On the theory of phase transformations with a nonuniform nucleation rate

An expression for the phase volume fraction in a system with a nonuniform nucleation rate is derived by using the geometrical-probabilistic approach. Examples of such systems considered here are (1) a plane layer (with nucleation in the midplane) and random planes in space, (2) an infinitely long cylinder (with nucleation on the axis) and random lines in space, and (3) a sphere (with nucleation at the center) and nucleation at random points. In each case, an expression for the phase volume fraction is derived for the time-dependent rates of nucleation and growth. The equivalence of homogeneous nucleation and nucleation at points is established.     

过热液氦均匀核化速率的确定

预测不同压力下过热液氦的均匀核化速率是十分重要的,它与液氦的极限过热度密切相关。文中通过回顾动力学理论、分子聚集理论、涨落理论等研究液体均匀核化的方法,对过热液氦的均匀核化速率进行了计算,并且对各种方法进行了比较与分析。结果表明,用能量涨落理论来计算过热液氦的均匀核化速率是一种比较合理的方法。     

Test of the validity of the adiabatic approximation in scattering theory

Exact solutions for the scattering of a fast projectile x on deuterium are compared with various versions of the fixed scatterers approximation. The content of the approximations for a nucleon and a different projectile is discussed. The calculations show the approximate agreement of angular distributions in forward direction and the amount of disagreement in the backward hemisphere. In the case of nucleon scattering the importance of nucleon exchange, neglected in the FSA, is explicitly demonstrated. As expected, the quality of the tested approximations rapidly improves with diminishing mass ratio M_x/M_N.     

On the validity of the narrow band approximation

The accuracy of the narrow band approximation is estimated. It is shown that, in order to assess the accuracy of the approximation, not only the form of the source function but also the form of the integrand is required. The accuracy is improved when the integrand is symmetric.     

Classical theory of homogeneous nucleation in superheated liquids and its experimental verification

This work summarizes the cycle of investigations devoted to determination of the character of superheated liquid boiling-up in a glass capillary at the boundary of the attainable superheating. The brief history of studies is followed by a brief introduction into the theory of homogeneous nucleation. The result of the targeted experiments determining stationarity of a random process of a supercritical embryo generation is considered. From the experiments it may be concluded that the process is unsteady. Based on a large selection of life spans of superheated liquids, the authors have made parametric and nonparametric evaluations of the functions of distribution and dependence of boiling-up frequency on time. The comparison of the obtained results with exponential distribution shows significant differences that also prove the nonstationarity of the studied random process. Special experiments and calculations for evaluation of homogeneity of the superheated liquid boilingup at the boundary of attainable superheating are considered. It is shown that in the experiments with glass capillary, the boiling-up occurs on the wall. As the most convincing evidence of heterogeneity of the superheated liquid boiling-up in a glass capillary the authors provide the results of high-speed video filming in a silylated and clean capillaries.     

On the validity of the quasi-particle approximation in nuclear physics

The validity of the quasi-particle approximation for the two-point function in nuclear physics is tested by means of one-particle strengths taken from (d, p) reactions. It is found that in general the quasi-particle approximation is not justified.     

Transient time in homogeneous nucleation

The problem of the transient time in nucleation is studied. The size-dependent transient time at a constant temperature is defined and the approximate analytical solution is found and compared with the exact numerical solution for the model Li₂O.2 SiO₂ melt. It is shown that the analytical solution for the size-dependent transient time is in agreement with the numerical result.     

On the homogeneous nucleation and propagation of dislocations under shock compression

The dynamic response of crystalline materials subjected to extreme shock compression is not well understood. The interaction between the propagating shock wave and the material’s defect occurs at the sub-nanosecond timescale which makes in situ experimental measurements very challenging. Therefore, computer simulation coupled with theoretical modelling and available experimental data is useful to determine the underlying physics behind shock-induced plasticity. In this work, multiscale dislocation dynamics plasticity (MDDP) calculations are carried out to simulate the mechanical response of copper reported at ultra-high strain rates shock loading. We compare the value of threshold stress for homogeneous nucleation obtained from elastodynamic solution and standard nucleation theory with MDDP predictions for copper single crystals oriented in the [0 0 1]. MDDP homogeneous nucleation simulations are then carried out to investigate several aspects of shock-induced deformation such as; stress profile characteristics, plastic relaxation, dislocation microstructure evolution and temperature rise behind the wave front. The computation results show that the stresses exhibit an elastic overshoot followed by rapid relaxation such that the 1D state of strain is transformed into a 3D state of strain due to plastic flow. We demonstrate that MDDP computations of the dislocation density, peak pressure, dynamics yielding and flow stress are in good agreement with recent experimental findings and compare well with the predictions of several dislocation-based continuum models. MDDP-based models for dislocation density evolution, saturation dislocation density, temperature rise due to plastic work and strain rate hardening are proposed. Additionally, we demonstrated using MDDP computations along with recent experimental reports the breakdown of the fourth power law of Swegle and Grady in the homogeneous nucleation regime.     

