ISS Well, the longest-lived particle, not counting the neutron, is the muon – a kind of “brother” of the electron.
Takeoff weight – 340 kgWing area – 47.4 m2Flight speed – 4 m / sEngine power – 12 HP from.
Known for:for the first time a gasoline engine was installed on an aircraft and a special method of aircraft control was developed – the so-called “blanking”. The method consisted in simultaneously changing the position of the center of gravity of the apparatus and changing the curvature of the ends of the wings, which were literally bent with the help of tension cables.
The idea of creating an airplane took on more or less real contours in the middle of the 19th century. But for the implementation of the idea there was not enough theoretical justification, and most importantly, a lightweight and sufficiently powerful engine. The flight of the first aircraft became possible after the invention of the gasoline internal combustion engine.
A distinctive feature of the first aircraft was the presence of a large number of braces supporting the wings: the flight speed was very low, and therefore, wings of a very large area were needed to provide lift.
Braces are structural elements of an aircraft, most often metal cables that support the wing from sagging under its own weight and from deformation under the action of aerodynamic forces.
The pilot’s seat was open to “all winds.”
The Wilber Brothers and Orville Wright
Wilber was born on April 16, 1867 in the village of Millville, near Newcastle, Indiana, and Orville, on August 19, 1871, in Dayton, Ohio. Their father was a bishop, as a result of which the family had to move frequently until they settled in Dayton in 1884. Studying at the brothers’ school cannot be called successful. The idea of creating a free-flying vehicle heavier than air captivated them in 1899. This was due not least to the numerous experiments of Otto Lilienthal.
Next: The first “heavy aircraft”. “Ilya Muromets” B (Russia)
Fractals have been known for almost a century, are well studied and have numerous applications in life. This phenomenon is based on a very simple idea: an infinite number of shapes, infinite in beauty and variety, can be obtained from relatively simple structures using just two operations – copying and scaling.
This concept has no strict definition. Therefore, the word “fractal” is not a mathematical term. This is usually the name given to a geometric shape that satisfies one or more of the following properties:
has a complex structure at any magnification; is (approximately) self-similar; has a fractional Hausdorff (fractal) dimension, which is more topological; can be built with recursive procedures.
At the turn of the 19th and 20th centuries, the study of fractals was more episodic than systematic, because earlier mathematicians mainly studied “good” objects that were amenable to research using general methods and theories. In 1872, the German mathematician Karl Weierstrass constructed an example of a continuous function that is nowhere differentiable. However, its construction was entirely abstract and difficult to perceive. Therefore, in 1904, the Swede Helge von Koch invented a continuous curve, which has no tangent anywhere, and it is quite simple to draw. It turned out that it has the properties of a fractal. One of the variants of this curve is called the “Koch snowflake”.
The ideas of self-similarity of figures were picked up by the Frenchman Paul Pierre Levy, the future mentor of Benoit Mandelbrot. In 1938 he published his article “Plane and spatial curves and surfaces, consisting of parts similar to the whole”, which describes another fractal – the Levy C-curve. All of these above fractals can be conditionally attributed to one class of constructive (geometric) fractals.
Another class is dynamic (algebraic) fractals, which include the Mandelbrot set. The first studies in this direction date back to the beginning of the 20th century and are associated with the names of the French mathematicians Gaston Julia and Pierre Fatou. In 1918, Julia’s nearly two hundred-page work was published, devoted to iterations of complex rational functions, in which Julia sets were described – a whole family of fractals closely related to the Mandelbrot set. This work was awarded the prize of the French Academy, but it did not contain a single illustration, so it was impossible to appreciate the beauty of the objects discovered. Despite the fact that this work made Julia famous among the mathematicians of the time, it was quickly forgotten.
The attention to the works of Julia and Fatou turned again only half a century later, with the advent of computers: it was they who made the wealth and beauty of the world of fractals visible. After all, Fatou could never look at the images that we now know as images of the Mandelbrot set, because the required amount of calculations cannot be done manually. The first person to use a computer for this was Benoit Mandelbrot.
