短脉冲激光与介质相互作用的扩散模型

推导了扩散近似方程,通过半无限大均匀介质计算,用扩散理论分析解验证了数值方法的有效性.模拟了光在非均匀介质内的传输过程,给出了介质内光通量随时间变化的空间分布.结果表明,该基于扩散模型的数值方法能够模拟短脉冲光在强散射介质中的传播过程以及漫散射光的时间变化特性,并且借助于光通量空间分布能够准确模拟非均匀介质内内含物的位置.     

Transport and Diffusion in a Random Medium

We consider particle transport in a spatially random medium, the transport governed by the traditional, linear, time- and space-dependent transport equation for “host and guest.” The scattering is elastic and isotropic; there is no absorption. If the host medium has uniform density we know that an initial burst will, in time, approach the solution to the time-dependent diffusion equation. In the case of random medium we find that for a large class of such media the asymptotic behavior is unchanged by the stochasticity; there is neither renormalization of the equation nor the diffusion co-efficient.The nature of the correlation between fluctuations of density at large separation plays an important role in the analysis.     

Interference related corrections to classical gas diffusion in a system of small heterogeneities

Diffusion of an ideal gas in a system of small spherical heterogeneities (collective of particles and a system of small cavities in homogeneous medium) is considered. The effective diffusion coefficient is calculated using methods of multiple scattering theory. Some possible contribution to diffusion of multiple passing closed loops on the trajectory of a molecule is considered. The interest to such loops is related to constructive interference of amplitudes corresponding to two alternative ways of the loop passing (clockwise and counterclockwise). This interference always exists, irrespective to the medium disorder. In this paper, we show that the interference corrections to classical diffusion lead to appearance of low frequency macroscopic oscillations of the gas concentration and complete stagnation of the diffusion process. The latter resembles the Anderson localization of electrons in a system of impurities in an ideal lattice.     

Influence of octupole photoionization transitions on the angular distribution of photoelectrons from solids with account for elastic scattering

Using the transport theory approach, equations are derived for the angular dependence of XPS intensities from semi-infinite solids taking into account elastic scattering of photoelectrons and non-dipolar transitions up the second-order corrections. The unpolarized excitation source is considered. The elastic scattering is the main term smearing the non-dipolar contribution in complete analogy with smearing of dipole contribution. Some additional terms are shown to be negligible in comparison with the main term for complete sets of emission and azimuth angles, three representative single scattering albedo values and several representative sets of the second-order non-dipolar parameters. The photoelectron angular distributions are calculated for Al 2s and Ag 3d lines using transport theory and Monte-Carlo simulation. The Monte-Carlo calculations are in agreement with transport theory approach.     

The role of surface tension in elastic wave scattering in an inhomogeneous poroelastic medium

It is well known that many porous media such as rocks have heterogeneities at nearly all scales. We applied Biot's poroelastic theory to study the propagation of elastic waves in isotropic porous matrix with spherical inclusions. It is assumed that the heterogeneity dimension exceeds significantly the pore size. Modified boundary conditions on poroelastic interface are used to take into account the surface tension effects. The effective wavenumber is calculated using the Waterman and Truell multiple scattering theory, which relates the effective wave number to the amplitude of the wave field scattered by a single inclusion. The calculations were performed for a medium containing fluid-filled cavities or porous inclusions contrasting in saturating fluid elastic properties. The results obtained show that when we consider elastic wave propagation in poroelastic medium containing soft inclusions, it is necessary to take into account the capillary pressure. The influence of the surface tension depends on the diffraction parameter and it is a maximum in the low frequency range.     

The mechanism of Landau-Rumer relaxation of thermal and high-frequency phonons in cubic crystals of germanium,silicon, and diamond

Transverse phonon relaxation according to the Landau-Rumer mechanism is considered for an isotropic medium and crystals of germanium, silicon, and diamond possessing a cubic symmetry. The energy of elastic deformation caused by the anharmonicity of vibrations of the cubic crystal lattice is expressed via the second-and third-order moduli of elasticity. Using the known values of these elastic moduli, parameters determining the frequencies of the transverse phonon relaxation in the Landau-Rumer mechanism are evaluated for the germanium, silicon, and diamond crystals. It is shown that the dependence of the relaxation frequency on the wavevector of thermal and high-frequency phonons sharply differs from the classical Landau-Rumer relationship both in the isotropic medium and in the cubic crystals. It is established that the observed peculiarities in the relaxation frequency are related to the angular dependence of the probability of anharmonic scattering and the anisotropy of elastic properties of the germanium, silicon, and diamond crystals. A new method is proposed for the experimental determination of the relaxation frequency of high-frequency phonons as a function of the wavevector using the temperature dependence of the coefficient of absorption of high-frequency ultrasound.     

