Description Of Phase Transitions Research Articles

Tutorials: Physics-informed machine learning methods of computing 1D phase-field models

Phase-field models are widely used to describe phase transitions and interface evolution in various scientific disciplines. In this Tutorial, we present two neural network methods for solving them. The first method is based on physics-informed neural networks (PINNs), which enforce the governing equations and boundary/initial conditions in the loss function. The second method is based on deep operator neural networks (DeepONets), which treat the neural network as an operator that maps the current state of the field variable to the next state. Both methods are demonstrated with the Allen–Cahn equation in one dimension, and the results are compared with the ground truth. This Tutorial also discusses the advantages and limitations of each method, as well as the potential extensions and improvements.

Lagrangian modelling of reactive contaminant transport in the multi-component marine medium

The particle-tracking method for transporting radionuclides in multicomponent ocean medium (water and multifractional suspended and deposited sediments) is considered using a probabilistic approach for simulating interaction processes between several states of radioactivity. The state transformations as a result of reactions of the first order were described using the master equation for the probability of the particle being in the given state. Transition probabilities between all possible states can be obtained from the numerical solution of the matrix master equation that is derived in the paper. In the first approximation, the Euler method was used to obtain a solution for the next time step. This approach can be applied to any linear system of equations describing phase transitions with any number of states, but it requires small values of the transition probabilities to ensure only a single-phase change during one time step. The paper also focuses on deriving the Lagrangian interface conditions between the water column and bottom deposition. To apply the probabilistic approach, the boundary conditions were considered as the reaction terms in a thin near-bottom interface layer in which boundary conditions were converted into source terms. For this layer, the corresponding master equation was derived to obtain transitional probabilities for particle states. The developed approaches were tested on numerical and analytical solutions of two test cases. It was found that the optimal thickness of the interface layer must be larger than the maximum vertical displacement of the particle during the one-time step, but it must be small enough to approximate the condition of uniform distribution of concentration in this layer.

Comparative study on phase transition behaviors of fractional molecular field theory and random-site Ising model

Fractional molecular field theory (FMFT) is a phenomenological theory that describes phase transitions in crystals with randomly distributed components, such as the relaxor-ferroelectrics and spin glasses. In order to verify the feasibility of this theory, this paper fits it to the Monte Carlo simulations of specific heat and susceptibility versus temperature of two-dimensional (2D) random-site Ising model (2D-RSIM). The results indicate that the FMFT deviates from the 2D-RSIM significantly. The main reason for the deviation is that the 2D-RSIM is a typical system of component random distribution, where the real order parameter is spatially heterogeneous and has no symmetry of space translation, but the basic assumption of FMFT means that the parameter is spatially uniform and has symmetry of space translation.

Effect of surface roughness on phase transition timing in megaampere pulsed-power–driven exploding conductors

An understanding of material phase transitions in megaampere pulsed-power–driven exploding conductors is important for predicting the growth of hydrodynamic instabilities in magneto-inertial fusion concepts. This study analyzes phase transitions in electrical conductor explosions using 1D Lagrangian and 2D arbitrary Lagrangian–Eulerian resistive magnetohydrodynamic simulations to show that micrometer-scale surface roughness can lead to the electrothermal instability (ETI), a feedback effect that concentrates resistive heating and leads to early melting and ablation. Simulations of the Mykonos electrothermal instability II (METI-II) experiment show melting begins 19% sooner for machined rods with micrometer-scale surface roughness than for rods without these features. The surface magnetic field is 41 T around the initial region of melt, representing a lower magnitude than both the 86 T from 1D simulations and the 85 T threshold reported elsewhere. In 2D simulations with micrometer-scale surface roughness, temperature measurements indicate the critical point temperature of aluminum is reached 17% faster in comparison with 1D simulations. Values from 2D simulations with surface roughness align with predictions from ETI theory, and the observed temperature redistribution further supports the ETI as an underlying mechanism. Simulation results are validated against experimental photonic Doppler velocimetry data. This study shows 1D simulations are adequate to model conductors with sub-micrometer-scale surface roughness in this high-energy-density regime; however, 2D or 3D simulations are required to capture the full range of physics for accurately describing phase transitions in conductors with micrometer-scale or larger surface roughness.

