One-dimensional diffusion of vacancies on an Sr/Si(100)-c(2×4) surface

An Sr/Si（100）-c（2 ×4） surface is investigated by high-resolution scanning tunneling microscopy （STM） and scanning tunneling spectroscopy （STS）. The semiconductor property of this surface is confirmed by STS. The STM images of this surface shows that it is bias-voltage dependent and an atomic resolution image can be obtained at an empty state under a bias voltage of 1.5 V. Furthermore, one-dimensional （ID） diffusion of vacancies can be found in the room-temperature STM images. Sr vacancies diffuse along the valley channels, which are constructed by silicon dimers in the surface. Weak interaction between Sr and silicon dimers, low metal coverage, surface vacancy, and energy of thermal fluctuation at room temperature all contribute to this 1D diffusion.

Domain of attraction of quasi-stationary distribution for one-dimensional diffusions

We study quasi-stationarity for one-dimensional diffusions killed at 0, when 0 is a regular boundary and ＋∞ is an entrance boundary. We give a necessary and sufficient condition for the existence of exactly one quasistationary distribution, and we also show that this distribution attracts all initial distributions.

Analytical Solution to the One-Dimensional Advection-Diffusion Equation with Temporally Dependent Coefficients

In a one-dimensional advection-diffusion equation with temporally dependent coefficients three cases may arise: solute dispersion parameter is time dependent while the flow domain transporting the solutes is uniform, the former is uniform and the latter is time dependent and lastly the both parameters are time dependent. In the present work analytical solutions are obtained for the last case, studying the dispersion of continuous input point sources of uniform and increasing nature in an initially solute free semi-infinite domain. The solutions for the first two cases and for uniform dispersion along uniform flow are derived as particular cases. The dispersion parameter is not proportional to the velocity of the flow. The Laplace transformation technique is used. New space and time variables are introduced to get the solutions. The solutions in all possible combinations of increasing/decreasing temporal dependence are compared with each other with the help of graphs. It has been observed that the concentration attenuation with position and time is the fastest in case of decreasing dispersion in accelerating flow field.

Comparison of Numerical Approximations of One-Dimensional Space Fractional Diffusion Equation Using Different Types of Collocation Points in Spectral Method Based on Lagrange’s Basis Polynomials

Recently many research works have been conducted and published regarding fractional order differential equations. There are several approaches available for numerical approximations of the solution of fractional order diffusion equations. Spectral collocation method based on Lagrange’s basis polynomials to approximate numerical solutions of one-dimensional (1D) space fractional diffusion equations are introduced in this research paper. The proposed form of approximate solution satisfies non-zero Dirichlet’s boundary conditions on both boundaries. Collocation scheme produce a system of first order Ordinary Differential Equations (ODE) from the fractional diffusion equation. We applied this method with four different sets of collocation points to compare their performance.

LOCAL ONE-DIMENSIONAL ASE-I SCHEME FOR 2D DIFFUSION EQUATION

A local alternating segment explicit - implicit method for the solution of 2D diffusion equations is presented in this paper .The method is unconditionally stable and has the obvious property of parallelism. Some numerical experiments show the method is not only simple but also more accurate.

Anomalous energy diffusion and heat conduction in one-dimensional system

We propose a new concept, the centre of energy, to study energy diffusion and heat conduction in a one-dimensional hard-point model. For the diatom model, we find an anomalous energy diffusion as （x2） - tβ with β = 1.33, which is independent of initial condition and mass rate. The present model can be viewed as the model composed by independent quasi-particles, the centre of energy. In this way, heat current can be calculated. Based on the theory of dynamic billiard, the divergent exponent of heat conductivity is estimated to be α = 0.33, which is confirmed by a simple numerical calculation.

Small Random Perturbations of One-Dimensional Diffusion Processes

In the present paper we consider the small random perturbations of one-dimensional diffosion processes. By virtue of stochastic analysis methods, we investigate the asymptotics of the mean exit times and probabilistical estimates of the exit times as the perturbations tend to zero.

