A computational approach towards modelling dislocation transmission across phase boundaries

To study the nanoscopic interaction between edge dislocations and a phase boundary within a two-phase microstructure the effect of the phase contrast on the internal stress field due to the dislocations needs to be taken into account. For this purpose a 2D semi-discrete model is proposed in this paper. It consists of two distinct phases, each with its specific material properties, separated by a fully coherent and non-damaging phase boundary. Each phase is modelled as a continuum enriched with a Peierls–Nabarro (PN) dislocation region, confining dislocation motion to a discrete plane, the glide plane. In this paper, a single glide plane perpendicular to and continuous across the phase boundary is considered. Along the glide plane bulk induced shear tractions are balanced by glide plane shear tractions based on the classical PN model. The model's ability to capture dislocation obstruction at phase boundaries, dislocation pile-ups and dislocation transmission is studied. Results show that the phase contrast in material properties (e.g. elastic stiffness, glide plane properties) alone creates a barrier to the motion of dislocations from a soft to a hard phase. The proposed model accounts for the interplay between dislocations, external boundaries and phase boundary and thus represents a suitable tool for studying edge dislocation–phase boundary interaction in two-phase microstructures.     

Absorption and generation of electromagnetic waves by structural inhomogeneities of solid

The integrability conditions of the electromagnetic field equations in a continuum with defects and their wave solutions are found. The following dislocation effects on the electromagnetic wave propagation in a continuous medium are investigated: the change in the direction of the electromagnetic wave propagation in a continuous medium; the rotation of the polarization plane of electromagnetic field wave in a continuous medium; the excitation of longitudinal components of the electromagnetic wave in a continuous medium and the change in the electromagnetic wave intensity related to this phenomenon. The energy balance equation for the electromagnetic field in a continuum with a stationary distribution of dislocation is found and it is shown that an electromagnetic wave excites exciton modes localized at dislocations in the solid.     

SH-wave propagation and resonance phenomena in a periodically layered composite structure with a crack

This paper presents a dynamic analysis of time-harmonic plane SH-waves propagating in periodically multilayered elastic composites with a strip-like crack. The total wave field in the multilayered elastic structure is described as a sum of incident wave field modeled by the transfer matrix method and the scattered wave field governed by an integral representation containing the crack-opening-displacement. The integral equation derived from the boundary conditions on the crack-faces is solved numerically by a Galerkin method. The paper focuses on resonant and non-resonant regimes of anti-plane wave motion in a stack of elastic layers weakened by a single strip-like crack and wave localization in the vicinity of the crack. The scattered extra displacement induced by the presence of the crack is investigated in detail for both situations of high and low contrast in material properties. Numerical results for the average crack-opening-displacement, the transmission coefficient, the stress intensity factor and the average energy flow are presented and discussed to reveal wave resonance and localization phenomena within the band-gaps and the pass-bands.     

On the electromagnetic energy density and energy transfer rate in a medium with dispersion due to conduction

The simplest dispersion relation determined by dissipation due to conduction is considered; the electromagnetic energy density in a plane monochromatic wave and its (phase and group) velocity are determined, as well as the energy and momentum transfer rates. It is shown that the energy density at low frequencies in this case has the form of the electrostatic density, in which the permittivity is replaced by its real part, and the energy transfer rate in a plane electromagnetic wave is equal to the phase velocity. The group velocity may exceed the speed of light.     

弯晶的沟道效应

本文引入正弦平方势,将弯晶中的粒子运动方程化为常力矩作用下的摆方程,并用非线性力学方法,详细讨论了系统的相平面特征,分析了相平面上奇点分布和相对运动对系统稳定性的影响,从系统的临界状态出发导出了动力学允许的临界参数和可能偏转的最大能量;此外,还考察了小振幅近似下的粒子运动行为,发现该系统具有软弹簧特征,用Jacobian椭圆函数和第一类全椭圆积分严格求解了运动方程和振动周期,导出了低能带电粒子在弯晶中的空间分布和动量分布。 关键词：     