Lorentz violation emergence in a superconductivity phase transition scenario

In this letter, we use a condensation of topological defects mechanism to show how a Lorentz-violating (LV) term can emerge. The approach used here was originally developed to describe phase transitions due to a vortice proliferation in systems such as superconductors. First, as a consequence of our approach, we obtain a Podolsky-like LV term as a result of this work. Second, a condensation of topological defects in the theory restores the original Lorentz symmetric phase of the theory. The approach presented here can be seen as an early description of a mechanism to describe a phase transition between a Lorentz symmetric phase and a non-symmetric one. Besides the usage of this mechanism to show how LV terms can emerge, we also show how to extend the condensation mechanism to scalar theories. The condensation mechanism was originally designed for gauge theories. As a result, our scalar extension recovers the Ginzburg-Landau (GL) description of both regular and non-local superconductors. The GL description, in our approach, arises as a consequence of the condensation of topological defects.

A Simple Highly Accurate Algebraic Model of Phase Transitions on Square, Hexagonal, and Triangular Flat Faces

A simple, highly accurate algebraic model is proposed for describing phase transitions on flat faces of square, hexagonal, and triangular structures. The model is derived using the cluster variational approach within the Ising model and expressed in an analytical form by choosing a basic closed-form cluster of the minimal size for each facet structure with nearest neighbors of z = 3 (triangular), 4 (square), and 6 (hexagonal). The new model provides three times more accurate equations for molecular distributions of particles in the Ising model than earlier analytical expressions. The model’s analytical equations allow direct calculations of molecular distributions. (Only iterative numerical means were used earlier to obtain results of the same accuracy.) The effect of refinements when considering correlation effects in the new model is compared to traditional mean-field and quasi-chemical (QCA) approximations when calculating isotherms and pair and cluster distribution functions. Analytical expressions are obtained for the critical temperature of a segregation-type phase transition.

From Vlasov Equation to Degenerate Nonlocal Cahn-Hilliard Equation

We provide a rigorous mathematical framework to establish the hydrodynamic limit of the Vlasov model introduced in Takata and Noguchi (J. Stat. Phys. 172:880-903, 2018) by Noguchi and Takata in order to describe phase transition of fluids by kinetic equations. We prove that, when the scale parameter tends to 0, this model converges to a nonlocal Cahn-Hilliard equation with degenerate mobility. For our analysis, we introduce apropriate forms of the short and long range potentials which allow us to derive Helmhotlz free energy estimates. Several compactness properties follow from the energy, the energy dissipation and kinetic averaging lemmas. In particular we prove a new weak compactness bound on the flux.

Probing the Critical Nucleus Size in the Metal-Insulator Phase Transition of VO_{2}.

In a first-order phase transition, critical nucleus size governs nucleation kinetics, but the direct experimental test of the theory and determination of the critical nucleation size have been achieved only recently in the case of ice formation in supercooled water. The widely known metal-insulator phase transition (MIT) in strongly correlated VO_{2} is a first-order electronic phase transition coupled with a solid-solid structural transformation. It is unclear whether classical nucleation theory applies in such a complex case. In this Letter, we directly measure the critical nucleus size of the MIT by introducing size-controlled nanoscale nucleation seeds with focused ion irradiation at the surface of a deeply supercooled metal phase of VO_{2}. The results compare favorably with classical nucleation theory and are further explained by phase-field modeling. This Letter validates the application of classical nucleation theory as a parametrizable model to describe phase transitions of strongly correlated electron materials.

SECOND-ORDER PHASE TRANSITIONS IN CRYSTALLINE MEDIA UNDER THE TEMPERATURE EFFECTS

Various approaches to describe phase transitions in crystalline media are considered: Landau phenomenological approach of second-order phase transitions as well as Kolmogorov’s, Avrami’s and Christian’s theories of crystallization. An analysis of the existing approaches indicates that they do not always adequately describe the experimental results. A qualitative model for describing the dependence of a crystalline substance heat capacity on temperature at a constant volume is proposed in this paper. The model describes the change in the number of particles of a new phase of a crystalline substance at a constant volume and is based on Einstein principle of detailed balance. An expression for metal heat capacity adequately corresponded to Dulong-Petit heat capacity is obtained. A model for describing the dependence of heat capacity on temperature in case of phase transitions is proposed.

THE STATE OF THE PROBLEM OF THE JOINT MOVEMENT OF FLUID IN THE PORE SPACE

This article discusses the problems of studying the issue of joint motion of liquids in the porous space. The article provides the construction of a mathematical model of the theory of ltration, which describes phase transitions. The main diculty in constructing this model is associated with the fact that free interphase boundaries create regions that change over time, and it is required to nd the temperature or concentration elds of substances in them. In this case, the coordinates of the considered phase boundaries are not initially specied and must be calculated already in the process of solving. For this, a derivation of the averaged equation for the problem of nding the rupture surface during the movement of two incompressible viscous liquids in the pores of the soil skeleton was proposed. The article deals with the case when the skeleton is an absolutely rigid body. The rationale was given for the choice of an averaged ltration model instead of a microscopic one. The main research methods are classical methods of mathematical physics, functional analysis and computation methods of the theory of partial dierential equations, as well as dierence methods. The formulation of the problem is given, and the denition of a generalized solution for solving the problem is provided. Next, an averaged model is derived and the existence of at least one generalized solution to the problem is proved.

