Theory Of Phase Transitions Research Articles

Finite difference model for predicting road surface ice formation based on heat transfer and phase transition theory

Icy pavement surface significantly reduces the skid resistance of roads, and is an important cause of traffic accidents in winter. Reliable road surface icing prediction models are of great significance for decision making in winter road maintenance. This paper developed a finite difference model for predicting road surface ice formation based on heat transfer and phase transition theory. The input data included the meteorological data and road material properties. The output of the model included not only the road surface temperature, but also the road surface condition and ice thickness. To achieve this, the governing equation and boundary conditions were established based on the heat transfer theory. The energy exchanges during the transformation between ice and water were considered by calculating the latent heat based on the phase transition theory. The finite difference method was used to solve the above heat transfer problem. A series of laboratory experiments were designed and conducted to verify the accuracy of the prediction model. And an equation was established to estimate the time required for all surface water to condense into ice when necessary climatic factors were available. With the validated model, the effects of road materials and climatic factors on pavement surface ice formation were analyzed. The results show that cement concrete pavements are more likely to freeze than asphalt concrete pavement. Pavement consisted of a low-conductivity bottom layer, and high-conductivity surface and middle layers, is more suitable for preventing road surface ice in winter. The prediction model is useful for transportation agencies to understand the mechanism of road ice formation and ensure traffic safety in winter.

Дискретная модель эволюции информации сложной системы вблизи точки фазового перехода

Landau's theory of phase transitions and Frenkel's theory of heterophase fluctuations, due to their simplicity and efficiency, have acquired the status of universal theories that have numerous applications in various branches of science and technology. One of the important scientific directions in the development of the theory is the study of changes in information in complex systems. To date, an urgent task is the development of multilevel mathematical models of the dynamics of the transition of a macroscopic system to a new phase state, based on the analysis of changes in Shannon information. The paper proposes a discrete model of the phase transition at the microscopic level. The discrete phase transition model differs from the models used in the Landau and Frenkel theory by a smaller scale, which leads to a greater dependence on random factors. The model is based on the theory of Markov processes and the principle of maximum information or information entropy. The main mathematical apparatus is the Kolmogorov equations. For clarity, Kolmogorov graphs are used. Work results. A stochastic model of the phase transition at the microlevel is constructed. The model remains adequate both near the phase transition point and far from it. An estimate of the intensity of the evolution of the entropy of the system is given. The dynamics of phase change during transitions of the first and second order is obtained. Conditions for phase equilibrium are obtained for phase transitions of the first and second kind. A stochastic interpretation of the phenomenon of hysteresis at the microscopic level is given. The results obtained are in accordance with the principles of Landau and Frenkel's theory. The results of the work have prospects for application in forecasting crises of complex systems based on the dynamics of information changes.

Phase transitions driven by topological excitations and their tensor network approach

The fundamental concepts of phases of matter and thermal phase transitions constitute the cornerstone of our understanding of the physical universe. The historical development of the phase transition theory from Landau's spontaneous symmetry breaking paradigm to modern topological phase transition theories represents a major milestone in the evolution of numerous scientific disciplines. From the perspective of emergent philosophy, the interplay of topological excitations leads to enriched physical phenomena. One prominent prototype is the Berezinskii-Kosterlitz-Thouless (BKT) phase transition, where unbinding of integer vortices occurs in the absence of spontaneous breaking of continuous <i>U</i>(1) symmetry. Using the state-of-the-art tensor network methods, we express the partition function of the two-dimensional <i>XY</i>-related system in terms of a product of one-dimensional transfer operators. From the singularities of the entanglement entropy of the one-dimensional transfer operator, we accurately determine the complete phase diagram of the partition function. This method provides new insights into the emergent phenomenon driven by topological excitations, and sheds new light on future studies of 2D systems with continuous symmetries.

Effective medium theory for mechanical phase transitions of fiber networks.

Networks of stiff fibers govern the elasticity of biological structures such as the extracellular matrix of collagen. These networks are known to stiffen nonlinearly under shear or extensional strain. Recently, it has been shown that such stiffening is governed by a strain-controlled athermal but critical phase transition, from a floppy phase below the critical strain to a rigid phase above the critical strain. While this phase transition has been extensively studied numerically and experimentally, a complete analytical theory for this transition remains elusive. Here, we present an effective medium theory (EMT) for this mechanical phase transition of fiber networks. We extend a previous EMT appropriate for linear elasticity to incorporate nonlinear effects via an anharmonic Hamiltonian. The mean-field predictions of this theory, including the critical exponents, scaling relations and non-affine fluctuations qualitatively agree with previous experimental and numerical results.

