Parallel Diffusion Research Articles

Application of preoperative advanced diffusion magnetic resonance imaging in evaluating the postoperative recurrence of lower grade gliomas

BackgroundRecurrence of lower grade glioma (LrGG) appeared to be unavoidable despite considerable research performed in last decades. Thus, we evaluated the postoperative recurrence within two years after the surgery in patients with LrGG by preoperative advanced diffusion magnetic resonance imaging (dMRI).Materials and methods48 patients with lower-grade gliomas (23 recurrence, 25 nonrecurrence) were recruited into this study. Different models of dMRI were reconstructed, including apparent fiber density (AFD), white matter tract integrity (WMTI), diffusion tensor imaging (DTI), diffusion kurtosis imaging (DKI), neurite orientation dispersion and density imaging (NODDI), Bingham NODDI and standard model imaging (SMI). Orthogonal Partial Least Squares-Discriminant Analysis (OPLS-DA) was used to construct a multiparametric prediction model for the diagnosis of postoperative recurrence.ResultsThe parameters derived from each dMRI model, including AFD, axon water fraction (AWF), mean diffusivity (MD), mean kurtosis (MK), fractional anisotropy (FA), intracellular volume fraction (ICVF), extra-axonal perpendicular diffusivity (De⊥), extra-axonal parallel diffusivity (De∥) and free water fraction (fw), showed significant differences between nonrecurrence group and recurrence group. The extra-axonal perpendicular diffusivity (De⊥) had the highest area under curve (AUC = 0.885), which was significantly higher than others. The variable importance for the projection (VIP) value of De⊥ was also the highest. The AUC value of the multiparametric prediction model merging AFD, WMTI, DTI, DKI, NODDI, Bingham NODDI and SMI was up to 0.96.ConclusionPreoperative advanced dMRI showed great efficacy in evaluating postoperative recurrence of LrGG and De⊥ of SMI might be a valuable marker.

Influence of electron cyclotron current drive on the pressure crashes caused by the 2/1 double tearing modes

Abstract A module with self-consistent evolution of driven current is developed and coupled with the resistive-MHD equations in the three-dimensional, toroidal, and nonlinear simulation code (CLT). The driven current equation is solved with a second-order accuracy symmetric scheme, which exhibits good conservation properties. With the new module, we find that the driven current can self-consistently concentrate inside the magnetic island when the parallel diffusion of the driven current is sufficiently large. The efficiency of the driven current on tearing mode suppression will then be much higher than those with stationary distributions. With the new module, the influence of electron cyclotron current drive (ECCD) on the nonlinear evolution of the 2/1 double tearing modes (DTMs) is investigated. When co-ECCD deposits on the outer resonant surface, the local magnetic shear is reduced, and the growth rates of the DTMs decrease; if ctr-ECCD deposits on the outer resonant surface, the local magnetic shear increases, and the DTMs become more unstable. However, things will be different if ECCD deposits on the inner resonant surface since the local magnetic shear is negative. The co-ECCD deposited on the inner resonant surface increases the negative shear and then promotes the growth of the DTMs; while the ctr-ECCD suppresses the DTMs. It is also found that the off-axis and central pressure crashes associated with the 2/1 DTMs can be converted to each other by properly depositing the driven current. To convert a central crash to an off-axis crash, the co-ECCD should be deposited on the outer resonant surface, or the ctr-ECCD deposited on the inner resonant surface. While, the co-ECCD should be deposited on the inner rational surface, or the ctr-ECCD deposited on the outer rational surface to convert an off-axis crash to a central crash. The co- or ctr-ECCD should be larger than a threshold for such transitions, and the threshold value is mainly determined by the location of the inner resonant surface.

Acral lentiginous melanoma in situ on the palm with a diffuse parallel furrow pattern

Acral lentiginous melanoma in situ on the palm with a diffuse parallel furrow pattern

Multiphase modeling of pressure-dependent hydrogen diffusivity in fractal porous structures of acrylonitrile butadiene rubber-carbon black composites with different fillers

