scholarly journals The q-Phase Transition and Critical Scaling Laws near the Band-Crisis Point of Chaotic Attractors

1989 ◽  
Vol 82 (5) ◽  
pp. 879-896 ◽  
Author(s):  
T. Yoshida ◽  
S. Miyazaki ◽  
H. Mori ◽  
T. Kobayashi ◽  
T. Horita ◽  
...  
Keyword(s):  
Phase Transition ◽  
Scaling Laws ◽  
Chaotic Attractors ◽  
Critical Scaling

The Order of Phase Transition of Solvable DNA Melting Models

2003 ◽  
Vol 17 (16) ◽  
pp. 885-896 ◽  
Author(s):  
Su-Long Nyeo ◽  
I-Ching Yang
Keyword(s):  
Phase Transition ◽  
Hydrogen Bonds ◽  
Short Range ◽  
Scaling Laws ◽  
Dna Melting ◽  
Thermodynamic Quantities ◽  
Base Pairs ◽  
Order Of Phase Transition ◽  
Exactly Solvable ◽  
Dna Models

The phase transition of DNA molecules is studied in an exactly solvable formalism with the Morse and Deng–Fan potentials for the interstrand hydrogen bonds of nucleotide base pairs. It is shown that although the two potentials have different short-range behaviors, the thermodynamic quantities of the DNA system in these potentials enjoy the same scaling laws with the associated critical exponents, which are explicitly calculated. These exactly solvable DNA models are shown to exhibit a phase transition of the second order and the results of the analysis agree with previous studies.

Critical scaling theory of generalized phase transition and its universality

2000 ◽  
Vol 9 (6) ◽  
pp. 450-458 ◽  
Author(s):  
Cai Shao-hong ◽  
Hu Lin ◽  
Dai Ling-jiang ◽  
Ji Shi-yin ◽  
Li Jian-shi ◽  
...  
Keyword(s):  
Phase Transition ◽  
Scaling Theory ◽  
Critical Scaling

scholarly journals Phase Transition in Dynamical Systems: Defining Classes of Universality for Two-Dimensional Hamiltonian Mappings via Critical Exponents

2009 ◽  
Vol 2009 ◽  
pp. 1-22 ◽  
Author(s):  
Edson D. Leonel
Keyword(s):  
Phase Transition ◽  
Critical Exponents ◽  
Scaling Laws ◽  
Scaling Function ◽  
Initial Conditions ◽  
Invariant Tori ◽  
Dynamical Variable ◽  
Two Dimensional ◽  
Control Parameters ◽  
Average Value

A phase transition from integrability to nonintegrability in two-dimensional Hamiltonian mappings is described and characterized in terms of scaling arguments. The mappings considered produce a mixed structure in the phase space in the sense that, depending on the combination of the control parameters and initial conditions, KAM islands which are surrounded by chaotic seas that are limited by invariant tori are observed. Some dynamical properties for the largest component of the chaotic sea are obtained and described in terms of the control parameters. The average value and the deviation of the average value for chaotic components of a dynamical variable are described in terms of scaling laws, therefore critical exponents characterizing a scaling function that describes a phase transition are obtained and then classes of universality are characterized. The three models considered are: The Fermi-Ulam accelerator model, a periodically corrugate waveguide, and variant of the standard nontwist map.

PHASE TRANSITION, GEOMETROTHERMODYNAMICS AND CRITICAL EXPONENTS OF BARDEEN BLACK HOLE

2014 ◽  
Vol 23 (04) ◽  
pp. 1450040
Author(s):  
JIE-XIONG MO
Keyword(s):  
Phase Transition ◽  
Black Hole ◽  
Specific Heat ◽  
Critical Exponents ◽  
Transition Point ◽  
Scaling Laws ◽  
Phase Transition Point ◽  
Invariant Metrics ◽  
Thermodynamic Quantities ◽  
Transition Structure

In this paper, we investigate the phase transition of Bardeen black hole for the first time. First, we calculate thermodynamic quantities and correct the misuse of formula in former literature. Second, we investigate in detail the behavior of specific heat. We not only discuss the influence of parameter on phase transition, but also show the three-dimensional behavior of the specific heat. It is shown that phase transition takes place from a locally unstable large black hole to a locally stable small black hole. It is also shown that the location of phase transition point is proportional to the charge. Meanwhile, we study the behavior of the inverse of the isothermal compressibility and find that it diverges at the phase transition point. Thirdly, we build up geometrothermodynamics to examine the phase transition structure. It is shown that Legendre invariant thermodynamic scalar curvature diverges exactly where the specific heat diverges, which leads to the conclusion that the Legendre invariant metrics can correctly produce the behavior of the phase transition structure. Furthermore, to gain a thorough understanding of critical behavior, we calculate the relevant critical exponents and examine the scaling laws. It is shown that they are in agreement with the scaling laws.

