Finite volume Kolmogorov-Johnson-Mehl-Avrami theory

We study the Kolmogorov-Johnson-Mehl-Avrami theory of phase conversion in finite volumes. For the conversion time we find the relationship tau(con)=tau(nu)[1+f(d)(q)]. Here d is the space dimension, tau(nu) the nucleation time in the volume V, and f(d)(q) a scaling function. Its dimensionless argument is q=tau(ex)/tau(nu), where tau(ex) is an expansion time, defined to be proportional to the diameter of the volume divided by expansion speed. We calculate f(d)(q) in one, two, and three dimensions. The often considered limits of phase conversion via either nucleation or spinodal decomposition are found to be volume-size dependent concepts, governed by simple power laws for f(d)(q).     

A damage model based on failure threshold weakening

A variety of studies have modeled the physics of material deformation and damage as examples of generalized phase transitions, involving either critical phenomena or spinodal nucleation. Here we study a model for frictional sliding with long-range interactions and recurrent damage that is parameterized by a process of damage and partial healing during sliding. We introduce a failure threshold weakening parameter into the cellular automaton slider-block model which allows blocks to fail at a reduced failure threshold for all subsequent failures during an event. We show that a critical point is reached beyond which the probability of a system-wide event scales with this weakening parameter. We provide a mapping to the percolation transition, and show that the values of the scaling exponents approach the values for mean-field percolation (spinodal nucleation) as lattice size L is increased for fixed R. We also examine the effect of the weakening parameter on the frequency-magnitude scaling relationship and the ergodic behavior of the model.     

Curvature-dependent surface tension of a growing droplet

A ghost interface simulation technique is developed and applied to supersaturated Lennard-Jones liquid-vapor interfaces. It is shown that the surface tension decreases approximately linearly with the supersaturation ratio and that it vanishes at the spinodal. The effect leads to a curvature-dependent surface tension since, it is argued, the local supersaturation of the vapor above a droplet is greater than in the bulk due to slow diffusion in the vapor phase. An analytic approximation is given for the local supersaturation ratio, and an analytic expression for this contribution to Tolman's length is derived. The theory gives a smaller critical radius and reduces the free energy barrier to nucleation compared to classical homogeneous nucleation theory, which have important implications for the kinetics of droplet and bubble formation.     

Monte Carlo methods for the study of phase transitions and phase equilibria

Monte Carlo methods can predict macroscopic properties of N-body systems from the (classical) Hamiltonian describing the interactions between the particles and hence can serve as a basic tool of equilibrium statistical mechanics, avoiding uncontrolled approximations. However, a necessary ingredientis the control of finite size effects. For this purpose, the finite size scaling analysis of suitable distribution functions is a powerful tool. The basic ideas of this approach will be discussed, including extensions to critical phenomena where the hyperscaling relation between critical exponents is violated (colloid-polymer mixtures in random media as a realization of the random field Ising model, phase transitions caused by competition of interfacial and surface effects, etc.) Finite size effects on two-phase coexistence cause the existence of a van-der-Waals-like loop, but it has a completely different origin, the “spinodal” reflecting the “droplet evaporation/condensation” transition. Also the possibility to extract interface free energies is discussed.     

Bubble dynamics in a strong first-order quark-hadron transition

We investigate the dynamics of a strong first-order quark-hadron transition driven by cubic interactions via homogeneous bubble nucleation in the Friedberg-Lee model.The one-loop effective thermodynamic potential of the model and the critical bubble profiles have been calculated at different temperatures and chemical potentials.By taking the temperature and the chemical potential as variables,the evolutions of the surface tension,the typical radius of the critical bubble,and the shift in the coarse-grained free energy in the presence of a nucleation bubble are obtained,and the limit on the reliability of the thin-wall approximation is also addressed accordingly.Our results are compared to those obtained for a weak first-order quark-hadron phase transition;in particular,the spinodal decomposition is relevant.     

Failure of length scaling in Wilson's ϵ expansion

We show that length scaling of the four-point scattering amplitude in Wilson's ? expansion is not consistent in the order of ?³. However, in conformity with conformal invariance at the critical point, momentum scaling in a given channel is consistent. This latter method permits us to calculate the dimension of the field φ² at the critical point without recourse to length scaling and one finds $\text{d}{}_{\mathrm{\phi }}\text{2 =}\text{d}\text{2}\text{?}\text{1}\text{ν}\text{to O}\text{(?}{}^2\text{)}$ as if length scaling were true. However, this does not imply Kadanoff's relation 2?α = νd which is predicted on length scaling. Indeed the above-mentioned inconsistency makes impossible the determination of α by these methods.     