Embedding of Particle Waves in a Schwarzschild Metric Background

The special and general relativity theories are used to demonstrate that the velocity of an unradiative particle in a Schwarzschild metric background, and in an electrostatic field, is the group velocity of a wave that we call a particle wave, which is a monochromatic solution of a standard equation of wave motion and possesses the following properties. It generalizes the de Broglie wave. The rays of a particle wave are the possible particle trajectories, and the motion equation of a particle can be obtained from the ray equation. The standing particle wave equation generalizes the Schrödinger equation of wave amplitudes. The particle wave motion equation generalizes the Klein–Gordon equation; this result enables us to analyze the essence of the particle wave frequency. The equation of the eikonal of a particle wave generalizes the Hamilton–Jacobi equation; this result enables us to deduce the general expression for the linear momentum. The Heisenberg uncertainty relation expresses the diffraction of the particle wave, and the uncertainty relation connecting the particle instant of presence and energy results from the fact that the group velocity of the particle wave is the particle velocity. A single classical particle may be considered as constituted of geometrical particle wave; reciprocally, a geometrical particle wave may be considered as constituted of classical particles. The expression for a particle wave and the motion equation of the particle wave remain valid when the particle mass is zero. In that case, the particle is a photon, the particle wave is a component a classical electromagnetic wave that is embedded in a Schwarzschild metric background, and the motion equation of the wave particle is the motion equation of an electromagnetic wave in a Schwarzschild metric background. It follows that a particle wave possesses the same physical reality as a classical electromagnetic wave. This last result and the fact that the particle velocity is the group velocity of its wave are in accordance with the opinions of de Broglie and of Schrödinger. We extend these results to the particle subjected to any static field of forces in any gravitational metric background. Therefore we have achieved a synthesis of undulatory mechanics, classical electromagnetism, and gravitation for the case where the field of forces and the gravitational metric background are static, and this synthesis is based only on special and general relativity.     

Stochastic electrodynamics. I. On the stochastic zero-point field

This is the first in a series of papers that present a new classical statistical treatment of the system of a charged harmonic oscillator (HO) immersed in an omnipresent stochastic zero-point (ZP) electromagnetic radiation field. This paper establishes the Gaussian statistical properties of this ZP field using Bourret's postulate that all statistical moments of the stochastic field plane waves at a given space-time point should agree with their corresponding quantized field vacuum expectations. This postulate is more than adequate to derive the Planck spectrum classically via Boyer's and Theimer's methods, but it requires that the stochastic amplitude of each linearly polarized plane wave in the field contain two independent Gaussian random variables, not just a random phase as has sometimes been assumed. In the succeeding papers in the series, the total motion of a charged HO is described by a fully renormalized dipole-approximation Abraham-Lorentz equation. This leads without further approximation to the following major results concerning this stochastic electrodynamics (SED) of the HO: i) The ensemble-average Liouville equation for the oscillator-ZP field system in the presence of an arbitrary applied classical radiation field is exactly equivalent to the usual time-dependent Schrödinger equation supplemented by an explicit radiation reaction vector potential similar to that of the Crisp-Jaynes-Stroud theory; ii) this SED Schrödinger equation for the HO is incomplete, insmuch as there exists a companion equation that restricts initial conditions such that the corresponding Wigner phase-space distribution is always positive; iii) the wave function of the SED Schrödinger equation has thea priori significance of position probability amplitude; iv) first-order transition rates predicted for the HO by this theory agree with those predicted by quantum electrodynamics for resonance absorption and spontaneous emission, which occurs with no triggering necessary; and v) if SED is taken seriously, then the concepts of quantized energies and photons must be abandoned.     