Band Propagation, Scaling Laws and Phase Transition in a Precipitate System. I: Experimental Study

2012 ◽  
Vol 116 (18) ◽  
pp. 4427-4437 ◽  
Author(s):  
Mazen Al-Ghoul ◽  
Manal Ammar ◽  
Rabih O. Al-Kaysi
Keyword(s):  
Phase Transition ◽  
Experimental Study ◽  
Scaling Laws

scholarly journals Determining the nonequilibrium criticality of a Gardner transition via a hybrid study of molecular simulations and machine learning

2021 ◽  
Vol 118 (11) ◽  
pp. e2017392118
Author(s):  
Huaping Li ◽  
Yuliang Jin ◽  
Ying Jiang ◽  
Jeff Z. Y. Chen
Keyword(s):  
Machine Learning ◽  
Phase Transition ◽  
Critical Exponents ◽  
Spin Glasses ◽  
Scaling Laws ◽  
Finite Size ◽  
Three Dimensions ◽  
Aging Effects ◽  
Correlation Lengths ◽  
Nonequilibrium Phase

Apparent critical phenomena, typically indicated by growing correlation lengths and dynamical slowing down, are ubiquitous in nonequilibrium systems such as supercooled liquids, amorphous solids, active matter, and spin glasses. It is often challenging to determine if such observations are related to a true second-order phase transition as in the equilibrium case or simply a crossover and even more so to measure the associated critical exponents. Here we show that the simulation results of a hard-sphere glass in three dimensions are consistent with the recent theoretical prediction of a Gardner transition, a continuous nonequilibrium phase transition. Using a hybrid molecular simulation–machine learning approach, we obtain scaling laws for both finite-size and aging effects and determine the critical exponents that traditional methods fail to estimate. Our study provides an approach that is useful to understand the nature of glass transitions and can be generalized to analyze other nonequilibrium phase transitions.

Scanning-probe and information-concealing machine learning intermediate hexatic phase and critical scaling of solid-hexatic phase transition in deformable particles

2022 ◽  
Author(s):  
Weichen Guo ◽  
Bao-Quan Ai ◽  
Liang He
Keyword(s):  
Machine Learning ◽  
Phase Transition ◽  
Correlation Length ◽  
Continuous Phase ◽  
Scanning Probe ◽  
Learning Approaches ◽  
Two Dimensional ◽  
Critical Scaling ◽  
Hexatic Phase ◽  
Deformable Particles

Abstract We investigate the two-dimensional melting of deformable polymeric particles with multi-body interactions described by the Voronoi model. We report machine learning evidence for the existence of the intermediate hexatic phase in this system, and extract the critical exponent $\nu\approx0.65$ for the divergence of the correlation length of the associated solid-hexatic phase transition. Moreover, we clarify the discontinuous nature of the hexatic-liquid phase transition in this system. These findings are achieved by directly analyzing system's spatial configurations with two generic machine learning approaches developed in this work, dubbed ``scanning-probe'' via which the possible existence of intermediate phases can be efficiently detected, and ``information-concealing'' via which the critical scaling of the correlation length in the vicinity of generic continuous phase transition can be extracted. Our work provides new physical insights into the fundamental nature of the two-dimensional melting of deformable particles, and establishes a new type of generic toolbox to investigate fundamental properties of phase transitions in various complex systems.