A finite element-spherical harmonics radiation transport model for photon migration in turbid media

In this paper, we solve the steady-state form of the Boltzmann transport equation in homogeneous and heterogeneous tissue-like media with a finite element-spherical harmonics (FE-P_N) radiation transport method. We compare FE-transport and diffusion solutions in terms of the ratio of absorption to reduced scattering coefficient, (μ_a/μ_s′) and the anisotropy factor g. Two different scattering phase function formulas are employed to model anisotropic scattering in the slab media with high g-value. Influence of void-like heterogeneities, and of their boundaries with the surrounding medium on the transport of photons are also examined.     

Diffusion near an interface via onsager-type equations

Summary Onsager-type transport equations, as were derived in a previous paper by the authors, are applied to the diffusion of test particles near the interface of a scattering medium with a perfect absorber. Temperature and density profiles are obtained for different types of scattering cross-section.     

Inelastic collisions of medium energy atomic elements in solids

The stopping of medium atomic elements in solids has been calculated in the framework of classical approximation, taking into account elastic and inelastic collisions. The calculations are based on the 1) revised equations for the law of energy and impulse conservation, which were earlier used to describe inelastic collisions of atomic particles, 2) theory of quasi-small angle scattering, 3) power potential of LNS, and 4) limitation of the maximum distance of atoms approach determined by the interatomic distance in solids. Analytical equations have been obtained to calculate 1) a differential cross-section of elastic scattering in the presence of inelastic collisions, 2) energy transferred, 3) cross-sections of elastic and inelastic stopping, and penetration depth. Implantation into solids was found to be of threshold character.     

A transport model and numerical simulation of the high-frequency dynamics of three-dimensional beam trusses

The theory of microlocal analysis shows that the energy density associated with the high-frequency vibrations of a three-dimensional Timoshenko beam satisfies a Liouville-type transport equation. In the present application, the material of the beam is assumed to be isotropic. Its parameters are allowed to vary along the beam axis at length scales much larger than the wavelength of the high-frequency waves traveling in it. Moreover, the curvature and torsion of the beam are accounted for. The first part of the paper focuses on the derivation of the transport model for a single three-dimensional beam. In order to extend this model to beam trusses, the reflection/transmission phenomena of the energy fluxes at junctions of beams are described by power flow reflection/transmission operators in a subsequent part. For numerical simulations, a discontinuous Galerkin finite element method is used on account of the discontinuities of the energy density field at the junctions. Thus, a complete mechanical-numerical modeling of the linear transient dynamics of beam trusses is proposed. It is illustrated by numerical examples highlighting some remarkable features of high-frequency vibrations: The onset of a diffusive regime characterized by energy equipartition rules at late times. Energy diffusion is prompted by the multiple reflection/transmission of waves at the junctions, with possible mode (polarization) conversions. This is the regime applicable to the statistical energy analysis of structural acoustics systems. The main purpose of this research is to develop an effective strategy to simulate and predict the transient response of beam trusses impacted by acoustic or mechanical shocks.     

On the anisotropy of a heterogeneous medium with respect to the diffusion of neutrons I

Equations are derived for the diffusion of monoenergetic neutrons in a stratified heterogeneous medium. The neutron sources are plane and are located at infinity. The problem of homogenization and anisotropy of the heterogeneous medium is solved on the assumption of microscopic isotropy of scattering of the neutrons. The problem is solved quite generally (general position of the source, active and inactive medium). It confirms the conclusions reached in paper [3]from the more general point of view and is again in disagreement with the conclusions of paper [8].This disagreement is explained by the use of equations of the kinetic theory of the diffusion of neutrons.     

Effective potential theory of atom-solid surface elastic scattering

A new quantum mechanical theory of atom-solid surface elastic scattering is formulated, based on the idea of effective potentials. Two such quantities are defined in the present approach, one, the “optical potential”, regulating specular scattering, and the second, the “transition potential”, responsible for diffractive scattering. Rigorous equations are obtained for the above mentioned quantities, by using field-theoretic techniques, and an approximation scheme is worked out explicitly. The main computational aspect of the present theory requires the solution of an uncoupled integro-differential equation and the formulation can be easily extended to consider more complicated scattering processes.     