Energy flow model considering near field energy for predictions of acoustic energy in low damping medium

The Acoustic Energy Flow Boundary Element Method (AEFBEM) is developed to predict the acoustic energy density and intensity of an engineering system. Up to now, the acoustic energy flow model has been used only for analysis of high frequencies or radiation noise because of plane wave and far-field assumptions. In this research, a new energy flow governing equation that can consider the near field acoustic energy term and spherical wave characteristics is derived successfully to predict the acoustic energy density and intensity of a system in the medium-to-high frequency range. A near field term of acoustic energy in spherical coordinate is added to the relationship between energy density and energy flow. But with the far-field assumption, this term vanishes, so the relationship between energy density and energy flow becomes the same as that of the plane wave. By considering the near field energy term without far-field assumption, the energy density at medium frequencies can be estimated. However, the governing equation has to be numerically manipulated for use in the analysis of complex structures; therefore, the Boundary Element Method (BEM) is implemented. AEFBEM is a numerical analysis method formulated by applying the boundary element method to an acoustic energy flow governing equation. It is very powerful in predicting the acoustic energy density and intensity of complex structures in medium-to-high frequency ranges, and can analyze interior noise and radiating sound. To verify its validity, several numerical results are provided. BEM and AEFBEM were compared with respect to energy density, and the results from both methods were similar.     

Study on the validity region of Energy Finite Element Analysis

The validity domain of Energy Finite Element Analysis (EFEA) is studied in this paper. The validity region and criterion of EFEA are studied theoretically from the formation of reverberant plane wave field, one of the main assumptions of EFEA. The studies are acquired by virtue of the equation of radiative energy transfer method, a similar wave method that can express the direct field and its conversion relationship with reverberant field exactly. The result shows that the SEA criterion of diffuse field derived by Le Bot can be used as a good indicator for the EFEA validity. Numerical simulations on a rectangular plate with different physical parameters are applied to validate the criterion. The validity region and the diagrams of validity of EFEA are assessed and discussed. Some noteworthy conclusions about EFEA are drawn.     

晶体摆动场辐射系统的全局分叉与混沌行为

引入正弦平方势,在经典力学框架内和偶极近似下,考虑到运动阻尼和非线性影响,把粒子在晶体摆动场中的运动方程化为具有阻尼项和受迫项的广义摆方程.利用Jacob椭圆函数和椭圆积分分析了无扰动系统的相平面特征,并解析地给出了系统的解和粒子振动周期; 进一步利用Melnikov方法分析相平面上三类轨道的分叉性质和进入Smale马蹄意义下的混沌行为,找到系统的全局分叉与系统进入混沌的临界条件.结果表明,系统的临界条件与它的物理参数有关,只需适当调节这些参数就可以原则上避免、抑制分叉或混沌的出现. 关键词： 晶体摆动场辐射 Melnikov方法 分叉 混沌     

Evolution equation for radiance and coherence

If the field of applications of radiometry is restricted to energy calculations of optical systems then the theorem about invariant of the phase radiance (or the reduced radiance) along the light ray takes the form of Liouville's equation. This differential equation is a good basis for the traditional radiometry of Lambertian sources, as well as radiometry of the quasi-homogeneous sources. It is known that the wave analogue of phase radiance is the Wigner definition function. This wave analogy helps to clarify the limits of applicability of the concepts and approximations, e.g. properties of optical media in which the radiation transfer can be described by Liouville's equation.     

Radiative transfer theory with time delay for the effect of pulse entrapping in a resonant random medium: General transfer equation and point-like scatterer model