Critical exponents of the Ising model on low-dimensional fractal media

The critical behavior of the Ising model on fractal substrates with noninteger Hausdorff dimension d_H<2 and infinite ramification order is studied by means of the short-time critical dynamic scaling approach. Our determinations of the critical temperatures and critical exponents β, γ, and ν are compared to the predictions of the Wilson-Fisher expansion, the Wallace-Zia expansion, the transfer matrix method, and more recent Monte Carlo simulations using finite-size scaling analysis. We also determined the effective dimension (d_ef), which plays the role of the Euclidean dimension in the formulation of the dynamic scaling and in the hyperscaling relationship d_ef=2β/ν+γ/ν. Furthermore, we obtained the dynamic exponent z of the nonequilibrium correlation length and the exponent θ that governs the initial increase of the magnetization. Our results are consistent with the convergence of the lower-critical dimension towards d=1 for fractal substrates and suggest that the Hausdorff dimension may be different from the effective dimension.     

Monte Carlo study of the effect of perturbations on critical droplets

We present a Monte Carlo study of the effect of perturbations on critical or nucleation droplets in both classical and spinodal nucleation. Locating the saddle point with an intervention technique, we determine that the effect of perturbations at the saddle point depends on their location in the droplet. We find that the most effective perturbations occur at the location of the maximum growth rate where the droplet is allowed to nucleate and grow unperturbed. Moreover, the decay of sufficiently perturbed droplets follows a path that can be best characterized as a growth mode in reverse, specifically the decay of classical droplets is at the surface and that of spinodal droplets at the center independent of the location of the perturbation.     

调幅分解及形核对相分离作用机理研究

以SCN-30wt%H₂O, SCN-50 wt%H₂O和SCN-80 wt%H₂O三组透明体系, 在恒温场下实现了形核和调幅分解两种过程; 在此基础上, 施加温度梯度, 研究了第二相液滴的迁移运动规律. 结果表明, 相分离在临界成分体系以调幅分解方式进行, 在另外两种体系中以形核长大方式进行; 调幅分解与形核过程相比, 反应进行得更快, 液滴长大到同一尺寸所需时间仅为形核所需时间的1/3—1/2. 且临界成分体系有更大的不混溶间隙, 所以第二相液滴具有更多迁移时间, 揭示了偏晶体系相分离过程中在临界成分处易获得壳-核组织的内在机理. 在单向温度场中, 测量了不同半径的液滴迁移速率, 并且与理论Marangoni迁移速率值作比较, 发现液滴迁移速率和Marangoni理论迁移速率符合较好. 说明了在较好地抑制自然对流条件下Marangoni迁移对于相分离过程起主要作用.     

Elucidating the mechanism of nucleation near the gas-liquid spinodal

We have constructed a multidimensional free energy surface of nucleation of the liquid phase from the parent supercooled and supersaturated vapor phase near the gas-liquid spinodal. In particular, we remove the Becker-Doring constraint of having only one growing cluster in the system. Close to the spinodal, the free energy, as a function of the size of the largest cluster, develops surprisingly a minimum at a subcritical cluster size. It is this minimum at intermediate size that is found to be responsible for the barrier towards further growth of the nucleus at large supersaturation. An alternative free energy pathway involving the participation of many subcritical clusters is found near the spinodal where the growth of the nucleus is promoted by a coalescence mechanism. The growth of the stable phase becomes collective and spatially diffuse, and the significance of a "critical nucleus" is lost for deeper quenches.     

Computational materials design of filled tetrahedral compound magnetic semiconductors

Based on first-principles calculations within the density functional theory, materials design of filled tetrahedral compound magnetic semiconductors is proposed. By using the Korringa–Kohn–Rostoker coherent potential approximation, electronic structures of Mn-doped LiZnAs, LiZnP and LiZnN are calculated. First, by estimating free energy, phase diagrams of these systems are predicted. It is shown that these systems are phase separating systems and favor spinodal decomposition. However, by introducing Li vacancies, spinodal decomposition is strongly suppressed and Mn can be doped up to high concentration. Moreover, the introduced Li vacancies induce ferromagnetic interaction between Mn and thus we can expect high Curie temperature (T_C) in these systems. To see the chemical trend, electronic structure and T_C of Li(Zn, Cr)As are also calculated.     

Nucleation rate of the quark-gluon plasma droplet at finite quark chemical potential

The nucleation rate of quark-gluon plasma (QGP) droplet is computed at finite quark chemical potential. In the course of computing the nucleation rate, the finite size effects of the QGP droplet are taken into account. We consider the phenomenological flow parameter of quarks and gluons, which is dependent on quark chemical potential and we calculate the nucleation rate of the QGP droplet with this parameter. While calculating the nucleation rate, we find that for low values of quark phenomenological parameter ?? _q , nucleation rate is negligible and when ?? _q increases, nucleation rate increases significantly.     