Механизм распухания облучаемого оксидного ядерного топлива. Часть I. Режим штатного облучения

The fuel swelling during normal operation is considered within the framework of 1st kind phase transition theory. It is shown that the phase transition occurs in the supersaturated sold solution of vacancy-impurity complexes – Xe with vacancies in uranium dioxide. The analysis of fuel swelling and fission gas release from fuel doped with different additives during normal operation was carried out.

Order parameters in Dicke model

Dicke model provides describing the superradiance effect when the spontaneous emission of a great number of excited two-level atoms is running in a correlated way due to their interaction via field. The process is identical to a giant dipole emission. Since the ordering takes place, it is interesting to study the possibility for using the terms of phase transition theory in such physical situation. Equilibrium properties of Dicke type models were studied for a long time because of their relevance for explaining some phenomena in matter-field interaction. The existence of an ordered phase in the emitter subsystem together with macroscopic photon mode filling is established, wherein the correct solution requires the Bogolyubov concept of quasiaverages to exclude the phase uncertainty of quasispin component structures <R+> and <R-> (for the concentrated model). In this paper, the behavior of similar order parameters for the non-equilibrium process description is analyzed and using the order parameter <R+R-> associated with the squared electric dipole moment of the emitter complex is substantiated. Such fact justifies <R3> application in the literature devoted to the superradiance theory. The situation with quasiaverages is compared with the problem of uniformity breaking in the numerical modeling.

Formation of dissipative structures in microscopic models of mixtures with species interconversion

The separation of substances into different phases is ubiquitous in nature and important scientifically and technologically. This phenomenon may become drastically different if the species involved, whether molecules or supramolecular assemblies, interconvert. In the presence of an external force large enough to overcome energetic differences between the interconvertible species (forced interconversion), the two alternative species will be present in equal amounts, and the striking phenomenon of steady-state, restricted phase separation into mesoscales is observed. Such microphase separation is one of the simplest examples of dissipative structures in condensed matter. In this work, we investigate the formation of such mesoscale steady-state structures through Monte Carlo and molecular dynamics simulations of three physically distinct microscopic models of binary mixtures that exhibit both equilibrium (natural) interconversion and a nonequilibrium source of forced interconversion. We show that this source can be introduced through an internal imbalance of intermolecular forces or an external flux of energy that promotes molecular interconversion, possible manifestations of which could include the internal nonequilibrium environment of living cells or a flux of photons. The main trends and observations from the simulations are well captured by a nonequilibrium thermodynamic theory of phase transitions affected by interconversion. We show how a nonequilibrium bicontinuous microemulsion or a spatially modulated state may be generated depending on the interplay between diffusion, natural interconversion, and forced interconversion.

Full quantum theory of nonequilibrium phonon condensation and phase transition

Fr\"olich condensation is a room-temperature nonequilibrium phenomenon which is expected to occur in many physical and biological systems. Though predicted theoretically a half century ago, the nature of such condensation remains elusive. In this Letter, we derive a full quantum theory of Fr\"ohlich condensation from the Wu-Austin Hamiltonian and present for the first time an analytical proof that a second-order phase transition induced by nonequilibrium and nonlinearity emerges in the large-$D$ limit with and without decorrelation approximation. This critical behavior cannot be witnessed if external sources are treated classically. We show that the phase transition is accompanied by large fluctuations in the statistical distribution of condensate phonons and that the Mandel-Q factor which characterizes fluctuations becomes negative in the limit of excessive external energy input. In contrast with the cold atom equilibrium BEC, the Fr\"ohlich condensate is a result of the nonequilibrium driving where the pump plays a role of setting the number of particles, and the medium plays a role of setting the temperature. Hence, BEC can either arise by reducing the medium temperature at fixed pump (equilibrium case), or by increasing the pump at fixed medium temperature (nonequilibrium case).

