadronic collision is given by
 
<math>
\sigma_{ij \rightarrow k} = \sum_{i, j} \int d x_1 d x_2 d\hat{t} f_i^1(x_1, Q^2) f_j^2(x_2, Q^2) \frac{d\hat{\sigma}_{ij \rightarrow k}}{d\hat{t}},
</math>
 
with
 
* ''x'', ''Q''<sup>2</sup>: longitudinal momentum fraction and momentum transfer
* <math>\hat{\sigma}_{ij \rightarrow k}</math>: perturbative QCD cross section for the reaction ''ij''&nbsp;→&nbsp;''k''
* <math>f_i^a(x, Q^2)</math>: parton distribution function for finding particle species ''i'' in beam ''a''.
 
Elementary cross sections <math>\hat{\sigma}</math> are e.g. calculated to the leading order of perturbation theory in Peskin & Schroeder (1995), section 17.4. A review of various parameterizations of parton distribution functions and the calculation in the context of Monte Carlo event generators is discussed in T. Sjöstrand ''et al.'' (2003), section 7.4.1.
 
==Jet fragmentation==
 
Perturbative [[Quantum_chromodynamics|QCD]] calculations may have colored partons in the final state, but only the colorless hadrons they ultimately produce are observed experimentally. Thus, to describe what is observed in a detector as a result of a given process, all outgoing colored partons must first undergo parton showering and then combination of the produced partons into hadrons. The terms ''fragmentation'' and ''hadronization'' are often used interchangeably in the literature to describe soft [[Quantum_chromodynamics|QCD]] radiation, formation of hadrons, or both processes together.  
 
As the parton which was produced in a hard scatter exits the interaction, the strong coupling constant will increase with its separation.  This increases the probability for [[Quantum_chromodynamics|QCD]] radiation, which is predominantly shallow-angled with respect to the originating parton.  Thus, one parton will radiate gluons, which will in turn radiate {{SubatomicParticle|Quark}}{{SubatomicParticle|Antiquark}} pairs and so on, with each new parton nearly collinear with its parent.  This can be described by convolving the spinors with fragmentation functions <math>P_{ji}\!\left(\frac{x}{z}, Q^2\right)</math>, in a similar manner to the evolution of parton density functions. This is described by a Dokshitzer-Gribov-Lipatov-Altarelli-[[Giorgio Parisi|Parisi]] ([[DGLAP]]) type equation
 
<math>\frac{\partial}{\partial\ln Q^2} D_{i}^{h}(x, Q^2) = \sum_{j} \int_{x}^{1} \frac{dz}{z} \frac{\alpha_S}{4\pi} P_{ji}\!\left(\frac{x}{z}, Q^2\right) D_{j}^{h}(z, Q^2)</math>
 
Parton showering produces partons of successively lower energy, and must therefore exit the region of validity for perturbative [[Quantum_chromodynamics|QCD]]. Phenomenological models must then be applied to describe the length of time when showering occurs, and then the combination of colored partons into bound states of colorless hadrons, which is inherently not-perturbative.  One example is the [[Lund_string_model|Lund String Model]], which is implemented in many modern [[Event_generator|event generators]].
 
==References==
 
* [http://dx.doi.org/10.1016/0370-1573(83)90080-7 B. Andersson ''et al.'', "Parton Fragmentation and String Dynamics", ''Phys. Rep.'' '''97(2&ndash;3)''', 31&ndash;145 (1983).]
* [http://arxiv.org/abs/hep-ph/9305266 S. D. Ellis, D. E. Soper, "Successive Combination Jet Algorithm For Hadron Collisions", ''Phys. Rev.'' '''D48''', 3160&ndash;3166 (1993).]
* [http://arxiv.org/abs/nucl-th/0302077 M. Gyulassy ''et al.'', "Jet Quenching and Radiative Energy Loss in Dense Nuclear Matter", in R.C. Hwa & X.-N. Wang (eds.), ''Quark Gluon Plasma 3'' (World Scientific, Singapore, 2003).]
* J. E. Huth ''et al.'', in E. L. Berger (ed.), ''Proceedings of Research Directions For The Decade: Snowmass 1990'', (World Scientific, Singapore, 1992), 134. [http://lss.fnal.gov/archive/test-preprint/fermilab-conf-90-249-e.shtml (Preprint at Fermilab Library Server)]
* [http://physics.weber.edu/schroeder/qftbook.html M. E. Peskin, D. V. Schroeder, "An Introduction to Quantum Field Theory" (Westview, Boulder, CO, 1995)].
* [http://arxiv.org/abs/hep-ph/0308153 T. Sjöstrand ''et al.'', "Pythia 6.3 Physics and Manual", Report LU TP 03-38 (2003).]
* [http://www.arxiv.org/abs/hep-ph/0412013 G. Sterman, "QCD and Jets", Report YITP-SB-04-59 (2004).]
 
