Finite-size scaling investigation of the liquid-liquid critical point in ST2 water and its stability with respect to crystallization

Kesselring, Tobias; Lascaris, Erik; Franzese, Giancarlo; Buldyrev, Sergey V.; Herrmann, Hans J.; Stanley, H. Eugene

doi:10.1063/1.4808355

Cited by 63 publications

(44 citation statements)

References 100 publications

(212 reference statements)

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“…For example, the low degree nodes are the key nodes that influence the dynamic robustness, while structural robustness is largely influenced by hubs [114]. Note that some dynamic systems can spontaneously recover after a breakdown [39,[107][108][109][110]115,116].…”

Section: Discussionmentioning

confidence: 99%

“…An entire class of real-world dynamic complex systems can spontaneously recover after their collapse [39,[107][108][109][110]. For example, the Internet can initially fail after a severe attack, and then after a period of time, recover; a human brain can spontaneously recover after an epileptic attack; a traffic network returns to its normal state after a period of gridlock; and a financial network may, after a period of time, recover after having a large fraction of its constituents fail.…”

Section: Spontaneous Recovery In Dynamical Networkmentioning

confidence: 99%

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Recent Progress on the Resilience of Complex Networks

Gao

Liu

et al. 2015

Energies

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Many complex systems in the real world can be modeled as complex networks, which has captured in recent years enormous attention from researchers of diverse fields ranging from natural sciences to engineering. The extinction of species in ecosystems and the blackouts of power girds in engineering exhibit the vulnerability of complex networks, investigated by empirical data and analyzed by theoretical models. For studying the resilience of complex networks, three main factors should be focused on: the network structure, the network dynamics and the failure mechanism. In this review, we will introduce recent progress on the resilience of complex networks based on these three aspects. For the network structure, increasing evidence shows that biological and ecological networks are coupled with each other and that diverse critical infrastructures interact with each other, triggering a new research hotspot of "networks of networks" (NON), where a network is formed by interdependent or interconnected networks. The resilience of complex networks is deeply influenced by its interdependence with other networks, which can be analyzed and predicted by percolation theory. This review paper shows that the analytic framework for Energies 2015, 8 12188 NON yields novel percolation laws for n interdependent networks and also shows that the percolation theory of a single network studied extensively in physics and mathematics in the last 60 years is a specific limited case of the more general case of n interacting networks. Due to spatial constraints inherent in critical infrastructures, including the power gird, we also review the progress on the study of spatially-embedded interdependent networks, exhibiting extreme vulnerabilities compared to their non-embedded counterparts, especially in the case of localized attack. For the network dynamics, we illustrate the percolation framework and methods using an example of a real transportation system, where the analysis based on network dynamics is significantly different from the structural static analysis. For the failure mechanism, we here review recent progress on the spontaneous recovery after network collapse. These findings can help us to understand, realize and hopefully mitigate the increasing risk in the resilience of complex networks.

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Section: Discussionmentioning

confidence: 99%

Section: Spontaneous Recovery In Dynamical Networkmentioning

confidence: 99%

Recent Progress on the Resilience of Complex Networks

Gao

Liu

et al. 2015

Energies

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“…2c we focus on the state point (3240 K, 0.3 GPa) which lies near the LLCP and on the liquid-liquid phase transition line. This is clearly demonstrated by the "phase flipping" [28,29] between LDL and HDL that becomes visible when we plot how the density changes with time (see inset of Fig. 2c).…”

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confidence: 95%

Tunable Liquid-Liquid Critical Point in an Ionic Model of Silica

Lascaris

2016

Phys. Rev. Lett.

