Brazuca, a Pogorelov's ball

posted by @ulaulaman about #Brazuca #geometry #WorldCup2014 #Brazil2014

Brazuca is the ball of the World Cup 2014. The particular pattern of its surface is a consequence of the Pogorelov's theorem about convex polyhedron:

A domain is convex if the segment joining any two of its points is completely contained within the field.
Now consider two convex domains in the plane whose boundaries are the same length.⁽¹⁾

Now we can create a solid using the two previous domains: we must simlply connect every point of one boundary with a point of the other boundary, obtaining a convex polyhedron, like showed by Pogorelov in 1970s.

The object you have built consists of two developable surfaces glued together on edge.

Instead of using two domains, you can, for example, start from six convex domains as the "square faces" of a cube. On the edges of each of these areas, you choose four points, as the vertices of the "square". We assume that the four "corners" that you have chosen are like the vertices, that is to say that the domains have angles in these points.⁽¹⁾

The damages of the heavy metal

by @ulaulaman via @verascienza about #heavymetal #chemistry #health

A heavy metal is any metal or metalloid of environmental concern. The term originated with reference to the harmful effects of cadmium, mercury and lead, all of which are denser than iron. It has since been applied to any other similarly toxic metal, or metalloid such as arsenic, regardless of density. Commonly encountered heavy metals are chromium, cobalt, nickel, copper, zinc, arsenic, selenium, silver, cadmium, antimony, mercury, thallium and lead.

Heavy metals have a lot of detrimental effects on our body:

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Aluminum - Damage to the central nervous system, dementia, memory loss
Antimony - Damage to heart, diarrhea, vomiting, stomach ulcer
Arsenic - Lymphatic cancer, liver cancer, skin cancer
Barium - Increased blood pressure, paralysis
Bismuth - Dermatitis, stomatitis, colitis, diarrhea
Cadmium - Diarrhea, stomach pains, vomiting, bone fractures, damage to the immune, psychological disorders
Chrome - Damage to the kidneys and liver, respiratory problems, lung cancer, death
Copper - Irritation of the nose, mouth and eyes, liver cirrhosis, brain damage and kidney
Gallium - Irritation of the throat, difficulty 'breathing, pain in the chest
Hafnium - Irritation of eyes, skin and mucous membranes
Indium - Damage to the heart, kidneys and liver
Iridium - Irritation of the eyes and digestive tract
Lanthanum - Lung cancer, liver damage
Lead - Fruits, vegetables, meats, cereals, wine, cigarettes contain. Cause brain damage, dysfunction at birth, kidney damage, learning disabilities, destruction of the nervous system
Manganese - Blood clotting, glucose intolerance, disorders of the skeleton
Mercury - Destruction of the nervous system, brain damage, DNA damage
Nickel - Pulmonary embolism, breathing difficulties, asthma and chronic bronchitis, allergic skin reaction
Palladium - Very toxic and carcinogenic, irritant
Platinum - Alterations of DNA, cancer, and damage to intestine and kidney
Rhodium - Stains the skin, potentially toxic and carcinogenic
Ruthenium - Very toxic and carcinogenic, damage to the bones
Scandium - Pulmonary embolism, threatens the liver when accumulated in the body
Silver - Used as a coloring agent E174, headache, breathing difficulties, skin allergies, with extreme concentration it causes coma and death
Strontium - Lung cancer, in children difficulty of bone development
Tantalum - Irritation to the eyes and to the skin, upper respiratory tract lesion
Thallium - Used as a rat poison, stomach damage, nervous system, coma and death for those who survive the remain Thallium nerve damage and paralysis
Tin - Irritation of the eyes and skin, headaches, stomach aches, difficulty to urinate
Tungsten - Damage to the mucous membranes and membranes, eye irritation
Vanadium - heart and cardiovascular disorders, inflammation of the stomach and intestine
Yttrium - Very toxic, lung cancer, pulmonary embolism, liver damage

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via verascienza

The Championships' Final

by @ulaulaman via @Airi_Talk about #WorldCup2014 #Brazil2014 predictions: #ESP-#GER

Jürgen Gerhards, Michael Mutz and Gert Wagner developed an economic model in order to predict the results of the football team during the international cups. The researchers evaluated the market value of every player and described every team with an economic price: in this way they predict the winners in 2006 (World Cup: Italy), 2008 (Euro Cup: Spain), 2010 (WC: Spain), 2012 (EC: Spain). Starting from the previous results, the three researchers realized the board of the challenges from the eighth:

The predicted final will be between Spain and Germany, with Spain favorite, but there is a little hope for the other teams, first of all Brazil: in 2012 the model didn't predict the other team in the final game of the Euro Cup: Italy, that should not have reached even into the semi-finals:

Marketization and globalization have changed professional soccer and the composition of soccer teams fundamentally. Against the background of these shifting conditions this paper investigates the extent to which the success of soccer teams in their national leagues is determined by (a) the monetary value of the team expressed in its market value, (b) inequality within the team, (c) the cultural diversity of the team, and (d) the degree of turnover among team members. The empirical analyses refer to the soccer season 2012/13 and include the twelve most important European soccer leagues. The findings demonstrate that success in a national soccer championship is highly predictable; nearly all of our hypotheses are confirmed. The market value of the team is, in today's world, by far the most important single predictor of athletic success in professional soccer.

