Condensed Matter Theory

Abstract:

We investigate synchronization caused by long-range hydrodynamic interaction in a two-dimensional, substrated array of rotors with random intrinsic frequencies. The rotor mimics a flagellated bacterium that is attached to the substrate ("bacterial carpet") and exerts an active force on the fluid. Transition from coherent to incoherent regimes is studied numerically, and the results are compared to a mean-field theory. We show that quite a narrow distribution of the intrinsic frequency is required to achieve collective motion in realistic cases. The transition is gradual, and the critical behavior is qualitatively different from that of the conventional globally coupled oscillators. The model not only serves as a novel example of non-locally coupled oscillators, but also provides insights into the role of intrinsic heterogeneities in living and artificial microfluidic actuators.

Abstract:

The fact that ice oats because of the hydrogen bonding imposing a perfect tetrahedrally coordinated network, linking them into six-membered rings with much empty space between the molecules (Franzese and Stanley, p. 105), is perhaps the best known of what are widely seen as a long list of curiosities. Water’s maximum density at 4°C and its unusually high thermal capacity are also familiar anomalies. Many others, however, are less celebrated but are surely as noteworthy. Both the melting and boiling points of water are unexpectedly high when it is placed in the sequence of group VI hydrides. So Lyndell-Bell and Debenedetti remind us by this extrapolation, although not by this imagery, that ice placed in a gin and tonic would melt at -100°C and a cup of tea should be prepared at -80°C. Not only that, but the effect of supercooling is also remarkable, so that at ambient pressure it can reach -41°C, whereas at 2 kbar it may be as low as -92°C (Franzese and Stanley, p. 102). These authors also remind us that if the supercooling is very rapid the water fails to crystallize and becomes a glass. This is of more than passing interest because in its high density form it is “the most abundant ice in the universe, where it is found as a frost on interstellar grains” (Franzese and Stanley, p. 103). This is not the only regime in which water becomes amorphous. In the hydration layer associated with a peptide, the water again has glasslike properties “with a very rough potential-energy landscape and slow hopping between local potential minima” (Ball, p. 56).