On a reconsideration of classical nucleation theory

A correct account of the collective motion of a cluster does not require the Lothe-Pound correction; furthermore, this correction is shown to contradict the laws of thermodynamics.     

Extended (n/v)-Stillinger cluster for use in the theory of homogeneous nucleation

In this paper we develop a theory for an extended version of the (n/v)-Stillinger cluster that has been used in nucleation theory, where n means the number of particles constituting the cluster characterized by the volume v. The "extended cluster" incorporates some of the surrounding supersaturated vapor. This cluster, although requiring more extensive simulation than the original (n/v)-Stillinger cluster, is almost devoid of approximation. It maintains the non-ad-hoc nature of the original (n/v)-Stillinger cluster implicitly. The theory of the cluster is also applicable to clusters which avoid redundancy by some other means than the so-called "connectivity requirement." Simulation of the extended cluster is now being implemented and will be used in the theory of the homogeneous nucleation rate.     

On the post-Newtonian approximation of the Einstein-Cartan-Sciama-Kibble theory

The post-Newtonian approximation of the Einstein-Cartan-Sciama-Kibble or ECSK theory is developed. It is used to obtain a drastic reduction on the density of the source needed to detect the spin. It is also proved that if we know the structure of the source, up to order ¯v, the spin can be detected, and if we know it up to order ¯v² the theory can be verified.Supported by a scholarship from the Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET).     

On the eikonal approximation in the theory of transition radiation

The transition radiation of relativistic electrons in nonuniform media is considered. Based on the equivalent photon method and the eikonal approximation in wave mechanics, a method for describing this process is proposed. For the case in which the permittivity depends on several coordinates, equations for the spectral-angular density of transition radiation are obtained. The main results obtained in the Born and eikonal approximations of the theory of transition radiation are compared. The equations obtained are used to analyze the transition radiation process for a fiberlike target.     

On the post-Newtonian approximation of the ECSK theory II

We complete the PNA program for the ECSK theory. We find the general post-Newtonian equations of motion for the source. The different components of the complete affine connection, the torsion, and the energy-momentum tensor, as well as the conservation theorems of the theory, are developed for the case of an ideal fluid with spin in order to find the post-Newtonian trajectories of test particles exterior to the sources distribution. The main results are compared with the corresponding ones of general relativity.Supported by a scholarship from the Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET).     

Analytical calculation of the nucleation rate for first order phase transitions beyond the thin wall approximation

First order phase transitions in general proceed via nucleation of bubbles. A theoretical basis for the calculation of the nucleation rate is given by the homogeneous nucleation theory of Langer and its field theoretical version of Callan and Coleman. We have calculated the nucleation rate beyond the thin wall approximation by expanding the bubble solution and the fluctuation determinant in powers of the asymmetry parameter. The result is expressed in terms of physical model parameters. Received: 18 August 1999 / Published online: 14 October 1999     

On the validity of the variational approximation in discrete nonlinear Schrödinger equations

The variational approximation is a well known tool to approximate localized states in nonlinear systems. In the context of a discrete nonlinear Schrödinger equation with a small coupling constant, we prove error estimates for the variational approximations of site-symmetric, bond-symmetric, and twisted discrete solitons. This is shown for various trial configurations, which become increasingly more accurate as more parameters are taken. It is also shown that the variational approximation yields the correct spectral stability result and controls the oscillatory dynamics of stable discrete solitons for long but finite time intervals.     

On the validity of the inclusion of geometrical shadowing functions in the multiple-scatter Kirchhoff approximation

The validity of the geometrical shadowing functions for use in calculations of the light distribution scattered from a rough surface is investigated. By the use of the multiple-scatter Kirchhoff approximation, single- and double-scattered contributions are calculated with and without the incident, intrasurface and scatter-shadowing functions. Explicit conditions are given for the validity of the geometrical shadowing functions.     

On the Born-Oppenheimer approximation of wave operators in molecular scattering theory

In this paper we study the diatomic molecular scattering by reducing the number of particles through Born-Oppenheimer approximation. Under a non-trapping assumption on the effective potential of the molecular Hamiltonian we use semiclassical resolvent estimates to show that non-adiabatic corrections to the adiabatic (or Born-Oppenheimer) wave operators are small. Furthermore we study the classical limit of the adiabatic wave operators by computing its action on quantum observables microlocalized by use of coherent states.