drift velocity and super conduction

Page 2 - Seeking answers? Join the AnandTech community: where nearly half-a-million members share solutions and discuss the latest tech.

johanfprins

Junior Member
Aug 6, 2010
10
0
0
I am not going to comment on the extracts posted by William Gaatjies in detail since the interpretation of the results of what he has quoted, by the researchers who measured these results, is naive. Yes there are two gaps involved in the ceramic superconductors, and yes when you inject a large number of charge carriers the energy through the superconductor can be approximated by sort of "wave" of charge-carriers. But it is also transported when a SINGLE charge is injected. How can a single charge-carrier cause ALL the charge carriers within the superconductor to suddenly move as a "wave"?

There is a single, simple mechanism that models superconduction in both the low temperature metals and the ceramics. I have been blocked from publishing this model since it proves without a doubt that the charge-carriers are NOT PAIRS but fermions. I already wrote a book about it 5 years ago, but it seems that the elementary physics in that book is just too advanced for modern-day physicists to understand. This model predicts that the ceramic materials have a ceiling for the critical temperature at about 250 K: Exactly where these materials became stuck twenty years ago.

I have now written a second book aimed at people who have not been lobotomized by studying physics at a university.
 

TecHNooB

Diamond Member
Sep 10, 2005
7,460
1
76
I am not going to comment on the extracts posted by William Gaatjies in detail since the interpretation of the results of what he has quoted, by the researchers who measured these results, is naive. Yes there are two gaps involved in the ceramic superconductors, and yes when you inject a large number of charge carriers the energy through the superconductor can be approximated by sort of "wave" of charge-carriers. But it is also transported when a SINGLE charge is injected. How can a single charge-carrier cause ALL the charge carriers within the superconductor to suddenly move as a "wave"?

There is a single, simple mechanism that models superconduction in both the low temperature metals and the ceramics. I have been blocked from publishing this model since it proves without a doubt that the charge-carriers are NOT PAIRS but fermions. I already wrote a book about it 5 years ago, but it seems that the elementary physics in that book is just too advanced for modern-day physicists to understand. This model predicts that the ceramic materials have a ceiling for the critical temperature at about 250 K: Exactly where these materials became stuck twenty years ago.

I have now written a second book aimed at people who have not been lobotomized by studying physics at a university.

what is it about your theory other physicists don't believe? you should be able to narrow it down and deliver a succinct answer so that noobs like me can ponder over it. :)
 

johanfprins

Junior Member
Aug 6, 2010
10
0
0
what is it about your theory other physicists don't believe? you should be able to narrow it down and deliver a succinct answer so that noobs like me can ponder over it. :)

The first thing that they do not want to believe is that the charge-carriers are not electron-pairs but are singly-charged. The next thing they do not want to believe is that these charge-carriers are stationary (anchored) when there is no current flowing: i.e. That such a phase must be an insulator. The fact is that if it were not an insulator, an applied electric-field will not be cancelled at the positions of the charge-carriers, and it will be impossible to measure a zero voltage as is measured for all superconductors.

This means that when injecting charge-carriers into such a phase, the resultant current must be transported by these anchored charge-carriers (localized orbitals) and it must happen without them being accelerated; since if they are accelerated then one must measure a voltage. This means that a charge-carrier must obtain energy in another manner than from acceleration to move on. It sounds impossible BUT:

The latter is possible owing to Heisenberg's relationship of energy and time NOTE THIS IS NOT AN UNCERTAINTY RELATIONSHIP AS CLAIMED IN TEXT BOOKS; What it actually does is to allow an electron-wave (or orbital) to borrow energy (delta)E as long as it is not done for a time limit longer than (delta)t. In other words, it allows such an anchored orbital to obtain enough energy TO BREAK FREE AND MOVE ON TO FIND ANOTHER ANCHOR POSITION.

Thus when injecting a charge-carrier it reaches the first orbital at the contact: This orbital is displaced by the incoming charge carrier since the latter orbital can borrow the required energy to move on to the next adjacent orbital and replace this orbital, which then borrows energy to move on and so forth. Since acceleration is not required one cannot measure a voltage: And since the required energy is borrowed and returned every time, there is no remaining energy which requires dissipation.

