Multiple Diffusion Research Articles

Simplified Simulation Method of Diffusers for Indoor Non-Uniform Temperature Distribution: A Case Study in Shanghai

The specific air jet of a diffuser is formed by the complex internal structure, which affects the outlet airflow distribution of the diffuser directly and the indoor environment distribution indirectly. If the diffusers are developed based on their actual geometry structure and their boundary conditions are set as their inlet flowrate, the simulated indoor temperature distribution will be more accurate. However, it is noted that many problems may arise, such as model complexity, many grid cells, and slow convergence of calculations. Therefore, this paper focuses on a simplified method for four-way square diffusers in a computational fluid dynamics (CFD) simulation of indoor non-uniform temperature distribution. Firstly, the airflow distribution is simulated on the outlet air supply cross-section of the diffuser. Then, according to the outflow characteristics of the diffuser, the diffuser model is simplified and simulated in an experimental room. Finally, the temperature distribution at the 1.2 m height plane is obtained from CFD simulation and compared with the experimental results. The results show that the 68-point air supply opening model can well simulate the effects of the outlet airflow distribution of the diffuser, and the simulated indoor temperature distribution meets the experiment results well. The deviations for three scenarios are between −7.4~1.7% and the average deviation is −3.0%, while the root mean square error of temperature for three scenarios is 0.7 °C, 0.7 °C, and 1.0 °C, respectively. The results also demonstrate the mutual influence of the airflow from different diffusers and the indoor non-uniform temperature distribution under the action of multiple diffusers. The proposed method can contribute to balancing the model complexity and the accuracy in CFD simulation, especially for multiple diffusers in the room.

Attention-based fusion of multiple graphheat networks for structural to functional brain mapping

Over the last decade, there has been growing interest in learning the mapping from structural connectivity (SC) to functional connectivity (FC) of the brain. The spontaneous fluctuations of the brain activity during the resting-state as captured by functional MRI (rsfMRI) contain rich non-stationary dynamics over a relatively fixed structural connectome. Among the modeling approaches, graph diffusion-based methods with single and multiple diffusion kernels approximating static or dynamic functional connectivity have shown promise in predicting the FC given the SC. However, these methods are computationally expensive, not scalable, and fail to capture the complex dynamics underlying the whole process. Recently, deep learning methods such as GraphHeat networks and graph diffusion have been shown to handle complex relational structures while preserving global information. In this paper, we propose a novel attention-based fusion of multiple GraphHeat networks (A-GHN) for mapping SC-FC. A-GHN enables us to model multiple heat kernel diffusion over the brain graph for approximating the complex Reaction Diffusion phenomenon. We argue that the proposed deep learning method overcomes the scalability and computational inefficiency issues but can still learn the SC-FC mapping successfully. Training and testing were done using the rsfMRI data of 1058 participants from the human connectome project (HCP), and the results establish the viability of the proposed model. On HCP data, we achieve a high Pearson correlation of 0.788 (Desikan-Killiany atlas with 87 regions) and 0.773 (AAL atlas with 86 regions). Furthermore, experiments demonstrate that A-GHN outperforms the existing methods in learning the complex nature of the structure-function relation of the human brain.

Mathematical Modeling of Oxygen Diffusion from Capillary to Tissues during Hypoxia through Multiple Points Using Fractional Balance Equations with Memory.

The diffusion of oxygen through capillary to surrounding tissues through multiple points along the length has been addressed in many clinical studies, largely motivated by disorders including hypoxia. However relatively few analytical or numerical studies have been communicated. In this paper, as a compliment to physiological investigations, a novel mathematical model is developed which incorporates the multiple point diffusion of oxygen from different locations in the capillary to tissues, in the form of a fractional dynamical system of equations using the concept of system of balance equations with memory. Stability analysis of the model has been conducted using the well known Routh-Hurwitz stability criterion. Comprehensive analytical solutions for the differntial equation problem in the new proposed model are obtained using Henkel transformations. Both spatial and temporal variation of concentration of oxygen is visualized graphically for different control parameters. Close correlation with simpler models is achieved. Diffusion is shown to arise from different points of the capillary in decreasing order along the length of the capillary i.e. for the different values of z. The concentration magnitudes at low capillary length far exceed those further along the capillary. Furthermore with progrssive distance along the capillary, the radial distance of diffusion decreases, such that oxygen diffuses only effectively in very close proximity to tissues. The simulations provide a useful benchmark for more generalized mass diffusion computations with commercial finite element and finite volume software including ANSYS FLUENT.

