Tracer diffusion in the presence of segregating obstacles

Tracer diffusion in an alloy in which the trajectories of one of the species is biased is examined as a model of mass transport with attendant segregation to extended defects (e.g., dynamic strain ageing, grain-boundary segregation). More specifically, we employ Monte Carlo simulation to describe the nonequilibrium diffusive behavior of the components of a two-dimensional lattice gas comprising A and B atoms wherein one of the species (B) interacts with randomly distributed line defects to create equilibrium atmospheres at late times. Various kinetic assumptions and defect densities are explored to highlight the role of B-atom mobility and defect interaction strength on the transport behavior of the A atoms. From the calculated instantaneous diffusivity, several diffusive regimes are then identified and related to evolving segregation profiles and, in particular, to the free area available for diffusion.     

快中子照相模拟分析与实验验证

首次系统地推导出快中子照相像素值形成解析式, 建立图像反差不等式, 并利用该不等式首次对图像对比度与源强、照射时间和散射之间的关系进行说明. 并在像素值解析式基础上编制快中子照相模拟程序, 利用该程序对空间分辨率和图像对比度进行模拟, 并与实验对照, 研究结果表明空间分辨率模拟效果好于实验, 图像对比度模拟效果与实验相当. 最后通过对狭缝、方孔以及多材质组成的复杂样品模拟并与实验对照, 结果显示模拟效果与实验照片在反差灵敏度效果上非常一致, 该模拟计算方法可为实验设计和工程应用提供参考.     

Novel multisection design of anisotropic diffusion phantoms

Diffusion-weighted magnetic resonance imaging provides access to fiber pathways and structural integrity in fibrous tissues such as white matter in the brain. In order to enable better access to the sensitivity of the diffusion indices to the underlying microstructure, it is important to develop artificial model systems that exhibit a well-known structure, on the one hand, but benefit from a reduced complexity on the other hand. In this work, we developed a novel multisection diffusion phantom made of polyethylene fibers tightly wound on an acrylic support. The phantom exhibits three regions with different geometrical configuration of fibers: a region with fibers crossing at right angles, a region with parallel fibers and homogeneous density, and, finally, a region with parallel fibers but with a gradient of fiber density along the axis of symmetry. This gives rise to a gradual change of the degree of anisotropy within the same phantom. In this way, the need to construct several phantoms with different fiber densities is avoided, and one can access different fractional anisotropies in the same experiment under the same physical conditions. The properties of the developed phantom are demonstrated by means of diffusion tensor imaging and diffusion kurtosis imaging. The measurements were performed using a diffusion-weighted spin-echo and a diffusion-weighted stimulated-echo pulse sequence programmed in-house. The influence of the fiber density packing on the diffusion parameters was analyzed. We also demonstrate how the novel phantom can be used for the validation of high angular resolution diffusion imaging data analysis.     

Density profile and flow of miscible fluid with dissimilar constituent masses

A computer simulation model is used to study the density profile and flow of a miscible gaseous fluid mixture consisting of differing constituent masses (m_A=m_B/3) through an open matrix. The density profile is found to decay with the height ∝exp (−m_A(B)h), consistent with the barometric height law. The flux density shows a power-law increase ∝(p_c−p)^μ with μ2.3 at the porosity 1−p above the pore percolation threshold 1−p_c.     

Monte Carlo algorithm for drift and diffusion of ions in anisotropic,non-homogeneous media

A new Monte Carlo algorithm for ion transport in two-dimensional anisotropic media is reported. It is based on physical considerations of drift and diffusion in anisotropic media with or without an impermeable boundary. Inhomogeneities in the medium and electric field can be taken into account by averaging along the ion trajectory. The algorithm has been applied to the calculation of ion transport in liquid crystal displays and has been successfully compared with a finite difference program on a one-dimensional liquid crystal structure.     