All superconductors can be modeled by this mechanism as well as those aspects known about them that cannot be modeled by the traditional models like the Ginzberg-Landau model or the BCS model, or whatever. These theoreticians should have listened to the late Bernd Matthias when he warned that the their models cannot be correct because they are not predictive. As Pauli would have commented: They are not even wrong!

To summarize: Since the charge-carriers are not accelerated, a voltage is not required to drive them along; and since the energy is borrowed and returned as allowed by quantum mechanics, there is no residual energy which needs to be dissipated by scattering. That is why a circular current can run in perpetuity. As the second law of thermodynamics mandates, such perpetual motion is only possible when the "engine" performing it obtains energy to do work and after having done the work it returns ALL the energy back to the source.

If I lost you, please return with more questions.
 
May 11, 2008
19,787
1,220
126
Can you comment on this research mr Prins ?

Sometimes i play advocate of the devil according to an old strategic saying: "Know your adversary " ^_^

I do not know much about it as i would like to know, as such i just relay what i read. It seems other researchers have claimed to found evidence for cooper pairs. However, they have come up with another explanation. What is your idea on what is happening when a superconductor comes in contact with a ferromagnetic material ?

http://www.sciencedaily.com/releases/2010/12/101201100013.htm

http://prb.aps.org/abstract/PRB/v82/i6/e060505

Unfortunately, the pdf is not for free. I also do not have a subscription for it.
According to the article, they found a loophole :

If it were possible to eliminate electrical resistance we could reduce our electric bill significantly and make a significant contribution to solving the energy problem, if it were not for a few other problems. Many metals as well as oxides demonstrate a superconductive state, however only at low temperatures. The superconductive effect results from Cooper pairs that migrate through the metal together "without resistance." The electrons in each Cooper pair are arranged so that their composite angular momentum is zero. Each electron has an angular momentum, the so-called spin, with a value of 1/2. When one electron spins counterclockwise (-1/2) and the other clockwise (+1/2), the total of the two spin values is zero. This effect, found only in superconductors, is called the singlet state.

If a superconductor is brought into contact with a ferromagnetic material, the Cooper pairs are broken up along the shortest path and the superconductor becomes a normal conductor. Cooper pairs cannot continue to exist in a singlet state in a ferromagnetic material. Researches at RUB (Prof. Konstantin Efetov, Solid State Physics) among others have, however, theoretically predicted a new type of Cooper pair, which has a better chance of survival in ferromagnetic materials. In such Cooper pairs the electrons spin in parallel with one another so that they have a finite spin with a value of 1. Since this angular momentum can have three orientations in space, it is also known as the triplet state. "Obviously there can also be only one certain, small fraction of Cooper pairs in a triplet state, which then quickly revert to the singlet state" explained Prof. Kurt Westerholt. "The challenge was to verify these triplet Cooper pairs experimentally."


Superconductors allow us to produce highly sensitive detectors for magnetic fields, which even allow detection of magnetic fields resulting from brain waves. These detectors are called SQUID's (superconducting quantum interference devices) -- components which use the superconductive quantum properties. The central feature in these components consists of so-called tunnel barriers with a series of layers made up of a superconductor, insulator and another superconductor. Quantum mechanics allows a Cooper pair to be "tunneled" through a very thin insulating layer. Tunneling of a large number of Cooper pairs results in a tunnel current. "Naturally the barrier cannot be too thick, otherwise the tunnel current subsides. A thickness of one to two nanometers is ideal," according to Prof. Hermann Kohlstedt (CAU).

If part of the tunnel barrier is replaced by a ferromagnetic layer, the Cooper pairs are broken up while they are still in the barrier and do not reach the superconductor on the other side. The tunnel current decreases drastically. "Triplet Cooper pairs can, however, be tunneled much better through such a ferromagnetic barrier," says Dirk Sprungmann, who was involved as Ph.D. student. If we are successful in converting a portion of the singlet Cooper pairs to triplet Cooper pairs, the tunnel current should be significantly stronger and be able to pass through a thicker ferromagnetic layer. This is precisely what the physicists in Bochum and Kiel tested. They allowed the Cooper pairs to pass through ferromagnetic barriers with thicknesses of up to 10 nanometers. With this attempt the physicists achieved a double success. On the one hand they were able to experimentally verify the existence of triplet Cooper pairs, and, on the other, they demonstrated that the tunnel current is greater than for singlet Cooper pairs in conventional tunnel contacts. "These new ferromagnetic tunnel barriers may possibly be used for new types of components," states Dr. Martin Weides (Santa Barbara). With their research findings the scientists confirmed, among other things, the theoretical work of a Norwegian research team published only a few weeks before.


