Phase Transition In Model Research Articles

A thermoviscoelastic model for the one-way and two-way shape memory effects of semi-crystalline polymers

Both one-way and two-way shape memory effects induced by crystallization and melting transitions have been recently demonstrated in several semi-crystalline polymers. The paper proposes a novel thermoviscoelastic phase transition model accounting for the underlying mechanisms of the material. The nonlinear Adam-Gibbs model of structural relaxation and a modified Eying model of viscous flow are incorporated to characterize the thermomechanical behaviors of the amorphous phase. Another main feature of the model lies in the characterization of the formation and melting of the crystalline phase based on a theory of multiple natural configurations. Comparisons with uniaxial shape memory experiments show that the model can well reproduce the stress-strain-temperature responses in different loading conditions.

Modelling strategy for tailorable mechanics and thermochemically driven shape memory effect in amorphous polymers

Thermochemically responsive shape-memory polymers (SMPs) with biocompatibility and variable stiffness have shown great potential in biomedical applications. However, it is difficult to characterize the relaxation behavior and visco-elastoplastic deformation of this kind of SMPs due to the complex interactions between polymer segments and solvent molecules. Herein, a thermo-chemo-mechanical coupling model was proposed to predict the shape-memory behavior and thermomechanical properties of SMPs at different solvent volume fractions and temperatures. By combining the Vrentas–Duta free volume theory and the Flory-Huggins theory, the effect of free volume change on the Gibbs free energy, chemical potential, thermal expansion coefficient, and relaxation time of SMPs was investigated. Subsequently, these functions were substituted into the Maxwell and Boyce models to characterize the visco-elastoplastic mechanical behavior of thermochemically responsive SMPs under large deformation. Based on the phase transition model, the chemical plasticizing effect of solvent molecules on the glass transition temperature, shape-recovery strain, and yield strength of SMPs was further investigated. The numerical results are in good agreement with the experimental results. The proposed model is expected to provide theoretical guidance for designing SMPs with tailorable mechanics.

Non-analyticity in holographic complexity near critical points

The region near a critical point is studied using holographic models of second-order phase transitions. In a previous paper, we argued that the quantum circuit complexity of the vacuum (C 0) is the largest at the critical point. When deforming away from the critical point by a term the complexity has a piece non-analytic in τ, namely . Here, as usual, and ξ is the correlation length and there are possible logarithmic corrections to this expression. That was derived using numerical results for the Bose–Hubbard model and general scaling considerations. In this paper, we show that the same is valid in the case of holographic complexity providing evidence that the results are universal, and at the same time providing evidence for holographic computations of complexity.

Critical dynamics in holographic first-order phase transition

We study the critical phenomena of the dynamical transition from a metastable state to a stable state in the model of first-order phase transition via two different triggering mechanisms. Three universal stages during the fully nonlinear evolution are extracted. On the one side, by perturbing the scalar source, an isolated seed nucleus is injected into an initial homogeneous state in the supercooled region. For critical parameters of the seed nucleus, the real-time dynamics reveal that the system will converge to a critically unstable state. For supercritical parameters, the system exhibits a phase separation, while for subcritical parameters falls back to homogeneous. The shape independence of the seed nucleus is also investigated, which implies that the critical phenomena are universal. On the other side, we propose a novel mechanism to render the critical phenomena via a collision of two gravitational shock waves on the dual geometries. Specifying an inhomogeneous momentum density, the initial system can be also attracted to a critically unstable state. Aside from these dynamical constructions, we also quantitatively analyze the critical nucleus preventing the system from reaching the final phase separation. We find the depth of the critical nucleus increases almost linearly with the temperature, which implies that the hotter the supercooled state is, the harder for it to trigger phase separation.

Numerical research on the cavitation effect induced by underwater multi-point explosion near free surface

In this study, the cavitation effect induced by two charges in underwater explosions near free surfaces is numerical researched by two dimensional compressible multiphase fluids based on a four-equation system with a phase transition model. The occurrence of the generation, development, and collapse of cavitation in two-charge underwater explosions near free surfaces can be captured directly. The detailed density, pressure, and vapor volume fraction contours during the interaction process are obtained and can better reveal the characteristic underlying the cavitation, free surface, and explosion bubbles. Numerical results reveal that the cavitation domain has expanded to an area much deeper than the explosion bubble location in two-charge underwater explosions, which should be paid enough attention due to its influence on the input load of underwater structures. The detailed density and pressure contours during the interaction process can also be captured and can better reveal the mechanism underlying the explosion bubble, cavitation, and surface wave dynamics. The present results can expand the currently limited database of multiphase fluid in underwater explosions and also provide new insights into the strong nonlinear interaction between underwater explosion and cavitation, which provides a deep understanding of multi-point explosions.

