Condensed concepts

 A friend recently showed me that solid gallium can melt in your hand. I did not know this. I was quite familiar with liquid mercury, but not gallium.  The existence of elemental gallium was predicted by Mendeleev in 1869 after he constructed the periodic table. It was discovered within six years. He was able to predict that it would have a low-melting temperature, based on extrapolations from the known melting temperatures of elements close to it in the periodic table. Solid gallium is soft enough to be cut with a knife. Three different stable crystal structures for solid gallium are shown below. The phase diagram of pure gallium is shown below. Note the negative slope of the phase boundary between the liquid and the solid alpha-Ga. This is like water. It follows from the Clausius-Clapeyron equation that the solid state has lower density than the liquid state. Gallium is the only elemental metal with this property. (The semi-metals antinomy and bismuth also do). Gallium remains l

  I am currently working on the proofs and index for Condensed Matter Physics: A Very Short Introduction . It is wonderful to have got to this stage. It is slated for release on December 29. It can be pre-ordered from Oxford UP (GDP 9) , Amazon  (US $12), Book Depository  (US $16), ...

Significant understanding of emergent phenomena in quantum materials has come from the study of model Hamiltonians such as those associated with the names Hubbard, Anderson, Kondo, Heisenberg, Kitaev, Haldane, BCS,... I had not appreciated until recently that an early key to the Modern Synthesis of evolutionary biology (that brought together Darwinian natural selection with Mendelian genetics) was the development of simple mathematical models. The discussion below is taken from Towards a unified science of cultural evolution  Alex Mesoudi, Andrew Whiten and Kevin N. Laland  Significant advances were made in the study of biological [micro]evolution before its molecular basis was understood, in no small part through the use of simplified mathematical models, pioneered by Fisher (1930), Wright (1931), and J.B.S. Haldane (1932)...   Mathematical models such as [those for cultural evolution and gene-culture coevolution] are often treated with suspicion and even hostility by some social sc