Model investigation of non-thermal phase transition in high energy collisions

The non-thermal phase transition in high energy collisions is studied in detail in the framework of random cascade model. The relation between the characteristic parameter A_p, of phase transition and the rank q of moment is obtained using Monte Carlo simulation, and the existence of two phases in self-similar cascading multiparticle systems is shown. The relation between the critical point qc of phase transition on the fluctuation parameter a is obtained and compared with the experimental results from NA22. The same study is carried out also by analytical calculation under central limit approximation. The range of validity of the central limit approximation is discussed.     

A two-gradient approach for phase transitions in thin films

Motivated by solid-solid phase transitions in elastic thin films, we perform a Γ-convergence analysis for a singularly perturbed energy related to second order phase transitions in a domain of vanishing thickness. Under a two-wells assumption, we derive a sharp interface model with an interfacial energy depending on the asymptotic ratio between the characteristic length scale of the phase transition and the thickness of the film. In each case, the interfacial energy is determined by an explicit optimal profile problem. This asymptotic problem entails a nontrivial dependance on the thickness direction when the phase transition is created at the same rate as the thin film, while it shows a separation of scales if the thin film is created at a faster rate than the phase transition. The last regime, when the phase transition is created at a faster rate than the thin film, is more involved. Depending on growth conditions of the potential and the compatibility of the two phases, we either obtain a sharp interface model with scale separation, or a trivial situation driven by rigidity effects.     

Mesures pluriharmoniques et comparaison de deux théories du potentiel au bord

To explore the possibility of developing a phase transition theory in quantum lattice systems within the C¹-framework, the notion of phase transition free states on UHF algebras is introduced and the relationship between phase transition free states and unique KMS states are studied.     

Dynamics of water evaporation fronts

The evolution and shapes of water evaporation fronts caused by long-wave instability of vertical flows with a phase transition in extended two-dimensional horizontal porous domains are analyzed numerically. The plane surface of the phase transition loses stability when the wave number becomes infinite or zero. In the latter case, the transition to instability is accompanied with reversible bifurcations in a subcritical neighborhood of the instability threshold and by the formation of secondary (not necessarily horizontal homogeneous) flows. An example of motion in a porous medium is considered concerning the instability of a water layer lying above a mixture of air and vapor filling a porous layer under isothermal conditions in the presence of capillary forces acting on the phase transition interface.     

Evolution of a Condensation Surface in a Porous Medium near the Instability Threshold

We consider the dynamics of a narrow band of weakly unstable and weakly nonlinear perturbations of a plane phase transition surface separating regions of soil saturated with water and with humid air; during transition to instability, the existing stable position of the phase transition surface is assumed to be sufficiently close to another phase transition surface that arises as a result of a turning point bifurcation. We show that such perturbations are described by a Kolmogorov–Petrovskii–Piskunov type equation.     

Ultradisperse-Diamond Nanoclusters. Fractal Structure and Diamond–Graphite Phase Transition

A systematic study of the diamond–graphite structural phase transition in ultradisperse-diamond clusters obtained by the detonation technique is reported. Samples of two types, differing in the kinetics of detonation-product cooling, were investigated. The phase transition was achieved under heating in an inert atmosphere in the temperature range 720–1400 K. X-ray characterization showed the ultradisperse-diamond, irrespective of the cooling rate used, to be a cluster material possessing a diamond structure with a characteristic nanocrystal size of 44 Å. The diamond–graphite structural phase transition in ultradisperse diamond is shown to start from the cluster surface inwards at T_pt≈1200 K, i.e., at substantially lower temperatures than is the case with bulk diamond single crystals. Ultradisperse-diamond clusters are shown to be fractal objects and the character of variation of the fractal dimension in the course of the diamond–graphite phase transition is studied.     