光在随机增益介质中的放大

 结合环形腔理论,运用蒙特卡罗法模拟了光子在介质中的随机行走。研究了倍频Nd:YAG（脉宽6 ns,频率20 Hz）脉冲激光器作为泵浦光,在TiO₂ / 若丹明 B有机增益介质中,散射微粒的颗粒密度和泵浦光面积对随机激光器阈值强度的影响。模拟结果表明：随机激光阈值和光子在增益介质中的随机行走路程长度和光子通过边界返回增益区和非增益区的几率有关。随着泵浦光面积的增加,随机激光器阈值降低;增益介质中散射颗粒密度的增加降低了随机激光器的阈值。     

模体大小对MC程序计算速度与精度的影响研究

蒙特卡罗程序的计算速度与计算模型的体积大小有一定关联。 通过改变模体的厚度， 发现除在尾部有限范围内会出现差异外， 薄模体与厚模体的结果差别很小， 然而却可以获得模拟效率的指数性提升。 通过改变模体的宽度， 发现窄模体与宽模体相比， 只要宽度比照射野半影大， 对模拟效率的影响都很小； 而当宽度与照射野半影区重合时， 效率就有一定程度的提高， 同时对剂量结果影响很小。 将此研究结果用于临床头部实例， 获得了计算速度的显著提升。     

密闭实验大厅内散射中子注量的模拟研究

为能够快速评判实验测试方案和预估实验结果,建立了中子体通量的快速估算模型。理论上,封闭空间中子平均体通量与特征长度的平方成反比,且中子体通量的大小能反映散射中子注量强弱。采用蒙特卡罗模拟方法,计算得到了密闭实验大厅内中子的体通量,以及不同位置处的散射中子注量,并将模拟得到的体通量和散射中子注量拟合成便于工程实践中应用的解析表达式,拟合结果与模拟结果的相对偏差小于10%。研究结果表明,球形空间内中子的体通量与球半径的1.905次方成反比;密闭实验大厅的中子体通量与大厅横截面宽度的1.948次方成反比,与长宽比的0.775次方成反比;球形空间结构内,每个源中子的平均径迹长度约为半径的5.4倍,而长方体密闭实验大厅内,单个源中子的平均径迹长度为大厅特征尺度的2~3倍。     

Validation of practical diffusion approximation for virtual near infrared spectroscopy using a digital head phantom

Light propagation in the digital head phantom for virtual near infrared spectroscopy and imaging is calculated by diffusion theory. In theory, diffusion approximation is not valid in a low-scattering cerebrospinal fluid (CSF) layer around the brain. The optical path length and spatial sensitivity profile predicted by the finite element method based upon the diffusion theory are compared with those predicted by the Monte Carlo method to validate a practical implementation of diffusion approximation to light propagation in an adult head. The transport scattering coefficient of the CSF layer is varied from 0.01 to 1.0 mm⁻¹ to evaluate the influence of that layer on the error caused by diffusion approximation. The error is practically ignored and the geometry of the brain surface such as the sulcus structure in the digital head phantom scarcely affects the error when the transport scattering coefficient of the CSF layer is greater than 0.3 mm⁻¹.     

Comparison between fixed and Gaussian steplength in Monte Carlo simulations for diffusion processes

We analyze the different degrees of accuracy of two Monte Carlo methods for the simulation of one-dimensional diffusion processes with homogeneous or spatial dependent diffusion coefficient that we assume correctly described by a differential equation. The methods analyzed correspond to fixed and Gaussian steplengths. For a homogeneous diffusion coefficient it is known that the Gaussian steplength generates exact results at fixed time steps Δt. For spatial dependent diffusion coefficients the symmetric character of the Gaussian distribution introduces an error that increases with time. As an example, we consider a diffusion coefficient with constant gradient and show that the error is not present for fixed steplength with appropriate asymmetric jump probabilities.     

