On the theory of transient nucleation at the intermediate stage of phase transitions

The evolution of a system of growing aggregates in a macroscopically homogeneous medium with account of both the reduction in metastability and the continuing initiation of new nuclei is studied. The corresponding integro-differential model describing the intermediate stage of phase transitions is solved analytically for arbitrary nucleation kinetics and growth rates of nuclei. An exact solution of the Fokker–Planck equation is found with allowance for the diffusivity along the axis of nucleus radii. In limiting cases of purely kinetic and mixed kinetic-diffusion rates of crystal growth for a special form of diffusivity, the obtained solutions transform to earlier known expressions.     

Enhancement of stochastic resonance in distributed systems due to a selective coupling

Recent massive numerical simulations have shown that the response of a "stochastic resonator" is enhanced as a consequence of spatial coupling. Similar results have been analytically obtained in a reaction-diffusion model, using nonequilibrium potential techniques. We now consider a field-dependent diffusivity and show that the selectivity of the coupling is more efficient for achieving stochastic-resonance enhancement than its overall value in the constant-diffusivity case.     

Interference model of femtosecond laser pulse conical emission in dispersive medium

A simple interference model is proposed for conical emission frequency-angular spectrum formation during the filamentation of femtosecond laser pulse in a nonlinear dispersive medium. The model allows to obtain analytical expressions for frequency-angular distributions of the supercontinuum spectral components of pulses at different wavelengths in media with arbitrary material dispersion law. The model reproduces the supercontinuum frequency-angular spectrum transformation for the case of laser pulse splitting into several subpulses and for multiple refocusing of the light field in filament. Frequency-angular spectra analytically calculated from the proposed interference model are in good agreement with the results of numerical simulations performed for the filamentation of femtosecond laser pulses in fused silica.     

Moisture diffusivity in structure of random fractal fiber bed

A theoretical expression related to effective moisture diffusivity to random fiber bed is derived by using fractal theory and considering both parallel and perpendicular channels to diffusion flow direction. In this Letter, macroporous structure of hydrophobic nonwoven material is investigated, and Knudsen diffusion and surface diffusion are neglected. The effective moisture diffusivity predicted by the present fractal model are compared with water vapor transfer rate (WVTR) experiment data and calculated values obtained from other theoretical models. This verifies the validity of the present fractal diffusivity of fibrous structural beds.     

Dynamical behaviour of stochastic dust charge fluctuations

The dynamics of stochastic dust charge fluctuations is investigated. An inhomogeneous Burgers equation with a linear forcing term is derived in which the Burgers term is proportional to the diffusivity of dust charge fluctuations. This novel equation is solved analytically. Possibility of turbulence due to stochastic charge fluctuations is highlighted.     

Transport of energetic particles by microturbulence in magnetized plasmas

Transport of energetic particles by the microturbulence in magnetized plasmas is studied in gyrokinetic simulations of the ion temperature gradient turbulence. The probability density function of the ion radial excursion is found to be very close to a Gaussian, indicating a diffusive transport process. The particle diffusivity can thus be calculated from a random walk model. The diffusivity is found to decrease drastically for high energy particles due to the averaging effects of the large gyroradius and orbit width, and the fast decorrelation of the energetic particles with the waves.     

Calculation of superdiffusion for the Chirikov-Taylor model

It is widely known that the paradigmatic Chirikov-Taylor model presents enhanced diffusion for specific intervals of its stochasticity parameter due to islands of stability, which are elliptic orbits surrounding accelerator mode fixed points. In contrast with normal diffusion, its effect has never been analytically calculated. Here, we introduce a differential form for the Perron-Frobenius evolution operator in which normal diffusion and superdiffusion are treated separately through phases formed by angular wave numbers. The superdiffusion coefficient is then calculated analytically resulting in a Schloemilch series with an exponent beta=3/2 for the divergences. Numerical simulations support our results.     

双相滞热传导的振动现象

本文用解析的方法研究了双相滞热传导的振动现象,给出了热传导振动发生的条件.发现传热介质的尺寸越小,热扩散系数越大,易引发温度场的振动现象.     

Ageing evaluation of thermal barrier coatings by thermal diffusivity

Ceramic thermal barrier coatings (TBC) are widely applied for protecting from combustion gases hot path components of gas turbines for both aero- and land-based applications. In order to prevent the detachment of TBC, it would be essential to monitor their degradation in terms of sintering kinetic. As sintering strongly affects also the thermal diffusivity of TBC, the idea is to measure the latter parameter to account for the former. The technique to measure thermal diffusivity using pulsed thermography is described, together with the model that leads to the identification of TBC diffusivity. Tests and results on specimens artificially aged are reported.     

Dark spatial solitons in discrete cubic media with self- and cross-phase modulation

We analytically study the background stability of dark strongly localized vectorial modes in discrete cubic media with self- and cross-phase modulation. The instability regions are identified as a function of the linear and non-linear coupling strength as well as the ratio between the background amplitudes of the two components. The respective instability gain is calculated. Approximate analytical solutions for vectorial discrete solitons of different topologies are derived. The analytical results obtained are confirmed by direct numerical simulations.     

