Anisotropic Diffusion Process Research Articles

Anisotropic grain boundary diffusion process in textured sintered and hot-deformed Nd-Fe-B magnets

A systematic study of the dependence of the Grain Boundary Diffusion Process (GBDP) on texture using Dy and Dy-Nd-Cu in microcrystalline sintered and nanocrystalline hot deformed Nd-Fe-B magnets was performed. Diffusion parallel or perpendicular to the texture direction, the nominal c-axes orientation in the polycrystals, was investigated. By measuring thin slices from the respective samples, coercivity as a function of (i) magnet thickness and (ii) diffusion depth was obtained showing that GBDP efficiency depends on the diffusion direction, diffusion source as well as the grain morphology originating from the magnet production route. In nanocrystalline hot deformed magnets perpendicular diffusion is superior due to the platelet-like shape of the grains. Microcrystalline sintered magnets consist of equiaxed grains hence the main effects originate in anisotropic lattice diffusion and pole surface hardening. The magnetic properties are correlated with a comprehensive analysis of microstructure, chemistry and magnetization reversal.

Random walk on spheres method for solving anisotropic transient diffusion problems and flux calculations

Abstract The Random Walk on Spheres (RWS) algorithm for solving anisotropic transient diffusion problems based on a stochastic learning procedure for calculation of the exit position of the anisotropic diffusion process on a sphere is developed. Direct generalization of the Random Walk on Spheres method to anisotropic diffusion equations is not possible, therefore, we have numerically calculated the probability density for the exit position on a sphere. The first passage time is then represented explicitly. The method can easily be implemented to solve diffusion problems with spatially varying diffusion coefficients for complicated three-dimensional domains. Particle tracking algorithm is highly efficient for calculation of fluxes to boundaries. We apply the developed algorithm for solving an exciton transport in a semiconductor material with a threading dislocation where the measured functions are the exciton fluxes to the semiconductor’s substrate and on the dislocation surface.

Three Dimensional Surface Preserving Smoothing

We propose a new anisotropic diffusion process for removing noise from MRI images without distorting the edges. The method is based on a simple principle: any diffusion that increases a gradient at neighbouring pixels should be prohibited. From this principle, we deduce an inequality that allows diffusion along the edges but not across them. We introduce promising results using synthetic data with various types of noise as well as real MRI scans.

Control method for periodically faceted surfaces and application on AlGaAs/GaAs (6 3 1) heterostructures

Recently, the set of advantages of assembling quasi-one dimensional quantum wire heterostructures by molecular beam epitaxy over high-index orientations has been exhibited, including merging the benefits of both integer-dimension extremes while ruling out their flaws. Nonetheless, hitherto a shallow knowledge of their growth evolution has been barely gathered and thereupon a scarce design control could only be achieved. In this paper we impart a profound survey of the growth phenomena present on the GaAs (631) surface in addition of a method that enhances the reflection high-energy electron diffraction in situ characterization performed upon the mesoscopic periodic corrugation in the course of homoepitaxial growth by molecular beam epitaxy and for the first time in literature, during heteroepitaxy. The fundamentals of the unparalleled corrugation uniformity are expanded in terms of a novel perspective for the surface reconstruction and anisotropic diffusion process. Furthermore, an inverse Weissenberg-RHEED method is proposed to enhance the design control over the mesoscopic corrugation in situ, optimizing the production cycle of quasi-one dimensional QWRs and enabling a proper framework in pursuit for application into higher performance electro-optical devices.

The effect of inter-particle hydrodynamic and magnetic interactions in a magnetorheological fluid

A magnetorheological fluid, which consists of magnetic particles suspended in a viscous fluid, flows freely with well-dispersed particles in the absence of a magnetic field, but particle aggregation results in flow cessation when a field is applied. The mechanism of dynamical arrest is examined by analysing interactions between magnetic particles in a magnetic field subject to a shear flow. An isolated spherical magnetic particle undergoes a transition between a rotating state at low magnetic field and a static orientation at high magnetic field. The effect of interactions for spherical dipolar and polarisable particles with static orientation is examined for an unbounded dilute viscous suspension. There are magnetic interactions due to the magnetic field disturbance at one particle caused by the dipole moment of another, hydrodynamic interactions due to the antisymmetric force moment of a non-rotating particle in a shear flow, and a modification of the magnetic field due to the particle magnetic moment density. When there is a concentration variation, the torque balance condition results in a disturbance to the orientation of the particle magnetic moment. The net force and the drift velocity due to these disturbances is calculated, and the collective motion generated is equivalent to an anisotropic diffusion process. When the magnetic field is in the flow plane, the diffusion coefficients in the two directions perpendicular to the field direction are negative, implying that concentration fluctuations are unstable in these directions. This instability could initiate field-induced dynamical arrest in a magnetorheological fluid.