Abstract

A pulse propagation of a vector electromagnetic wave field in a discrete random medium under the condition of Mie resonant scattering is considered on the basis of the Bethe–Salpeter equation in the two-frequency domain in the form of an exact kinetic equation which takes into account the energy accumulation inside scatterers. The kinetic equation is simplified using the transverse field and far wave zone approximations which give a new general tensor radiative transfer equation with strong time delay by resonant scattering. This new general radiative transfer equation, being specified in terms of the low-density limit and the resonant point-like scatterer model, takes the form of a new tensor radiative transfer equation with three Lorentzian time-delay kernels by resonant scattering. In contrast to the known phenomenological scalar Sobolev equation with one Lorentzian time-delay kernel, the derived radiative transfer equation does take into account effects of (i) the radiation polarization, (ii) the energy accumulation inside scatterers, (iii) the time delay in three terms, namely in terms with the Rayleigh phase tensor, the extinction coefficient and a coefficient of the energy accumulation inside scatterers, respectively (i.e. not only in a term with the Rayleigh phase tensor). It is worth noting that the derived radiative transfer equation is coordinated with Poynting's theorem for non-stationary radiation, unlike the Sobolev equation. The derived radiative transfer equation is applied to study the Compton–Milne effect of a pulse entrapping by its diffuse reflection from the semi-infinite random medium when the pulse, while propagating in the medium, spends most of its time inside scatterers. This specific albedo problem for the derived radiative transfer equation is resolved in scalar approximation using a version of the time-dependent invariance principle. In fact, the scattering function of the diffusely reflected pulse is expressed in terms of a generalized time-dependent Chandrasekhar H-function which satisfies a governing nonlinear integral equation. Simple analytic asymptotics are obtained for the scattering function of the front and the back parts of the diffusely reflected Dirac delta function incident pulse, depending on time, the angle of reflection, the mean free time, the microscopic time delay and a parameter of the energy accumulation inside scatterers. These asymptotics show quantitatively how the rate of increase of the front part and the rate of decrease of the rear part of the diffusely reflected pulse become slower with transition from the regime of conventional radiative transfer to that of pulse entrapping in the resonant random medium.     

Wave chaos and mode-medium resonances at long-range sound propagation in the ocean

We study how the chaotic ray motion manifests itself at a finite wavelength at long-range sound propagation in the ocean. The problem is investigated using a model of an underwater acoustic waveguide with a periodic range dependence. It is assumed that the sound propagation is governed by the parabolic equation, similar to the Schrodinger equation. When investigating the sound energy distribution in the time-depth plane, it has been found that the coexistence of chaotic and regular rays can cause a "focusing" of acoustic energy within a small temporal interval. It has been shown that this effect is a manifestation of the so-called stickiness, that is, the presence of such parts of the chaotic trajectory where the latter exhibit an almost regular behavior. Another issue considered in this paper is the range variation of the modal structure of the wave field. In a numerical simulation, it has been shown that the energy distribution over normal modes exhibits surprising periodicity. This occurs even for a mode formed by contributions from predominantly chaotic rays. The phenomenon is interpreted from the viewpoint of mode-medium resonance. For some modes, the following effect has been observed. Although an initially excited mode due to scattering at the inhomogeneity breaks up into a group of modes its amplitude at some range points almost restores the starting value. At these ranges, almost all acoustic energy gathers again in the initial mode and the coarse-grained Wigner function concentrates within a comparatively small area of the phase plane.     

小孔衍射和近场散射数值计算的格林函数方法

从简谐光波满足的亥姆霍兹方程出发,将由格林定理得到的介质分界面上的积分方程转化为以表面上的光波及其导数为未知量的线性方程组,并对其进行数值求解,实现了光场的数值计算。然后将这一方法应用于亚波长尺度的小孔衍射的光波以及自仿射分形表面产生的随机光场及其在近场区域范围内的传播的计算。在随机表面产生的光场计算中．提出了类比推导夫琅禾费面上散斑场自相关函数的方法产生随机表面,以及计算其导数的傅里叶变换方法。对光场的计算结果表明,在近场范围内,光场随离开表面的距离的增加而迅速变化,其传播特性完全不同于光场在远场范围内的传播特性。     

激光驻波场中电子运动与能量分析

采用相对论Lorentz方程,数值计算了高能电子在线极化激光驻波场中的运动过程。计算结果表明,电子能量存在一个临界值,能量超过临界值的入射电子在驻波场中振荡运动的稳定平衡位置由波节变成波腹。在波腹处平行于电场入射的高能电子在强电场作用下速度和能量快速振荡,其振幅包络近似为余弦函数。而在波节处垂直于磁场入射的电子仅在Lorentz力作用下快速振荡,在穿过驻波中心前获得能量,穿过中心后失去能量,电子出射后能量均保持不变。     

