Gerade gefunden: Demolition City! Thematisch verwandt mit Crush the castle, allerdings diesmal mit Dynamitladungen. Einfaches Konzept, trotzdem Suchtgefahr…

Mit gezielten Dynamitladungen fällt alles…

The dirt on corrugations

Phys. Rev. E 79, 061308 (2009)

© STOCKPHOTO / ROS RAVBAR

Anyone who has driven long distances over unpaved dirt roads will be familiar with the washboard-like corrugations that can develop. Smoothing out these corrugations can be expensive; understanding how they form and how they might be prevented is thus of potentially great value.

It is commonly assumed that corrugations are created by the forced oscillation of the suspension systems of the cars that pass over them. But their period is usually far from the natural frequency of a typical car’s suspension.

To try to resolve the mystery, Anne-Florence Bitbol and colleagues have built an experiment to recreate similar effects in the lab. This involves dragging either a cylindrical wheel or a fixed rectangular plough blade around the circumference of a circular bed of sand. Above a certain speed, they find that both the wheel and the plough produce corrugations in the sand, proving that suspension effects are indeed unimportant. Moreover, they find that the speed at which the corrugations form changes with the weight and angle of attack of the plough, in a manner similar to that of the skipping of stones across the surface of a lake.

Hints for Epilson-Minus types:

*Remember Einstein’s Theory: E=MC2 (remember, you can take this to the next level by replacing the 2 with a 3)

*Remember this triangular law: a / sin A  =  b / sin B  =  c / sin C (unfortunately this has nothing to do with what we’re talking about)

*The shortest distance between two points is also the cheapest (unless there are armed gunmen along the route).

Just when you thought it couldn’t get any smaller, it did.

No I’m not talking about microprocessors or micro-microprocessors.

It’s all about the smallest particles in nature. It went from molecule to atom, to protons to quarks to gluons. The quarks with their colours and the gluons with their flavours. And now it’s down to spinons and holons. Read on.

Well, yes we’ve studied about this, right from the very primitive ‘Plum-Pudding model’ by J.J. Thompson which was abandoned (1911) on both theoretical and experimental grounds in favour of the Rutherford atomic model, in which the electrons describe orbits about a tiny positive nucleus.

And then, the nucleons (protons and electrons) were said to be made of quarks. Quarks associate with one another via the strong force to make up protons and neutrons, in much the same way that the latter particles combine in various proportions to make up atomic nuclei. There are six types, or flavours, of quarks that differ from one another in their mass and charge characteristics. These six quark flavours can be grouped in three pairs: up and down, charm and strange, and top and bottom. Quarks appear to be true elementary particles; that is, they have no apparent structure and cannot be resolved into something smaller. In addition, however, quarks always seem to occur in combination with other quarks or with antiquarks, their antiparticles, to form all hadrons—the so-called strongly interacting particles that encompass both baryons and mesons.  Quantum chromodynamics (QCD) : In this theory of strong interactions, whose breakthrough ideas were published in 1973, colour has nothing to do with the colours of the everyday world but rather represents a property of quarks that is the source of the strong force.

Then came the gluons, the so-called messenger particle of the strong nuclear force, which binds subatomic particles known as quarks within the protons and neutrons of stable matter as well as within heavier, short-lived particles created at high energies. Quarks interact by emitting and absorbing gluons, just as electrically charged particles interact through the emission and absorption of photons. Like quarks, the gluons carry a “strong charge” known as colour; this means that gluons can interact between themselves through the strong force.

And now, is it really true that they split the electron? This was what was published in ‘The Times Of India’ as on 4th August 2009:

Los superconductores a temperatura ambiente serían posibles si la ecuación empírica de Roeser, que parece verdadera, es realmente verdadera. La ecuación de Roeser relaciona la temperatura de transición en superconductores de alta temperatura con una longitud característica de su estructura cristalina microscópica que los autores denominan “distancia de dopado.” Una relación lineal (con errores menores del 0.02%) descubierta experimentalmente sin ninguna teoría que la sustente. ¿Estará el secreto de la superconductividad de alta temperatura oculto en la explicación de la ecuación de Roeser? Quizás sí, por ahora ya se han ofrecido algunas críticas, por ejemplo, no está claro como se calcula la llamada “distancia de dopado,” el procedimiento parece ad hoc. Sólo el tiempo lo dirá. Bee y Stefan de Backreaction nos comentan la noticia en “Röser’s equation,” July 27, 2009, y en “Röser’s equation, again,” August 03, 2009.

La tabla indica algunos de los valores mostrados en la figura. Esta extraída del artículo en el que los autores estudian esta correlación para pníctidos (superconductores de alta temperatura basados en hierro), en concreto Felix Huber, Hans Peter Roeser, Maria von Schoenermark, “A Correlation Between Tc of Fe-Based HT Superconductors and the Crystal Super Lattice Constants of the Doping Element Positions,” Proc. Int. Symp. Fe-Pnictide Superconductors, J. Phys. Soc. Jpn. 77 (2008) Supplement C pp. 142-144 (PDF gratis). La ecuación encontrada por Hans Peter Roeser, profesor del Institute of Space Systems en la Universidad de Stuttgart, Alemania, es la siguiente

4 π k m_e(2 x)² n^-2/3 = h²/ T_c

donde T_c es la temperatura crítica, k es la constante de Boltzmann, h es la contante de Planck, m_e es la masa del electrón, x es la distancia de dopado del cristal (que los autores calculan con una fórmula aparte, ver la figura de abajo) y n es el número de capas supraconductoras en el cristal (1,2,3, …). ¿Cómo se interpreta esta fórmula? Básicamente afirma que la longitud de onda de de Broglie de un par de Cooper en el superconductor a la temperatura de transición es proporcional a la “distancia de dopado” con un factor de origen geométrico en la estructura cristalina.

