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A new analysis by Princeton University researchers has uncovered patterns in primes that are similar to those found in the positions of atoms inside certain quasicrystals. Abstract available.
"Our analysis leads to an algorithm that enables one to predict primes with high accuracy. "
Uncovering multiscale order in the prime numbers via scattering
thewoodenwand, could that string-net fluid story be related to this: http://www.wired.com/2014/06/the-new-quantum-reality/ ?
"What if electrons were not elementary, but were the ends of long strings in a string-net liquid which becomes our space?"
A state or a phase corresponds to an organization of particles. A deformation in the organization represents a wave in the state. A new state of matter will usually support new kinds of waves. Wen and Levin found that, in a state of string-net liquid, the motion of string-nets correspond to a wave that behaved according to a very famous set of equations -- Maxwell's equations! The equations describe the behavior of light -- a wave of electric and magnetic field. "A hundred and fifty years after Maxwell wrote them down, ether -- a medium that produces those equations -- was finally found." says Wen.
That wasn't all. They found that the ends of strings are the sources of the electric field in the Maxwell's equations. In other words, the ends of strings behave like charged electrons. The string-end picture can even reproduce the Fermi statistics and the Dirac equation that describes the motion of the electrons. They also found that string-net theory naturally gave rise to other elementary particles, such as quarks, which make up protons and neutrons, and the particles responsible for some of the fundamental forces, such as gluons and the W and Z bosons.
From this, the researchers made another leap. Could the entire universe be modeled in a similar way? "Suddenly we realized, maybe the vacuum of our whole universe is a string-net liquid," says Wen. "It would provide a unified explanation of how both light and matter arise." So in their theory elementary particles are not the fundamental building blocks of matter. Instead, they emerge as defects or "whirlpools" in the deeper organized structure of space-time.
I am trying to represent this in terms of a set of Mathematical equations, a little help.
I figured it out, never mind.
Does anyone know how to represent 7/(1+81x^2) as a power series and find the first 5 coefficients in the series?
I got 7*sum(from 0 to infinity) (-1)^n * 81^n * x^(2n)
The first coefficient I got was 7 which is correct, but after that I'm getting wrong answers ie 2nd coefficient -567 is wrong....
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