Differential algebraic equation: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
en>Marupio
See also: Partial differential algebraic equations
 
en>GabeIglesia
m Fixed bolding
Line 1: Line 1:
In fact, over half the male population over the age of 40 will suffer from some form of impotence at some stage. When impotence is present, many men are reluctant to try invasive treatments. Disorders that narrow arteries and decrease blood inflow on the blood vessels can cause erectile dysfunction. Go native - top native trees to add to your landscaping. The number of people who are waking up to the benefits of taking charge of their health procedures is increasing exponentially as the grounds for doing so become more known. <br><br>Here are some remedies for impotence you can try tonight. Tadalafil works by inhibiting the enzyme PDE-5, and helps to increase the blood supply to the penis. It increases libido and strengthens reproducing organs. Even better from his gherkin's point of view: certain nuts are genuine aphrodisiacs. To stay healthy, it is critical to get peaceful rest for not less than 8 hrs on a daily basis. <br><br>Men who are impotent from diabetes must seek treatment every month and each month, the attending doctor must draw a blood test called HBA1C, or another blood test called fructosamine. Therefore, if you are considering boosting your testosterone either by using a natural testosterone supplement or by visiting your doctor for testosterone injections or creams, you should look online to get a feel for what products are working for other men. This herbal supplement is also found to be as a best cure for treating low libido problems. Poor flow of nitric oxide into the reproductive organ also can be a crucial reason for it. By witnessing the success of the anti-impotence pill, many manufactures started to produce drug similar to the innovator anti-impotence which would be more appealing to the general public. <br><br>If you are not completely satisfied with the results, you don't pay a cent. Foods such as salmon (and other oily fish), that are packed with Omega 3, which increases blood flow around the body and to the genitals is great for fighting impotence. These dangerous workouts are also the causes of impotence. You may be pleasantly surprised at the result when you're not trying as hard. A number of different conditions may cause impotence, including: -. <br><br>Overdose can create problem also so be aware about taking its dosages. I rolled bangs to make them just look like Bettie bangs and then I just cut Bettie bangs and dyed hair bright red and also black in the color. But  offers an unusually concentrated source, with 7% to 10% of its fatty acids available in the form of GLA. People suffering from conditions such as impotence or for those looking to acquire medical gadgets or HIV home test kits need not leave the comfort of their seat. &ldquo;I do not mean to shock the good sense of my readers by saying that an electrical property can be imparted to medicines, but I do affirm, that I can prepare medicines in such a way that they will possess latent electrical properties which are at once rendered active by coming in contact with the gastric fluids of the stomach.<br><br>When you have almost any queries regarding exactly where and the way to employ [http://www.eiaculazione-precoce.info/ herbal supplements for erectile dysfunction], you can contact us on the web site.
[[File:Atomic Interferometry.ogv|thumb|300px|Atomic interferometry.]]
 
An '''Atom interferometer''' is an [[interferometer]] based on exploiting the [[Wave-particle duality|wave]] character of atoms. Interferometers are often used to make high-precision comparisons of distances.  This can be used to constrain fundamental constants like the [[Gravitational Constant]] or possibly to detect [[Gravitational Waves]].<ref>S. Dimopoulos, et al., [http://adsabs.harvard.edu/cgi-bin/bib_query?arXiv:0712.1250 "Gravitational wave detection with atom interferometry"] ''Physics Letters B'' '''678''', 1 (2008).</ref>
 
==Overview==
 
[[Interferometry]] inherently depends on the [[wave]] nature of the object. As pointed out by [[Louis, 7th duc de Broglie|de Broglie]] in his PhD-thesis, particles, including [[atom]]s, can behave like waves (the so-called [[Wave-particle duality]], according to the general framework of [[quantum mechanics]]). More and more high precision experiments now employ atom interferometers due to their short [[de Broglie wavelength]]. Some experiments are now even using [[molecule]]s to obtain even shorter de Broglie wavelengths and to search for the limits of quantum mechanics.<ref>K. Hornberger et al., Rev. Mod. Phys. '''84''', 157(2011).</ref> In many experiments with atoms, the roles of matter and light are reversed compared to the [[laser]] based interferometers, i.e. the beam splitter and mirrors are lasers while the source instead emits matter waves (the atoms).
 
