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De los líquidos hasta la De los líquidos hasta la economía: el discreto encanto economía: el discreto encanto
de la física estadísticade la física estadísticaGerardo García Naumis
Cub. 37, Instituto de Física, UNAM. México D.F., Mexico.
Escuela de verano de la física, Agosto 2006
• IntroducciónIntroducción• Gases, líquidos y sólidos.Gases, líquidos y sólidos.• Materia Suave y Medios Granulares.Materia Suave y Medios Granulares.• BiofísicaBiofísica• Turbulencia, física del tráfico y Van Ghogh.Turbulencia, física del tráfico y Van Ghogh.• Econofísica.Econofísica.• Sociofísica.Sociofísica.• Teoría de la información: lenguaje, música, Teoría de la información: lenguaje, música,
reconstrucción de imágenes, etc.reconstrucción de imágenes, etc.• Teoría del caos.Teoría del caos.
• Conclusiones.Conclusiones.
Objetivo original: entender el comportamiento térmico de un sistema en términos de sus propiedades microscópicas.
En 1733 Daniel Bernoulli dedujo la ley de los gases ideales:
PV=NkT
usando la idea de que un gas es un “billar” donde las moléculas chocan contra las paredes.
Boltzmann: 1877
S=k lnW
Dado que son muchas partículas, Boltzmann usó “la estadística” para describir el comportamiento mecánico del sistema
W= # de estados microscópicos posibles del sistema con un volumen y temperatura dados. 1/W=probabilidad de que el sistema esté en cierto estado.
Esta fórmula conecta el mundo “macro “ con el “micro”
1902-Gibbs desarrolla la teoría de ensambles: en lugar de seguir un sistema en el tiempo, estudiamos un conjunto de réplicas idénticas del sistema en un tiempo dado
1905-Einstein desarrolla nuevos métodos que prueban la existencia de átomos gracias al movimiento browniano (premio Nobel). En 1927 desarrolla la estadística cuántica con Bose. Fermi la extiende para partículas como electrones,protones,
Muchas partículas+reglas entre ellos=Comportamiento Colectivo
Atomos+Fuerzas de Interacción=estructura de la materia
Carros+Interacción=física del tráficoPalabras+Gramática=Lenguaje Notas+Armonía=MúsicaAgentes económicos+Comercio=EconomíaPersonas+Interacción=SociedadGranos de arena+Interacción=física de medios granulares
¿Qué nos interesa en la actualidad? ¿Qué nos interesa en la actualidad?
•Cómo y porqué ocurren los cambios de fase.•¿Porqué fuera del equilibrio termodinámico no hay cambios de fase(formación de vidrios, plásticos, etc.)?•La formación de vidrios es uno de los problemas mas importantes de la Física Moderna.
1990's - The Nobel Prize in physics is awarded for research into the physics of polymers and liquid crystals. New biomaterials save lives through transplants and drug delivery systems. Polymers and semiconductors are being designed to emit light, while "smart" materials are being designed to
modify their own behavior in response to stress or damage.
The future of its commercial jet business is taking shape. The future is plastic -- and lots of it. Boeing's 777 is only 11% plastics, mostly in the tail section. But compo--sites will make up 100% of the Boeing 787's skin and 50% of all the materials in the plane. "We have always wanted to design in composites,"
Materia SuaveMateria Suave
•Espuma: ¿sólido,líquido o gas?Aplicaciones: procesos químicos, industria alimentos y farmacéutica,aleaciones aeronáutica, construcción,etc.
• Gelatina: ¿sólido o líquido? • ¿Quieres un look original? ¿O algo elegante y logrado?
Empieza con el pelo seco o ligeramente húmedo. Esparce el tamaño de una avellana entre tus manos. Te recomendamos que te pongas el gel por todo el pelo al principio, y luego vayas definiendo los detalles con tus dedos.
(aerogeles, etc.)
• Coloides y emulsiones(pinturas, medicamentos, leche, mayonesa, etc.)
• Cristales líquidos (pantallas, materiales inteligentes, etc.)
• Fluídos y fluidos complejos
Medios Granulares (¿líquidos o sólidos?)Medios Granulares (¿líquidos o sólidos?)
Granos, arena, industria farmacéutica, ingeniería de suelos, evitar avalanchas, etc.
Flowing Sand in SpaceNASA scientists are sending sand into Earth orbit to learn more about how soil
behaves during earthquakes. Their results will help engineers build safer structures on Earth and someday on other planets, too.
