scholarly journals From Critical Point to Critical Point: The Two-States Model Describes Liquid Water Self-Diffusion from 623 to 126 K

Molecules ◽  
2021 ◽  
Vol 26 (19) ◽  
pp. 5899
Author(s):  
Carmelo Corsaro ◽  
Enza Fazio
Keyword(s):  
Critical Point ◽  
Critical Points ◽  
Liquid Water ◽  
Dynamical Behavior ◽  
Configurational Entropy ◽  
Industrial Applications ◽  
Detailed Knowledge ◽  
Primary Role ◽  
Self Diffusion ◽  
Liquid States

Liquid’s behaviour, when close to critical points, is of extreme importance both for fundamental research and industrial applications. A detailed knowledge of the structural–dynamical correlations in their proximity is still today a target to reach. Liquid water anomalies are ascribed to the presence of a second liquid–liquid critical point, which seems to be located in the very deep supercooled regime, even below 200 K and at pressure around 2 kbar. In this work, the thermal behaviour of the self-diffusion coefficient for liquid water is analyzed, in terms of a two-states model, for the first time in a very wide thermal region (126 K < T < 623 K), including those of the two critical points. Further, the corresponding configurational entropy and isobaric-specific heat have been evaluated within the same interval. The two liquid states correspond to high and low-density water local structures that play a primary role on water dynamical behavior over 500 K.

Phase space correspondence between Jordan and Einstein frames

2021 ◽  
pp. 2150087
Author(s):  
Amin Salehi
Keyword(s):  
Phase Space ◽  
Critical Point ◽  
Critical Points ◽  
Dynamical Behavior ◽  
Cosmological Parameters ◽  
Jordan Frame ◽  
Field Equations ◽  
Theories Of Gravity ◽  
The Stability ◽  
Jordan And Einstein Frames

Scalar–tensor theories of gravity can be formulated in the Einstein frame or in the Jordan frame (JF) which are related with each other by conformal transformations. Although the two frames describe the same physics and are equivalent, the stability of the field equations in the two frames is not the same. Here, we implement dynamical system and phase space approach as a robustness tool to investigate this issue. We concentrate on the Brans–Dicke theory in a Friedmann–Lemaitre–Robertson–Walker universe, but the results can easily be generalized. Our analysis shows that while there is a one-to-one correspondence between critical points in two frames and each critical point in one frame is mapped to its corresponds in another frame, however, stability of a critical point in one frame does not guarantee the stability in another frame. Hence, an unstable point in one frame may be mapped to a stable point in another frame. All trajectories between two critical points in phase space in one frame are different from their corresponding in other ones. This indicates that the dynamical behavior of variables and cosmological parameters is different in two frames. Hence, for those features of the study, which focus on observational measurements, we must use the JF where experimental data have their usual interpretation.

scholarly journals Dynamical Behavior of some families of cubic functions in complex plane

2019 ◽  
Vol 24 (7) ◽  
pp. 122
Author(s):  
Mizal H. Alobaidi ◽  
Omar Idan Kadham
Keyword(s):  
Fixed Points ◽  
Critical Point ◽  
Complex Plane ◽  
Critical Points ◽  
Dynamical Behavior ◽  
Open Disc ◽  
Origin Point

The current study deals with the dynamical behavior of three cubic functions in the complex plane. Critical and fixed points of all of them were studied . Properties of every point were studied and the nature of them was determined if it is either attracting or repelling. First function  such that have two critical points  and three fixed points  such that is attracting when  is origin point As shown in figure (2).And  are attracting when  is the region specified by open disc  shown in figure (1.(c)).Second function  such that have two critical points   and three fixed points such that  is attracting when  and that its path is to the origin point as shown in figure (4).And  are attractive when  represents the open disc shown in the figure (3.(c)).Third function  such that  have one critical point  and three fixed points  is attracting that is path is the origin point and  are repelling as shown in figure (5). And all 2-cycles of  are repelling and unstable .   http://dx.doi.org/10.25130/tjps.24.2019.139

scholarly journals Global Phase Portrait and Bifurcation Diagram for a Multi-Parametric Linear System

