Angular anisotropy of group averaged absorption coefficient and its effect on the behavior of diffusion approach in radiative transfer

Multi-group method, a generally accepted procedure for handling the radiative transfer equation, is accompanied by the group averaged absorption coefficient, and actually the coefficient is angularly anisotropic. In the paper, we present a brief discussion how the anisotropy of the coefficient makes the material absorb photons at different rate in each direction, also study its effect on the diffusion approach by comparing the results calculated using multi-group diffusion and multi-group discrete ordinate SN for the isotropic and anisotropic group averaged absorption coefficients respectively, and find that the anisotropy deteriorates the behavior of diffusion approach.     

Self-diffusion in granular gases: Green-Kubo versus Chapman-Enskog

We study the diffusion of tracers (self-diffusion) in a homogeneously cooling gas of dissipative particles, using the Green-Kubo relation and the Chapman-Enskog approach. The dissipative particle collisions are described by the coefficient of restitution epsilon which for realistic material properties depends on the impact velocity. First, we consider self-diffusion using a constant coefficient of restitution, epsilon=const, as frequently used to simplify the analysis. Second, self-diffusion is studied for a simplified (stepwise) dependence of epsilon on the impact velocity. Finally, diffusion is considered for gases of realistic viscoelastic particles. We find that for epsilon=const both methods lead to the same result for the self-diffusion coefficient. For the case of impact-velocity dependent coefficients of restitution, the Green-Kubo method is, however, either restrictive or too complicated for practical application, therefore we compute the diffusion coefficient using the Chapman-Enskog method. We conclude that in application to granular gases, the Chapman-Enskog approach is preferable for deriving kinetic coefficients.     

Kinetic Description of Particle Interaction with a Gravitational Wave

The interaction of charged particles, moving in a uniform magnetic field, with a plane polarized gravitational wave is considered using the Fokker-Planck-Kolmogorov (FPK) approach. By using a stochasticity criterion, we determine the exact locations in phase space, where resonance overlapping occurs. We investigate the diffusion of orbits around each primary resonance of order m by deriving general analytical expressions for an effective diffusion coefficient. A solution of the corresponding diffusion equation (Fokker-Planck equation) for the static case is found. Numerical integration of the full equations of motion and subsequent calculation of the diffusion coefficient verifies the analytical results.     

Anisotropic diffusion in media with absorbing traps (application to the Keller–Dykhne theorem)

Anisotropic diffusion in multidimensional media with absorbing traps is investigated. It is shown that the diffusion asymptotic forms of the survival probability over long time intervals are determined by a new effective diffusion coefficient. Exact expressions derived for the effective diffusion coefficient generalize the well-known Dykhne–Keller 2D results to the 3D case. In other words, the dynamic diffusion approach is used for obtaining a generalization of the Dykhne–Keller theorem to the 3D case.     

Effective relaxation time of the impurity concentration in a medium with a slightly nonuniform diffusion coefficient

Based on the previously introduced integral criterion and a new approach to estimating the time characteristics of diffusion, the relaxation time of impurity concentration in a medium with a slightly nonuniform diffusion coefficient is determined. The diffusion coefficient profile that cuts the relaxation time is found.     

Variational estimates of the diffusion coefficient of cosmic rays in a random magnetic field

A variational method is used to obtain estimates of the effective particle transport coefficients in a random static magnetic field. The particle propagation is described by an anisotropic diffusion equation. The diffusion coefficient parallel to the local magnetic field is much greater than the transverse diffusion coefficient. For large-scale magnetic-field variations the diffusion is described by effective coefficients. The variational approach can be used to find the effective parallel and perpendicular diffusion coefficients. It was shown that the instability growth rate of the magnetic field lines determines the upper estimate of the effective transverse diffusion coefficient. Zh. éksp. Teor. Fiz. 114, 398–405 (August 1998)     

Hopping on a zig-zag course

We study the diffusion coefficient of Active Brownian particles in two dimensions. In addition to usual attributes of active motion we let the particles turn in preferred directions over random times. This angular motion is modeled by an effective Lorentz force with time dependent frequency switching between two values at exponentially distributed random times. The diffusion coefficient is calculated by the Taylor-Kubo formula where distributions found from a Fokker-Planck equation or from a continuous time random walk approach have been inserted for averaging. Eventually properties of the diffusion coefficient will be discussed.     