多机制半参数平滑转换回归模型——兼论我国宏观经济运行周期

本文结合多机制平滑转换回归模型和半参数平滑转换回归模型,提出多机制半参数平滑转换回归模型。对模型转换函数中的未知光滑有界函数采用级数估计,并给出了结合Back-fitting算法和非线性最小二乘法估计模型参数的具体执行步骤,随机模拟结果说明了本文模型和估计算法的可行性和灵活性。应用本文模型和估计算法对我国宏观经济运行周期的实证研究表明,我国经济增长的非线性结构可以分为四个显著不同的增长机制:扩张阶段、衰退阶段、收缩阶段、恢复阶段,并且宏观经济政策的作用有三到四个季度的迟滞效应。     

Branching of symmetric solution of molecular field equation

Branching of a completely symmetric solution of the molecular field equation is investigated under the assumption that the configuration space of a molecule is a certain groupQ. The scheme can be used to describe orientationally ordered and space-modulated structures. Phase transitions from an isotropic liquid to the nematic, cholesteric, and conic phases are considered. The relationship between the phase-transition characteristics (order, Curie point, symmetry of the newly formed phase) and the potential of the intermolecular interaction is established. Investigation of the isolated isotropic-liquid—two-axis-nematic phase transition point has shown that this is not always a second-order transition. The possible existence of a one-dimensional modulated structure having smectic-A symmetry is predicted. The corresponding phase transition follows a scenario different from that of the isotropic-liquid—smectic-A phase transition.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 90, No. 2, pp. 246–258, February, 1992.     

Renormalization group study of the melting of a two-dimensional system of collapsing hard disks

We consider the melting of a two-dimensional system of collapsing hard disks (a system with a hard-disk potential to which a repulsive step is added) for different values of the repulsive-step width. We calculate the system phase diagram by the method of the density functional in crystallization theory using equations of the Berezinskii–Kosterlitz–Thouless–Halperin–Nelson–Young theory to determine the lines of stability with respect to the dissociation of dislocation pairs, which corresponds to the continuous transition from the solid to the hexatic phase. We show that the crystal phase can melt via a continuous transition at low densities (the transition to the hexatic phase) with a subsequent transition from the hexatic phase to the isotropic liquid and via a first-order transition. Using the solution of renormalization group equations with the presence of singular defects (dislocations) in the system taken into account, we consider the influence of the renormalization of the elastic moduli on the form of the phase diagram.     

Shape memory and phase transitions for auxetic materials

We present a mathematical model describing the auxetic‐austenitic phase transition phenomenon by a second order shape memory phase transition. The typical properties of auxetic materials, as the negative Poisson ratio ν, are described by a function of the phase ?, called order parameter, which relates the phase transition with a change of the internal order structure of the material. In our model, the auxetic phase is represented by an order parameter ? = 1, which provides a negative Poisson's ratio, while the austenitic phase will be denoted by ? = 0. Copyright © 2013 John Wiley & Sons, Ltd.     

Hydrogen Storage: Modeling and Analytical Results

We present a thermomechanical model describing hydrogen storage by use of metal hydrides. The problem is considered as a phase transition phenomenon. The model is recovered by continuum mechanics laws, using a generalization of the principle of virtual power accounting for microscopic movements related to the phase transition. The resulting nonlinear PDE system is investigated from the point of view of existence, uniqueness, and regularity of solutions.     

DISCONTINUOUS TRAVELING WAVE ENTROPY SOLUTIONS OF A MODIFIED ALLEN-CAHN MODEL

This paper deals with the existence and the asymptotic behavior of discontinuous traveling wave entropy solutions for a modified Allen-Cahn model,in which,the usual Ficken-based model for phase transition is replaced with a more physical model with nonlinear diffusive flux. The discontinuous traveling waves correspond to the discontinuous phase transition phenomena.     

New parastatistics leading to classical thermodynamics: Physical interpretation

This paper presents UD-statistics almost coinciding with Gentile statistics for negative chemical potentials, but having another extension in the case of positive chemical potentials. The physical meaning of the metamorphosis of the phase transition of the third kind to the phase transition of the first kind is explained. The coincidence of isochores and isotherms in the supercritical domain corresponding to UD statistics is shown.     