What i in the past as many other people took for granted is something interesting :
When a material is made superconducting, and while a current is flowing the circuit is closed, only a dc current will flow for extended periods of time( maybe forever). But for AC current , this will not be the case. The current will not flow forever because the change of direction consumes energy from the "flowing" current.
If i understand correctly, this is the case yes ?

In your other post, you mentioned borrowing energy. It reminded me of something Richard P Feynman used as an explanation as well. :)
 
Last edited:

johanfprins

Junior Member
Aug 6, 2010
10
0
0
Can you comment on this research mr Prins ? I also do not have a subscription for it.
According to the article, they found a loophole :
According to me they are deluded. Cooper Pairs are not required for superconduction and probably do not even exist: also not in the form of parallel spins.
What i in the past as many other people took for granted is something interesting :
When a material is made superconducting, and while a current is flowing the circuit is closed, only a dc current will flow for extended periods of time( maybe forever). But for AC current , this will not be the case. The current will not flow forever because the change of direction consumes energy from the "flowing" current.
If i understand correctly, this is the case yes ?
Yes it is so since the charge-carriers cancel the applied electric field by becoming polarized. With an AC current the direction of polarization must change with every cycle. A vibrating dipole will radiate EM waves. Energy is thus dissipated. In the DC case no energy is dissipated at all.
In your other post, you mentioned borrowing energy. It reminded me of something Richard P Feynman used as an explanation as well. :)
You are of course correct since the Heisenberg relationship for energy and time is also (incorrectly though) used in quantum electrodynamics. Feynman could have solved the real physics if he did not accept Bohr's Principle of Complementarity. The latter is hogwash! Nobody has ever defined what a particle really is: So not knowing what it is, it means that it is utter nonsense to talk about wave-particle duality and "complementarity".
 
May 11, 2008
19,787
1,220
126
Well mr Prins, when ignoring the idea of cooper pairs. What do you think is going on with what is mentioned in the text when an superconductor and a ferromagnetic material come into contact with each other. In the text it is mentioned that the superconductor turns back into a "normal " conductor. Can you explain this with your model as well ? It would be a strong argument.

I am curious about this mechanism.

You give me to much credit. I am sure fresh young physics students into physics, quantum physics or QED know more then me and can perhaps learn a lot from you.

As a side step question :
When thinking of above, my strange mind for some reason does not let me go when wondering about the Peltier effect as well. I find the Peltier effect interesting and have difficulty understanding how vibrations of the atoms (which if i am correct is thermal energy) is moved away from one side to another when an electrical current is applied. effectively creating a cool side and a hot side with an Peltier element. The charge carriers ( i assume electrons) absorb the thermal vibration energy and move it to another part of the material. I cannot grasp that, can you explain it for me ?

It may be silly, but i just have some gut feeling the Peltier effect, Seebeck effect and the Thomson effect are something that is of interest as well in the search of the super conductor at usable temperatures. Although it seems that these effects no longer are present when a super conductor is super conducting. Maybe i wondering of to much though and i am wrong about it...


Anyway, as always i have a tendency to post songs from (according to me)good music.
I add this time a great song from singer Adele , rolling in the deep :

http://www.youtube.com/watch?v=lazyDlfaptM
I just have to give some counterweight against distortion that is called music these days...

And another from Caro Emerald:
http://www.youtube.com/watch?v=CPm-4gngEvs&feature=fvst


^_^
 
Last edited:

johanfprins

Junior Member
Aug 6, 2010
10
0
0
Well mr Prins, when ignoring the idea of cooper pairs. What do you think is going on with what is mentioned in the text when an superconductor and a ferromagnetic material come into contact with each other. In the text it is mentioned that the superconductor turns back into a "normal " conductor. Can you explain this with your model as well ? It would be a strong argument.
I am curious about this mechanism.
When you apply a magnetic field to a superconductor it increases the energy of the anchored orbitals and this decreases their density. When this decrease in density reaches a critical density, superconduction cannot occur anymore. The same happens when such a material comes into contact with a ferromagnetic material. If the magnetic field is strong enough to diminish the orbital density below a critical value, SC will stop: If not, superconduction will still be possible notwithstanding the presence of ferromagnetism.