La gran pregunta: Si la fórmula de Roeser es verdadera siempre, ¿pueden existir superconductores a temperatura ambiente, digamos 300 ºC? Como nos contesta Stefan en su blog, sí, es posible. Por ejemplo, para el material llamado LOFFA en la figura y en la tabla, la altura de la celda unidad es de 0.9 nm (similar a otros superconductores basados en hierro), y para una temperatura de transición de 25.5 ºKelvin, la distancia de dopado es de 5.22 nm. Multiplicando la temperatura por 16 = 4², ya alcanzamos la temperatura ambiente (408 ºKelvin o 135º C), lo que requiere reducir la distancia de dopado en un factor de 4, es decir, hasta 1.3 nm, o unas 1,5 veces la altura de la celda unidad del material. Imposible, no parece, bastaría un cociente de dopado del orden de 2/3.

Ante un resultado empírico tan aplastante como la figura que corona esta entrada uno se pregunta si no habrá alguna trampa oculta. ¿No habrán seleccionado los autores los materiales para los que la ley se cumple de “escándalo” obviando los demás? Los autores eligen un plano concreto en el calculan su distancia de dopado, ¿por qué dicho plano y no otro? Los materiales superconductores a alta temperatura son muy complejos. Las dudas son muchas. ¿Cómo resolverlas? El primer paso para verificar la ecuación de Roeser podría ser mediante simulaciones numéricas 3D de la ecuación de Schrödinger en una aproximación cuasi-clásica para los electrones. Es un problema computacionalmente intensivo pero creo que está al alcance de los supercomputadores actuales. Un segundo paso, mucho más difícil, será proponer un modelo teórico que explique dicha ley que, a priori, no parece fácil de obtener dado que la estructura cristalina de los materiales superconductores a alta temperatura, gracias a cierta dosis de dopantes, es muy complicada.

¿Permitirá la ley de Roeser predecir nuevos materiales con temperaturas de transición más altas que el récord actual? Yo personalmente no lo creo, pero no soy experto. Lo que sí es cierto es que si así fuera, caería un Premio Nobel con toda seguridad.

Por cierto, la teoría de cuerdas se inició al tratar de entender los diagramas o trayectorias de Tullio Regge por parte de Veneziano y otros. Eran unos diagramas empíricos que relacionaban el momento angular de hadrones (bariones y mesones) con la masa de sus resonancias (propuestos originalmente en 1957). Se pensó que eran claves para entender la fuerza nuclear fuerte en los 1960, pero más tarde la cromodinámica cuántica los destronó (a principios de los 1970). Más sobre trayectorias de Regge. Hoy en día explicamos muy bien los diagramas de Regge gracias a que los bariones están formados por quarks. ¿Pasará con la ecuación de Roeser algo parecido que con los diagramas de Regge?

Los interesados en más información técnica  para algunos cupratos pueden consultar la serie de artículos: H.P. Roeser, F.M. Huber, M.F. von Schoenermark, A.S. Nikoghosyan, F. Hetfleisch, M. Stepper, A. Moritz, “Doping patterns in N-type high temperature superconductors PLCCO and NCCO,” Acta Astronautica 65: 289-294, July-August 2009, H.P. Roeser, F.M. Huber, M.F. von Schoenermark, A.S. Nikoghosyan, “High temperature superconducting with two doping atoms in La-doped Bi-2201 and Y-doped Bi-2212,” Acta Astronautica 654: 489-494, August-September 2009, y H.P. Roeser, D.T. Haslam, F.M. Huber, J.S. López, M.F. von Schoenermark, A.S. Nikoghosyan, J. Vernerey, “Doping structure of the high temperature superconductor La2-ΔCa1+ΔCu2O6+δ,” Acta Astronautica, Article in Press, Corrected Proof, 2009.

Here is an intriguing photo at Astronomy Picture of the Day that purports to be a “true” optical illusion of 3 concurrent images of the sun rising over Gdansk Bay in Poland. I don’t know enough to determine if this was photoshopped or not. Check it out.

A WOW documentary video, showing how mathematics, physics theory and science in general evolves, and that NOTHING is certain!

Findings of Godel, Cantor, Boltzmann, and Turing.

This New York Times article on the Large Hadron Collider is disturbing for anyone who’s been looking forward to major scientific advancement coming out of Geneva anytime soon. I’ve done plenty of blogging on the LHC and was looking forward to it finally being up and running after the initial misfire. Looks like major problems are going to be a part of this project for a while to come.

From the first link:

The biggest, most expensive physics theory machine in the world is riddled with thousands of bad electrical connections.

Many of the magnets meant to whiz high-energy subatomic particles around a 17-mile underground racetrack have mysteriously lost their ability to operate at high energies.

Some physicists are deserting the European project, at least temporarily, to work at a smaller, rival machine across the ocean.

After 15 years and $9 billion, and a showy “switch-on” ceremony last September, the Large Hadron Collider, the giant particle accelerator outside Geneva, has to yet collide any particles at all.

But soon?

This week, scientists and engineers at the European Center for Nuclear Research, or CERN, are to announce how and when their machine will start running this winter.

That will be a Champagne moment. But scientists say it could be years, if ever, before the collider runs at full strength, stretching out the time it should take to achieve the collider’s main goals, like producing a particle known as the Higgs boson thought to be responsible for imbuing other elementary particles with mass, or identifying the dark matter that astronomers say makes up 25 percent of the cosmos.

The energy shortfall could also limit the collider’s ability to test more exotic ideas, like the existence of extra dimensions beyond the three of space and one of time that characterize life.

“The fact is, it’s likely to take a while to get the results we really want,” said Lisa Randall, a Harvard physicist who is an architect of the extra-dimension theory.