Dynamic phase transition theory

Thermodynamic conventions suffer from describing dynamical distinctions, especially when the structural and energetic changes induced by rare events are insignificant. By using the ensemble theory in the trajectory space, we present a statistical approach to address this problem. Rather than spatial particle-particle interaction which dominates thermodynamics, the temporal correlation of events dominates the dynamics. The zeros of dynamic partition function mark phase transitions in the space-time, i.e., dynamic phase transition (DPT), as Yang and Lee formulate traditional phase transitions, and hence determine dynamic phases on both sides of the zeros. Analogous to the role of temperature (pressure) as thermal (mechanical) potential, we interpret the controlling variable of DPT, i.e., dynamic field, as the dynamical potential. These findings offer possibility towards a unified picture of phase and phase transition.

Fracton critical point at a higher-order topological phase transition

The theory of quantum phase transitions separating different phases with distinct symmetry patterns at zero temperature is one of the foundations of modern quantum many-body physics. Here we demonstrate that the existence of a two-dimensional topological phase transition between a higher-order topological insulator (HOTI) and a trivial Mott insulator with the same symmetry eludes this paradigm. We present a theory of this quantum critical point (QCP) driven by the fluctuations and percolation of the domain walls between a HOTI and a trivial Mott insulator region. Due to the spinon zero modes that decorate the rough corners of the domain walls, the fluctuations of the phase boundaries trigger a spinon-dipole hopping term with fracton dynamics. Hence we find that the QCP is characterized by a critical dipole liquid theory with subsystem U(1) symmetry and the breakdown of the area law entanglement entropy which exhibits a logarithmic enhancement: $Lln(L)$. Using the density matrix renormalization group method, we analyze the dipole stiffness together with the structure factor at the QCP, which provides strong evidence of a critical dipole liquid with a Bose surface, UV-IR mixing, and a dispersion relation $\ensuremath{\omega}={k}_{x}{k}_{y}.$

The early universe scenario in FRW and K-K models: A study

The early Universe has been a subject of research for many cosmologists and it is reviewed and analyzed rigorously in cosmology recently. Thermal history and theory of phase transition coordinate us to elucidate the evolution of the Universe at its early stages and is interesting to get a gist of early universe behavior. At phase transition, effective potential plays a significant role for the kinds of transition that occurred during the evolution.  The temperature, at which phase transition occurs, can be determined at minimum effective potential.  It is also known fact that temperature of the Universe has changed considerably with its evolution.  The present work investigates the time-temperature relation in four- dimensional and five-dimensional cosmological models.  A comparison of time- temperature relation in FRW model with that of Kaluza-Klein (K-K) model demonstrates that temperature decreases faster in Kaluza-Klein model. The investigation demonstrates the important role played by extra dimension in the study of time-temperature relation at the early Universe scenario.

The Boltzmann distribution function for equilibrium fluctuations

A complex of issues related to the problem of proving the Boltzmann formula for the probability density (distribution) w(η) of the values of a certain set of parameters η of an equilibrium system is investigated. The classical Boltzmann formula expresses this distribution through the non-equilibrium free energy of the system F (η) , which depends on the mentioned parameters. This is possible because after the occurrence of fluctuations, the system finds itself in a non-equilibrium state, which evolves further to equilibrium. The specified parameters are chosen according to the problem under consideration. In the theory of phase transitions, they are called the order parameters. Questions under consideration include definition and construction of the free energy F (η) of a non-equilibrium system and distribution w(η ) for it in the microscopic theory. The approaches of Landau, Leontovich, and Peletminsky are discussed. It is proposed to investigate the results for states in the vicinity of equilibrium. The leading ideas of the research are considering the non-equilibrium state as being realized in the presence of an appropriate external field, using the Gibbs formula for the non-equilibrium system entropy, and applying the Boltzmann formula as a definition of the free energy of the non-equilibrium system. The article is a continuation of the authors' works and sets the task of clarifying some of their statements as well as simplifying and clarifying the calculations. Among other things, the following are discussed: the formula for the expansion of the free energy of the system in powers of the field, the simplification of the distribution w(η ) calculation, the normalization of the approximate expressions for the distribution w(η) , the possibilities of studying the free energy of the equilibrium system using our expression for the effective Landau Hamiltonian, the refinement of the calculation of the non-equilibrium free energy of a spatially inhomogeneous system, the investigation of new types of effective interactions with the Landau Hamiltonian.