The Peltier effect etc. are more complicated and cannot be answered on a thread. Suffice to say that the electron waves within a material change when you change the boundary conditions. For example, within an ideal metal at absolute zero temperature the waves are delocalized standing waves. When applying an electric-field, they superpose to form wave packets which can transport charge. Similar effects happen when you apply a temperature gradient. The point to remember is that there are NO "free electrons" within a metal since "free electrons" will not be able to chemically bond the atoms.
 
May 11, 2008
19,787
1,220
126
If i am seem harsh, i apologize.

I have to do a little background reading on the different types of semiconductors(1 and 2). Because i have difficulty grasping the effects of the ferromagnetic material. If i understand correctly, current models explain that a superconductor seems to push the magnetic field completely outside. When an external magnetic field is forced in, the super conducting effect can not be possible anymore because then it is no longer what exactly? To me it seems as a tuned oscillation but on different fields. I think i understand what you are trying to explain, a material is a complex tuned balanced formation of solitons that are all slightly detuned some way or another.
But then again i have conflict with understanding how the 45 tesla superconductor can still work. If only we would be able to know all the details...


But here is what i try to envision :
When it is a superconductor :

Is the electrical component fully tuned and matched or not fully tuned and matched ? Because the electrical component influences the magnetic component as well. And afcourse the magnetic component can influence the electrical component. The only way i can see it working is as what i stated in a post above. Removing disturbances such as thermal oscillations or distances that are causing waves from one soliton to bump into waves of another soliton. In effect causing the scattering. But when at the right distance and temperature, i can see a harmonic movement. And that is why direct current will work and not alternating current. Because the constant reversal of alternating current destroys the harmony of the waves the solitons are comprised of.


As a sidenote from my own personal crazy idea about physics :
I always try to visualize what is happening inside a solid material or a gas or ultimate vacuum. But to do so i cannot accept the particle model either. I always have the feeling that particles are solitons but comprised of waves on different fields, electrical field, magnetic field and gravitational field. The electrical wave packet enforces a similar oscillation in the magnetic field and the result is a magnetic oscillating wave packet enforcing again the same electrical oscillation. That is how i can envision a photon, a wavepacket that behaves like a particle(meaning a single separate entity but is in effect a soliton on different fields) but has very little gravitational field disturbance. it enforces it's own oscillation but does this i think the same way as electron's can "borrow" energy from quantum fluctuations. The photon is in effect ever existing because it is net 0 energy as long as it is in flight between source and destination. The energy used to create it is absorbed again when the photon is hitting a tuned target. If not, new photons must arise. The photon has a slight gravitational disturbance. It must have this, or gravitational redshift is not possible because a deformation in the gravitational field would otherwise go unnoticed by a photon or a group of photons. And this is not the case as is shown by time dilation and gravitational redshift.

Long ago the aether was seen as a perfect gas. Then everything was seen as particles in perfect empty space. Later on, it was realized that space was never empty and the virtual particles model arrived to explain measurements.
The aether idea was in principle restored.
As such, i could say we are existing in different fields, which is obvious. If i see everything in 3d, I have a 3d electrical space, 3d magnetic space, 3d gravitational space. Then i can envision it. But now i have the desire to think more about waves and the resulting waveforms.

This in 3d i can imagine and then the distance of the individual atoms and the effect in the lattice actually make sense :

electron707.gif



A mugshot of an electron :

electron_1.jpg




Another favorite of mine when it comes to music :
http://www.youtube.com/watch?v=9CppQF_nwn8

Please listen while watching the gif above... ^_^.



EDIT:

Here is the website i took the gif from :

http://www.glafreniere.com/

Christiaan Huygens, one of many great people...
 
Last edited:
May 11, 2008
19,787
1,220
126
Forgot to add my conclusion.

Mr Prins, what you explain, it reads to me as something that i can envision without any problem as waves only. I also see now why an external magnetic field can have an effect. Only for the superconductor still functioning in an external field of 45 tesla, i do not understand it.

The trick is to accept that nothing is stationary. Everything at the quantum level is constant moving. But when moving fast enough, it seems as standing still and when wanting to determine position or energy, it turns into a random guess because the result is experienced, the effect is experienced and not the multiple causes.