Critical Scaling Behavior of Microemulsion Systems

1984 ◽  
Vol 24 (02) ◽  
pp. 197-202 ◽  
Author(s):  
John S. Huang ◽  
Mahn Won Kim
Keyword(s):  
Phase Transition ◽  
Phase Boundary ◽  
Critical Point ◽  
Critical Phenomena ◽  
Scaling Laws ◽  
Continuous System ◽  
Universal Function ◽  
Scaling Behavior ◽  
Critical Phase ◽  
Classical Thermodynamics

Abstract We used dynamic light scattering to study the characteristic droplet size, in dilute single-phase microemulsions near the critical phase transition point. We found that there existed a general power-law dependence of f on point. We found that there existed a general power-law dependence of f on the reduced variable = . Here stands for any thermodynamic and system variables whose critical value is denoted by . The variables of interest in the present work are temperature and alkane carbon number (ACN). It is found that where = . This is observed both in water- and oil-internal microemulsions, independent of the surfactant properties. This behavior, known as the scaling behavior, was analyzed in terms of generalized homogeneous functions with as the degree of homogeneity. It turns out that only one of the reduced variables is an independent variable in these functions, greatly simplifying the description of the properties of microemulsions in the neighborhood of a critical phase boundary. Introduction Critical phenomena have been under intensive investigation for the past 20 years by physicists and physical chemists. There are several reasons for this subject to attract so much attention. SINGULARITIES. A large number of thermodynamic properties, especially ones related to the second-order derivative of the free energy, become singular (in a mathematical sense) at the critical point. UNIVERSALITY. There exists a universal description (scaling laws) of the singular behavior of all the corresponding thermodynamic parameters in a large number of vastly different systems. These range from simple liquid/gas mixtures, liquid crystals, and magnetic alloys to the quantum mechanical superfluids. NONCLASSICAL BEHAVIOR. Though critical properties are macroscopic properties pertaining to the bulk phases, classical thermodynamics is properties pertaining to the bulk phases, classical thermodynamics is inadequate to explain quantitatively what happens in the neighborhood of the critical points. NEW PARAMETERS. Geometric properties (such as the symmetry group of the so-called "order parameter") and spatial dimensionality of the system are more important than the nature of basic interactions that produce the phase transition. phase transition. Great progress has been achieved, both experimentally (such as dynamic light scattering) and theoretically (such as the powerful scaling laws and renormalization group theories), in the study of critical phenomena. As a result, a vast amount of knowledge has been accumulated on the subject in recent years. Critical phenomena may also play an important role in the understanding of the fundamental mechanism in EOR by microemulsions and micellar solutions. Microemulsions do exhibit unmistakable critical behavior in certain composition and temperature ranges near the cloud point of a homogeneous system. There are many ways to cause a homogeneous microemulsion to split into a multiphase system. When any of the system variables, such as the temperature, salinity, composition of the oil, and concentration of the dispersed phase, are changed in such a manner that the resultant phase transition occurs in the neighborhood of a plait point, which corresponds to a vanishing tie line, then the system will exhibit critical phenomena. All critical transitions are characterized by pronounced thermodynamic fluctuations. These fluctuations are described by a con-elation length that diverges at the critical point, causing a strong scattering of light known as the critical opalescence, a feature that is also observed in microemulsions. By definition, the correlation length diverges at the critical value, Zc, of the corresponding system variable, . Therefore, the reduced variable delta Z = Zc -Z expresses a measure of a "thermodynamic distance" to the critical point. We use the lower-case letter z = delta Z/Zc to denote the dimensionless scaled variables that are important for the description of the universal behavior of a microemulsion near a critical phase boundary. In the neighborhood of the critical point, the physical phase boundary. In the neighborhood of the critical point, the physical properties of the microemulsion systems depend on some universal function properties of the microemulsion systems depend on some universal function of scaled variables only, independent of the chemical makeup of the system. We call this the critical scaling behavior. Experimental Procedure MICROEMULSION SYSTEM. We have chosen two model microemulsions for our study. One is a simple pure three-component oil-continuous system containing pure normal alkanes, distilled water, and a surfactant commonly known as AOT. This surfactant, sodium di-2-ethyl hexylsulfosuccinate, was twice recrystallized from hexane over activated charcoal. The other is a water-continuous system composed of 8% NaCl brine solution, normal alkanes and a combined surfactant (hepta-ethoxylated octadecyl methyl ammonium-i-dodecyl-o-xylene sulfonates). SPEJ p. 197

Critical scaling laws in insulating spin glasses

1986 ◽  
Vol 54-57 ◽  
pp. 127-128 ◽  
Author(s):  
P. Beauvillain ◽  
C. Chappert ◽  
J.P. Renard ◽  
J. Seiden
Keyword(s):  
Spin Glasses ◽  
Scaling Laws ◽  
Critical Scaling
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