Minimal potentials with very many minima

We demonstrate, by construction, that simple renormalizable matrix potentials with S(N), as opposed to O(N), symmetry can exhibit an exponentially large number of inequivalent deep local minima.     

1H and 13C NMR of PMMA macromonomers and oligomers - end groups and tacticity

¹H NMR and ¹³C NMR have been used to study the end groups and tacticity in PMMA macromonomers and oligomers. These macromonomers are terminated almost exclusively in one vinylidene group per chain. The end group signals from the macromonomers are identified in both the ¹³C and ¹H NMR spectra. The spectra of the purified oligomers (n = 1-4) were used to aid in assignment. The macromonomers are predominantly syndiotactic, and the tacticity measured is consistent with Bernoullian statistics. The tetramer is a mixture of r and m isomers in a 4:1 ratio. It is shown that T₁ experiments can provide a useful method of distinguishing resonances due to low molecular weight impurities from those due to stereochemical or isomeric effects in macromonomers. The absence of internal double bonds was confirmed by isomerizing the vinylidene group of several oligomers and of the macromonomer, and verifying the absence of the isomerized signals in the NMR spectra of the original materials.     

Anticipating a new Golden Age

The standard model of fundamental interactions is remarkably successful, but it leaves an unfinished agenda. Several major questions seem ripe for exploration in the near future. I anticipate that the coming decade will be a Golden Age of discovery in fundamental physics.