Controlling the diffusion process via time-variable diffusion coefficient

The establishment of the steady-state dopant profile in a medium with a time-variable diffusion coefficient is considered within the approach proposed previously for estimating mass-and heat-transfer time characteristics. It is shown that the time it takes for the equilibrium concentration to set in may be increased or decreased by appropriately choosing the law of variation of the diffusion coefficient.     

Regression Analysis of Confocal FRAP and its Application to Diffusion in Membranes

In most biological processes, diffusion plays a critical role in transferring various bio-molecules to transfer desirable locations in an effective and energy-efficient manner. How fast molecules are transferred is measured by diffusion coefficients. Since each bio-molecules, in particular, signaling molecules have their unique diffusion coefficients and quantifying the diffusion coefficients help us to understand various time scales of both physiological and pathological processes in biological systems. Moreover, since diffusion profiles of a diffusant vary in different micro-environments of cell membranes, accurate diffusion coefficient also can provide a good picture of membrane landscapes as well as interactions of different membrane constituents. Currently, only a few experimental methods are available to assess the diffusion coefficient of a biomolecule of interest in live cells including Fluorescence Recovery After Photobleaching (FRAP). FRAP was developed to study diffusion processes of biomolecules in the cell membranes in the 1970s. Albeit its long history, the main principle of FRAP analysis has remained unchanged since its inception: fitting FRAP data to a theoretical diffusion model for the best fitting diffusion coefficient or using the relation between the half time of recovery and ROI size. In this study, we developed a flexible yet versatile confocal FRAP data analysis framework based on linear regression analysis which allows FRAP users to determine the diffusion from either single or multiple FRAP data points without data fitting. We also validated this approach for a series of fluorescently labeled soluble and membrane-bound proteins and lipids.

     

Finite-difference approach for the high-precision analysis of rotating-frame diffusion images

A finite-difference approach has been developed for precisely determining diffusion coefficient and T₁ relaxation time in fluid samples analyzed by magnetization-grating rotating-frame imaging (MAGROFI) with either a surface coil or a toroid cavity detector (TCD). This approach avoids shortcomings of phenomenologically based approximations, such as neglect of sample geometries with singularities at the confines of the sample volume, and accounts for the diffusive edge enhancement observed in fluid imaging. Error limits are discussed. The new method has been applied to the determination of the self-diffusion coefficient for MAGROFI experiments using TCDs filled with acetone.     

Fringe-pattern denoising based on discrete topological analysis

We present an effective way to solve the denoising problem of fringe patterns in optics interferometry. The proposed method is based on the topological analysis of an appropriate cost function. To overcome the blurring drawback of the linear diffusion approach, the linear diffusion coefficient at each edge is perturbed successively. The total variation of a discrete cost function can be taken as an indicator function to pick out the most suitable edges of pixels at which the diffusion coefficients are to be perturbed. Then, a filtered image can be obtained by using selected diffusion coefficients associated to the edges. We demonstrate the performance of the proposed method via application to numerically simulated and experimentally obtained fringe patterns.     

应用MRI研究CO2在癸烷中的扩散

应用核磁共振成像(MRI)技术可视化研究CO₂在癸烷中的扩散,在MRI系统采集图像的同时,应用双室压力衰减法（PVT法）监测压力,通过对MRI图像进行信号强度分析,可得到CO₂的无量纲浓度分布,然后基于菲克定律应用有限体积法可计算得出与扩散距离和扩散时间有关的扩散系数,并可得到任意扩散时间范围内的整体平均扩散系数,MRI方法得出的扩散平衡时间范围内的整体平均扩散系数与PVT法相比较误差为2.7%,并且与相似条件下的前人实验结论具有相同的数量级(10^–9)．根据实验结果得出,扩散系数沿扩散方向下降且随时间以指数形式降低,整体平均扩散系数随扩散时间的增加而减小．     

A highly sensitive radial diffusion measurement method for white matter tract investigation

This article describes a novel approach for local estimation of the radial diffusion coefficient (D(perpendicular)) in white matter (WM) regions containing well-oriented nervous fibers. The method is based on the assumption that the diffusion process in well-organized WM regions responds to a cylindrical symmetry. The increased precision in the estimation of D(perpendicular) provided by this local approach compared to standard techniques based on diffusion tensor imaging is demonstrated using numerical simulations. An in vivo validation of the technique is also provided, showing its application to the corpus callosum of six healthy volunteers, highlighting the sensitivity of the method. Assuming that D(perpendicular) is sensitive to myelin integrity, our technique has the potential to investigate pathophysiological aspects of several neurological and psychiatric disorders with improved precision in targeted WM tracts.     