In 1982, Mandelbrot’s book “The Fractal Geometry of Nature” was published, in which the author collected and systematized almost all the information about fractals available at that time and presented it in an easy and accessible manner. In his presentation, Mandelbrot made the main emphasis not on cumbersome formulas and mathematical constructions, but on the geometric intuition of the readers. Thanks to the illustrations obtained with the help of a computer, and historical tales, with which the author skillfully diluted the scientific component of the monograph, the book became a bestseller, and fractals became known to the general public. Their success among non-mathematicians is largely due to the fact that with the help of very simple constructions and formulas that a high school student can understand, images of amazing complexity and beauty are obtained. When personal computers became powerful enough, even a whole trend in art appeared – fractal painting, and almost any computer owner could do it. Now on the Internet you can easily find many sites dedicated to this topic.
Next: Geometric Fractals
What is discovered
The ATLAS collaboration performed a search for the production of WW-, ZZ-, and WZ-pairs with an invariant mass greater than 1 TeV. An excess in the form of a peak is seen in the 2 TeV region. The deviation is most pronounced in the WZ-channel, where the local statistical significance reached 3.4σ, the global – 2.9σ. After a new analysis of the same data, the significance sank, and the first data of Run 2 put the riddle on the brink of extinction altogether.
In other WZ-pair decay channels, no deviation is seen.
The distribution over the invariant mass of a WZ pair (left) and a ZZ pair (right) reconstructed from hadronic decays. The local statistical significance of the deviation from the background is shown at the bottom of the graphs. A source
September 2015. Usually, during hadronic decays of W and Z-bosons, the hadrons that have arisen fly in different directions and form several hadronic jets. However, if the bosons are moving with such high energy (boosted bosons), as here, all decay hadrons fly into about one cone and form one wide jet. In order to recognize its bosonic origin in this jet, the jet substructure technique was used. This is a relatively new and not yet tested technique, and it is doubtful that it has been properly optimized. This fact can turn out to be both a source of errors and a chance to enhance the result in the future.
The technique used does not allow one to reliably separate the W and Z bosons. The identification is carried out only by the invariant mass of each jet, and they overlap for W and Z. Therefore, the search for dibosones WW, WZ, and ZZ is by no means mutually exclusive; many events fell into all three classes.
ATLAS also studied the production of WZ and WW pairs in another decay channel, when W decays into leptons and the second boson into hadrons. If there really is a new heavy particle decaying into a WZ pair, it should also appear in this channel. However, no statistically significant deviation was found here. This further casts doubt on the reality of the effect.
The ATLAS result was published in June and collected 70 citations in three months. To theorists, the discovered peak seems very tempting, since it clearly resembles resonances or new heavy particles in a variety of New Physics models. But there is no consensus yet on what kind of particle it should be.
October 2015. The ATLAS Collaboration has released a large methodological article devoted to the art of reconstructing fast W-bosons from their hadronic decays.
December 2015. New ATLAS analysis shows that the two-boson burst is visible only in the hadronic decay channel and is not visible in the lepton and semi-lepton channels. When summed over all channels, the global statistical significance falls below 2σ, which casts strong doubts on the reality of this burst. Nevertheless, the final verdict should be postponed for now.
June 2016. ATLAS presented an analysis of the same process based on Run 2 data, and for all decay channels of W and Z bosons. Despite the fact that the data sometimes exceed expectations, this excess no longer looks like a peak at 2 TeV. In general, the situation is close to closing.
August 2016. The 2016 data on two-bosonic production with different decay channels, published by ATLAS at the ICHEP conference, finally close this deviation.
For links, see Hunting for new physics with boosted bosons // ATLAS Coll., 5 August 2016.ATLAS coll., Searches for heavy diboson resonances in pp collisions at √s = 13 TeV with the ATLAS detector // original arXiv: 1606.04833 [hep-ex].ATLAS coll., Combination of searches for WW, WZ, and ZZ resonances in pp collisions at √s = 8 TeV with the ATLAS detector // arXiv: 1512.05099 [hep-ex].ATLAS coll., Search for resonances with boson-tagged jets in 3.2 fb − 1 of pp collisions at √s = 13 TeV collected with the ATLAS detector // preliminary publication ATLAS-CONF-2015-073.ATLAS coll., Search for high-mass diboson resonances with boson-tagged jets in proton-proton collisions at √s = 8 TeV with the ATLAS detector // arXiv copy: 1506.00962 [hep-ex].