The limitation of the proposed collection efficiency for fiber probes on the visible and near-infrared diffuse spectroscopy

A fiber is usually used as a probe in visible and near-infrared diffuse spectra measurement. However, the use of different fiber probes in the same measurement may cause data mismatch problems. Our group has researched the influence of the parameters of fiber probe, including the aperture angle, on the diffuse spectrum by a modified Monte Carlo model. To eliminate the influence of the aperture angle, we proposed a fitted equation of correction coefficient to correct its difference in practical range. However, we did not discuss the limitation of this method. In this work, we explored the collection efficiency in different optical environment with Monte Carlo simulation method, and find the suitable conditions—weak absorbing and strong scattering media, for the proposed collection efficiency. Furthermore, we tried to explain the stability of the collection efficiency in this condition. This work gives suitable conditions for the collection efficiency. The use of collection efficiency can help reduce the influence of different measurement systems and is also helpful to the model translation.     

A Monte Carlo model for determination of binary diffusion coefficients in gases

A Monte Carlo method has been developed for the calculation of binary diffusion coefficients in gas mixtures. The method is based on the stochastic solution of the linear Boltzmann equation obtained for the transport of one component in a thermal bath of the second one. Anisotropic scattering is included by calculating the classical deflection angle in binary collisions under isotropic potential. Model results are compared to accurate solutions of the Chapman–Enskog equation in the first and higher orders. We have selected two different cases, H₂ in H₂ and O in O₂, assuming rigid spheres or using a model phenomenological potential. Diffusion coefficients, calculated in the proposed approach, are found in close agreement with Chapman–Enskog results in all the cases considered, the deviations being reduced using higher order approximations.     

Application of the spatial averaging theorem to radiative heat transfer in two-phase media

The spatial averaging theorem is applied to rigorously derive continuum-scale equations of radiative transfer in two-phase media consisting of arbitrary-type phases in the limit of geometrical optics. The derivations are based on the equations of radiative transfer and the corresponding boundary conditions applied at the discrete-scale to each phase, and on the discrete-scale radiative properties of each phase and the interface between the phases. The derivations confirm that radiative transfer in two-phase media consisting of arbitrary-type phases in the range of geometrical optics can be modeled by a set of two continuum-scale equations of radiative transfer describing the variation of the average intensities associated with each phase. Finally, a Monte Carlo based methodology for the determination of average radiative properties is discussed in the light of previous pertinent studies.     

Evaluation of fiber tracking from subsampled q-space data in diffusion spectrum imaging

Diffusion spectrum imaging (DSI) is capable of resolving crossing and touching fiber bundles in a given voxel. Acquisition of DSI data involves sampling large number of points in the q-space which significantly increases scan times. The scan times can be reduced by exploiting the symmetry of the q-space. In this study the fiber pathways for five (fornix, cingulum, superior longitudinal fasciculus, corticospinal tract, and crossing fibers in the centrum semiovale region) fiber bundles derived using three subsampled data sets of different sizes derived from the 257 samples in the q-space are compared. The coefficient of variation of the ratio of the number of fiber pathways for each subsample data set to the original data points, averaged over all the 10 subjects, was used for quantitatively investigating the effect of subsampling on the tractography. The effect of threshold angles on tractography is also investigated. The effect of subsampling on the orientation distribution function (ODF) was quantitatively evaluated using both scalar and vector measures derived from the ODF. A streamline tractography method that improves the curvature problem and reduces the local truncation error to further improve the mapping of fiber pathways is adapted. Analysis of the fiber pathways in ten normal subjects, based on qualitative and quantitative methods, shows that the 129 and 198 q-space points provide very similar result with angle of threshold between 41° and 45°. Based on the scan time advantage, 129 subsampled points appear to be adequate for tractography.     