Indoor experiments of a horizontal multiple effects diffusion solar still: Influence of heat input and the number of stages

<abstract> <p>Clean water is important for human life, and obtaining it with the least amount of energy is significant. This research aims to desalinate water using a horizontal multiple effects diffusion solar still (DSS). A small distillation device with an area of 10 × 10 cm<sup>2</sup> was designed and 3D printed. An electric heater was used to simulate solar radiation at 400, 700, and 1000 W/m<sup>2</sup>. The amount of water produced when using 1, 3, and 5 effects was recorded. The most notable results were: maximum water yield reached 1.93 kg/m<sup>2</sup> h at 1000 W/m<sup>2</sup>, at which the solar to vapor conversion efficiency was 107%. The daily water yields throughout the year were estimated, and the maximum production was 10.16 kg/m<sup>2</sup> during a day in June, when the global horizontal irradiance was 7.01 kWh/m<sup>2</sup>. The results were also compared with other distillation systems.</p> </abstract>

Effect of non-ideal mixture on flame–spray interaction in counterflow n-heptane/ethanol flames

This work presents a numerical study of bi-component n-heptane/ethanol spray flames in a counterflow to improve the understanding of the effect of non-ideal mixtures on the flame–spray interaction. The simulations of this spray configuration allow for the detailed examination of the real fluid behavior and its influence on gas-phase combustion kinetics for a wide range of relevant parameters, i.e., droplet composition, size, and gas strain rate. The results reveal that due to the large real activity coefficient of n-heptane and the resulting selective evaporation of the heavier component, the burning characteristics of the spray with a high initial ethanol content do not differ if non-ideal mixture is considered. Conversely, the flame structure with a low ethanol content is substantially different, and displacement of the flame towards the spray side of the configuration is found. A multiple reaction zone, displaying both partially-premixed and diffusion flames, exists, which is overestimated spatially if the fluid is assumed ideal. In general, the ideal prediction of real fluid would misinterpret the composition evaporation order, prolonging the droplet lifetime and consequently, enhancing the flame–spray interaction locally, which results in a lower flame temperature. A parameter characterizing the multicomponent droplet penetration is introduced, which highlights the appreciable non-ideal effects that vary with droplet size and composition, and most importantly, further demonstrates the necessity of considering the real fluid properties in design of next-generation engines with blended fuels.

Graphyne-based 3D porous structure and its sandwich-type graphene structure for alkali metal ion battery anode materials.

In order to develop candidate materials for more metal ion battery anodes, a three-dimensional (3D) porous structure 3D-PGY was designed based on graphyne, and a sandwich structure graphene/PGY/graphene (G/PGY/G) was constructed by adjusting the distance between two layers of graphene with 3D-PGY as the middle layer. Systematic calculations have shown that 3D-PGY is thermally and mechanically stable even at temperatures up to 1000 K. Li can migrate in multiple diffusion directions in two structures because of its smaller radius while Na and K ions can only migrate through the larger pores. The energy barriers of Li, Na and K ions in 3D-PGY are 0.18, 0.43 and 0.27 eV respectively. After forming the sandwich structure with graphene, the minimum energy barriers of Li, Na and K ions are decreased to 0.12, 0.37 and 0.24 eV, respectively. As the anode for Li, Na, and K ion batteries, the theoretical specific capacities of 3D-PGY are about 558 mA h g-1, and the average open circuit voltages of 3D-PGY and G/PGY/G are about 0.48/0.52/0.29 and 1.08/1.04/1.39 V, respectively. Finally, using ab initio molecular dynamics simulations, the diffusion coefficients for 3D-PGY at different temperatures, as well as for G/PGY/G at 400 K were obtained. The Li, Na and K ions in both structures can diffuse rapidly and have good rate capabilities. These excellent performances show that the graphyne-based 3D porous structure and its sandwich-type graphene structure are very promising for the development of new battery materials.

Influence of Diffusion Time and Temperature on Restricted Diffusion Signal: A Phantom Study.

