Choet al.Reply:

Abstract

Cho et al. Reply: It appears to us that Velasco et al. [1] have misconstrued the intent of our paper [2]. The purpose of using the overly simple 1D model in the first place was merely to verify that an appropriately chosen double-well potential can produce a realistically behaving pressure-dependent density maximum. The calculation was meant further to provide a valid yet understandable physical picture for the properties of this important substance, none then existing, and to give possible insights for later 3D computations.However, the 3D calculations performed by Velasco et al. used a potential model that is not closely related to any 3D model conceived or suggested by us. When they find no evidence for a density anomaly using such a model, they incorrectly conclude that the key to the density anomaly is not the multiple-well potential. They further claim that the analytic work of Stell and Hemmer (SH) [3] excludes the possibility of anomalous behavior from multiple-well potentials in 3D systems. As far as we can see, SH made no comments on such phenomena in 3D models at all. In fact, contrary to this point of view, Bell et al.[4] did find density maxima in 3D models with double-well potentials, but their particular choice of potentials gave an incorrect pressure dependence.Apparently, Velasco et al.[1] simply used our unmodified 1D potential in their 3D calculations. In our paper we stated that, "the water-water potential in computational models should be modified in such a way that it can provide a subsidiary second-neighbor oxygen-oxygen minimum near 3.4 Å, while keeping intact under appropriate thermodynamic conditions the open tetrahedral structure." This cannot be done by assuming a spherically symmetric double-well potential as in Ref. [1].A strong angular dependence [5] of the water-water potential enters in 3D because the normal O-H · · · O hydrogen bond must be present only within a narrow range of angles so as to allow the formation of a normal oxygen-oxygen van der Waals minimum near 3.4 Å. Kamb [6] has already discussed the possible necessity of these van der Waals interactions to offset energy losses caused by hydrogen bonds bending to form the much more compact O · · · O · · · O angles in the dense polymorph structures. Coulomb interactions employed in all commonly used potential models [7], and, of course, the Velasco et al. potential, have far too broad an angular dependence. Since the potential of Velasco et al. does not have close to the form we suggested, it is not surprising to us that no density anomalies were found.It is our opinion that the 3.4 Å potential minimum must be present in order to promote the formation of highdensity ice-II-like structure known to occur in the real liquid. See the differential scattering curves in Fig. 5 of Ref. [8]. A correctly behaving intermediate range 3D potential has been devised in our laboratory [9]. In this three-site model, H · · · H interactions have a standard

Structural anomalies for a three dimensional isotropic core-softened potential

“…Depending on the choice of the values of a, r 0 and c, this potential assumes several shapes ranging from a deep double well potential 44,45,46 to a repulsive shoulder 36 .…”

Thermodynamic and dynamic anomalies for a three-dimensional isotropic core-softened potential

“…Notwithstanding the progresses made by the models described above, a potential in which both the potential and the force are continuous functions and that exhibits all the thermodynamic and dynamic anomalies present in water is still missing. In this paper, we check if particles interacting with a core-softened potential similar to the one proposed by Cho et al [37,38,39] exhibit thermodynamic and dynamic anomalies similar to the ones present in water. Since the potential can have a variety of shapes, depending on its parameters, we study a soft ramp ( with continuous force) with two scale distances.…”

“…In this paper, we check if particles interacting with a core-softened potential similar to the one proposed by Cho et al [37,38,39] exhibit thermodynamic and dynamic anomalies similar to the ones present in water. Since the potential can have a variety of shapes, depending on its parameters, we study a soft ramp ( with continuous force) with two scale distances.…”

Confining Phase in Susy So(12) Gauge Theory With One Spinor and Several Vectors

“…Especially, physics of confining phase in N = 1 supersymmetric gauge theories was enriched (quantum deformed moduli space, "s-confinement"). These works have been also extended to the theories with various types of gauge groups and matter contents [3,4,5,6]. Furthermore, these theories have recently been applied to construction of models with dynamical supersymmetry breaking or SUSY composite models.…”