It is the same principle again as when wanting to see objects smaller then the wavelength of the medium used.

^_^

Yay.
 
May 11, 2008
19,787
1,220
126
Just when i think, i understand something i realize i still only see fragments of the hidden beauty of reality and i have to accept i do not understand it...
I realized i have difficulty connecting the orbitals to an aspect of the waves.
I have to dig deep in mathematics. Only if i know and understand the calculation, i can imagine and visualize the calculation. This is the case for every person by the way.

Something i learned :
It seems that Albert Einstein was more famous, but i just learned of a few very important people.
It seems Albert Einstein was using information from Henri Poincaré and Hendrik Lorentz as well.
Henri Poincaré and Albert Einstein both had their own view on relativity.
According to some, Einstein committed plagiarism on the work of Poincaré.
I do not know if this is true, i do know that when great minds think about the same subject at the same timeframe(being influenced by the same information), both will produce similar idea's.
Interesting read though and a must for those who wish to explore physics...
Let history be a source of information to the future...

Tchaikovsky :
http://www.youtube.com/watch?v=ph3h2IJAsgk&feature=related
 
Last edited:

komatta

Member
Oct 22, 2010
64
0
66
If all this is to believed, why have you not published this in a refereed journal? To which ones did you apply and why did they reject the paper?
 
May 11, 2008
19,787
1,220
126
Another research breakthrough in the field of super conductivity.


http://phys.org/news/2012-07-synchrotrons-superconductors-cold.html

Dr. Feizhou He observes a sample at the Canadian Light Source beamline where the superconductor data was gathered. Credit: Canadian Light Source Inc.

(Phys.org) -- The longstanding search for a room temperature superconductor is fueled by a tantalizing set of possible applications that sound like science fiction: infinitely long power lines that never lose energy, magnetically levitating trains, and incredibly fast quantum computers.

Superconductors have zero resistance, the electric equivalent to friction, when cooled below a specified temperature. The temperatures involved are alarmingly low, ranging from a couple of degrees above absolute zero to a balmy -135°C, still too cold for large scale practical use. Advances in high temperature superconductor research have been slow in part because their physics is poorly understood.

Now an international team of researchers has made a major breakthrough in understanding the limits of these materials. The collaboration, including researchers from the Canadian Light Source, University of Waterloo, and the University of British Columbia, used no less than four synchrotron facilities worldwide in order to confirm their results.

A synchrotron, like Saskatoon’s CLS, where some of the experiments were performed, is a football-field-sized source of brilliant light that enables scientists to study the microstructure and chemical properties of materials

The team found the first experimental evidence that a so-called “charge-density-wave instability” competes with superconductivity. Armed with this knowledge, scientists can start to design new materials that will bring superconductors out of the cold and into large-scale real world applications.

“Without very specific evidence it is like theorists are shooting in the dark. Our new data will narrow their target significantly” explained Canadian Light Source scientist Dr. Feizhou He.

The collaboration involved several prominent institutions, including the Max Planck Institute in Germany, Milan Polytechnic University and CNR-SPIN. The results were published this week in the journal Science.

More information: www.sciencemag.org/content/early/2012/07/11/science.1223532

A charge density wave seems to be the same as a spin density wave.

http://en.wikipedia.org/wiki/Spin_density_wave

Can somebody please explain it ?
I want to make sure if i understand it correctly and that it is what i imagined...
 
May 11, 2008
19,787
1,220
126
I am not going to comment on the extracts posted by William Gaatjies in detail since the interpretation of the results of what he has quoted, by the researchers who measured these results, is naive. Yes there are two gaps involved in the ceramic superconductors, and yes when you inject a large number of charge carriers the energy through the superconductor can be approximated by sort of "wave" of charge-carriers. But it is also transported when a SINGLE charge is injected. How can a single charge-carrier cause ALL the charge carriers within the superconductor to suddenly move as a "wave"?

There is a single, simple mechanism that models superconduction in both the low temperature metals and the ceramics. I have been blocked from publishing this model since it proves without a doubt that the charge-carriers are NOT PAIRS but fermions. I already wrote a book about it 5 years ago, but it seems that the elementary physics in that book is just too advanced for modern-day physicists to understand. This model predicts that the ceramic materials have a ceiling for the critical temperature at about 250 K: Exactly where these materials became stuck twenty years ago.