The hydrogen diffusivities of acrylonitrile butadiene rubber (NBR) composites with different types and contents of carbon black (CB) fillers were investigated in the exposure pressure range of 0.5–10 MPa using a volumetric analysis system. These measured diffusivities exhibited distinct pressure-dependent behavior. The diffusivities of unfilled NBR and NBR composites containing medium-thermal CB filler decreased from 39.7 × 10−11 m2/s to 9.4 × 10−11 m2/s as the pressure increased. On the other hand, the pressure-dependent diffusivities of NBR composites containing high-abrasion furnace, fast-extrusion furnace and semireinforcing furnace CB fillers revealed left-biased unimodal shaped curves, with peak values ranging from 19.7 × 10−11 m2/s to 5.6 × 10−11 m2/s. To model this observed behavior, the diffusion resistance theory with a heterogeneous NBR–CB composite and a fractal porous structure for H2 was introduced. The theoretical parallel diffusion resistance model was found to coexist independently as the surface, Knudsen, and bulk diffusion phases. This theoretical multiphase modeling was applied to the measured diffusivities, determining diffusion resistance parameters for each phase. The obtained individual parametric characteristics for each diffusion were interpreted by considering the CB filler content and volume fraction of the filler. As a result, the diffusivities calculated by multiphase diffusion modeling were in quite agreement with the measured diffusivities for all investigated specimens, where the determined squared correlation coefficient (R2) by fitting process was in the range from 0.69 to 0.97.

Parallel diffusion models promote high detail-fidelity photoacoustic microscopy in sparse sampling

Reconstructing sparsely sampled data is fundamental for achieving high spatiotemporal resolution photoacoustic microscopy (PAM) of microvascular morphology in vivo. Convolutional networks (CNN) and generative adversarial networks (GAN) have been introduced to high-speed PAM, but due to the use of upsampling in CNN-based networks to restore details and the instability in GAN training, they struggle to learn the entangled microvascular network structure and vascular texture features, resulting in only achieving low detail-fidelity imaging of microvascular. The diffusion models is richly sampled and can generate high-quality images, which is very helpful for the complex vascular features in PAM. Here, we propose an approach named parallel diffusion models (PDM) with parallel learning of Noise task and Image task, where the Noise task optimizes through variational lower bounds to generate microvascular structures that are visually realistic, and the Image task improves the fidelity of the generated microvascular details through image-based loss. With only 1.56% of fully sampled pixels from photoacoustic human oral data, PDM achieves an LPIPS of 0.199. Additionally, using PDM in high-speed 16x PAM prevents breathing artifacts and image distortion issues caused by low-speed sampling, reduces the standard deviation of the Row-wise Self-Correlation Coefficient, and maintains high image quality. It achieves high confidence in reconstructing detailed information from sparsely sampled data and will promote the application of reconstructed sparsely sampled data in realizing high spatiotemporal resolution PAM.

Toward Graph Self-Supervised Learning With Contrastive Adjusted Zooming.

Graph representation learning (GRL) is critical for graph-structured data analysis. However, most of the existing graph neural networks (GNNs) heavily rely on labeling information, which is normally expensive to obtain in the real world. Although some existing works aim to effectively learn graph representations in an unsupervised manner, they suffer from certain limitations, such as the heavy reliance on monotone contrastiveness and limited scalability. To overcome the aforementioned problems, in light of the recent advancements in graph contrastive learning, we introduce a novel self-supervised GRL algorithm via graph contrastive adjusted zooming, namely, G-Zoom, to learn node representations by leveraging the proposed adjusted zooming scheme. Specifically, this mechanism enables G-Zoom to explore and extract self-supervision signals from a graph from multiple scales: micro (i.e., node level), meso (i.e., neighborhood level), and macro (i.e., subgraph level). First, we generate two augmented views of the input graph via two different graph augmentations. Then, we establish three different contrastiveness on the above three scales progressively, from node, neighboring, to subgraph level, where we maximize the agreement between graph representations across scales. While we can extract valuable clues from a given graph on the micro and macro perspectives, the neighboring-level contrastiveness offers G-Zoom the capability of a customizable option based on our adjusted zooming scheme to manually choose an optimal viewpoint that lies between the micro and macro perspectives to better understand the graph data. In addition, to make our model scalable to large graphs, we use a parallel graph diffusion approach to decouple model training from the graph size. We have conducted extensive experiments on real-world datasets, and the results demonstrate that our proposed model outperforms the state-of-the-art methods consistently.