Diffusion MRI is a physical measurement method that quantitatively indicates the displacement of water molecules diffusing in voxels. However, there are insufficient data to characterize the diffusion process physically in a uniform structure such as a phantom. This study investigated the transitional relationship between structure scale, temperature, and diffusion time for simple restricted diffusion using a capillary phantom. We performed diffusion-weighted pulsed-gradient stimulated-echo acquisition mode (STEAM) MRI with a 9.4 Tesla MRI system (Bruker BioSpin, Ettlingen, Germany) and a quadrature coil with an inner diameter of 86 mm (Bruker BioSpin). We measured the diffusion coefficients (radial diffusivity [RD]) of capillary plates (pore sizes 6, 12, 25, 50, and 100 μm) with uniformly restricted structures at various temperatures (10ºC, 20ºC, 30ºC, and 40ºC) and multiple diffusion times (12-800 ms). We evaluated the characteristics of scale, temperature, and diffusion time for restricted diffusion. The RD decayed and became constant depending on the structural scale. Diffusion coefficient fluctuations with temperature occurred mostly under conditions of a large structural scale and short diffusion time. We obtained data suggesting that temperature-dependent changes in the diffusion coefficients follow physical laws. No water molecules were observed outside the glass tubes in the capillary plates, and the capillary plates only reflected a restricted diffusion process within the structure.We experimentally evaluated the characteristics of simple restricted diffusion to reveal the transitional relationship of the diffusion coefficient with diffusion time, structure scale, and temperature through composite measurement.

Numerical modeling of non-uniform indoor temperature distribution for coordinated air flow control

The indoor thermal environment is usually non-uniformly distributed in parameters such as temperature and velocity. For precise control of indoor environment, it is necessary to figure out the indoor non-uniform temperature distribution (INUTD) that empowers independently zone control according to the different requirements of occupants. Computational Fluid Dynamics (CFD) tool is usually used to obtain the INUTD, but it consumes huge computational resources and time, which may not be suitable for coupling with control system. To address this research question, this study proposes a numerical modeling method for predicting the INUTD and air flowrate response of multiple diffusers for coordinated air flow control. Firstly, we establish a dataset with 5000 cases, along with the results of INUTD for each case. Then two models, namely room thermal response model (RTRModel) and air flowrate prediction model (AFPModel), are developed by machine learning algorithms to predict indoor temperature and supply air flowrate, respectively. The results show that proposed models are both fast in prediction, less than 1 s for each case. The standard deviation of error in RTRModel developed with support vector machine algorithm is 0.0041 while that in AFPModel developed with Convolutional Neural Network algorithm is 0.0198. Further, a comparative analysis has been conducted between the AFPModel with and without optimization algorithm. The results reveal that using optimization algorithm is more accurate, but it takes more time. While numerical modeling can instantaneous response with qualified accuracy. The proposed method can contribute to independently zonal environment control and occupant-centered micro-environment control.

A cascade information diffusion prediction model integrating topic features and cross-attention

Information cascade prediction is a crucial task in social network analysis. However, previous research has only focused on the impact of social relationships on cascade information diffusion, while ignoring the differences caused by the characteristics of cascade information itself, which limits the performance of prediction results. We propose a novel cascade information diffusion prediction model (Topic-HGAT). Firstly, we extract features from different topic features to enhance the learned cascade information representation. To better implement this method, we use hypergraphs to better characterize cascade information and dynamically learn multiple diffusion sub-hypergraphs according to the time process; secondly, we introduce cross-attention mechanisms to learn each other's feature representations from the perspectives of both user representation and cascade representation, thereby achieving deep fusion of the two features. This solves the problem of poor feature fusion effect caused by simply calculating self-attention on learned user representation and cascade representation in previous studies; finally, we conduct comparative experiments on four real datasets, including Twitter and Douban. Experimental results show that the proposed Topic-HGAT model achieves the highest improvements of 2.91% and 1.59% on Hits@100 and MAP@100 indicators, respectively, compared to other 8 baseline models, verifying the rationality and effectiveness of the proposed Topic-HGAT model.

Event-triggered pinning passivity and synchronization of multiple spatial diffusion coupled reaction–diffusion neural networks

In this paper, the problem of the event-triggered pinning passivity and synchronization for multiple spatial diffusion coupled reaction–diffusion neural networks is investigated. Two types of multiple spatial diffusion coupled reaction–diffusion neural networks, with undirected and directed topologies, are considered. Combining the advantages of event-triggered and pinning control methods, event-triggered pinning controllers for these two networks are constructed. By imposing appropriate Lyapunov functionals and inequality techniques, several passivity and synchronization conditions are established for these two networks under the designed event-triggered pinning controllers. Moreover, the non-occurrence of the Zeno behavior in the proposed control is proved. Two numerical examples are illustrated to verify the effectiveness of the proposed criteria.