Jürgen Gerhards, Michael Mutz, Gert Wagner (2014). Die Berechnung des Siegers: Marktwert, Ungleichheit, Diversität und Routine als Einflussfaktoren auf die Leistung professioneller Fußballteams. Zeitschrift für Soziologie, Jg. 43, Heft 3, 231-250

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via University of Berlin, galileonet.it, airicerca.org

Soccer balls

#abstract about #soccer #WorldCup

Soccer balls are typically constructed from 32 pentagonal and hexagonal panels. Recently, however, newer balls named Cafusa, Teamgeist 2, and Jabulani were respectively produced from 32, 14, and 8 panels with shapes and designs dramatically different from those of conventional balls. The newest type of ball, named Brazuca, was produced from six panels and will be used in the 2014 FIFA World Cup in Brazil. There have, however, been few studies on the aerodynamic properties of balls constructed from different numbers and shapes of panels. Hence, we used wind tunnel tests and a kick-robot to examine the relationship between the panel shape and orientation of modern soccer balls and their aerodynamic and flight characteristics. We observed a correlation between the wind tunnel test results and the actual ball trajectories, and also clarified how the panel characteristics affected the flight of the ball, which enabled prediction of the trajectory.

Hong S. & Asai T. (2014). Effect of panel shape of soccer ball on its flight characteristics., Scientific reports, 4 DOI: 10.1038/srep05068

Portrait of an atom

by @ulaulaman about #hydrogen #atom #orbitals #Bohr #Rutherford #quantum_mechanics

The study of the structure of the atom is long story, and it begins with Democritus, or from the point of view of the modern science, with John Dalton in 1808: indeed he tried to fix in scientific terms the ideas of the greek philosopher and naturalist.
Dalton's theory was based on five fundamental points:

• matter is made of tiny building blocks called atoms, which are indivisible and indestructible;
• atoms of the same element are all equal to each other;
• the atoms of different elements combine with each other (via chemical reactions) in ratios of whole numbers and generally small, thus giving rise to compounds;
• atoms can be neither created nor destroyed;
• atoms of an element can not be converted into atoms of other elements.

As you can see, there are some other ideas correct and incorrect. We do, however, a jump of a century and we go to 1902 with Mr. Thomson, the first to propose an atomic model: he assumed that the atom was made up as a sort of cake, a positively charged sphere in which were scattered, like raisins, the electrons with a negative charge distribution such as to make the object as a whole neutral.
A few years later, however, in 1911, Rutherford devised and conducted an important experiment⁽¹⁾ in which he sent a beam of alpha particles against gold nuclei. The cross section observed, i.e. the surface on which the scattered particles resulting bump, it was too large to be compatible with the Thomson's hypothesis, but was compatible with that of Rutherford, namely that the atom was made up of a positive nucleus and by a number of electrons that revolved around the core itself at a large distance (compared to nuclear ones, of course).

However, this is not the last step: in 1913 Niels Bohr refined the Rutherford's model⁽²⁾. Accepted the planetary structure of the atom, Bohr suggested that the electrons in their rotational motion, could not occupy orbits at their leisure, but they must themselves at very specific distances from the nucleus: this is the dawn of quantum mechanics, that further refine the atomic model thanks to the famous Schroedinger's equation.

The atom, now, was intended as a postive nucleus consists of protons and neutrons, with a little cloud of electrons that moved around, and not on an orbital but in a sort of spherical cap. And these caps at different energy was recently directly observed by Aneta Stodolna's team^{(3, 4)}:

(...) an experimental method was proposed about thirty years ago, when it was suggested that experiments ought to be performed projecting low-energy photoelectrons resulting from the ionization of hydrogen atoms onto a position-sensitive two-dimensional detector placed perpendicularly to the static electric field, thereby allowing the experimental measurement of interference patterns directly reflecting the nodal structure of the quasibound atomic wave function.⁽³⁾

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via phys.org, io9

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(1) Rutherfor E. (1911). The scattering of α and β particles by matter and the structure of the atom, Philosophical Magazine Series 6, 21 (125) 669-688. DOI: 10.1080/14786440508637080
(2) Bohr N. (1913). On the constitution of atoms and molecules, Philosophical Magazine Series 6, 26 (151) 1-25. DOI: 10.1080/14786441308634955
(3) Stodolna, A., Rouzée, A., Lépine, F., Cohen, S., Robicheaux, F., Gijsbertsen, A., Jungmann, J., Bordas, C., & Vrakking, M. (2013). Hydrogen Atoms under Magnification: Direct Observation of the Nodal Structure of Stark States Physical Review Letters, 110 (21) DOI: 10.1103/PhysRevLett.110.213001
(4) Smeenk, C. (2013). A New Look at the Hydrogen Wave Function Physics, 6 (58) DOI: 10.1103/Physics.6.58

15 Sorting Algorithms in 6 Minutes

Visualization and "audibilization" of 15 Sorting Algorithms in 6 Minutes.
Sorts random shuffles of integers, with both speed and the number of items adapted to each algorithm's complexity. The algorithms are: selection sort, insertion sort, quick sort, merge sort, heap sort, radix sort (LSD), radix sort (MSD), std::sort (intro sort), std::stable_sort (adaptive merge sort), shell sort, bubble sort, cocktail shaker sort, gnome sort, bitonic sort and bogo sort (30 seconds of it).
More information at the "Sound of Sorting"