SegLD: Achieving universal, zero-shot and open-vocabulary segmentation through multimodal fusion via latent diffusion processes

Open-vocabulary learning can identify categories marked during training (seen categories) and generalize to categories not annotated in the training set (unseen categories). It could theoretically extend segmentation systems to more universal applications. However, current open-vocabulary segmentation frameworks are primarily suited for specific tasks or require retraining according to the task, and they significantly underperform in inferring seen categories compared to fully supervised frameworks. Therefore, we introduce a universal open-vocabulary segmentation framework based on the latent diffusion process (SegLD), which requires only a single training session on a panoptic dataset to achieve inference across all open-vocabulary segmentation tasks, and reaches SOTA segmentation performance for both seen and unseen categories in every task. Specifically, SegLD comprises two stages: in the first stage, we deploy two parallel latent diffusion processes to deeply fuse the text (image caption or category labels) and image information, further aggregating the multi-scale features output from both latent diffusion processes on a scale basis. In the second stage, we introduce text queries, text list queries, and task queries, facilitating the learning of inter-category and inter-task differences through the computation of contrastive losses between them. Text queries are then further fed into a Transformer Decoder to obtain category-agnostic segmentation masks. Then we establish classification loss functions for the type of text input during training, whether image captions or category labels, to help assign a category label from the open vocabulary to each predicted binary mask. Experimental results show that, with just a single training session, SegLD significantly outperforms other contemporary SOTA fully supervised segmentation frameworks and open-vocabulary segmentation frameworks across almost all evaluation metrics for both known and unknown categories on the ADE20K, Cityscapes, and COCO datasets. This highlights SegLD’s capability as a universal segmentation framework, with the potential to replace other segmentation frameworks and adapt to various segmentation domains. The project link for SegLD is https://zht-segld.github.io/.

Preparation of surgical meshes using self-regulating technology based on reaction-diffusion processes

While reaction-diffusion processes are utilized in multiple scientific fields, these phenomena have seen limited practical application in the polymer industry. Although self-regulating processes driven by parallel reaction and diffusion can lead to patterned structures, most polymeric products with repeating subunits are still prepared by methods that require complex and expensive instrumentation. A notable, high-added-value example is surgical mesh, which is often manufactured by weaving or knitting. In our present work, we demonstrate how the polymer and the biomedical industry can benefit from the pattern-forming capabilities of reaction-diffusion. We would like to propose a self-regulating method that facilitates the creation of surgical meshes from biocompatible polymers. Since the control of the process assumes a thorough understanding of the underlying phenomena, the theoretical background, as well as a mathematical model that can accurately describe the empirical data, is also introduced and explained. Our method offers the benefits of conventional techniques while introducing additional advantages not attainable with them. Most importantly, the method proposed in this paper enables the rapid creation of meshes with an average pore size that can be adjusted easily and tailored to fit the intended area of application.Graphical abstract

Modeling of pulse and relaxation of high-rate Li/CFx-SVO batteries in implantable medical devices

We present a Hybrid Multiphase Porous Electrode Theory (Hybrid-MPET) model that accurately predicts the performance of Medtronic’s implantable medical device battery lithium/carbon monofluoride (CFx) - silver vanadium oxide (SVO) under both low-rate background monitoring and high-rate pulsing currents. The distinct properties of multiple active materials are reflected by parameterizing their thermodynamics, kinetics, and mass transport properties separately. Diffusion limitations of Li+ in SVO are used to explain cell voltage transient behavior during pulse and post-pulse relaxation. We also introduce change in cathode electronic conductivity, Li metal anode surface morphology, and film resistance buildup to capture evolution of cell internal resistance throughout multi-year electrical tests. We share our insights on how the Li+ redistribution process between active materials can restore pulse capability of the hybrid electrode, allow CFx to indirectly contribute to capacity release during pulsing, and affect the operation protocols and design principles of batteries with other hybrid electrodes. We also discuss additional complexities in porous electrode model parameterization and electrochemical characterization techniques due to parallel reactions and solid diffusion pathways across active materials. We hope our models can complement future experimental research and accelerate development of multi-active material electrodes with targeted performance.