A Novel Technique for Controlling Anisotropic Ion Diffusion: Bulk Single‐Crystalline Metallic Silicon Clathrate (Adv. Mater. 9/2022)

Anisotropic Ion Diffusion An anisotropic ion diffusion process is developed, as reported by Masaya Fujioka and co-workers in article number 2106754. This technique can homogeneously extract Na+ from a type-II Si clathrate regardless of the size of the single crystal while maintaining high crystallinity, by skillfully exploiting the difference in the chemical potentials as a driving force. The synthesis concept behind the technique is expected to expose new exploration areas for thermodynamically metastable materials.

A region based remote sensing image fusion using anisotropic diffusion process

ABSTRACT The aim of remote sensing image fusion is to merge the high spectral resolution multispectral (MS) image with high spatial resolution panchromatic (PAN) image to get a high spatial resolution MS image with less spectral distortion. The conventional pixel level fusion techniques suffer from the halo effect and gradient reversal. To solve this problem, a new region-based method using anisotropic diffusion (AD) for remote sensing image fusion is investigated. The basic idea is to fuse the ‘Y’ component only (of YCbCr colour space) of the MS image with the PAN image. The base layers and detail layers of the input images obtained using the AD process are segmented using the fuzzy c-means (FCM) algorithm and combined based on their spatial frequency. The fusion experiment uses three data sets. The contributions of this paper are as follows: i) it solves the chromaticity loss problem at the time of fusion, ii) the AD filter with the region-based fusion approach is brought into the context of remote sensing application for the first time, and iii) the edge info in the input images is retained. A qualitative and quantitative comparison is made with classic and recent state-of-the-art methods. The experimental results reveal that the proposed method produces promising fusion results.

Existence theory for the EED inpainting problem

An existence theory is developed for an elliptic boundary value problem in image analysis known as edge-enhancing diffusion (EED) inpainting. The EED inpainting problem aims at restoration of missing data in an image as the steady state of a nonlinear anisotropic diffusion process where the known data provide Dirichlet boundary conditions. The existence of a weak solution is established by applying the Leray–Schauder fixed point theorem, and it is shown that the set of all possible weak solutions is bounded. Moreover, it is demonstrated that under certain conditions the sequences resulting from iterative application of the operator from the existence theory contain convergent subsequences.

First-principles prediction of Hittorf's violet phosphorene as a promising candidate of anode material for Li- and Na-ion batteries

Hittorf's violet phosphorus is the most stable phosphorus allotrope with a layered structure. The corresponding Hittorf's violet phosphorene, a more stable two-dimensional semiconducting structure than black phosphorene, is a promising two-dimensional material for electronic and optoelectronic devices. In this work, the adsorption and anisotropic diffusion process of Li and Na atoms have been studied using first-principles calculations. The adsorption energies of Li and Na atoms are calculated to be 1.65 and 1.32 eV, respectively. Based on the structural nature of Hittorf's violet phosphorene, two possible diffusion paths (in-trench diffusion and inter-trench diffusion) are proposed and investigated. The results of transition state calculation indicate that in-trench diffusion of metal atom has lower barrier that inter-trench diffusion, indicating the significant anisotropic diffusion of Li and Na atom on Hittorf's violet phosphorene. Our work suggests the promising application of Hittorf's violet phosphorene in ion batteries research and development.