The schmidt number of pure continuous-variable bipartite entangled states and the method of its calculation

The Schmidt number—the measure of entanglement of pure states of a continuous-variable bipartite system—is analytically calculated for a simple model of photon-atom scattering.     

Chaotic mixing of granular material in slowly rotating containers as a discrete mapping

Chaotic mixing of granular material in a two-dimensional slowly rotating noncircular container in the absence of granular diffusivity is studied analytically and numerically as a discrete mapping. The noncircularity of a drum produces a time periodic disturbance and chaotization of the flow field. The location of the fixed points of the mapping and the separatrices of the hyperbolic points are determined in a closed analytical form.(c) 1999 American Institute of Physics.     

Different methods of calculating the pinning energy of plane vortices in a 3D Josephson medium: A comparative study

The pinning energy of plane (laminar) vortices in a 3D Josephson medium is calculated within a continuous vortex model considering functions of two types: V=1−cosϕ and V= 2/π⁴ϕ²(2π−ϕ)². The shape and energy of the stable and unstable vortices are found with an algorithm for the exact numerical solution of a set of difference equations. The vortex magnetic and Josephson energies diverge. The magnetic and Josephson components of the pinning energy are close in magnitude but differ in sign; as a result, the total pinning energy is smaller than its components by one order of magnitude. This result is confirmed analytically. An analytical computing method within the continuous vortex model is suggested. This method preserves the difference terms in the energy expression. The magnetic energy found by this method differs from the Josephson energy in magnitude, and the magnetic component of the pinning energy is opposite in sign to the Josephson component. Comparative analysis of the approximate approaches to energy calculation within the continuous vortex model when the difference terms are retained and when they are replaced by derivatives is performed. It is shown that the continuous vortex model gives incorrect values of the Josephson and magnetic components of the pinning energy. The actual values are several tens or several hundreds of times higher than those obtained with the continuous vortex model. Yet, since the Josephson and magnetic components of the pinning energy have different signs, the exact value of the total pinning energy and the approximate value obtained within the continuous vortex model differ insignificantly.     

A framework for quality control and parameter optimization in diffusion tensor imaging: theoretical analysis and validation

In this communication, a theoretical framework for quality control and parameter optimization in diffusion tensor imaging (DTI) is presented and validated. The approach is based on the analytical error propagation of the mean diffusivity (D(av)) obtained directly from the diffusion-weighted data acquired using rotationally invariant and uniformly distributed icosahedral encoding schemes. The error propagation of a recently described and validated cylindrical tensor model is further extrapolated to the spherical tensor case (diffusion anisotropy approximately 0) to relate analytically the precision error in fractional tensor anisotropy (FA) with the mean diffusion-to-noise ratio (DNR). The approach provided simple analytical and empirical quality control measures for optimization of diffusion parameter space in an isotropic medium that can be tested using widely available water phantoms.     

Magnetic instability of a two-dimensional Anderson non-Fermi liquid

We show that in the Anderson model for a two-dimensional non-Fermi liquid a magnetic instability can lead to the itinerant electron ferromagnetism. The critical temperature and the susceptibility of the paramagnetic phase have been analytically calculated. The usual Fermi behavior is re-obtained by taking the anomalous exponent to be zero.     

New scenario to chaos transition in the mappings with discontinuities

We consider a many-parametric piecewise mapping with discontinuity. That is a one-dimensional model of singular dynamic system. The stability boundary are calculated analytically and numerically. New typical features of stable cycle structures and scenario to chaos transition provoked by discontinuity are found.     

在双电极对激光器中激光感生介质扩散的影响

从理论上研究了在ＣＯ２激光器中双电极对对激光感生介质扩散的影响，讨论了激光感生介质的扩散系数，传播速率以及感生介质密度并采用复化Ｓｉｍｐｓｏｎ公式进行了数值计算。所得结果在双电级对激光器的设计中有重要意义。     

Combustion waves in a model with chain branching reaction and their stability

In this paper the travelling wave solutions in the adiabatic model with the two-step chain branching reaction mechanism are investigated both numerically and analytically in the limit of equal diffusivity of reactant, radicals and heat. The properties of these solutions and their stability are investigated in detail. The behaviour of combustion waves are demonstrated to have similarities with the properties of non-adiabatic one-step combustion waves in that there is a residual amount of fuel left behind the travelling waves and the solutions can exhibit extinction. The difference between the non-adiabatic one-step and adiabatic two-step models is found in the behaviour of the combustion waves near the extinction condition. It is shown that the flame velocity drops down to zero as the extinction condition is reached. Prospects of further work are also discussed.     

利用WBEPM模型和稳定变分法计算氦原子的极化率和色散系数

以最弱受约束电子势模型(WBEPM)理论为基础,建立了计算氦原子多极动态极化率和相互作用色散系数的稳定变分方法.导出了该方法中所涉及的矩阵元和线性方程组的解析表达式.作为应用,具体计算了基态氦原子的极化率和两体色散系数,将计算结果与用其他方法所得到的结果进行了比较, 数据基本一致.