I have now written a second book aimed at people who have not been lobotomized by studying physics at a university.

This is just a wild guess, but a proposed paper how fotosynthesis actually works, might give a clue about how excitons move around in a wave when fotosynthesis is happening on a large scale.

Since this is not my experience field so i had to look it up :
"An exciton is a bound state of an electron and an electron hole which are attracted to each other by the electrostatic Coulomb force. • Attraction between the electron and the hole causes their motion to be correlated and the resultant electron-hole pair is known as an exciton."

Suppose this also works in a superconductor in a similar way :
And it is not scattering because the electron exists everywhere while moving around when the conductor is in a superconducting state. Perhaps something like that. That would explain the single carrier and multiple carriers behave the same.
We know that pressure and temperature deforms the atom lattice and therefore causes some kind of geometric change that is favorable for electrons moving around without scattering, superconducting state : There is no electrical Ohmic resistance.
Like in this state electrons are harmonically lifting along the movements of the atoms and moving smoothly in time without being stopped for short moments or bumped upon, creating vibrations and accelerations and decelerations and this will cause bremsstrahlung. Bremsstrahlung is electromagnetic radiation and it is released.
The electrons move like a wave over all atoms in such an atom lattice or the entire superconductor ? It is everywhere at once. I do not know. It is fun to wonder about...
The electrons stay in coherence while the material is in superconductive state and experience decoherence when the wire has normal resistance AKA the electrons scatter, the experience deflection paths in classical view and experience bremsstrhalung and also then absorb the brehmsstralung again. That photon is like the marble in a pinball machine and the electrons are like the sides the marble bashes into. Just a view from a classical representation that is easy to imagine.

That also makes me wonder if an electrical signal through a superconductor while superconducting moves at the speed of light or moves with limited speed : The velocity factor must be taken into account...

This video explains excitons and perhaps it is similar , i know that in metals (Hydrogen atoms in a very compressed state, AKA high pressure also behaves like a metal) there is a sea of free electrons but some of the superconductive materials are in fact ceramics with special gemometric atom lattices because of the composition of the superconductive ceramic. And then excitons may apply ? I am just guessing here.

The video :
How an exciton moves as a wave simultaneously through all the chlorophyll molecules to the reaction center...
That is what the paper is proposing. The exciton is everywhere at once: Superposition... That is Quantum Mechanical stuff.
Fotosynthesis seems to happen with 100% efficiency. No electrons lost...

This youtube video about fotosynthesis might give a clue what is going on in those ceramic superconductors as well.

For more information :
 
Last edited:
May 11, 2008
19,787
1,220
126
With knowing this all, how could superconduction happen ?

To explain it from different subjects :

This is interesting to know : Geometric changes in atom lattices.

How does the wave pass and how does electron scattering and therefore Ohmic resistance happen ?
My weird idea is that in the lattice the atoms move from position and therefore the phases line up so the electrons can move along without experiencing jumps in the phase. This during superconducting state. If we see the particles as spherical matterwaves, they all have their own oscillation.
And their own wavelenghts. I guess the trick is that these wavelengths are either fixed or variable and that by tuning the temperature and the pressure and knowing the wavelength of the atoms used (the elements) the phases line up.
So the electrons can move like a sinusoidal wave along. In normal rsistive state, the phase do not align up and jumps occur. If you would visualize it, it would look like an electron scattering around. If you take a fixed point on the wave and see that point as a particle.

Thinking quantum mechanics stuff.
When i look at this coherence, it could mean that the phases line up.
And decoherence happens when the phases doe not line up any longer and a jump occurs. No more harmony or ongoing matter waves.
For more information, see this website about spherical standing waves :


For more explanation how the geometric changes can influence the behavior of a material see this veritasium video about titinol. The alloy know for its properties to change shape depending on temperature.
The interesting part of the video ~(17:50) is when they bend the material and let it relax. It produces heat or it takes heat energy from it surroudings depending if it is bend or relaxed.



It is just having fun. Might be right, might be wrong. I am kind of in superposition here... :)

I guess particles are jumps in phases , so we got a lot of those oscillations. And that seems to match up with all the virtual particles ideas. So, we all exist because of jumps in phases.

My man...
Ain't that something...
:yum:
 
Last edited: