The experimental and theoretical studies of supercooled liquid water strongly suggest that the two liquid waters and their liquid-liquid critical point (LLCP) exist at low temperature. However, the decisive experimental evidence of the LLCP has not been obtained because of the rapid crystallization of liquid water in the "no-man's land." Here, we observed experimentally the pressure-induced pol...

Water is characterized by a density anomaly whose origin is a matter of debate. Theoretical works have shown that two of the proposed explanations, the second-critical-point hypothesis and the singularity-free scenario, have the same microscopic origin, but arise from different choices of parameters, such as the hydrogen bond strength or geometry. We consider a Hamiltonian model proposed by Sas...

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We study an eigenvalue problem by a non-smooth critical point theory. Under general assumptions, we prove the existence of at least one solution as a minimum of a constrained energy functional. We apply some results on critical point theory with symmetry to provide a multiplicity result.

An asymptotically exact solution is presented for the two-impurity Kondo model for a finite region of the parameter space surrounding the critical point. This region is located in the most interesting intermediate regime where RKKY interaction is comparable to the Kondo temperature. After several exact simplifications involving reduction to one dimension and abelian bosonization, the critical p...

Deuteron spin-lattice relaxation time (TJ measurements of binary mixtures 2,6-lut idine/D20 have been done near the lower critical solution point (Tc L), e = (T — Tg L)/Tc 10~. Singularities are observed at Tc L . The changes in the slope of Ti (H) = / ( T ) can be interpreted as due to the effect of concentration changes on Ty and simultaneously strong overlaping of H N M R signals from coexis...