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Recently it was shown that the WAC model for liquid silica [L. V. Woodcock, C. A. Angell, and P. Cheeseman, J. Chem. Phys. 65, 1565Phys. 65, (1976] is remarkably close to having a liquid-liquid critical point (LLCP). We demonstrate that increasing the ion charge separates the global maxima of the response functions, while reducing the charge smoothly merges them into a LLCP; a phenomenon that might be experimentally observable with charged colloids. An analysis of the Si and O coordination numbers suggests that a sufficiently low Si/O coordination number ratio is needed to attain a LLCP.PACS numbers: 64.70.Ja, 61.20.JaTetrahedral liquids tend to display a range of phenomena that are anomalous in comparison to "simple" liquids [1]. The showcase example here is liquid water, which displays a large number of anomalies, such as an increase of the self-diffusion upon compression (diffusion anomaly) and an increase of the density as it is cooled (density anomaly). In water, many of these anomalies are highly pronounced in the supercooled regime, far below the melting line. Of particular interest are the seemingly divergent behaviors of both the isobaric heat capacity C P [2, 3] and isothermal compressibility K T [4] upon cooling. Unfortunately these experiments are limited by homogeneous nucleation, and crystallization rapidly occurs as the temperature approaches −40To explain both the anomalies and this divergent behavior, several scenarios have been proposed [5][6][7] among which the liquid-liquid critical point (LLCP) scenario [6] has received the most attention [8,9]. According to this scenario two metastable liquids exist deep in the supercooled regime: a high-density liquid phase (HDL) that is highly diffusive, and a low-density liquid phase (LDL) that is more structured and less diffusive. These two metastable phases are separated by a first-order-like liquid-liquid phase transition (LLPT) line that ends at a critical point. In the one-phase region beyond any critical point the response functions remain finite and display a locus of maxima or minima that near the critical point merges with the locus of correlation length maxima, known as the Widom line [10][11][12]. According to this scenario it is the response function extrema originating from the LLCP that account for many of the anomalies of water.The LLCP scenario could also explain the anomalies found in other tetrahedral liquids. For example, a LLCP has been found in the Stillinger-Weber model for liquid silicon [13,14]. Another candidate is liquid silica, SiO 2 . Simulations of the BKS silica model [15] and the WAC silica model [16] show hints of a possible LLCP at low temperatures [17][18][19], however, more recent studies have questioned its existence in these models [20,21]. Nonetheless, in the P T -plane the isochores of the WAC model are remarkably close to crossing. As the crossing of isochores is a clear indicator of a phase transition [20,22], one may therefore conclude that the WAC model is remarkably close to having a LLCP.It is important to ...

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“…This hypothesized liquid-liquid coexistence, terminated by a critical point, is not directly accessible to bulk-water experiments because it is presumably located a few degrees below the line of homogeneous nucleation of ice [2,4,5]. Fresh approaches to resolving the question of the existence of water's polyamorphism are especially desirable in view of conflicting reports on simulations in water-like models [6][7][8][9][10][11][12][13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Behavior of supercooled aqueous solutions stemming from hidden liquid–liquid transition in water

Biddle

Holten

Анисимов

2014

The Journal of Chemical Physics

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A popular hypothesis that explains the anomalies of supercooled water is the existence of a metastable liquid-liquid transition hidden below the line of homogeneous nucleation. If this transition exists and if it is terminated by a critical point, the addition of a solute should generate a line of liquid-liquid critical points emanating from the critical point of pure metastable water. We have analyzed thermodynamic consequences of this scenario. In particular, we consider the behavior of two systems, H2O-NaCl and H2O-glycerol. We find the behavior of the heat capacity in supercooled aqueous solutions of NaCl, as reported by Archer and Carter, to be consistent with the presence of the metastable liquid-liquid transition. We elucidate the non-conserved nature of the order parameter (extent of "reaction" between two alternative structures of water) and the consequences of its coupling with conserved properties (density and concentration). We also show how the shape of the critical line in a solution controls the difference in concentration of the coexisting liquid phases.

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Finite-size scaling investigation of the liquid-liquid critical point in ST2 water and its stability with respect to crystallization

Cited by 63 publications

References 100 publications

Recent Progress on the Resilience of Complex Networks

Recent Progress on the Resilience of Complex Networks

Tunable Liquid-Liquid Critical Point in an Ionic Model of Silica

Behavior of supercooled aqueous solutions stemming from hidden liquid–liquid transition in water

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