Reducing anisotropic effects on oxygen separation performance of K2NiF4-type membranes by adjusting grain size

The microstructure of membranes (especially the grain size) has a considerable influence on their oxygen separation performance. Numerous studies focused on isotropic materials such as perovskites, while only a few investigated anisotropic K2NiF4-type materials due to their complex oxygen ion transport paths. In this work, a series of K2NiF4-type (Pr0.9La0.1)1.9Ni0.74Cu0.21Ga0.05O4+δ ((PL)1.9NCG) dense membranes, with a grain size of 8.2–166.4 μm2, were prepared by adjusting the sintering conditions. The oxygen permeation fluxes through the (PL)1.9NCG membranes displayed a unique concave curve as a function of the grain size, with an initial decrease when the grain size increased from 8.2–62.1 μm2, followed by an increase when the grain size exceeded the critical value (62.1 μm2). As the structure, density, and surface exchange rates of the (PL)1.9NCG membranes were found to alter slightly with the grain size, the differences in the oxygen permeability were deduced to be originating from the anisotropic bulk diffusion process. Therefore, adjusting the grain size is an effective strategy for enhancing the oxygen permeability of anisotropic membranes.

Noise reducing performance of anisotropic diffusion filter and circular median filter in digital images

The speckle noise is one of the prominent features found in ultrasound images and it tends to degrade the quality of the image. There is a historic success in the works towards this approach particularly in the medical field related to image de-speckling. In this paper, a scale-space nonlinear anisotropic diffusion process and circular median filter is being combined with un-sharp masking to filter out the speckle noise from the ultrasound images. However, the performance evaluation and the comparison of both the filters are being done at each level of the process by comparing the various parameters of image quality measures. The nonlinear anisotropic diffusion filter has found to be performing better by two decimal point values in comparison to the circular median filter.

Fractional anisotropic diffusion equation in cylindrical brush model

In this work, we have suggested a neat method of obtaining the fractional diffusion equation for an anomalous anisotropic diffusion process using fractal brush structure as a background medium. For the sake of completeness, we intend to present an analytical solution in the case of the Dirichlet boundary condition. Finally, some notes and remarks are represented to show the vital role of a physical or biological system that exhibits a multiple trapping process.

A global sparse gradient based coupled system for image denoising

We consider a coupled system for image denoising, which consists of an anisotropic diffusion equation and a global sparse gradient model (GSG). The global sparse gradient model is used to estimate the edge map from the noisy image accurately and robustly. The anisotropic diffusion process is guided by the edge map. Furthermore, we prove the existence and uniqueness of the solutions of the coupled system with Dirichlet initial–boundary value problem. Finally, comparing with the edge indicators based on local methods, experimental results demonstrate that our proposed method has the state-of-the-art performance among the PDE-based anisotropic diffusion approaches both in objective measurement and visual evaluation.

Single image fog removal algorithm in spatial domain using fractional order anisotropic diffusion

This paper presents a novel image defogging algorithm using fractional-order anisotropic diffusion equation. The proposed algorithm uses the airlight map extracted from the foggy model as the initial image in the anisotropic diffusion process. The iterative diffusion process improves this airlight map. The anisotropic diffusion process is generalized to the order of any real number between [1, 2) using the Riemann-Liouville definition of the fractional order derivatives. The formulation of the iterative process is carried out in the spatial domain to have a simple and computationally efficient implementation. Simulation results validate that the proposed algorithm is outperforming over few of the existing algorithms. The comparison study is carried out using different metrics like contrast gain, colorfulness index, contrast-to-noise ratio and visible edges ratio.

Coherent noise reduction of phase images in digital holographic microscopy based on the adaptive anisotropic diffusion.

The suppression of coherent noise can produce higher-quality reconstructed images in digital holographic microscopy. A robust and effective phase coherent noise denoising algorithm is proposed in this paper that combines the anisotropic diffusion equation and the phase quality map. In order to accurately identify the noise and signal pixels, we introduce the phase quality map and edge detection to quantify the quality of the pixel information. In addition, a synthetic diffusion function is established to control the speed of the anisotropic diffusion process based on the quality coefficient. Several experiments have been carried out to validate the effectiveness of the proposed algorithm for coherent noise reduction. The results demonstrate that the proposed algorithm can reduce coherent noise and preserve edge details well.

Convexity dependent anisotropic diffusion for mode detection in cluster analysis

Abstract In cluster analysis, regions of high local density of data points, which might correspond to significant clusters, can be found from the modes of the underlying probability density function (pdf). However, due to irregularities in the data distribution, the modes and the valleys of the pdf are often ill defined so that mode detection can lead to poor results. In this paper, an anisotropic diffusion process is proposed in order to reinforce the smoothing of the pdf in the modal regions where it is concave and in the valleys where it is convex, while preserving the boundaries between them. This adaptive smoothing procedure is combined with a strategy which consists in applying a forward diffusion when the pdf is concave and a backward diffusion when it is convex. Iterations of this convexity dependent anisotropic diffusion tend to enhance the modes and to deepen the valleys of the underlying pdf, so that mode detection becomes trivial. Experiment and comparative results with some well-known clustering algorithms over simulated datasets show the effectiveness of the proposed clustering method.

