Maths in my town

May 29, 2010

I live in a little beautiful town, Santander in the north coast of Spain and I want to give my congratulations to a local mathematician Francisco Santos who has refuted the Hirsch conjecture.

Conjecture   Let $ P $ be a convex $ d $polytope with $ n $ facets. Then the diameter of the graph of the polytope $ P $ is at most $ n-d $.

What haven’t been proved for d≥4 and remains unresolved for 50 years.

The proof will be presented at the 100 Years in Seattle (The mathematics of Klee and Grunbaum) conference in end-July, this year.

But there is even an entry in the Wikipedia and a lot of references in the web,  what as I’ve read in the local newspaper interview, astonished Francisco Santos for such a quick reaction in the emedia. 

Here you have a part of this work published a few months ago December 2009

My humble congratulations.

Why Soap bubbles are possible?

May 29, 2010

How many times since I was a child I`ve got distracted while I wash the dishes by  making soap bubbles? so many, because they are enigmatic, like the most beautiful things in nature. Why his shape is so perfectly espherical?Why they shine in iridescent colors? What is the cause of the way they  arrange when they stick each other together? How could I make they take longer to explode? 

 I give you some formal mathematical expressions that need to be commented but give an idea about how something so simple hides complexity.

For a bubble of radius r, the pressure from the film surface tension is given by the Laplace-Young law

(1)

 

where and are the inner and outer radii of the bubble, respectively, and is the surface tension of the fluid. Letting r be the average of and (actually, ) gives

(2)

 

About the sound the bubble make when it explode there is another equation for the natural frequency

given in the following expression:

where:

gamma is the ratio of specific heat of the fluid

P sub zero is the steady state pressure

R sub zero is the steady state radius

rho is the density of the fluid

And here the instant when the subject of study disappear

Some thing else to think about….

Solar cells in Colors

May 15, 2010

A dream in the green energy  has been developed. New transparent solar cells in colors . They can capture the indirect light not only direct sun rays.  With an efficiency of 12% and a low cost of  $2.1/W.

Their developers based in Jerusalem hope to improve this figures  almost to 20% and $ 0.98/W  for the next couple of years.  It is a fifth of the actual cost for the usual cells wich uses high percentage of silicium and not use fluorescent nanoparticles.

The possibilities for green architecture are open to imagination.

Nuclear Fusion

May 12, 2010

Why is this way of energy so thoroughly pursued by scientific community?

Because the energy produced by the union of two primary light nuclei  into a heavier one is very high and the residues have low radioactivity.
Not all fusion reactions produce the same energy, the most common one is Deuterium + Tritium = Helium + neutron that produces 17,6 MeV , but even the easiest to produce is very hard to achieve.

There are many engineers , and physicists working hard in finding the way to produce fusion as a real source of energy.

One of the methods in which the scientist  believe harder  is Inertial Confinement Fusion
basically it works making to coincide numerous high power lasers in a dense metal, hohlraum , that produces X-rays of very high energy making the  nuclei  reach incredible high temperatures boosting the fusion probabilit

The premises in wich it is being proved this kind of fusion are  NIF (National Ignition Facility) in US and  LMJ (Laser Mega Joule) in France, with the same energy than NIF, but 240  laser beams instead  192, what gives  more flexibility (and complexity) to the installation.

 Some NIF  images 

Today North Korean newspapers published they succeed in fusion using this method. The coincidence with the birthday of the deceased  founder of  korea  festivity, the militar interest in nuclear weapons of the country and the luck of evidences makes the information not very trustful.

String, Superstring & p-branas Theory

May 12, 2010


To make it short, I will say that it is a complex mathematical theory grown to solve the quantum gravity problem. There is no way to explain the gravity with the quantum physics so it spoils the efforts to have a complete physic theory. It involves to think in particles like the electron not as a point but like a string with different vibrational states. The solution passes through adding dimensions until eleven,some of them only can be seen or applied at a microscopic scale.