Glass transition and crystallization process of hard magnetic bulk Nd60Al10Fe20Co10 metallic glass

Glass transition and crystallization process of bulk Nd60Al10Fe20Co10 metallic glass were investigated by means of dynamic mechanical thermal analysis (DMTA), differential scanning calorimetry (DSC), X-ray diffraction (XRD) and scanning electronic microscopy (SEM). It is shown that the glass transition and onset crystallization temperature determined by DMTA at a heating rate of 0.167 K/s are 480 and 588 K respectively. The crystallization process of the metallic glass is concluded as follows: amorphous α→α′＋metastable FeNdAl novel phase →α′＋primary δ phase→primary δ phase＋eutectic δ phase Nd3Al phase＋Nd3Co phase. The appearance of hard magnetism in this alloy is ascribed to the presence of amorphous phase with highly relaxed structure. The hard magnetism disappeared after the eutectic crystallization of amorphous phase.     

A model of incomplete phase transitions of gas hydrates in a porous medium

The kinetics of incomplete phase transitions of gas hydrates in a porous medium is considered. In such transformations, the solid hydrate and its decomposition products coexist in extended regions. The conservation laws that take into account mass, momentum, and energy transfer between the components of the medium are formulated. The concept of phase transition dissipation is introduced. A general form of the constitutive relations, which is necessary and sufficient for the entropy inequality to be satisfied in any processes involving a change of state of the medium, is found. A potential of the skeleton that takes into account the surface energy, the latent energy of the phase transition and the temperature dependence is proposed. A thermodynamically consistent kinetic equation is formulated. The conditions under which the phase transition of a hydrate begins and is completed are found. The problem of isothermal dissociation of a hydrate when the pressure on part of the boundary of the body is reduced is examined. The influence of several parameters of the model on the seepage of the decomposition products is investigated.     

A thermodynamically consistent Ginzburg–Landau model for superfluid transition in liquid helium

In this paper, we propose a thermodynamically consistent model for superfluid-normal phase transition in liquid helium, accounting for variations of temperature and density. The phase transition is described by means of an order parameter, according to the Ginzburg–Landau theory, emphasizing the analogies between superfluidity and superconductivity. The normal component of the velocity is assumed to be compressible, and the usual phase diagram of liquid helium is recovered. Moreover, the continuity equation leads to a dependence between density and temperature in agreement with the experimental data.     

Gauge theory of the liquid-glass transition in static and dynamical approaches

We propose static and dynamical formulations of the liquid-glass transition theory based on the glass gauge theory and the fluctuation theory of phase transitions. In accordance with the proposed theory, the liquid-glass transition is an unattainable second-order phase transition blocked by a premature critical slowing of the gauge field relaxation caused by the system frustration. We show that the proposed theory qualitatively agrees well with experimental data.     

Phase transition for dielectric breakdown model

In this paper, the phase transition for DBM when ν varies is investigated by using real-space renormalization-group method. The result demonstrates that there are phase transitions for almost all the value of ν, and we find a new result that the larger ν is, the larger the value of phase transition point q_c is.     

Existence and stability results for the hyperbolic Stefan problem with relaxation

Summary The aim of this paper is to study a phase transition model, based on the Cattaneo-Fourier constitutive law for the heat flux and on a relaxed constitutive law for the phase variable. In turn, the model describes fast processes of melting and crystallization with supercooling and superheating effects. We give existence and stability results for the former phase transition problem. Uniqueness is deduced from the stability result On leave from: Lavrent'ev Institute of Hydrodynamics, 630090 Novosibirsk, Academy of Sciences of Russia, Russia.     

Instability of the Phase Transition Front during Water Injection into High-Temperature Rock

Water injection into a high-temperature geothermal reservoir saturated with superheated vapor is investigated. A solution to the one-dimensional problem in the form of a traveling wave is found. It is shown that there exist two types of solutions which correspond to the boiling of water and the condensation of vapor. In the condensation regime with high initial pressure, vapor ahead of the phase transition front is shown to be in a supercooled state. For moderate or law initial pressure, solutions with condensation and boiling are thermodynamically consistent. Linear stability of the phase transition surface between the water and vapor regions is analyzed. It is shown that the phase transition front moving at constant velocity is always unstable.