Mean-Shift segmentation and PDE-based nonlinear diffusion: toward a common variational framework for foreground/background document image segmentation

The presence of noise in images of degraded documents limits the direct application of segmentation approaches and can lead to the presence of a number of different artifacts in the final segmented image. A possible solution is the integration of a pre-filtering step which may improve the segmentation quality through the reduction of such noise. This study demonstrated that combining the Mean-Shift clustering algorithm and the tensor-driven diffusion process into a joint iterative framework produced promising results. For instance, this framework generates segmented images with reduced edge and background artifacts when compared to results obtained after applying each method separately. This improvement is explained by the mutual interaction of global and local information, introduced, respectively, by the Mean-Shift and the anisotropic diffusion. Another point of note is that the anisotropic diffusion process smoothed images while preserving edge continuities. The convergence of this framework was defined automatically under a stopping criterion not previously defined when the diffusion process was applied alone. To obtain a fast convergence, the common framework utilizes the speedup algorithm of the Fukunaga and Hostetler Mean-Shift formulation already proposed by Lebourgeois et al. (International Conference on Document Analysis and Recognition (ICDAR), pp 52–56, 2013). This new variant of the Mean-Shift algorithm produced similar results to the original one, but ran faster due to the application of the integral volume. The first application of this framework was document ink bleed-through removal where noise is stemmed from the interference of the verso side on the recto side, thus perturbing the legibility of the original text. Other categories of images could also be subjected to the proposed framework application.

Calibrating second-moment matrix for better shape adaptation with bias term from directional filter bank

Anisotropic diffusion is an important noise reduction process in many pattern recognition systems. The local orientations and shape are encoded in a descriptor, called second-moment matrix, to be used as the central part of the process. For a noisy image, it becomes hard to find the elements of the matrix with reasonable accuracy. Two layers of subsequent Gaussian smoothing are applied conventionally: One is referred to as noise scale and the other integration scale. It is still not guaranteed that a second-moment matrix is correctly aligned with underlying pattern flow directions. It is largely believed that the integration scale handles this orientation discrepancy. Therefore, some researchers suggested a space-dependent integration scale strategy. We propose here a calibration strategy using directional filterbank (DFB). The second-moment matrix is rotated to go along the proper ridge directions with an angle correction term from DFB. The experiments conducted show promise for the calibrated anisotropic diffusion process in terms of improved recognition rate over that of the un-calibrated process.

Spectral-spatial adaptive and well-balanced flow-based anisotropic diffusion for multispectral image denoising

Anisotropic diffusion can provide better compromise between noise reduction and edge preservation. In multispectral images, there exist different spatial local structures in the same band. Therefore, the levels of smoothing of anisotropic diffusion process should conform to both of image spectral and spatial features. In this paper, we present an effective denoising algorithm by integrating the spectral-spatial adaptive mechanism into a well-balanced flow (WBF) based anisotropic diffusion model, in which an adjustable weighted function is introduced to perform the appropriate levels of smoothing and enhancing according to different feature scales. Moreover, we make the fidelity term in the model to be adaptive by replacing the original noisy signal with the last evolution of the smoothed image. Consequently, the proposed algorithm can better control the diffusion behavior than traditional multispectral diffusion-based algorithms. The experimental results verify that our algorithm can improve visual quality of the image and obtain better quality indices.

2D self-assembly of phenylene–vinylene tectons at the liquid–highly oriented pyrolytic graphite interface: from chain length effects to anisotropic guest–host dynamics

Here we report the synthesis and characterization of a series of new phenylene–vinylene tectons. The study by scanning tunneling microscopy of their supramolecular self-assembly at the interface between a phenyloctane solution and highly oriented pyrolytic graphite demonstrates that variation of concentration and length of alkyl chains led to the formation of different networks, a compact one and a nanoporous one, with a fine control of the lattice parameters. The study of guest–host properties of the nanoporous network revealed a selectivity toward guest compounds according to their shape and size. Moreover, the statistical analysis of pore-to-pore guest dynamics evidences an anisotropic diffusion process.