A unified theory of free energy functionals and applications to diffusion

SignificanceThe free energy functional is a central component of continuum dynamical models used to describe phase transitions, microstructural evolution, and pattern formation. However, despite the success of these models in many areas of physics, chemistry, and biology, the standard free energy frameworks are frequently characterized by physically opaque parameters and incorporate assumptions that are difficult to assess. Here, we introduce a mathematical formalism that provides a unifying umbrella for constructing free energy functionals. We show that Ginzburg-Landau framework is a special case of this umbrella and derive a generalization of the widely employed Cahn-Hilliard equation. More broadly, we expect the framework will also be useful for generalizing higher-order theories, establishing formal connections to microscopic physics, and coarse graining.

Thermal-Hydraulic-Mechanical Coupling Research on Overburden Pressure Mitigated Ice Lens Growth in the Freezing Soil

Frost heave induced ground surface uplift can have a destructive impact on infrastructures when freezing methods are used for underground construction. The complexity of overburden pressure and the coupled heat and mass transport interaction and their relation to different water flow rates make frost heave modelling an interesting but challenging task. A frost heave model describing phase transition and multiphase interactions (liquid-crystal-soil matrix) is presented in this paper and used to investigate the kinetic growth of the ice lens. By introducing water activity determined growth rate of ice crystals, the micro- and mesophysical mechanisms underlying ice lens growth involve ice crystal nucleation, crystallization, phase transition, and water migration in the frozen fringe are explored. This work indicates that the frozen fringe thickness, the ice crystals growth and the cryogenic-suction in the frozen fringe are particularly significant in determining the ice lens growth kinetics (frost heave) under different overburden pressures. The variation in ice lens growth under various overburden pressures appears to be controlled by the water flow path, cryogenic-suction, and permeability of the frozen fringe. This research reveals the kinetic growth of the ice lens, and helps to evaluate and mitigate geological hazards when artificial ground freezing is applied.

Формирование фазовых состояний PbFe-=SUB=-0.5-=/SUB=-Nb-=SUB=-0.5-=/SUB=-O-=SUB=-3-=/SUB=-: описание на основе многоминимумных моделей

Two ferroelectric phase transitions are observed in the PbFe0.5Nb0.5O3 crystal. The first is between the cubic and tetragonal phase, the second is between the tetragonal and monoclinic phases. To describe phase transitions and emerging phases, a statistical model is proposed, based on the composition of two multi-minimum models - a six-minima model for the Pb cation and an eight-minima model for the Nb cation. Adjusting the model parameters, makes it possible to reproduce all the characteristic features of the thermodynamic behavior of the crystal. The most interesting is the formation of a ferroelectric, complexly ordered monoclinic phase with Cm symmetry. It is shown that the mentioned monoclinic phase arises due to the fact that the first-order phase transition to the rhombohedral ferroelectric phase occurs in the presence of an "external field" of tetragonal symmetry. The contribution of the subsystems of Pb and Nb cations to the features of the dielectric and structural properties of the crystal is estimated.

Study of the activation barrier of metastable liquid crystallization by metadynamics

The crystallization of Lennard-Jones fluid under weak supercooling was studied in molecular dynamics simulation with the metadynamics method. The Steinhardt parameter Q6 for a group of particles around a random atom and the system's potential energy were chosen to describe phase transition. The change in collective variables was observed in the process of overcoming the activation barrier of crystallization. The critical nucleus formation data were obtained. Keywords: metadynamics, Lennard-Jones fluid, metastability, activation barrier.

Formation of phase states in PbFe-=SUB=-0.5-=/SUB=-Nb-=SUB=-0.5-=/SUB=-O-=SUB=-3-=/SUB=-: Description based on multiminima models

Two ferroelectric phase transitions are observed in the PbFe0.5Nb0.5O3 crystal. The first is between the cubic and tetragonal phase, the second is between the tetragonal and monoclinic phases. To describe phase transitions and emerging phases, a statistical model is proposed, based on the composition of two multi-minimum models --- a six-minima model for the Pb cation and an eight-minima model for the Nb cation. Adjusting the model parameters, makes it possible to reproduce all the characteristic features of the thermodynamic behavior of the crystal. The most interesting is the formation of a ferroelectric, complexly ordered monoclinic phase with Cm symmetry. It is shown that the mentioned monoclinic phase arises due to the fact that the first-order phase transition to the rhombohedral ferroelectric phase occurs in the presence of an "external field" of tetragonal symmetry. The contribution of the subsystems of Pb and Nb cations to the features of the dielectric and structural properties of the crystal is estimated. Keywords: ferroelectric relaxors, phase transitions, multiminima models, ferroelectric monoclinic phase.

