We calculate the ideal-glass-transition line for adhesive hard spheres in the temperature-volumefraction plane within the framework of the mode-coupling theory. We find two intersecting lines, controlled by the hard-core and the adhesive part of the potential respectively, giving rise to two different mechanisms for structural arrest. In the glass region we identify the presence of a glassglass-transition line ending in a cusp bifurcation which causes, even in the close by liquid region, a logarithmic decay of correlations.PACS numbers: 64.70.Pf, 82.70.DdThe crossover from a liquid to an amorphous solid, observed near the calorimetric glass transition temperature T g , exhibits as a precursor phenomenon an anomalous dynamics, called glassy dynamics. Its evolution is connected with a critical temperature T c above T g . It has been studied extensively in the recent literature of the glass-transition problem, both experimentally [1][2][3][4][5], numerically [6,7] and theoretically [8,9]. Experiments around T c have been interpreted in the frame of the mode-coupling theory (MCT) for structural relaxation. MCT deals primarily with closed equations of motion for the normalized density-fluctuation-correlation functions Φ q (t) for wavevector moduli q. The equilibrium structure enters as input in these equations via the static structure factor S q . The theory explains T c as a glass-transition singularity resulting as a bifurcation phenomenon for the self-trapping problem of density fluctuations. Below T c

In this article we study in detail the Q-vector dependence of the collective dynamics in simulated deeply supercooled SPC/E water. The evolution of the system has been followed for 250 ns at low T , allowing a clear identification of a two step relaxation process. We present evidence in favor of the use of the mode coupling theory for supercooled liquid as framework for the description of the slow α-relaxation dynamics in SPC/E water, notwithstanding the fact that the cage formation in this system is controlled by the formation of an open network of hydrogen bonds as opposed to packing constraints, as in the case of simple liquids.

We present mode-coupling equations for the description of the slow dynamics observed in supercooled molecular liquids close to the glass transition. The mode-coupling theory (MCT) originally formulated to study the slow relaxation in simple atomic liquids, and then extended to the analysis of liquids composed by linear molecules, is here generalized to systems of arbitrarily shaped, rigid molecules. We compare the predictions of the theory for the q-vector dependence of the molecular nonergodicity parameters, calculated by solving numerically the molecular MCT equations in two different approximation schemes, with "exact" results calculated from a molecular dynamics simulation of supercooled water. The agreement between theory and simulation data supports the view that MCT succeeds in describing the dynamics of supercooled molecular liquids, even for network forming ones.

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