OPTIMAL TEMPERATURE DISTRIBUTION FOR A NONISOTHERMAL CAHN-HILLIARD SYSTEM IN TWO DIMENSIONS WITH SOURCE TERM AND DOUBLE OBSTACLE POTENTIAL

In this note, we study the optimal control of a nonisothermal phase field system of Cahn-Hilliard type that constitutes an extension of the classical Caginalp model for nonisothermal phase transitions with a conserved order parameter. It couples a Cahn-Hilliard type equation with source term for the order parameter with the universal balance law of internal energy. In place of the standard Fourier form, the con­stitutive law of the heat flux is assumed in the form given by the theory developed by Green and Naghdi, which accounts for a possible thermal memory of the evolution. This has the consequence that the balance law of internal energy becomes a second-order in time equation for the thermal displacement or freezing index, that is, a primitive with respect to time of the temperature. Another particular feature of our system is the presence of the source term in the equation for the order parameter, which entails further mathematical difficulties because the mass conservation of the order parameter is no longer satisfied. In this paper, we study the case that the double-well potential driving the evolution of the phase transition is given by the nondifferentiable dou­ble obstacle potential, thereby complementing recent results obtained for the differentiable cases of regular and logarithmic potentials. Be­sides existence results, we derive first-order necessary optimality condi­tions for the control problem. The analysis is carried out by employing the so-called deep quench approximation in which the nondifferentiable double obstacle potential is approximated by a family of potentials of logarithmic structure for which meaningful first-order necessary opti­mality conditions in terms of suitable adjoint systems and variational inequalities are available. Since the results for the logarithmic poten­tials crucially depend on the validity of the so-called strict separation property which is only available in the spatially two-dimensional situ­ation, our whole analysis is restricted to the two-dimensional case.

On the classical critical behavior of the specific heat capacity of a model of structural phase transitions with a long-range interaction

The critical specific heat capacity c of a d-dimensional model describing structural phase transitions in an anharmonic crystal with a long-range interaction (decreasing at large distances r as r −d−σ , 0 < σ ≤ 2) is studied near the classical critical point Tc . At temperatures T > Tc and for dimensions σ < d < 2σ (σ and 2σ are the lower and the upper critical dimensions, respectively) the critical specific heat capacity is obtained in the form c ≈ 1 − Dεαs , where D > 0 and αs < 0 depend only on the ratio d/σ, and ε = T/Tc −1 is a measure of the deviation from the critical point. For three fixed values of the ratio d/σ the dependence c ≈ c(ε) is graphically presented. It is shown that at all temperatures T ≤ Tc the specific heat capacity retains its maximum value, c max = 1. The critical exponent αs , obtained here, coincides with that of the known mean spherical model, while c max is different for the two models.

Keynote lecture. Constitutive modelling of phase transitions in granular soils

The use of numerical codes for simulating the propagation phase of fast landslides requires the definition of constitutive relationships suitable for the description of the mechanical behaviour of granular soils, under both solid and fluid conditions. In this paper, the authors briefly illustrate a constitutive modelling approach interpreting the material as a bi-phasic continuum, according to which the solid phase may behave like a solid, under quasi-static conditions, and a fluid, under collisional/dynamic conditions. The model presented seems to satisfactorily reproduce a series of results obtained by using a discrete element numerical code on mono and polydisperse granular specimens. The constitutive model has been implemented in a Material Point Method code to solve boundary value problems, in which strain rate large values are expected to influence the material response.

Manipulating topological Hall-like signatures by interface engineering in epitaxial ruthenate/manganite heterostructures.

Topologically protected non-trivial spin textures (e.g. skyrmions) give rise to a novel phenomenon called the topological Hall effect (THE) and have promising implications in future energy-efficient nanoelectronic and spintronic devices. Here, we have studied the Hall effect in SrRuO3/La0.42Ca0.58MnO3 (SRO/LCMO) bilayers. Our investigation suggests that pure SRO has hard and soft magnetic characteristics but the anomalous Hall effect (AHE) in SRO is governed by the high coercivity phase. We have shown that the proximity effect of a soft magnetic LCMO on SRO plays a critical role in interfacial magnetic coupling and transport properties in SRO. Upon reducing the SRO thickness in the bilayer, the proximity effect becomes the dominant feature, enhancing the magnitude and temperature range of THE-like signatures. The THE-like features in bilayers can be explained by a diffusive Berry phase transition model in the presence of an emergent magnetic state due to interface coupling. This work provides an alternative understanding of THE-like signatures and their manipulation in SRO-based heterostructures, bilayers and superlattices.