Numerical investigation of flows with condensation in micronozzles

The paper considers the numerical simulation of the flow of argon with account for the condensation process in the micronozzle and behind it. To describe phase transitions, the initial mathematical model of viscous heat-conducting gas flow is supplemented with the equation of formation and growth of condensation nuclei in the flow. The developed mathematical model allows for simulating the process of gas condensation at low pressures and temperatures. It is shown that the condensate mass fraction in the flow is not less than 1% at the pressure and temperature of 5 bar and 200 K, respectively, when argon flows out of a micronozzle to the environment with the pressure of 0.01 Pa. At the nozzle exit, the size of condensed particles reaches 80 angstroms. The obtained results confirm the necessity to take into account the condensation phenomenon in micronozzle flows of inert gases.

Phase Behaviors of Giant Surfactants with Different Numbers of Fluorinated Polyhedral Oligomeric Silsesquioxane "Heads" and One Poly(ethylene oxide) "Tail" at the Air-Water Interface.

Giant surfactants with different numbers of aryl-trifluorovinyl ether-functionalized polyhedral oligomeric silsesquioxane (FVPOSS) heads and one poly(ethylene oxide) (PEO) tail, (FVPOSS)n-PEO227, are precisely synthesized. The phase behaviors of (FVPOSS)n-PEO227 at the air-water interface were investigated through surface pressure measurements (isotherm and hysteresis experiments) and the Brewster angle microscopy. Upon increasing the number of FVPOSS heads, the interfacial behaviors of these giant surfactants greatly change. More phase transitions occur during the compression as the number of FVPOSS heads increased from one to two and three. The evolution of morphologies of Langmuir films and compression-expansion hysteresis curves further illustrate phase transitions at the air-water interface. Furthermore, molecular mechanisms to describe phase transitions of (FVPOSS)n-PEO227 at the interface are put forward. This study deepens the understanding of interfacial phase behaviors of special giant surfactants and provides knowledge of nanostructure design and construction at the interface.

Compounds Produced by the Pyrolysis of Powders and Dusts Present in the Alimentary Industry

ABSTRACT Under certain conditions dust explosions occur in the alimentary industry. Following ATEX and other guidelines have not eliminated accidents. Therefore, more knowledge is needed. The current work delivers experimental results describing phase transitions and decomposition of dusts. Dusts from wheat flour, chili powder, corn starch, milk powder, cocoa powder, and by-product of grain are investigated. The temperature of pyrolisation has been identified using TGA to be in the range [250°C, 600°C] in air and [300°C, 450°C] in nitrogen. It was found that the compositions of the pyrolysis gases depend on temperature. Carbon monoxide, carbon dioxide, methane, and hydrogen were the main contributors to the pyrolysis gases. The distributions are described with a polynomial or Gaussian fit. The current paper proposes coefficients for Gaussian polynomials expressing the concentration for the four primary pyrolysis gases.

Natural Convection Melting Influence on the Thermal Resistance of a Brick Partially Filled with Phase Change Material

The constant growth of urban agglomerations with the development of transport networks requires the optimal use of energy and new ways of storing it. Energy efficiency is becoming one of the main challenges of modern engineering. The use of phase change materials in construction expands the possibilities of accumulating and storing solar energy, as well as reducing energy consumption. In this study, we consider the problem of the effect of natural convection on heat transfer in a building block containing a phase change material. Heat transfer, taking into account melting in brick, was analyzed at various temperature differences. The mathematical model was formulated in the form of time-dependent equations of conjugate natural convection using non-dimensional stream function, vorticity, and temperature. The equations describing melting, taking into account natural convection, were solved using the finite difference method. Smoothing parameters were used to describe phase transitions in the material. As a result of calculations, local characteristics of heat and mass transfer at various points in time were obtained, as well as changes in temperature profiles on the side surfaces. It is shown that with a large volume of melt, natural convection increases heat loss by more than 10%.

Model Variational Phase Transition Problem in Continuum Mechanics

We formulate and study the model variational problem describing phase transitions in two-phase media. Based on this study, we obtain an information about properties of solutions to the problem on equilibrium of a two-phase medium in the traditional statement.