2020 ◽  
Vol 55 (4) ◽  
Author(s):  
Jorge Rodríguez Contreras ◽  
Alberto Reyes Linero ◽  
Juliana Vargas Sánchez
Keyword(s):  
Linear System ◽  
Critical Point ◽  
Phase Portrait ◽  
Bifurcation Diagram ◽  
Critical Points ◽  
Global Dynamics ◽  
Parametric Surfaces ◽  
Critical Points At Infinity ◽  
Global Phase Portrait ◽  
The Stability

The goal of this article is to conduct a global dynamics study of a linear multiparameter system (real parameters (a,b,c) in R^3); for this, we take the different changes that these parameters present. First, we find the different parametric surfaces in which the space is divided, where the stability of the critical point is defined; we then create a bifurcation diagram to classify the different bifurcations that appear in the system. Finally, we determine and classify the critical points at infinity, considering the canonical shape of the Poincaré sphere, and thus, obtain a global phase portrait of the multiparametric linear system.

Expanding the calculation of activation volumes: Self-diffusion in liquid water

2018 ◽  
Vol 148 (13) ◽  
pp. 134105 ◽  
Author(s):  
Zeke A. Piskulich ◽  
Oluwaseun O. Mesele ◽  
Ward H. Thompson
Keyword(s):  
Liquid Water ◽  
Self Diffusion

scholarly journals Bifurcation and global dynamical behavior of the f(T) theory

2014 ◽  
Vol 29 (07) ◽  
pp. 1450033 ◽  
Author(s):  
Chao-Jun Feng ◽  
Xin-Zhou Li ◽  
Li-Yan Liu
Keyword(s):  
Dynamical System ◽  
Critical Points ◽  
Initial Conditions ◽  
Dynamical Behavior ◽  
Nonlinear Effects ◽  
Local Analysis ◽  
Local Method ◽  
Initial Values ◽  
Bifurcation Phenomenon

Usually, in order to investigate the evolution of a theory, one may find the critical points of the system and then perform perturbations around these critical points to see whether they are stable or not. This local method is very useful when the initial values of the dynamical variables are not far away from the critical points. Essentially, the nonlinear effects are totally neglected in such kind of approach. Therefore, one cannot tell whether the dynamical system will evolute to the stable critical points or not when the initial values of the variables do not close enough to these critical points. Furthermore, when there are two or more stable critical points in the system, local analysis cannot provide the information on which the system will finally evolute to. In this paper, we have further developed the nullcline method to study the bifurcation phenomenon and global dynamical behavior of the f(T) theory. We overcome the shortcoming of local analysis. And, it is very clear to see the evolution of the system under any initial conditions.

scholarly journals A method to estimate statistical errors of properties derived from charge-density modelling

2018 ◽  
Vol 74 (3) ◽  
pp. 170-183 ◽  
Author(s):  
Bertrand Fournier ◽  
Benoît Guillot ◽  
Claude Lecomte ◽  
Eduardo C. Escudero-Adán ◽  
Christian Jelsch
Keyword(s):  
Charge Density ◽  
Least Squares ◽  
Critical Point ◽  
Critical Points ◽  
Property Values ◽  
Density Model ◽  
Interaction Energies ◽  
Topological Properties ◽  
A Charge ◽  
Density Modelling

Estimating uncertainties of property values derived from a charge-density model is not straightforward. A methodology, based on calculation of sample standard deviations (SSD) of properties using randomly deviating charge-density models, is proposed with theMoProsoftware. The parameter shifts applied in the deviating models are generated in order to respect the variance–covariance matrix issued from the least-squares refinement. This `SSD methodology' procedure can be applied to estimate uncertainties ofanyproperty related to a charge-density model obtained by least-squares fitting. This includes topological properties such as critical point coordinates, electron density, Laplacian and ellipticity at critical points and charges integrated over atomic basins. Errors on electrostatic potentials and interaction energies are also available now through this procedure. The method is exemplified with the charge density of compound (E)-5-phenylpent-1-enylboronic acid, refined at 0.45 Å resolution. The procedure is implemented in the freely availableMoProprogram dedicated to charge-density refinement and modelling.