Decorrelation and phase-shift of coda waves induced by local changes: multiple scattering approach and numerical validation

We report on theoretical predictions of the decorrelation and phase-shift of coda waves induced by local changes in multiple scattering media. Using the multiple scattering formalism, we show that both expressions (decorrelation and phase-shift) involve a same sensitivity kernel based on the intensity transport in the medium. We compare the kernels based on the diffusion approximation with the ones based on the radiative transfer approximation, showing that the latter is more accurate at short times or for changes located close to the source or the receiver. We also perform a series of numerical simulations of wave propagation (finite differences) to validate our models in different configurations.     

Multiple scattering, optical potential, and N-body approaches to elastic two-fragment collisions

Two-fragment elastic scattering problems are often studied using multiple scattering theories such as those due to Watson along with Feshbach-type optical potentials. These conventional methods are re-examined, rephased, and generalized using the language and techniques of contemporary N-particle scattering theory. A special realization of the latter theory is developed which is especially useful for relating the older and newer methods. This is facilitated by maintaining the same off-shell continuations of the scattering operators in both approaches. In particular, a set of connected-kernel scattering integral equations is introduced which provides a consistent N-particle framework for the calculation of that definition of the optical potential possessing the Feshbach off-shell continuation. These equations exhibit a multiple-scattering substructure and therefore allow the systematic generalization of some of the usual low-order approximations.     

Combined nuclear-molecular resonance inelastic scattering of x rays

We report on theoretical and experimental studies of nuclear inelastic scattering in a molecular crystal, whose atoms experience both molecular and lattice vibrations. In this case scattering proceeds as combined nuclear-molecular resonance inelastic scattering. The lattice vibrations give rise to inelastic scattering around the molecular resonances with an energy dependence identical to that around the nuclear resonance. The incoherent nature of the scattering in the molecular resonances results in a proper balance of elastic and inelastic components, which has important implications for studies of heterogeneous systems.     

Stimulated Raman Scattering at Induced Acoustic Vibrations of Elastic Particles in Suspensions Placed in an Optical Cavity

The stimulated low-frequency Raman scattering at acoustic vibrations of elastic inclusions in a liquid heterogeneous medium placed in an external open optical cavity has been investigated. The amplitudes of stationary field oscillations in the cavity at the frequencies of the excitation and the first Stokes component are found within a two-dimensional model. The specific features of the oscillation in dependence of the parameters of the cavity and Raman-active medium have been studied based on the simulation results.     

On formulation of a transition matrix for electroporoelastic medium and application to analysis of scattered electroseismic wave

On the basis of Pride's theory (1994) which couples Biot's theory for poroelastic medium (1956) and Maxwell equations via flux/force transport equations, we extend Yeh et al. (2004) approach for poroelastic medium to develop a transition matrix for electroporoelastic medium. The transition matrix, which relates the coefficients of scattered waves to those of incident waves, is then derived through the application of Betti's third identity and the associated orthogonality conditions for the electroporoelastic medium. To illustrate the application, a simple case of the scattering problem of a spherical electroporoelastic inclusion, embedded within the surrounding electroporoelastic medium subjected to an incident plane compressional wave is considered.     

Kinetic approach to the envelope equation for a relativistic electron beam propagating through a scattering gas-plasma medium in the presence of the reverse plasma current with an arbitrary radial profile

A kinetic approach is applied to derive the transport equations, the virial equation, the dynamic-equilibrium equation, and the envelope equation for an axially symmetric paraxial relativistic electron beam propagating through a scattering gas-plasma medium in the presence of a reverse plasma current with a radial density profile that is generally different from the beam density profile. The equations obtained include additional terms that account for this difference.     

Nonclassical transport in fractal media with a diffusion barrier

We investigate the impurity transport in a randomly heterogeneous fractal medium with a diffusion barrier. The barrier is due to low permeable medium surrounding the source. The transport regimes and asymptotic (large-distance) concentration distributions are found. The presence of the diffusion barrier results in the retardation of the transport regimes at short times. As regards the asymptotic concentration distribution, the barrier influence persists for long times as well.