Depending the vibration the string is performing we see, an electron, photon or a quark. The theory evolved into the superstring theory to include the fermion behaviour using supersymmetry.

The fundamental idea  it is that particles are strings in resonant vibration at a frequency equal to Planck length,under wich appear the quantum gravity.

The superstring theory can be explain with conventional three-dimensional fluid mechanics considering the strings  vortex made of yarns .This is known as Cladín theory, and it has been used to explain even black holes.

In the 90’s Physicist were disturbed by the discovering of  five different String theories, during what is called  The Second Superstring Revolution, and a new unified theory born. Was the M Theory, were strings were substituted by membranes with dimensions varying between 10  to 26 . So a 1-brana is a string, and a p-brana is a generic membrane in a 10-26 dimension space or bulk.

This theories have been criticized as pseudo science due to they are not falsable. (See falsationism)
See a conference about all this stuff

Carbon nanotubes

May 6, 2010

This structures have amazing properties, that can break the limits imposed by other materials in conducting electricity, resistance among others. The remarkable fact is that superconductivity appears around 30K, what gives them an important place in the HCTS (High Critical Temperature Superconductors)

The predecessor carbon based structure was the C60 buckyball,

Both  are part of the same family compounds, the fullerenes,which are made of  graphene linked hexagonal rings; but they may also contain pentagonal (or sometimes heptagonal) rings.

The nanotubes are cylinders  that can be closed by a half  buckyball  in each extreme, may have only one wall or more, and different wrapping  angles in the way the graphite lattice was curved to form the cylinder. 

This is a great place to read about his Properties

The arc-evaporation method, which produces the best quality nanotubes, involves passing a current of about 50 amps between two graphite electrodes in an atmosphere of helium.
But if you don’t have a laboratory, you can do your virtual nanotubes with this superb application made by a research team of the Granada University (Spain)nanotubes simulation

Laser light

May 4, 2010

 

Let me explain what laser is in a few words.

The word laser is an acronym for Light Amplification by Stimulated Emission of Radiation. 

Visible light is a mixture of different wavelengths

Laser light is the result of filter one of this wavelengths and boost his intensity by rebooting into a cavity wich  length between the mirrors inside, is a multiple of the  wavelength  in order  to generate constructive interactions. 

The source of the light, the way to increase the intensity, and the materials used make the difference in the numerous  lasers developed.

 

Aurora Borealis

May 4, 2010

This is one of the meteorological phenomenon I wish I could see in my life.

Most people knows about his beauty but not so many knows about his origin.

It is provoked by the sun wind, wich excites energetically the ions in the atmosphere most of them oxygen and nitrogen, and after they lose that extra energy emitting his spectroscopic light. Ions accumulates in the poles where the magnetic field of the earth is stronger , that is the cause why Auroras only happen in the North pole named Aurora Borealis or in the South pole named Aurora Australis.

Yellow to green tones comes from the emission of oxygen , blues come from the nitrogen and less common colors red and purple from the helium ions. 

The images need no words

                

What wind tunnels are for

May 3, 2010

I suppose I am not the only one who is interested in knowing how the air force is studied in engineering or other issues related with elements moving at high-speed.
The wind tunnels are used to apply controled wind speeds to the structure studied, in order to take all the necessary measurements to minimize the  resistant forces.
Here you are AEROLAB specialized in the design, fabrication, installation and calibration of aerospace wind tunnels.

Enjoy this high standard car images in a wind tunnel test

Origami is not only for fun

April 20, 2010

Can you do a paper bird? perhaps you can find new applications to this enterteining hobby.

In March of 1995, Japanese scientists used origami concepts to pack and deploy a solar power array in the research vessel called Space Flight Unit (SFU). On Earth, the solar array was folded into a compact parallelogram, and then in space, it was expanded into a solar sail. The method of folding the solar panels is called “Miura-ori”, in honor of Koryo Miura, a professor in Tokyo University, who developed the fold.


How it works