The generalized convective Cahn–Hilliard equation: Symmetry classification, power series solutions and dynamical behavior

2019 ◽  
Vol 31 (02) ◽  
pp. 2050024
Author(s):  
Zhi-Yong Zhang ◽  
Kai-Hua Ma ◽  
Li-Sheng Zhang
Keyword(s):  
Power Series ◽  
Critical Points ◽  
Driving Force ◽  
Series Solution ◽  
Dynamical Behavior ◽  
Compressive Force ◽  
Power Series Solution ◽  
Symmetry Classification ◽  
Hilliard Equation ◽  
Cahn Hilliard Equation

We first perform a complete Lie symmetry classification of the generalized convective Cahn–Hilliard equation. Then using the obtained symmetries, we mainly study the convective Cahn–Hilliard equation, of which a new power series solution is constructed. In particular for the crystal surface growth processes, the truncated series solution shows that the surface structures include peaks and valleys, and can exhibit different evolution trends with the driving force varying from compressive force to tensile force. Moreover, there exist several critical points for the driving force, where the surface configurations take the jump changes and show different features on the both sides of such critical points. According to the effects of driving forces, we analyze the dynamical features of crystal growth.

scholarly journals Ice is born in low-mobility regions of supercooled liquid water

2019 ◽  
Vol 116 (6) ◽  
pp. 2009-2014 ◽  
Author(s):  
Martin Fitzner ◽  
Gabriele C. Sosso ◽  
Stephen J. Cox ◽  
Angelos Michaelides
Keyword(s):  
Liquid Water ◽  
Dynamical Behavior ◽  
Supercooled Liquid ◽  
Ice Nucleation ◽  
Water Molecules ◽  
Ice Crystal ◽  
Surrounding Water ◽  
Dynamical Heterogeneity ◽  
Complex Dynamical Behavior

When an ice crystal is born from liquid water, two key changes occur: (i) The molecules order and (ii) the mobility of the molecules drops as they adopt their lattice positions. Most research on ice nucleation (and crystallization in general) has focused on understanding the former with less attention paid to the latter. However, supercooled water exhibits fascinating and complex dynamical behavior, most notably dynamical heterogeneity (DH), a phenomenon where spatially separated domains of relatively mobile and immobile particles coexist. Strikingly, the microscopic connection between the DH of water and the nucleation of ice has yet to be unraveled directly at the molecular level. Here we tackle this issue via computer simulations which reveal that (i) ice nucleation occurs in low-mobility regions of the liquid, (ii) there is a dynamical incubation period in which the mobility of the molecules drops before any ice-like ordering, and (iii) ice-like clusters cause arrested dynamics in surrounding water molecules. With this we establish a clear connection between dynamics and nucleation. We anticipate that our findings will pave the way for the examination of the role of dynamical heterogeneities in heterogeneous and solution-based nucleation.

scholarly journals II. On the critical state of gases

1880 ◽  
Vol 30 (200-205) ◽  
pp. 323-329 ◽  
Keyword(s):  
Critical Point ◽  
Critical Points ◽  
Critical State ◽  
Atmospheric Pressure ◽  
Boiling Point ◽  
Chemical Society ◽  
Boiling Points ◽  
Intermediate Condition ◽  
Specific Volumes

In a paper read before the Chemical Society, in May, 1879, I gave an account of a method of determining what is termed by Kopp the “specific volumes” of liquids; that was shown to be the volume of liquid at its boiling-point, at ordinary atmospheric pressure, obtainable from 22,326 volumes of its gas, supposed to exist at 0°. Being desirous of extending these researches, with the view of ascertaining such relations at higher temperatures, since April, 1879, I have made numerous experiments, the results of, and deductions from which I hope to publish before long. The temperatures observed vary from the boiling-points of the liquids examined, to about 50° above their critical points; and in course of these experiments I have noticed some curious facts, which may not be unworthy of the attention of the Society. It is well known that at temperatures above that which produces what is termed by Dr. Andrews the “critical point” of a liquid, the substance is supposed to exist in a peculiar condition, and Dr Andrews purposely abstained from speculating on the nature of the matter, whether it be liquid or gaseous, or in an intermediate condition, to which no name has been given. As my observations bear directly on this point, it may be advisable first to describe the experiments I have made, and then to draw the deductions which appear to follow from them.

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