==Interferometer types==
 
While the use of atoms offers easy access to higher frequencies (and thus accuracies) than [[light]], atoms are affected much more strongly by [[gravity]]. In some apparatuses, the atoms are ejected upwards and the interferometry takes place while the atoms are in flight, or while falling in free flight. In other experiments gravitational effects by free acceleration are not negated; additional forces are used to compensate for gravity. While these guided systems in principle can provide arbitrary amounts of measurement time, their [[quantum coherence]] is still under discussion. Recent theoretical studies indicate that coherence is indeed preserved in the guided systems, but this has yet to be experimentally confirmed.
 
The early atom interferometers deployed slits or wires for the beam splitters and mirrors. Later systems, especially the guided ones, used light forces for splitting and reflecting of
the matter wave.<ref>R. M. Rasel et al.,Phys. Rev. Lett. '''75''', 2633 (1995).</ref>
 
===Examples===
{| border=1
!Group
!Year
!Atomic Species
!Method
!Measured effect(s)
|-
!Pritchard
|1991
|[[Sodium|Na]], Na<sub>2</sub>
|Nano-fabricated [[Diffraction grating|gratings]]
|Polarizability, Index of Refraction
|-
!Clauser
|1994
|[[Potassium|K]]
|Talbot-Lau interferometer
|
|-
!Zeilinger
|1995
|[[Argon|Ar]]
|Standing light wave diffraction gratings
|
|-
!Sterr
|
|
|[[Ramsey interferometry#The Ramsey-Bordé Interferometer|Ramsey-Bordé]]
|Polarizability,<br/>[[Aharonov–Bohm effect]]: exp/theo <math>0.99 \pm 0.022</math>,<br/>Sagnac <math>0.3 rad / s \sqrt{Hz}</math>
|-
!Kasevich
|
|
|[[Doppler effect|Doppler]] on falling atoms
|[[Gravimeter]]: <math>3 \cdot 10^{-10}</math><br/>Rotation: <math>2\cdot 10^{-8} /s /\sqrt{Hz}</math>,<br/>[[fine structure constant]]: <math>\alpha\pm 1.5 \cdot 10^{-9}</math>
|-
!Berman
|
|
|Talbot-Lau
|
|}
 
==History==
The separation of matter wave packets from complete atoms was first observed by Esterman and Stern in 1930, when a Na beam was diffracted off a surface of NaCl.<ref>I. Estermann & [[Otto Stern]], ''Zeits. F. Physik'' '''61''', 95 (1930).</ref>  The first modern atom interferometer reported was a Young's-type [[double slit]] experiment with metastable helium atoms and a microfabricated double slit by Carnal and Mlynek<ref>O. Carnal & J. Mlynek, ''Phys. Rev. Lett.'' '''66''', 2689 (1991).</ref> in 1991, and an interferometer using three microfabricated diffraction gratings and Na atoms in the group around Pritchard at MIT.<ref>D.W. Keith, C.R. Ekstrom, Q.A. Turchette & D.E. Pritchard, ''Phys. Rev. Lett.'' '''66''', 2693 (1991).</ref> Shortly afterwards, an optical version of Ramsey spectrometer typically used in atomic clocks was recognized also as an atom interferometer at the [[Physikalisch-Technische Bundesanstalt|PTB]] in Braunschweig, Germany.<ref>F. Riehle, Th. Kisters, A. Witte, J. Helmcke & Ch. J. Bordé, ''Phys. Rev. Lett.'' '''67''', 177 (1991).</ref> The largest physical separation between the partial wave packets of atoms was achieved using laser cooling techniques and stimulated Raman transitions by S. Chu and coworkers in Stanford.<ref>M. Kasevich & S. Chu, ''Phys. Rev. Lett.'' '''67''', 181 (1991).</ref>
 
<!--See [[Wikipedia:Footnotes]] for an explanation of how to generate footnotes using the <references/)> tags-->
==See also==
*A. D. Cronin, J. Schmiedmayer, D. E. Pritchard, „Optics and interferometry with atoms and molecules“ Rev. Mod. Phys. '''81''', (2009).
*[[Electron interferometer]]
*C. S. Adams, M. Sigel & J. Mlynek, "Atom Optics", ''Phys. Rep.'' '''240''', 143 (1994). Overview of the atom-light interaction
*P. R. Berman [Editor], ''Atom Interferometry''. Academic Press (1997). Detailed overview of atom interferometers at that time (good introductions and theory).
*[http://www.physics.berkeley.edu/research/packard/Competition/Gyros/LaserRingGyro/Steadman/StedmanReview1997.pdf Stedman Review of the Sagnac Effect]
 
==See also==
*[[Ramsey interferometry]]
 
==References==
<references/>
 
{{DEFAULTSORT:Atom Interferometer}}
[[Category:Interferometers]]