Modelling interdiffusion in epitaxial multilayer structures using X-ray simulation techniques

The analysis of X-ray diffraction data forms an important non-destructive technique for the study of interdiffusion in multilayer structures. A frequently used approach is that of Fleming et al. in which the characteristic X-ray diffraction satellites from a superlattice structure are shown to be related to the corresponding Fourier components of the real space composition modulation. This relationship is derived assuming the strain to be small although the limitations on this parameter are unclear. To clarify this limitation the Fleming technique has been tested for a range of x values, and hence strain, using as examples a series of model multilayer CdTe:Cd_1-xMn_xTe structures. The approach has been to use a simulation technique based on the kinematical theory of X-ray diffraction to model the X-ray rocking curves from a series of structures in which the Mn diffusion profiles had been calculated using a particular value of the diffusion coefficient D. The values of the diffusion coefficient, derived from the diffraction data using the Fleming method, agree with the input D at low x values but differ for high x, high strain, structures and a criterion is suggested for the range of validity of the method.     

Analytical and numerical studies of angular correlation function of waves scattered from randomly distributed cylinders

The analytical solution for the angular correlation function of scattered waves from randomly distributed infinitely long cylinders is obtained using the second-order approximation with a modified attenuation coefficient. The approach is based on the coherent summation of the scattered waves which preserves the interference effects such as backscattering enhancement. The modification of the transport attenuation coefficient includes the contribution due to the incoherent wave. By comparing with the exact numerical simulations, we found that the correction factor is given by (1-μ¯) which also appears in the diffusion equation. The present approach gives good agreement with numerical and experimental results.     

Thermal diffusivity measurement of insulating material using infrared thermography

The article presents the results of research developing methods for determining the coefficient of thermal diffusivity of thermal insulating material. This method applies a periodic heating as an excitation and an infrared camera is used to measure the temperature distribution on the surface of tested material. In simulation study, the usefulness of known analytical solution of the inverse problem was examined using a three-dimensional model of the phenomenon of heat diffusion in the sample of tested material. To solve the coefficient inverse problem, an approach using artificial neural network is proposed. The measurements were performed on an experimental setup equipped with a ThermaCAM PM 595 infrared camera and frame grabber. The experiment allowed to verify the chosen 3D model of heat diffusion phenomenon and to determine suitability of the proposed test method.     

基尔霍夫近似下激光海面漫反射组网通信特性

 针对激光点对点通信方式的不足,根据舰艇编队通信的实际需要,提出了利用海面作为激光漫反射媒介的一对多的组网通信方法,并且采用基尔霍夫近似的方法对激光海面漫反射通信的特性进行了研究。通过对激光光束入射海面后产生的散射场的分析计算,采用遮蔽函数对计算过程中的阴影效应加以修正,得出了较为准确的2维激光海面双站散射系数和后向散射系数,并进行了实验验证,说明了激光海面漫反射组网通信方法的可行性。     

Photothermal deflection measurement of effective gas diffusion coefficient of a porous medium

In this work, an effective gas diffusion coefficient of a porous medium was measured using photothermal deflection (PD) technique. An in-house made Loschmidt diffusion cell with a photothermal-deflection probe were employed to measure the effective gas diffusion coefficient of a gas diffusion layer (GDL) with a porosity ε ≈ 0.7. The concentration evolutions of CO₂ in O₂ with and without the GDL were measured, respectively, using a transverse normal PD technique. The concentration variations were used to deduce the gas diffusion coefficients in the presence and absence of the GDL by solving mass diffusion equations. The effective gas diffusion coefficient of the GDL was calculated from the diffusion coefficients using a model of an equivalent resistance to diffusion and found to be 4.39 × 10^-6 m²s^-1, demonstrating that PD technique can be employed to determine the effective gas diffusion coefficient of a porous medium.