Metastability in a long range one-dimensional Ising model

Decay of the metastable state of the one-dimensional Ising model with an x^-α potential is investigated using instanton (critical droplet) techniques. Calculations indicating that the analytic structure of the free energy is modified by droplet-droplet interactions for 1 < α ? 1.2 are presented.     

Domain growth in chiral phase transitions

We study the kinetics of chiral phase transitions in quark matter. We discuss the phase diagram of this system in both a microscopic framework (using the Nambu-Jona-Lasinio model) and a phenomenological framework (using the Landau free energy). Then, we study the far-from-equilibrium coarsening dynamics subsequent to a quench from the chirally-symmetric phase to the massive quark phase. Depending on the nature of the quench, the system evolves via either spinodal decomposition or nucleation and growth. The morphology of the ordering system is characterized using the order-parameter correlation function, structure factor, domain growth laws, etc.     

Fusion of the extended modified liquid drop model for nucleation and dynamical nucleation theory

We present a new phenomenological approach to nucleation, based on the combination of the "extended modified liquid drop" model and dynamical nucleation theory. The new model proposes a new cluster definition, which properly includes the effect of fluctuations, and it is consistent both thermodynamically and kinetically. The model is able to predict successfully the free energy of formation of the critical nucleus, using only macroscopic thermodynamic properties. It also accounts for the spinodal and provides excellent agreement with the result of recent simulations.     

Predicting initial nucleation events occurred in a metastable nanodroplet during acoustic droplet vaporization

Acoustic droplet vaporization (ADV) capable of converting liquid perfluorocarbon (PFC) micro/nanodroplets into gaseous microbubbles has gained much attention due to its medical potentials. However, its physical mechanisms for nanodroplets have not been well understood due to the disappeared superharmonic focusing effect and the prominent Laplace pressure compared to microdroplets, especially for the initial ADV nucleation occurring in a metastable PFC nanodroplet. The classical nucleation theory (CNT) was modified to describe the ADV nucleation via combining the phase-change thermodynamics of perfluoropentane (PFP) and the Laplace pressure effect on PFP nanodroplets. The thermodynamics was exactly predicted by the Redlich–Kwong equation of state (EoS) rather than the van der Waals EoS, based on which the surface tension of the vapor nucleus as a crucial parameter in the CNT was successfully obtained to modify the CNT. Compared to the CNT, the modified CNT eliminated the intrinsic limitations of the CNT, and it predicted a larger nucleation rate and a lower ADV nucleation threshold, which agree much better with experimental results. Furthermore, it indicated that the nanodroplet properties exert very strong influences on the nucleation threshold instead of the acoustic parameters, providing a potential strategy with an appropriate droplet design to reduce the ADV nucleation threshold. This study may contribute to further understanding the ADV mechanism for PFC nanodroplets and promoting its potential theranostic applications in clinical practice.     

On the nucleation of hadronic domains in the quark-hadron transition

We present numerical results on bubble profiles, nucleation rates and time evolution for a weakly first-order quark-hadron phase transition in different expansion scenarios. We confirm the standard picture of a cosmological first-order phase transition, in which the phase transition is entirely dominated by nucleation. We also show that, even for expansion rates much lower than those expected in heavy-ion collisions nucleation is very unlikely, indicating that the main phase conversion mechanism is spinodal decomposition.     

ε-expansion calculations for spin-glasses

The critical properties of the spin-glass transition proposed by Edwards and Anderson are studied using the minimal subtraction method. The universal ratio of the second correction to scaling amplitude to the square of the first for the order parameter susceptibility χ₀ is calculated to first order in ε(ε=6?d). Comparison is made with Fisch and Harris' high temperature series analysis which incorporated Rudnick-Nelson-type corrections to scaling. Within the same formalism the critical exponents are calculated to second order in ε. They agree with the first order ε expansion of Harris, Lubensky and Chen.     

Properties of metastable ising models evolving under the Swendsen-Wang dynamics

The behavior of the metastable nearest neighbor Ising model governed by Swendsen-Wang dynamics (SW) is investigated ind=2. The results are compared to those obtained in standard Metropolis dynamics. Both the SW and Metropolis systems are observed to decay from the metastable state via the formation of nucleating droplets. Nucleation rates are measured and found to agree with those predicted by classical nucleation theory. The growth rates of the droplets are observed to differ between the two dynamics. In addition, the dynamic critical exponentz is measured in a mean-field (Curie-Weiss) metastable Ising model at the spinodal. It is found that for SW dynamics,z=2. Since this is the same value as that obtained in the Metropolis case, this result shows that SW does not change the dynamical universality class at the spinodal.