A Nearly Analytic Discrete Method for One-dimensional Unsteady Convection-dominated Diffusion Equations

In this paper, a nearly analytic discretization method for one-dimensional linear unsteady convection-dominated diffusion equations and viscous Burgers’ equation as one of the nonlinear equation is considered. In the case of linear equations, we find the local truncation error of the scheme is O(τ 2 + h4) and consider the stability analysis of the method on the basis of the classical von Neumann’s theory. In addition, the nearly analytic discretization method for the one-dimensional viscous Burgers’ equation is also constructed. The numerical experiments are performed for several benchmark problems presented in some literatures to illustrate the theoretical results. Theoretical and numerical results show that our method is to be higher accurate and nonoscillatory and might be helpful particularly in computations for the unsteady convection-dominated diffusion problems.

Alternating Group Explicit Iterative Methods for One-Dimensional Advection-Diffusion Equation

The finite difference method such as alternating group iterative methods is useful in numerical method for evolutionary equations and this is the standard approach taken in this paper. Alternating group explicit (AGE) iterative methods for one-dimensional convection diffusion equations problems are given. The stability and convergence are analyzed by the linear method. Numerical results of the model problem are taken. Known test problems have been studied to demonstrate the accuracy of the method. Numerical results show that the behavior of the method with emphasis on treatment of boundary conditions is valuable.

On the stability of lattice boltzmann equations for one-dimensional diffusion equation

Stability analysis of lattice Boltzmann equations(LBEs)on initial conditions for onedimensional diffusion is performed.Stability of the solution of the Cauchy problem for the system of linear Bhatnaghar–Gross–Krook kinetic equations is demonstrated for the cases of D1Q2 and D1Q3 lattices.Stability of the scheme for D1Q2 lattice is analytically analyzed by the method of differential approximation.Stability of parametrical scheme is numerically investigated by von Neumann method in parameter space.As a result of numerical analysis,the correction of the hypothesis on transfer of stability conditions of the scheme for macroequation to the system of LBEs is demonstrated.

Subdiffusion of Dipolar Gas in One-Dimensional Quasiperiodic Potentials

Considering the discrete nonlinear Schrodinger model with dipole-dipole interactions （DDIs）, we comparatively and numerically study the effects of contact interaction, DDI and disorder on the properties of diffusion of dipolar condensate in one-dimensional quasi-periodic potentials. Due to the coupled effects of the contact interaction and the DDI, some new and interesting mechanisms are found： both the DDI and the contact interaction can destroy localization and lead to a subdiffusive growth of the second moment of the wave packet. However, compared with the contact interaction, the effect of DDI on the subdiffusion is stronger. Furthermore and interestingly, we find that when the contact interaction （λ1） and DDI （A2） satisfy λ1 ≥ 2λ2, the property of the subdiffusion depends only on contact interaction; when λ1 ≤ 2λ2, the property of the subdiffusion is completely determined by DDI. Remarkably, we numerically give the critical value of disorder strength v＊ for different values of contact interaction and DDI. When the disorder strength v ≥ v＊, the wave packet is localized. On the contrary, when the disorder strength v ≤ v＊, the wave packet is subdiffusive.

GAN与Diffusion在传统纹样设计中的实验研究

传统纹样是中国优秀传统文化的重要组成部分,传统人工设计已经无法满足纹样的现代设计需求,生成式AI为传统纹样设计提供了新的设计路径和方法。文章将生成式AI应用于传统纹样设计中,通过适配实验优选基于GAN的Style GAN和基于Diffusion的Stable Diffusion两种主流图像生成模型进行实验,采用技术分析与艺术分析相结合,对实验结果进行多角度、多维度对比分析,为设计师选择生成设计方法提供参照。实验结果表明,两个模型均能满足基本的艺术设计需求。Style GAN模型生成的纹样图像更接近真实图像的分布,具有更高的图像质量和多样性;Stable Diffusion模型能较好地传承传统纹样的基因,艺术性与创造性兼具,更加符合传统纹样的艺术设计需求。

Discontinuous Legendre Wavelet Galerkin Method for One-Dimensional Advection-Diffusion Equation

This paper presents discontinuous Legendre wavelet Galerkin (DLWG) approach for solving one-dimensional advection-diffusion equation (ADE). Variational formulation of this type equation and corresponding numerical fluxes are devised by utilizing the advantages of both the Legendre wavelet bases and discontinuous Galerkin (DG) method. The distinctive features of the proposed method are its simple applicability for a variety of boundary conditions and able to effectively approximate the solution of PDEs with less storage space and execution. The results of a numerical experiment are provided to verify the efficiency of the designed new technique.