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.

Thermal free-surface immersed-boundary lattice Boltzmann method for free surface flows with a liquid-solid phase transition

This paper reports on the progress of the liquid-solid phase transition modeling of water in open channel flow by using the lattice Boltzmann method with the immersed boundary modification. The phase transition in a fluid flow has a moving interface between the liquid and solid state, which leads complicated treatments in existing numerical models. By applying the immersed boundary modification in the lattice Boltzmann method and the non-iterative enthalpy approach for the separation of the states, the moving boundary of the melting or solidification front is solved without any difficulty. The ice bed and the submerged ice cover under dynamic flow conditions is exercised to demonstrate the model performance. The model is extremely suitable in the formulation in terms of its simple and compact framework extendable to any dimensions.

Simulation Analysis of Emptying the Explosives in Projectiles with Electromagnetic Heating

This paper concerns a new method for projectile disposal by emptying the explosives in projectiles with electromagnetic heating. It explains the basic principles of the emptying technology via electromagnetic heating. A multiphysical analysis model coupled with an electromagnetic, thermal, fluid and phase transition model is established, and the explosive melting simulation is conducted based on this model. The dynamic phase transition process of the explosive from solid to liquid is simulated, and the electric field, magnetic field and thermal field distribution characteristics during the process are analyzed. Furthermore, the effect of excitation current characteristics on the phase transition of the explosive is given, which shows that the explosive melting process is controllable by setting the excitation current amplitude or frequency. This paper provides a new method for the disposal of end-of-life projectiles, which is more controllable, safe and environmentally friendly.

Statistical Multifragmentation Model within the Extended Morphological Thermodynamics Approach

On the basis of the morphological thermodynamics, we develop an exactly solvable version of the statistical multifragmentation model for the nuclear liquid-gas phase transition. It is shown that the hard-core repulsion between spherical nuclei generates only the bulk (volume), surface, and curvature parts of the free energy of the nucleus, while the Gaussian curvature one does not appear in the derivation. The phase diagram of the nuclear liquid-gas phase transition is studied for a truncated version of the developed model.

Theoretical and experimental study on rotating heat pipe towards thermal error control of motorized spindle

The thermal equilibrium time (TET) is extremely long, and the thermal elongation (TE) is obvious because the heat dissipation performance (HDP) is weak and the temperature gradient is significant for the high-speed motorized spindle (HSMS). Aiming at the above problems, a new rotating heat pipe (RHP) is designed towards the HSMS cooling and thermally induced error (TIE) control according to the working condition and geometric size constraint of the HSMS, and the theoretical and experimental studies are conducted on the designed RHP. To verify the heat transfer performance (HTP), the gas-liquid phase transition model is established for the designed RHP. A new test platform is constructed to simulate the actual service condition of the RHP and measure its HTP, and the experimental study is carried out for the designed RHP to get the optimal design parameters of the RHP. The temperatures and HTP obtained by the gas-liquid phase transition model agree well with the measured data. Finally, the designed RHP is embedded into the HSMS to increase the HDP and control the TIE. The fluid-thermal-solid interaction characteristic (FTSIC) models are established for the HSMS with the RHP and traditional fluid-cooled HSMS (FCHSMS) without the RHP. The results show that the designed RHP is effective to realize the HSMS cooling and TIE control, and finally the designed RHP and established FTSIC models are verified by carrying out the thermal behavior experiments.

Dynamical structural phase transition model of the electrical behavior of NiTi

A general phenomenological model of the kinetics of thermally induced structural phase transitions in multi-phase alloys is introduced for arbitrary numbers of lattice phases and transitions. The model is based on a system of ODEs yielding the temporal evolution of lattice phase fractions caused by temperature variation described by a heat balance equation. The kinetics of each transition are modeled by temperature rates of phase fractions rather than sigmoids, where an extra multiplicative parameter describing the shape of the transition rate curves is introduced. The model is applied to the electrical behavior of thin NiTi filaments by relating its resistivity to the relative proportions of three main structural phases, namely Martensite, Austenite and an intermediate phase, known as R-phase. The model yields resistivity time-series for successive heating/cooling cycles. Computer simulations are compared to previously published resistivity measurements on filaments self-heated by time-varying currents of various frequencies and passively heated samples.