PSDCLS: Parallel simultaneous diffusion–confusion image cryptosystem based on Latin square

Today, due to the unparalleled growth of multimedia data sharing, especially digital images, between users over insecure channels in real-time applications, cryptography algorithms have gained increasing attention for the secure and efficient transmission. In classical chaos-based image cryptosystems, the confusion and diffusion operations are often applied as two separate and independent phases, which threatens the cryptosystem security. To address these problems, in this paper, a fast image cryptosystem based on parallel simultaneous diffusion–confusion strategy has been proposed using Latin squares, called PSDCLS. It consists of three main steps. First, the initial parameters of the Hénon-Sine chaotic map are produced from SHA256 of both the plain image content and the user’s secret key. Second, a chaos-based random Latin square is constructed by employing the chaotic sequence produced through the Hénon-Sine chaotic map. Third, a parallel simultaneous diffusion–confusion scheme is proposed by using Latin square and vectorization technique to overcome the problems of computational complexity and high risk of separable and iterative confusion–diffusion operations in the classical chaos-based image cryptosystems. To analyze and evaluate the security and performance of PSDCLS cryptosystem, we conducted extensive simulations and experiments on various benchmark images. Experimental results and analyses show that PSDCLS achieves excellent scores for information entropy (>7.99), correlation coefficients close to 0, key space (2512), NPCR (>99.60%), UACI (>33.46%). The encryption time for test images of size 512 × 512 and 512×512×3 was around 0.026 and 0.081 s, respectively. Therefore, PSDCLS is highly robust against common cryptographic attacks and serves as a swift cryptosystem for real-time encryption applications. The source code of PSDCLS is accessible at: https://github.com/EbrahimZarei64/PSDCLS.

Transport of energetic particles in turbulent space plasmas: pitch-angle scattering, telegraph, and diffusion equations

Introduction: In this article, we revisit the pitch-angle scattering equation describing the propagation of energetic particles through magnetized plasma. In this case, solar energetic particles and cosmic rays interact with magnetohydrodynamic turbulence and experience stochastic changes in the pitch-angle. Since this happens over an extended period of time, a pitch-angle isotropization process occurs, leading to parallel spatial diffusion. This process is described well by the pitch-angle scattering equation. However, the latter equation is difficult to solve analytically even when considering special cases for the scattering coefficient.Methods: In the past, a so-called subspace approximation was proposed, which has important applications in the theory of perpendicular diffusion. Alternatively, an approach based on the telegraph equation (also known as telegrapher’s equation) has been developed. We show that two-dimensional subspace approximation and the description based on the telegraph equation are equivalent. However, it is also shown that the obtained distribution functions contain artifacts and inaccuracies that cannot be found in the numerical solution to the problem. Therefore, an N-dimensional subspace approximation is proposed corresponding to a semi-analytical/semi-numerical approach. This is a useful alternative compared to standard numerical solvers.Results and Discussion: Depending on the application, the N-dimensional subspace approximation can be orders of magnitude faster. Furthermore, the method can easily be modified so that it can be used for any pitch-angle scattering equation.

Cosmic-ray diffusion in two local filamentary clouds

Context. Hadronic interactions between cosmic rays (CRs) and interstellar gas have been probed in γ rays across the Galaxy. A fairly uniform CR distribution is observed up to a few hundred parsecs from the Sun, except in the Eridu cloud, which shows an unexplained 30–50% deficit in GeV to TeV CR flux. Aims. To explore the origin of this deficit, we studied the Reticulum cloud, which shares notable traits with Eridu: a comparable distance in the low-density region of the Local Valley and a filamentary structure of atomic hydrogen extending along a bundle of ordered magnetic-field lines that are steeply inclined to the Galactic plane. Methods. We measured the γ-ray emissivity per gas nucleon in the Reticulum cloud in the 0.16–63 GeV energy band using 14 years of Fermi-LAT data. We also derived interstellar properties that are important for CR propagation in both the Eridu and Reticulum clouds, at the same parsec scale. Results. The γ-ray emissivity in the Reticulum cloud is fully consistent with the average spectrum measured in the solar neighbourhood, but this emissivity, and therefore the CR flux, is 1.57 ± 0.09 times larger than in Eridu across the whole energy band. The difference cannot be attributed to uncertainties in gas mass. Nevertheless, we find that the two clouds are similar in many respects: both have magnetic-field strengths of a few micro-Gauss in the plane of the sky; both are in approximate equilibrium between magnetic and thermal pressures; they have similar turbulent velocities and sonic Mach numbers; and both show magnetic-field regularity with a dispersion in orientation lower than 10°–15° over large zones. The gas in Reticulum is colder and denser than in Eridu, but we find similar parallel diffusion coefficients around a few times 1028 cm2 s−1 in both clouds if CRs above 1 GV in rigidity diffuse on resonant, self-excited Alfvén waves that are damped by ion-neutral interactions. Conclusions. The loss of CRs in Eridu remains unexplained, but these two clouds provide important test cases to further study how magnetic turbulence, line tangling, and ion-neutral damping regulate CR diffusion in the dominant gas phase of the interstellar medium.