Revision as of 05:14, 19 December 2013

File:Atomic Interferometry.ogv

An Atom interferometer is an interferometer based on exploiting the wave character of atoms. Interferometers are often used to make high-precision comparisons of distances. This can be used to constrain fundamental constants like the Gravitational Constant or possibly to detect Gravitational Waves.[1]

Overview

Interferometry inherently depends on the wave nature of the object. As pointed out by de Broglie in his PhD-thesis, particles, including atoms, can behave like waves (the so-called Wave-particle duality, according to the general framework of quantum mechanics). More and more high precision experiments now employ atom interferometers due to their short de Broglie wavelength. Some experiments are now even using molecules to obtain even shorter de Broglie wavelengths and to search for the limits of quantum mechanics.[2] In many experiments with atoms, the roles of matter and light are reversed compared to the laser based interferometers, i.e. the beam splitter and mirrors are lasers while the source instead emits matter waves (the atoms).

Interferometer types

While the use of atoms offers easy access to higher frequencies (and thus accuracies) than light, atoms are affected much more strongly by gravity. In some apparatuses, the atoms are ejected upwards and the interferometry takes place while the atoms are in flight, or while falling in free flight. In other experiments gravitational effects by free acceleration are not negated; additional forces are used to compensate for gravity. While these guided systems in principle can provide arbitrary amounts of measurement time, their quantum coherence is still under discussion. Recent theoretical studies indicate that coherence is indeed preserved in the guided systems, but this has yet to be experimentally confirmed.

The early atom interferometers deployed slits or wires for the beam splitters and mirrors. Later systems, especially the guided ones, used light forces for splitting and reflecting of the matter wave.[3]

Examples

Group Year Atomic Species Method Measured effect(s)
Pritchard 1991 Na, Na2 Nano-fabricated gratings Polarizability, Index of Refraction
Clauser 1994 K Talbot-Lau interferometer
Zeilinger 1995 Ar Standing light wave diffraction gratings
Sterr Ramsey-Bordé Polarizability,
Aharonov–Bohm effect: exp/theo 0.99±0.022,
Sagnac 0.3rad/sHz
Kasevich Doppler on falling atoms Gravimeter: 31010
Rotation: 2108/s/Hz,
fine structure constant: α±1.5109
Berman Talbot-Lau

History

The separation of matter wave packets from complete atoms was first observed by Esterman and Stern in 1930, when a Na beam was diffracted off a surface of NaCl.[4] The first modern atom interferometer reported was a Young's-type double slit experiment with metastable helium atoms and a microfabricated double slit by Carnal and Mlynek[5] in 1991, and an interferometer using three microfabricated diffraction gratings and Na atoms in the group around Pritchard at MIT.[6] Shortly afterwards, an optical version of Ramsey spectrometer typically used in atomic clocks was recognized also as an atom interferometer at the PTB in Braunschweig, Germany.[7] The largest physical separation between the partial wave packets of atoms was achieved using laser cooling techniques and stimulated Raman transitions by S. Chu and coworkers in Stanford.[8]

See also

  • A. D. Cronin, J. Schmiedmayer, D. E. Pritchard, „Optics and interferometry with atoms and molecules“ Rev. Mod. Phys. 81, (2009).
  • Electron interferometer
  • C. S. Adams, M. Sigel & J. Mlynek, "Atom Optics", Phys. Rep. 240, 143 (1994). Overview of the atom-light interaction
  • P. R. Berman [Editor], Atom Interferometry. Academic Press (1997). Detailed overview of atom interferometers at that time (good introductions and theory).
  • Stedman Review of the Sagnac Effect

See also

References

  1. S. Dimopoulos, et al., "Gravitational wave detection with atom interferometry" Physics Letters B 678, 1 (2008).
  2. K. Hornberger et al., Rev. Mod. Phys. 84, 157(2011).
  3. R. M. Rasel et al.,Phys. Rev. Lett. 75, 2633 (1995).
  4. I. Estermann & Otto Stern, Zeits. F. Physik 61, 95 (1930).
  5. O. Carnal & J. Mlynek, Phys. Rev. Lett. 66, 2689 (1991).
  6. D.W. Keith, C.R. Ekstrom, Q.A. Turchette & D.E. Pritchard, Phys. Rev. Lett. 66, 2693 (1991).
  7. F. Riehle, Th. Kisters, A. Witte, J. Helmcke & Ch. J. Bordé, Phys. Rev. Lett. 67, 177 (1991).
  8. M. Kasevich & S. Chu, Phys. Rev. Lett. 67, 181 (1991).