Diffusion-Ordered Spectroscopy (DOSY) as a Powerful NMRMethod to Investigate Molecular Mobitiesand IntermolecularInteractions in Complex Oil Mixtures.

Studying the characteristics and molecular mechanisms of liquid self-diffusion coefficient and viscosity changes is of great significance for, e.g., chemical and petroleum processing. As an example of a highly complex liquid, asphaltene-free high-acid and high-viscosity crude oil and its extracted fractions were studied by comparing their 1H DOSY diffusion maps. The crude oil exhibited a polydisperse diffusion distribution, including multiple diffusion portions with diffusion coefficients much smaller than that of any single fraction in independent diffusion. The main mechanism that leads to the decreases in the diffusion coefficients of crude oil is attributed to diffusion resistance enhanced by Dynamical Molecular-Interaction Networks (DMINs), rather than by enlargement of the diffusion species caused by molecular aggregation. Constructed through the synergistic interactions of various polar molecules in crude oil, DMINs dynamically bind polar molecules, trap polarizable molecules, and spatially hinder the free motion of non-polar molecules. Overall, this reduces the diffusion coefficients of all molecular. This study demonstrates that DOSY is a powerful NMR method to investigate molecular motion abilities in complex mixtures. In addition, the insights in the influence of the interaction matrix on the molecular mobility also help to understand the contribution of "structural viscosity" to the viscosity of heavy oil.

Analysis of global stability and asymptotic properties of a Cholera model with multiple transmission routes, spatial diffusion and incomplete immunity

A novel reaction diffusion model is proposed, in this paper, to consider the impacts on the spatially heterogeneity, horizontal and environmental transmission, incomplete immunity and exposed individuals on the spread and control of Cholera. Firstly, the existence of the solution of this model, the boundedness and the existence of the global attractor are investigated. The basic reproduction number R0 of model is further defined, and then the threshold results of its global dynamics are established based on R0. In particular, we analyze the asymptotic behavior of the steady state when the diffusion rate is small or large in susceptible and exposed individuals. With the help of numerical simulations, we found that the spread of susceptible individuals does not change the spatial distribution of the disease and the local epidemic risk level during the spread of the disease in different regions, while the spread of exposed individuals has an important effect on the spatial distribution of the infected population.

Dual Stratification Effects on Mixed Convective Electro-magnetohydrodynamic Flow over a Stretching Plate with Multiple Slips and Cross Diffusion

This paper analyzed the effects of dual stratification on mixed convective electro-magnetohydrodynamic flow over stretching plates with multiple slips. With the aid of the similarity transformation technique were, the governing boundary equations, that were partial differential equations, were changed to a couple of ordinary differential equations and then solved with fourth order Runge Kutta method and Newton’s Raphson shooting techniques. It was observed that the magnetic field, Buoyancy ratio, permeability, momentum slip parameters, Dufour, Soret and Brinkmann numbers made the thermal boundary layer thickness to increase but the solutal stratification, electric field, chemical reaction, solutal slip, suction, thermal slip and thermal stratification parameters, Prandtl, Richardson and Lewis number decreased the thickness of the thermal boundary layer. The Buoyancy ratio, permeability, momentum slip, thermal slip and thermal stratification parameters and Soret number enhanced the solutal boundary layer thickness.

Longitudinal evolution of diffusion metrics after left hemisphere ischaemic stroke