ICHEP 2016: Burst at 2 TeV closed // “Elements”, 19.08.2016.Multichannel analysis casts doubt on the reality of the peak at 2 TeV, “Elements”, 27.12.2015.ATLAS develops a method for the analysis of heavy wide jets https://123helpme.me/synthesis-essay/ // “Elements”, 27.10.2015.There is a curious deviation in ATLAS and CMS data at 2 TeV // “Elements”, 15.06.2015.ATLAS saw a hint of a new superheavy particle // N + 1, 16.06.2015.
Lifetimes of elementary particles
● – leptons███ – light hadrons● – light hadrons and “strange” hadrons (contain an s-quark)███ – “enchanted” and “adorable” hadrons● – “charmed” hadrons (contain a c-quark)● – “lovely” hadrons (contain a b-quark)● – participants of electroweak interactions███ – measurement methods
If strong decays were grouped in the vicinity of yoctoseconds, electromagnetic ones – in the vicinity of attoseconds, then weak decays are “blown away for everyone” – they cover as much as 27 orders of magnitude on the time scale!
At the edges of this unimaginably wide range are two “extreme” cases.
The decays of the top quark and particles-carriers of the weak interaction (W and Z-bosons) occur in about 0.3 cc = 3 · 10−25 s. These are the fastest decays among all elementary particles and, in general, the fastest processes reliably known to modern physics. It turns out this way because these are decays with the highest energy release.The longest-lived elementary particle, the neutron, lives for about 15 minutes. Such a huge time by the standards of the microworld is explained by the fact that this process (beta decay of a neutron into a proton, an electron and an antineutrino) has a very low energy release. This energy release is so weak that under suitable conditions (for example, inside an atomic nucleus), this decay may already be energetically unfavorable, and then the neutron becomes completely stable. Atomic nuclei, all matter around us, and we ourselves exist only thanks to this amazing weakness of beta decay.
In the interval between these extremes, most weak decays are also more or less compact. They can be divided into two groups, which we will conventionally call: fast weak decays and slow weak decays.
The decay of the lovely B− meson into a charmed D0 meson with the emission of an electron and an antineutrino is one example of a rather fast decay due to weak interaction
Fast decays are decays with a duration of about a picosecond. So, the numbers in our world are surprisingly formed, that the lifetimes of several tens of elementary particles fall into a narrow range of values from 0.4 to 2 ps. These are the so-called charmed and adorable hadrons – particles that contain a heavy quark.
Picoseconds are great, they are invaluable from the point of view of a collider experiment! The fact is that in 1 ps a particle will have time to fly a third of a millimeter, and a modern detector measures such large distances easily. Thanks to these particles, the picture of the collision of particles at the collider becomes “easy to read” – here there was a collision and the birth of a large number of hadrons, and over there, a little further away, secondary decays took place. The lifetime becomes directly measurable, which means that it becomes possible to find out what kind of particle it was, and only then use this information for a more complex analysis.
Slow weak decays are decays that start from hundreds of picoseconds and extend over the entire nanosecond range. This includes a class of so-called “strange particles” – numerous hadrons containing a strange quark. Despite their name, for modern experiments they are not at all strange, but on the contrary, the most ordinary particles. They just looked strange in the 50s of the last century, when physicists suddenly began to discover them one after another and did not quite understand their properties. By the way, it was the abundance of strange hadrons that pushed physicists half a century back to the idea of quarks.
From the point of view of a modern experiment with elementary particles, nanoseconds are a lot. This is so much that the particle ejected from the accelerator simply does not have time to decay, but pierces the detector, leaving its mark in it. Of course, it will then get stuck somewhere in the substance of the detector or in the rocks around it and disintegrate there. But physicists no longer care about this decay, they are only interested in the trace that this particle left inside the detector. So for modern experiments such particles look almost stable; they are therefore called the “intermediate” term – metastable particles.
Well, the longest-lived particle, not counting the neutron, is the muon – a kind of “brother” of the electron. It does not participate in strong interactions, it does not disintegrate due to electromagnetic forces, so only weak interactions remain for it. And since it is quite light, it lives for 2 microseconds – an entire epoch on the scale of elementary particles.
On March 30, 2010, collisions of protons with a total energy of 7 TeV began at the Large Hadron Collider.