Landau theory for the Mpemba effect through phase transitions

The Mpemba effect describes the situation in which a hot system cools faster than an identical copy that is initiated at a colder temperature. In many of the experimental observations of the effect, e.g. in water and clathrate hydrates, it is defined by the phase transition timing. However, none of the theoretical investigations so far considered the timing of the phase transition, and most of the abstract models used to explore the Mpemba effect do not have a phase transition. We use the phenomenological Landau theory for phase transitions to identify the second order phase transition time, and demonstrate with a concrete example that a Mpemba effect can exist in such models.

Mechanical behavior of thermally-induced shape memory polymer composites thin-wall tube in non-uniform thermal field: Experiments and simulations

Thermally-induced shape memory polymer composites (SMPCs) have the capability to self-deploy when stimulated by a specific temperature. As a basic component of deployable truss structure, SMPCs thin-wall circular tubes will undergo complex non-linear deformation and changing thermal boundary conditions during application. This article aims to research the mechanical behavior of thermally-induced SMPCs thin-wall circular tubes in a non-uniform thermal field. Thermal properties of SMPCs including thermal conductivities and coefficients of thermal expansion are tested as fundamental temperature-dependent parameters. A 500 mm-long SMPCs thin-wall tube is conducted in the flattening-folding-cooling-reheating experiments through a specially manufactured loading apparatus. Combining phase transition theory and Fourier heat conduction, a coupling algorithm is proposed to describe the thermo-mechanical behavior of SMPCs, which is implemented by the user subroutines VUMAT by commercial finite element analysis packages ABAQUS. By comparing the results from the simulation of the non-uniform thermal field, the simulation of the uniform thermal field and experiments, the coupling algorithm is verified, and the effect on SMPCs from the non-uniform thermal field is given.

On behaviors of porous shape memory polymer under different loading conditions

Shape memory polymer (SMP) has drawn much attention in the fields of aerospace, microsystems and biomedicine as a typical smart material with unique shape memory properties. The porous SMPs (P-SMPs) have been manufactured for the applications of reduce noise and insulate thermal. A constitutive model of P-SMPs that proposed based on phase transition theory has been investigated in this work. First, combining Mori–Tanaka method and phase transition theory, a modified micromechanics constitutive model of P-SMPs has been presented to describe the thermal-mechanical behavior of P-SMPs. Then, a series of experiments including uniaxial tension, stress relaxation and thermal cycling test have been conducted to determine the parameters of the modified constitutive model. Finally, the correctness of the proposed constitutive model has been verified by comparing the results of the thermodynamic cycle process including heating recovery and cooling loading stages obtained by the numerical simulation results and thermodynamic cycle experiment. The results show that with a porosity f = 0.1, the strain and stress mean square errors of the constitutive model based on the phase transition theory are 0.22 and 0.0102, respectively, which means that the constitutive model proposed based on phase transition theory can reflect the shape memory properties of P-SMP materials.

Explorations on properties of ε′ phase and new crystalline phase of Fe3Ge alloy under high pressures

We calculated the lattice dynamics, elasticity, electron spin polarizability P(EF), and electron specific heat coefficient γ of the L12-Fe3Ge crystalline alloy under high pressure using first-principles method based on density functional theory. By comparing the lattice dynamics and elasticity of the ferromagnetic and non-magnetic systems, it can be found that the spontaneous magnetization of the system induces the dynamic stability of the system at low pressure (less than 6 GPa). Furthermore, the magnetostriction induced by the spontaneous magnetization enhances the elastic modulus of the system. With the increase of pressure, in the pressure range of 130-290 GPa where the spin magnetic moment of the system decreases sharply, the elastic modulus exhibits an abnormal behavior, which leads to double peaks in Poisson's ratio v and Pugh's ratio B/G, correspondingly, double valleys appear in shear modulus G, Young's modulus E and Debye temperature ΘD, which are associated with dynamic instability in the 130-290 GPa. Finally, for the phonon spectrum at 260 GPa with a significant imaginary frequency, the metastable orthogonal Fmmm structure is obtained using the soft mode phase transition theory. After comparing the enthalpy differences with different structures, it is found that the ferromagnetic Fmmm structure is a metastable phase, which is dynamic stable at 0 GPa and 260 GPa.