Abstract White matter is often severely affected after human ischaemic stroke. While animal studies have suggested that various factors may contribute to white matter structural damage after ischaemic stroke, the characterization of damaging processes to the affected hemisphere after human stroke remains poorly understood. Thus, the present study aims to thoroughly describe the longitudinal pattern of evolution of diffusion magnetic resonance imaging metrics in different parts of the ipsilesional white matter after stroke. We acquired diffusion and anatomical images in 17 patients who had suffered from a single left hemisphere ischaemic stroke, at 24–72 h, 8–14 days and 6 months post-stroke. For each patient, we created three regions of interest: (i) the white matter lesion; (ii) the perilesional white matter; and (iii) the remaining white matter of the left hemisphere. We extracted diffusion metrics (fractional anisotropy, mean, axial and radial diffusivities) for each region and conducted two-way repeated measures ANOVAs with stage post-stroke (acute, subacute and chronic) × regions of interest (white matter lesion, perilesional white matter and remaining white matter). Fractional anisotropy values stayed consistent across time-points, with significantly lower values in the white matter lesion compared to the perilesional white matter and remaining white matter tissue. Fractional anisotropy values of the perilesional white matter were also significantly lower than that of the remaining white matter. Mean, axial and radial diffusivities in the white matter lesion were all decreased in the acute stage compared to perilesional white matter and remaining white matter, but significantly increased in both the subacute and chronic stages. Significant increases in mean and radial diffusivities in the perilesional white matter were seen in the later stages of stroke. Our findings suggest that various physiological processes are at play in the acute, subacute and chronic stages following ischaemic stroke, with the infarct territory and perilesional white matter affected by ischaemia at different rates and to different extents throughout the stroke recovery stages. The examination of multiple diffusivity metrics may inform us about the mechanisms occurring at different time-points, i.e. focal swelling, axonal damage or myelin loss.

Hyperchaotic image encryption using DNA coding and discrete cosine transform

Achieving privacy over sensitive data is challenging in digital communication. In an effort to realize this aim, we propose hyperchaotic image encryption through DNA (deoxyribonucleic acid) coding and the discrete cosine transform (DCT). This multi-layered security algorithm comprises advanced levels of confusion and multiple diffusion techniques. The diffusion among the pixel values is attained by employing DNA operations among pixel values and the random sequence generated from the hyperchaotic map. Thereafter, the data sequence is scrambled through the baker map in order to permute the data points. Later, the partially encrypted image is further diffused and compressed through the DCT for lightweight communication. The significant contribution of this algorithm is the excellent improved quality of encryption through a double chaotic DNA encoded scheme. The statistical results are competitive in support of the robustness of the scheme and have shown resistance against the underlying cryptanalytic attacks. The performance of the scheme is evaluated in terms of diverse metrics via entropy, correlation coefficient, PSNR (Peak Signal-to-Noise Ratio), Chi-squared values, etc., and are determined to be more efficient and outperforms some existing state of art techniques.

Robust H∞ Pinning Synchronization for Multiweighted Coupled Reaction-Diffusion Neural Networks.

This article focuses on the robust H∞ synchronization of two types of coupled reaction-diffusion neural networks with multiple state and spatial diffusion couplings by utilizing pinning adaptive control strategies. First, based on the Lyapunov functional combined with inequality techniques, several sufficient conditions are formulated to ensure H∞ synchronization for these two networks with parameter uncertainties. Moreover, node-based pinning adaptive control strategies are devised to address the robust H∞ synchronization problem. In addition, some criteria of H∞ synchronization for these two networks under parameter uncertainties are developed via edge-based pinning adaptive controllers. Finally, two numerical examples are presented to verify our results.

Thermal analysis of bioconvective nanofluid flow over a sphere in presence of multiple diffusions and a periodic magnetic field

The current work intends to describe the heat and mass transfer in the mixed bioconvective flow of nanofluid along the sphere. This analysis also takes into account the influences of a periodic magnetic field and the diffusions of species concentrations such as liquid ammonia and liquid hydrogen. The physical problem is represented as a collection of connected nonlinear partial differential equations with appropriate boundary constraints using the Boussinesq approximation. The Buongiorno two-phase model is utilized to examine the nanoparticle's effect on the fluid. The governing equations are represented in the dimensionless form by using nonsimilar transformations. Further, the implicit finite difference scheme and the technique of quasilinearization are employed for numerical computation. Graphs are used to discuss the findings. The skin friction coefficient increases by about 27%, and the heat transfer rate to the fluid from the surface decreases by about 30% when the periodic magnetic field escalates from 0 to 1. The nanoparticle's mass transfer rate increases by about 35% when the Lewis number grows from 5 to 10. Higher Peclet numbers are favorable to the skin friction coefficient and heat transfer rate, but not the microorganism's density number. The present numerical results obtained in this analysis were compared to earlier published work and found to be in excellent agreement.