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.

Parallel Diffusion Coefficient of Energetic Charged Particles in the Inner Heliosphere from the Turbulent Magnetic Fields Measured by Parker Solar Probe

Diffusion coefficients of energetic charged particles in turbulent magnetic fields are a fundamental aspect of diffusive transport theory but remain incompletely understood. In this work, we use quasi-linear theory to evaluate the spatial variation of the parallel diffusion coefficient κ ∥ from the measured magnetic turbulence power spectra in the inner heliosphere. We consider the magnetic field and plasma velocity measurements from Parker Solar Probe made during Orbits 5–13. The parallel diffusion coefficient is calculated as a function of radial distance from 0.062 to 0.8 au, and the particle energy from 100 keV to 1 GeV. We find that κ ∥ increases exponentially with both heliocentric distance and energy of particles. The fluctuations in κ ∥ are related to the episodes of large-scale magnetic structures in the solar wind. By fitting the results, we also provide an empirical formula of κ ∥ = (5.16 ± 1.22) × 1018 r 1.17±0.08 E 0.71±0.02 (cm2 s−1) in the inner heliosphere, which can be used as a reference in studying the transport and acceleration of solar energetic particles as well as the modulation of cosmic rays.

Multi-scale simulation of Mo–Ag laminated metal matrix composites with Mo–Ag diffusion layer and parallel gap resistance welding in solar cells

Thus far, Mo/Ag laminated metal matrix composites (LMMCs) have been widely used as interconnectors in solar cells. In order to enhance the connection strength between Mo–Ag LMMCs and solar cells, a multi-scale simulation technique (MSM) was utilised to simulate the parallel gap resistance welding (PGRW) process. This method involved molecular dynamics (MD) simulation and the finite element method (FEM). The structure of the Mo–Ag diffusion layer was examined by high-resolution transmission electron microscopy (HRTEM), which revealed a thickness of around 5 nm. It exhibited a wedge-shaped configuration that augmented the bonding between Mo and Ag. The characteristics of the Mo–Ag diffusion layer were computed using molecular dynamics (MD), which has a substantial influence on the properties of the interconnectors. The FEM model was provided with these characteristics, and a total of nine sets of orthogonal simulation experiments were devised. The findings indicate that when a voltage of 0.5 V is applied, the distance between the electrodes is 0.15 mm, and the pressure on the electrodes is 8.89 N, the temperature at the interface of the workpiece can reach 940 °C. Furthermore, the internal stress (90 MPa) remains below the material's yield strength (430 MPa). In addition, based on the specifications of nine sets of orthogonal trials, the interconnectors were welded to the solar cells, and further 45° tensile tests were performed on the resulting joints. According to the simulation, the connection strength can achieve a maximum value of 558 gf (5.47 N) using the optimal parameters. Meanwhile, the findings from electron backscatter diffraction (EBSD) revealed that the primary process involved in the connection mechanism of PGRW is the mutual diffusion and recrystallization that occur due to electrode pressure and resistance heat.

Real-time chaotic video encryption based on multi-threaded parallel confusion and diffusion

Due to the strong correlation among adjacent pixels, image encryption schemes typically perform multiple rounds of confusion and diffusion to protect images against various attacks. This is time-consuming and cannot meet the real-time requirements for video encryption. Existing works, therefore, realize video encryption by simplifying encryption process or selectively encrypting specific pixels, resulting in lower security compared to image encryption. This paper proposes a real-time chaotic video encryption strategy based on parallel computing. It splits video frame into sub-frames, creates a dedicated set of threads to concurrently perform confusion and diffusion operations on their respective sub-frames, and efficiently outputs encrypted frames. To assess its performance, two cryptosystems are implemented using different chaotic systems. Encryption speed evaluation demonstrates a significant acceleration in byte generation, confusion, and diffusion phases, enabling real-time encryption and decryption on different X86 platforms. The average encryption time is less than 42 ms, despite performing five rounds of confusion and diffusion operations on each frame. Statistical and security analysis prove that the deployed cryptosystems exhibit exceptional statistical properties and provide resistance to different attacks. Moreover, our method is adopted to implement a multi-user, real-time mobile video secure communication system using embedded systems, validating the feasibility of the proposed strategy for various application scenarios.