A dynamic hysteresis model for customized glass transition in amorphous polymer towards multiple shape memory effects

Coexistence of multiple and discrete segments as well as their distinctive hysteresis relaxations enables amorphous shape memory polymers (SMPs) exhibiting complex disordered dynamics, which is critical for the glass transition behavior to determine the shape memory effect (SME), but remained largely unexplored. In this study, a dynamic hysteresis model is proposed to explore the working principle and collective dynamics in discrete segments of amorphous SMPs, towards a dynamic connection between complex relaxation hysteresis and glass transition behavior, which can be applied for design and realization of multiple SMEs in the amorphous SMPs. In combination of free volume theory and Adam-Gibbs domain size model, a phase transition model is formulated to identify the working principle of dynamic relaxation hysteresis in the glass transition of amorphous SMP. Furthermore, constitutive relationships among relaxation time, strain, storage modulus, loss angle and temperature have been established to describe the dynamic connection between complex relaxation hysteresis and customized glass transition, which is then utilized to achieve multiple SMEs based on the extended Maxwell model. Finally, effectiveness of the proposed models is verified using experimental results of SMPs with multiple SMEs reported in literature.

Numerical analysis of energy stable weak Galerkin schemes for the Cahn–Hilliard equation

In this paper, we construct and analyze the energy-stable weak Galerkin schemes for the Cahn–Hilliard equation in the mixed form. The energy stability depends on the newly defined discrete energy functional. We propose two robust weak Galerkin schemes with extra stabilizing terms in time: the first-order conditionally energy stable scheme of which the stability does not depend on spatial mesh size, and the second-order unconditionally energy stable scheme. Energy stabilities and error estimates for the fully discrete schemes are obtained. Numerical experiments are provided to validate the theoretical results. A classical phase transition model is presented to show the energy stable property of the schemes.

Controlling topological phases of matter with quantum light

Controlling the topological properties of quantum matter is a major goal of condensed matter physics. A major effort in this direction has been devoted to using classical light in the form of Floquet drives to manipulate and induce states with non-trivial topology. A different route can be achieved with cavity photons. Here we consider a prototypical model for topological phase transition, the one-dimensional Su-Schrieffer-Heeger model, coupled to a single mode cavity. We show that quantum light can affect the topological properties of the system, including the finite-length energy spectrum hosting edge modes and the topological phase diagram. In particular we show that depending on the lattice geometry and the strength of light-matter coupling one can either turn a trivial phase into a topological one or viceversa using quantum cavity fields. Furthermore, we compute the polariton spectrum of the coupled electron-photon system, and we note that the lower polariton branch disappears at the topological transition point. This phenomenon can be used to probe the phase transition in the Su-Schrieffer-Heeger model.

Size-Dependent Nucleation in Crystal Phase Transition from Machine Learning Metadynamics.

In this Letter, we present a framework that combines machine learning potential (MLP) and metadynamics to investigate solid-solid phase transition. Based on the spectral descriptors and neural networks regression, we develop a scalable MLP model to warrant an accurate interpolation of the energy surface where two phases coexist. Applying it to the simulation of B4-B1 phase transition of GaN under 50GPa with different model sizes, we observe sequential change of the phase transition mechanism from collective modes to nucleation and growths. When the size is at or below 128 000atoms, the nucleation and growth appear to follow a preferred direction. At larger sizes, the nuclei occur at multiple sites simultaneously and grow to microstructures by passing the critical size. The observed change of the atomistic mechanism manifests the importance of statistical sampling with large system size in phase transition modeling.

Study on the mechanism and load characteristics of secondary cavitation near free surface in underwater explosion

Although the cavitation phenomenon in underwater explosion has been researched for more than 100 years, the phase transition models based on mass and heat exchange between liquid and its vapor phases have only been established in the past decade. In this study, the secondary cavitation phenomenon was first captured by phase transition based on a four-equation system. The bulk cavitation near the free surface induced by underwater explosion was numerically investigated, and three typical bulk cavitation cases were investigated to explore their motion mechanisms and load characteristics on hydrodynamics and phase transition generation. It was found that secondary bulk cavitation will occur only under the condition that both the initial shock wave intensity and the distance between the water surface and the explosion bubble are satisfied in a specific relationship. Producing bulk cavitation was difficult at a relatively deep detonation depth because of the weak rarefaction wave reflected from the water surface by smaller charges. The statistical data under the condition of small charge indicated that the duration of cavitation increases with the increase in charge weight but the growth trend slows down gradually. However, the maximum volume of cavitation increased linearly with an increase in the charge weight. The present results can expand the currently limited database of underwater explosion multiphase fluids and provide insight into the interactions between the shock wave, bulk cavitation, explosion bubble, and water surface.