晶体相场法研究应力状态及晶体取向对微裂纹尖端扩展行为的影响

采用晶体相场模拟研究了单向拉伸作用下初始应力状态、晶体取向角度对单晶材料内部微裂纹尖端扩展行为的影响, 以(111)晶面上的预制中心裂纹为研究对象探讨了微裂纹尖端扩展行为的纳观机理, 结果表明: 微裂纹的扩展行为主要发生在<011>(111)滑移系上, 扩展行为与扩展方向与材料所处的初始应力状态及晶体取向紧密相关. 预拉伸应力状态将首先诱发微裂纹尖端生成滑移位错, 进而导致晶面解理而实现微裂纹尖端沿[011]晶向扩展, 扩展到一定程度后由于位错塞积, 应力集中, 使裂纹扩展方向沿另一滑移方向[101], 并形成锯齿形边缘; 预剪切应力状态下, 微裂纹尖端首先在[101]晶向解理扩展, 并诱发位错产生, 形成空洞聚集型长大的二次裂纹, 形成了明显的剪切带; 预偏变形状态下微裂纹尖端则直接以晶面解理形式[101]在上进行扩展, 直至断裂失效; 微裂纹尖端扩展行为随晶体取向不同而不同, 较小的取向角度会在裂纹尖端形成滑移位错, 诱发空位而形成二次裂纹, 而较大的取向角下的裂纹尖端则以直接解理扩展为主, 扩展方向与拉伸方向几近垂直.     

Coherent quantum states of a relativistic particle in an electromagnetic plane wave and a parallel magnetic field

We analyze the solutions of the Klein–Gordon and Dirac equations describing a charged particle in an electromagnetic plane wave combined with a magnetic field parallel to the direction of propagation of the wave. It is shown that the Klein–Gordon equation admits coherent states as solutions, while the corresponding solutions of the Dirac equation are superpositions of coherent and displaced-number states. Particular attention is paid to the resonant case in which the motion of the particle is unbounded.     

Cross-slip in face centred cubic metals: a general full stress-field dependent activation energy line-tension model

Cross-slip is a thermally activated process by which a screw dislocation changes its slip plane. Understanding and modelling the activation barrier of the cross-slip process as a free-energy barrier that depends on the stress conditions at the vicinity of the dislocation is crucial. In this work, we employ the line-tension model for the cross-slip of screw dislocations in face-centred cubic (FCC) metals in order to calculate the energy barrier when both Escaig stresses are applied on the primary and cross-slip planes and Schmid stress is applied on the cross-slip plane. We propose a closed-form expression for the activation energy for cross-slip in a large range of stresses, without any fitting parameters. The results of the proposed model are in good agreement with previous numerical results and atomistic simulations. We also show that, when Schmid stress is applied on the cross-slip plane, the energy barrier is decreased, and in particular, cross-slip can occur even when the Escaig stress in the primary plane is smaller than that on the cross-slip plane. The proposed closed-form expression for the activation energy can be easily implemented in dislocation dynamics simulations, owing to its simplicity and universality. This will allow cross-slip to be more accurately related to macroscopic plasticity.     

Phase velocities of plane waves in a pipe with a flow whose velocity varies along the radius

The phase velocities of plane waves in a pipe filled with a moving acoustic medium are studied for different laws of flow velocity variation along the pipe radius. The wave equation is solved by the discretization method, which breaks the entire pipe volume into individual cylinders under the assumption that, within each of the cylinders, the flow velocity of the medium is constant. This approach makes it possible to reduce the solution to the wave problem to solving Helmholtz equations for individual cylinders. Based on boundary conditions satisfied at the boundaries between neighboring cylinders, a homogeneous system of linear algebraic equations is obtained. From this system, with the use of the scattering matrices, a simple dispersion equation is derived for determining the phase velocities of plane waves. The stability of the numerical solution to the dispersion equation with respect to the number of cylinders is investigated. The phase velocities of quasi-homogeneous and inhomogeneous waves in a pipe are numerically calculated and analyzed for different velocities of a moving medium and different laws of flow velocity variation along the radius. It is shown that the variation that occurs in the phase velocity of a homogeneous plane wave in a pipe due to the motion of the medium is identical to the mean flow velocity for different laws of flow velocity variation along the radius. For inhomogeneous plane waves, the phase velocity increment exceeds the mean flow velocity several times and depends on both the law of wave amplitude distribution along the radius and the law of the flow velocity variation along the radius.