Bioconvective periodic MHD Eyring-Powell fluid flow around a rotating cone: Influence of multiple diffusions and oxytactic microorganisms

Investigating the effects of periodic magnetic field and triple diffusion on bioconvection flow through a rotating cone populated by oxytactic bacteria and an Eyring-Powell fluid is innovative and significant. The magneto-bioconvection flow of an Eyring-Powell multi-diffusive fluid across a spinning cone is investigated in this paper, considering the effect of oxytactic microorganisms. The non-similar technique is used in the mathematical analysis of the flow over a spinning cone. The flow under consideration contains two diffusive species: liquid hydrogen and liquid oxygen. In light of the periodic magnetic field, the surface gradients, notably skin friction, exhibit wavy effects in the boundary layer domain. The governing equations for the fluid flow in the current flow problem, accompanied by heat diffusion, species diffusion, rotation, bioconvection, and periodic magnetic, are highly coupled nonlinear PDEs dependent on the proper initial and boundary conditions. Mangler's transformations convert them into non-dimensional forms, and numerical non-similar solutions are produced using implicit finite difference approximation and quasi-linearisation. The enriching values of bioconvective Rayleigh number Rb decline the velocity F, as a result, lessen the friction between the surrounding fluid and the cone's surface. The improving Peclet number Pe and microbial density difference σ reduced the microorganism density profile and heightened the microorganism density number Re-1/2Nn.

A 4D discrete Hopfield neural network-based image encryption scheme with multiple diffusion modes

A novel 4D chaotic map is proposed in this paper using the model of a self-feedback Discrete Hopfield Neural Network (DHNN) with nonlinear synaptic ICMIC (4D-IDHNN). Based on an analysis of chaos characteristics, including attractors, Lyapunov exponents, Bifurcation, Sample Entropy and CO algorithms, the 4D-IDHNN system demonstrates reasonable stochasticity and ergodicity, alongside a broad spectrum of hyperchaotic parameters. Based on the 4D-IDHNN system, we design a new Pixel-dependent bit-plane Chaotic random Diffusion (PbCrD) algorithm with high diffusion capability and security. To begin, the 4D-IDHNN system generates pseudo-random sequences to confuse the plaintext image pixel positions with Chaotic Magic Random Scramble (CMRS). Subsequently, the PbCrD algorithm can be employed to diffuse pixel values. With the initial value of 4D-IDHNN generated using the SHA-256 hash of plaintext image, the ability to resist plaintext attacks can be enhanced. The algorithm includes 24 diffusion modes, which is three times greater than the number of DNA rules, thereby enhancing the complexity of decryption. The proposed encryption algorithm has good effectiveness, robustness, and resistance to differential attacks based on simulations and security analyses.

Estimation of diffusion coefficients in NiCoFeCrAl multi-principal element alloy following an inventive design strategy of diffusion couples

An inventive design strategy of producing the diffusion couples for intersecting the diffusion paths in multicomponent space is described in Ni-Co-Fe-Cr-Al multi-principal element alloy. This, for the first time, facilitates the estimation of the tracer, intrinsic, and interdiffusion coefficients of all the elements purely experimentally in this quinary system. This was not possible until now following any other experimental methods. The tracer diffusion coefficients estimated in this quinary system are compared with the impurity and tracer diffusion coefficients in pure Ni, and at (or near) equiatomic compositions of binary Ni-Co, ternary Ni-Co-Cr, and quaternary Ni-Co-Fe-Cr systems. The relative mobilities of the elements are found to follow the trend DNi*≤DCo*<DFe*≤DCr*<DAl* in all the systems. However, the tracer diffusion coefficients of the elements first decrease and then increase with the increasing order of the systems. The contribution of the vacancy wind effect on certain cross-intrinsic diffusion coefficients is found to be very significant and cannot be ignored. The influence of the vacancy wind effect on interdiffusion coefficients is less significant than the intrinsic diffusion coefficients since interdiffusion coefficients are the average of multiple intrinsic diffusion coefficients. This may lead to the wrong statement that the vacancy wind effects are negligible. We have further shown that describing the relative diffusion rates of the elements with main interdiffusion coefficients instead of the tracer diffusion coefficients can be misleading or confusing. Different elements as the dependent variables of interdiffusion coefficients indicate a very different or even opposite trend of relative diffusivities in this system.