ENTENDIENDO COMO se mueven átomos en los seres vivos:ENTENDIENDO COMO se mueven átomos en los seres vivos:
In many systems, we are interested in following the temporal evolution In many systems, we are interested in following the temporal evolution
Failure in folding: Alzheimer's disease, cystic fibrosis, BSE (Mad Cow disease), an inherited form of emphysema, and even many cancers are believed to result from protein misfolding.
Noten como los pequeños vórtices se hacen grandotes…
Invariancia frente a “cambios de tamaño”, a lo cual le llamamos fractalidad
Ejemplos de fractales
El Himalaya visto desde un satélite
Coliflor
Paisaje generado por computadora usando “algoritmos fractales”
Rayo sobre Phoenix
Published online: 7 July 2006; | NATURE; News and Viws doi:10.1038/news060703-17 , 2006.Van Gogh painted perfect turbulenceThe disturbed artist intuited the deep forms of fluid flow.
Philip Ball
The Starry Night has really turbulent swirls. © AP Photo/Mary AltafferVincent van Gogh is known for his chaotic paintings and similarly tumultuous state of mind. Now a mathematical analysis of his works reveals that the stormy patterns in many of his paintings are uncannily like real turbulence, as seen in swirling water or the air from a jet engine.
Physicist Jose Luis Aragon at the National Autonomous University of Mexico and his co-workers have found that the Dutch artist's works
Troubled minds and perfect turbulence
Van Gogh's painting Starry night. Vincent Van Gogh painted some of his most captivating paintings towards the end of his life during periods of intense emotional instability. Everything in these later paintings seems to be turning and churning, creating a sense of turmoil which many people find remarkably poignant. Now a team of physicists, led by José Luis Aragón and Gerardo Naumis of the Autonomous University of Mexico, have uncovered part of the secret behind the emotional appeal of Van Gogh's later paintings: their curls and swirls adhere to the same physical laws as turbulent fluids found in nature.The team analysed three of Van Gogh's most curly paintings, Starry night, Road with cypress and star and Wheat field with crows, and checked if and how the results fit in with the physics of turbulence. As a measure of each painting's impact on the viewer they used the concept of luminosity, the intensity of the light reflected off different points on the canvas, which holds most of the information the human eye picks up on when viewing a scene. The team used their measurements to work out the probability that two points lying a certain distance apart are equally luminous. These probabilities give a good idea of how luminosity varies across the canvas, leading to a neat mathematical representation of a viewer's perception of the painting.
The Times, London July 15, 2006
Illness helped Van Gogh to capture the perfect stormBy Paul Simons and Jack Malvern
THE chaotic swirls of Vincent van Gogh’s later
paintings may owe as much to science as they do to art. Physicists believe that some of his works are uncannily accurate pictures of the complex mathematics of turbulence, the phenomenon behind bumpy aircraft rides, cloud formations and the flow of ocean currents.
Van Gogh had turbulence down to a fine art15 July 2006
Mark Buchanan Magazine issue 2560
The Dutch artist's later paintings reflect light in a way that mimics the physics of turbulence - perhaps that explains their emotional chaos
ART experts have long marvelled at the emotional chaos apparent in the later paintings of the Dutch artist Vincent Van Gogh. Perhaps that is because the
images reflect light in a way that mimics the physics of turbulence. At least that's the view of a team of physicists led of the National Autonomous
University of Mexico, who analysed several of Van Gogh's later paintings, including Starry Night, Road with Cypress and Star (see below) and Wheat Field with Crows.
Mathematically, they studied how the luminosity, which is a measure of the total amount of visible light reflected off the paintings, varied across the canvas. Specifically, they analysed the likelihood that two points a distance D apart would have the same, or
similar, brightness. In each of the paintings, they found that points further apart were statistically less likely to have similar luminosities.
Nuestros resultados mas recientes…
Economía: turbulencia en la bolsa de valores
Economía: distribución del ingreso
Un animales domina cierto territorio El entrar a un terriotorio ajeno produce peleas El animal perdedor es expulsado
Los animales desarrollan desigualdad social. Los animales dominantes hacen lo que quieren. Los débiles comen sólo lo que sobra. Esto limita su reproducción.
Example: hens exhibit this type of hierarchy: the pecking order.
En los animales hay jerarquías socialesEn los animales hay jerarquías sociales
SOCIOFISICASOCIOFISICA
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