Non-Arrhenius relaxation of the Heisenberg model with dipolar and anisotropic interactions

The dynamical properties of a 2D Heisenberg model with dipolar interactions and perpendicular anisotropy are studied using Monte Carlo simulations in two different ordered regions of the equilibrium phase diagram. We find a temperature defining a dynamical transition below which the relaxation suddenly slows down and the system apart from the typical Arrhenius relaxation to a Vogel-Fulcher-Tamann law. This anomalous behavior is observed in the scaling of the magnetic relaxation and may eventually lead to a freezing of the system. Through the analysis of the domain structures we explain this behavior in terms of the domains dynamics. Moreover, we calculate the energy barriers distribution obtained from the data of the magnetic viscosity. Its shape supports our comprehension of both, the Vogel-Fulcher-Tamann dynamical slowing down and the freezing mechanism.     

Static correlations of higher order and diffusion in an interacting lattice gas

For a lattice gas with extended hard core interaction on a square lattice the static correlation functions of higher order, which determine the average jump rate in the diffusion process, are calculated both by the Monte Carlo method and by analytic approximations. It is found that the superposition approximation is very inaccurate for the correlation functions of third and fourth order, but gives better results for the average jump rate. Up to concentrations ofc = 0.3 better consistency with the Monte Carlo data for both quantities is obtained by treating the site occupation numbers as Gaussian random variables and accordingly expressing the correlation functions of higher order by products of averages of two particle correlations. For concentrationsc > 0.3, however, a Bethe-Peierls cluster approximation is superior to the superposition approximation.The results of this paper were presented at the I.L.L, workshop Beyond Radial Distribution, Grenoble, July 15–16, 1985.     

Effects of random subject rotation on optimised diffusion gradient sampling schemes in diffusion tensor MRI

The choice of the number (N) and orientation of diffusion sampling gradients required to measure accurately the water diffusion tensor remains contentious. Monte Carlo studies have suggested that between 20 and 30 uniformly distributed sampling orientations are required to provide robust estimates of water diffusions parameters. These simulations have not, however, taken into account what effect random subject motion, specifically rotation, might have on optimised gradient schemes, a problem which is especially relevant to clinical diffusion tensor MRI (DT-MRI). Here this question is investigated using Monte Carlo simulations of icosahedral sampling schemes and in vivo data. These polyhedra-based schemes, which have the advantage that large N can be created from optimised subsets of smaller N, appear to be ideal for the study of restless subjects since if scanning needs to be prematurely terminated it should be possible to identify a subset of images that have been acquired with a near optimised sampling scheme. The simulations and in vivo data show that as N increases, the rotational variance of fractional anisotropy (FA) estimates becomes progressively less dependent on the magnitude of subject rotation (), while higher FA values are progressively underestimated as increases. These data indicate that for large subject rotations the B-matrix should be recalculated to provide accurate diffusion anisotropy information.     

Monte Carlo simulation of the effect of atomic diagonal transition on cluster diffusion

The effect of atomic diagonal transition on the cluster diffusion and its size dependence is simulated by kinetic Monte Carlo method. The thresholds of atomic diagonal transition barriers E_{dt} are found to be 0.2eV and 0.4eV, corresponding to with and without evaporation and condensation mechanism, respectively. The results indicate that the cluster diffusion is controlled primarily by the atomic diagonal transition, and the cluster diffusion coefficient D decreases drastically with increasing E_d when E_dE_{dt}, and the relationship between D and N changes into D∝N^{-1.08±0.027}.     

Emergence of complex networks from diffusion on fractal lattices. A special case of the Sierpinski gasket and tetrahedron

A new approach to the assemblage of complex networks displaying the scale-free architecture is proposed. While the growth and the preferential attachment of incoming nodes assure an emergence of such networks according to the Barabási–Albert model, it is argued here that the preferential linking condition needs not to be a principal rule. To assert this statement a simple computer model based on random walks on fractal lattices is introduced. It is shown that the model successfully reproduces the degree distributions, the ultra-small-worldness and the high clustering arising from the topology of scale-free networks.