== See also ==
* [[Dijet event]]
 
==External links==
 
* [http://www.thep.lu.se/~torbjorn/Pythia.html The Pythia/Jetset Monte Carlo event generator]
 
[[Category:Experimental particle physics]]

Latest revision as of 18:43, 22 November 2014

It is very common to have a dental emergency -- a fractured tooth, an abscess, or severe pain when chewing. Over-the-counter pain medication is just masking the problem. Seeing an emergency dentist is critical to getting the source of the problem diagnosed and corrected as soon as possible.



Here are some common dental emergencies:
Toothache: The most common dental emergency. This generally means a badly decayed tooth. As the pain affects the tooth's nerve, treatment involves gently removing any debris lodged in the cavity being careful not to poke deep as this will cause severe pain if the nerve is touched. Next rinse vigorously with warm water. Then soak a small piece of cotton in oil of cloves and insert it in the cavity. This will give temporary relief until a dentist can be reached.

At times the pain may have a more obscure location such as decay under an old filling. As this can be only corrected by a dentist there are two things you can do to help the pain. Administer a pain pill (aspirin or some other analgesic) internally or dissolve a tablet in a half glass (4 oz) of warm water holding it in the mouth for several minutes before spitting it out. DO NOT PLACE A WHOLE TABLET OR ANY PART OF IT IN THE TOOTH OR AGAINST THE SOFT GUM TISSUE AS IT WILL RESULT IN A NASTY BURN.

Swollen Jaw: This may be caused by several conditions the most probable being an abscessed tooth. In any case the treatment should be to reduce pain and swelling. An ice pack held on the outside of the jaw, (ten minutes on and ten minutes off) will take care of both. If this does not control the pain, an analgesic tablet can be given every four hours.

Other Oral Injuries: Broken teeth, cut lips, bitten tongue or lips if severe means a trip to a dentist as soon as possible. In the mean time rinse the mouth with warm water and place cold compression the face opposite the injury. If there is a lot of bleeding, apply direct pressure to the bleeding area. If bleeding does not stop get patient to the emergency room of a hospital as stitches may be necessary.

Prolonged Bleeding Following Extraction: Place a gauze pad or better still a moistened tea bag over the socket and have the patient bite down gently on it for 30 to 45 minutes. The tannic acid in the tea seeps into the tissues and often helps stop the bleeding. If bleeding continues after two hours, call the dentist or take patient to the emergency room of the nearest hospital.

Broken Jaw: If you suspect the patient's jaw is broken, bring the upper and lower teeth together. Put a necktie, handkerchief or towel under the chin, tying it over the head to immobilize the jaw until you can get the patient to a dentist or the emergency room of a hospital.

Painful Erupting Tooth: In young children teething pain can come from a loose baby tooth or from an erupting permanent tooth. Some relief can be given by crushing a little ice and wrapping it in gauze or a clean piece of cloth and putting it directly on the tooth or gum tissue where it hurts. The numbing effect of the cold, along with an appropriate dose of aspirin, usually provides temporary relief.

In young adults, an erupting 3rd molar (Wisdom tooth), especially if it is impacted, can cause the jaw to swell and be quite painful. Often the gum around the tooth will show signs of infection. Temporary relief can be had by giving aspirin or some other painkiller and by dissolving an aspirin in half a glass of warm water and holding this solution in the mouth over the sore gum. AGAIN DO NOT PLACE A TABLET DIRECTLY OVER THE GUM OR CHEEK OR USE THE ASPIRIN SOLUTION ANY STRONGER THAN RECOMMENDED TO PREVENT BURNING THE TISSUE. The swelling of the jaw can be reduced by using an ice pack on the outside of the face at intervals of ten minutes on and ten minutes off.

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