Modeling Ion Acceleration and Transport in Corotating Interaction Regions: The Mass-to-charge Ratio Dependence of the Particle Spectrum

We investigate the role of perpendicular diffusion in shaping the energetic ion spectrum in corotating interaction regions (CIRs), focusing on its mass-to-charge (A/Q) ratio dependence. We simulate a synthetic CIR using the EUropean Heliospheric FORecasting Information Asset and model the subsequent ion acceleration and transport by solving the focused transport equation incorporating both parallel and perpendicular diffusion. Our results reveal distinct differences in ion spectra between scenarios with and without perpendicular diffusion. In the absence of perpendicular diffusion, ion spectra near CIRs show a strong (A/Q) ϵ dependence with ϵ depending on the turbulence spectral index, agreeing with theoretical predictions. In contrast, the incorporation of perpendicular diffusion, characterized by a weak A/Q dependence, leads to similar spectra for different ion species. This qualitatively agrees with observations of energetic particles in CIRs.

Investigating apparent differences between standard DKI and axisymmetric DKI and its consequences for biophysical parameter estimates.

The purpose of the study is to identify differences between axisymmetric diffusion kurtosis imaging (DKI) and standard DKI, their consequences for biophysical parameter estimates, and the protocol choice influence on parameter estimation. Noise-free and noisy, synthetic diffusion MRI human brain data is simulated using standard DKI for a standard and the fast "199" acquisition protocol. First the noise-free "baseline" difference between both DKI models is estimated and the influence of fiber complexity is investigated. Noisy data is used to establish the signal-to-noise ratio at which the baseline difference exceeds noise variability. The influence of protocol choices and denoising is investigated. The five axisymmetric DKI tensor metrics (AxTM), the parallel and perpendicular diffusivity and kurtosis and mean of the kurtosis tensor are used to compare both DKI models. Additionally, the baseline difference is also estimated for the five parameters of the WMTI-Watson model. The parallel and perpendicular kurtosis and all of the WMTI-Watson parameters had large baseline differences. Using a Westin or FA mask reduced the number of voxels with large baseline difference, that is, by selecting voxels with less complex fibers. For the noisy data, precision was worsened by the fast "199" protocol but adaptive denoising can help counteract these effects. For the diffusivities and mean of the kurtosis tensor, axisymmetric DKI with a standard protocol delivers similar results as standard DKI. Fiber complexity is one main driver of the baseline differences. Using the "199" protocol worsens precision in noisy data but adaptive denoising mitigates these effects.

Anisotropic heat diffusion in stochastic magnetic fields

AbstractThe magnetic topology is a critical issue in fusion plasma research. An example is the Resonant Magnetic Perturbation (RMP), which controls the edge transport in tokamaks. However, the physics of how the RMP affects edge transport is not clear. One reason is the transport process on the stochastic magnetic field is poorly understood. This study examines anisotropic heat diffusion numerically to understand heat transport in stochastic magnetic fields. We developed a numerical model of an anisotropic temperature diffusion model, where the significant deviation of the parallel and perpendicular thermal conductivity exists. We applied this implementation to the realistic stellarator geometry with the stochastic magnetic field in the edge. The smooth temperature profile is obtained for the large perpendicular diffusion, although the magnetic field is stochastic. However, for another case of significant parallel diffusion, the small flattening of the temperature on the magnetic island in the stochastic region appears. That result suggests that the stochastic magnetic field can keep the finite temperature gradient if the connection length of the magnetic field line in the stochastic region is sufficiently long.

The Effect of Solar Wind on Charged Particles’ Diffusion Coefficients

The transport of energetic charged particles through magnetized plasmas is ubiquitous in interplanetary space and astrophysics, and the important physical quantities are the parallel and perpendicular diffusion coefficients of energetic charged particles. In this paper, the influence of solar wind on particle transport is investigated. Using the focusing equation, we obtain parallel and perpendicular diffusion coefficients, accounting for the solar wind effect. For different conditions, the relative importance of the solar wind effect to diffusion is investigated. It is shown that, when energetic charged particles are close to the Sun, for parallel diffusion, the solar wind effect needs to be taken into account. These results are important for studying energetic charged particle transport processes in the vicinity of the Sun.