Phase transition grade and microstructure of AdS black holes in massive gravity

Considering that under the framework of the massive gravity theory, the interaction between the mass gravitons and Schwarzschild black hole (BH) could make it carry a scalar charge, the phase transition process caused by this scalar charge is investigated in this analysis. The phase transition grade and microstructure of those BHs are investigated from both macroscopic and microscopic points of view. From the macroscopic point of view, it is found that Ehrenfest equations are satisfied at the phase transition critical point, which implies that the phase transition grade of those BHs is second-order. Based on the BH molecules model and Landau continuous phase transition theory, the phase transition of those BHs from the microcosmic point of view is analyzed. The critical exponents obtained from the two perspectives are consistent. By investigating the Ruppeiner geometry, the microstructure feature of those BHs is revealed. These results suggest that the phase transition of BH in massive gravity is a standard second-order phase transition at the critical point, and the microscopic details of those BHs are different from the Reissner–Nordström AdS BH in standard Einstein gravity.

Atomic-Scale Observation of Grain Boundary Dominated Unsynchronized Phase Transition in Polycrystalline Cu2 Se.

Phase transition is a physical phenomenon that attracts great interest of researchers. Although the theory of second-order phase transitions is well-established, their atomic-scale dynamics in polycrystalline materials remains elusive. In this work, second-order phase transitions in polycrystalline Cu2 Se at the transition temperature are directly observed by in situ aberration-corrected transmission electron microscopy. Phase transitions in microcrystalline Cu2 Se start at the grain boundaries and extend inside the grains. This phenomenon is more pronounced in nanosized grains. Analysis of phase transitions in nanocrystalline Cu2 Se with different grain boundaries demonstrates that grain boundary energy dominates unsynchronized phase transition behavior. This suggests that the energy of grain boundaries is the key factor influencing the energetic barrier for initiation of phase transition. The findings advance atomic-scale understanding of second-order phase transitions, which is crucial for the control of this process in polycrystalline materials.

Damage Mechanism and Modeling of Concrete in Freeze–Thaw Cycles: A Review

The deterioration of concrete microstructures in freeze–thaw (F–T) cycles is the primary reason for the reduction in the service life of concrete. This paper reviews recent progress in the theory of damage mechanisms and damage models of concrete in F–T cycles. It is a detailed review of the salt-freeze coupling condition, microstructure testing, and models for the evolution of concrete properties that are subjected to F–T damage. Summarized in this paper are the deterioration theory of water phase transition; the mechanism of chloride-F–T and sulfate-F–T damage; the microstructure testing of hydration products, pore structure, microcracks, and interfacial transition zones (ITZ). Furthermore, F–T damage models for the macrostructure are presented. Finally, the issues that are existing in the research and outlook of concrete F–T damage are highlighted and discussed. This paper is helpful in understanding the evolution of F–T damage, and also provides a comprehensive insight into possible future challenges for the sustainable design and specifications of concrete in cold environments.

Modulation of polar dynamics with oxygen vacancies in Zn doped BaZr0.1Ti0.9O3

Zinc modified barium zirconium titanate ceramics have been fabricated by the solid-state reaction method. Crystallographic analysis shows that the ceramics exhibit tetragonal crystal structure with P4mm symmetry. The polar behavior of Zn doped BaZr0.1Ti0.9O3 [BZT] differs from the pure BZT compound, as observed from ferroelectric analysis. As a result of doping, the P-E loops become pinched and linear in the low field region as well as P-E loop characteristics transformed from single hysteresis to double hysteresis behavior. Double hysteresis behavior emerging in BZT ferroelectrics validates the leading characteristic of defective dipoles. The defect dipoles provide restoring force to the spontaneous dipoles and ease the recovery of domain towards its original orientation. To validate the role of defects dipoles in the synthesized ceramics, we performed P-E hysteresis measurement under field cooling protocol. P-E loops of field cooled doped-ceramics transformed into single hysteresis curve and shifts on field scale, which further confirms that the double hysteresis feature is associated with defects dipoles rather than antiferroelectric ordering. The normalized entropy curves, ΔS(E,T,x)/ΔSmax(E,TC,x), for x = 0–6%, follow the scheme of master curve with two reference temperatures and consistent with second-order phase transition theory. The dielectric spectroscopy and Arrott plot approach collectively reveal that Zn doping causes sharpening of Landau free energy profiles and doping increases the depth of double-well potential and lowers the polar dynamics. The room temperature energy storage efficiency (η∼83,x=6%) of BZT is significantly modified. Our study reveals that the interplay between ferroelectric dipoles and point defects opens a novel route toward the realization of efficient energy storage performance.