基于Stable Diffusion的虚拟人形象预设计的应用与研究

对当前AIGC在虚拟形象预设计方面的现状及影响进行了分析和探讨。以Stable Diffusion为例,详细介绍了工程构建和实现,对相关模块的作用、运行环境、使用方法及其指令等多个方面进行了综合叙述、分析和探讨,针对使用不同采样方法、不同采样参数及不同训练模型生成图片效果的优劣进行了说明及展示。随后,通过项目实例,完整地展示了人物形象预设计的过程。最后,对AIGC等新技术可能带来的社会影响进行了预测和总结。

Diffusion and reaction mechanism of limestone and quartz in fluxed iron ore pellet roasting process

The increase to the proportion of fluxed pellets in the blast furnace burden is a useful way to reduce the carbon emissions in the ironmaking process.In this study,the interaction between calcium carbonate and iron ore powder and the mineralization mechanism of fluxed iron ore pellet in the roasting process were investigated through diffusion couple experiments.Scanning electron microscopy with energy dispersive spectroscopy was used to study the elements’diffusion and phase transformation during the roasting process.The results indicated that limestone decomposed into calcium oxide,and magnetite was oxidized to hematite at the early stage of preheating.With the increase in roasting temperature,the diffusion rate of Fe and Ca was obviously accelerated,while the diffusion rate of Si was relatively slow.The order of magnitude of interdiffusion coefficient of Fe_(2)O_(3)-CaO diffusion couple was 10^(−10) m^(2)·s^(−1) at a roasting temperature of 1200℃for 9 h.Ca_(2)Fe_(2)O_(5) was the initial product in the Fe_(2)O_(3)-CaO-SiO_(2) diffusion interface,and then Ca_(2)Fe_(2)O_(5) continued to react with Fe_(2)O_(3) to form CaFe_(2)O_(4).With the expansion of the diffusion region,the sillico-ferrite of calcium liquid phase was produced due to the melting of SiO_(2) into CaFe_(2)O_(4),which can strengthen the consolidation of fluxed pellets.Furthermore,andradite would be formed around a small part of quartz particles,which is also conducive to the consolidation of fluxed pellets.In addition,the principle diagram of limestone and quartz diffusion reaction in the process of fluxed pellet roasting was discussed.

Value of multiple models of diffusion-weighted imaging to predict hepatic lymph node metastases in colorectal liver metastases patients

BACKGROUND About 10%-31% of colorectal liver metastases(CRLM)patients would concomitantly show hepatic lymph node metastases(LNM),which was considered as sign of poor biological behavior and a relative contraindication for liver resection.Up to now,there’s still lack of reliable preoperative methods to assess the status of hepatic lymph nodes in patients with CRLM,except for pathology examination of lymph node after resection.AIM To compare the ability of mono-exponential,bi-exponential,and stretchedexponential diffusion-weighted imaging(DWI)models in distinguishing between benign and malignant hepatic lymph nodes in patients with CRLM who received neoadjuvant chemotherapy prior to surgery.METHODS In this retrospective study,97 CRLM patients with pathologically confirmed hepatic lymph node status underwent magnetic resonance imaging,including DWI with ten b values before and after chemotherapy.Various parameters,such as the apparent diffusion coefficient from the mono-exponential model,and the true diffusion coefficient,the pseudo-diffusion coefficient,and the perfusion fraction derived from the intravoxel incoherent motion model,along with distributed diffusion coefficient(DDC)andαfrom the stretched-exponential model(SEM),were measured.The parameters before and after chemotherapy were compared between positive and negative hepatic lymph node groups.A nomogram was constructed to predict the hepatic lymph node status.The reliability and agreement of the measurements were assessed using the coefficient of variation and intraclass correlation coefficient.RESULTS Multivariate analysis revealed that the pre-treatment DDC value and the short diameter of the largest lymph node after treatment were independent predictors of metastatic hepatic lymph nodes.A nomogram combining these two factors demonstrated excellent performance in distinguishing between benign and malignant lymph nodes in CRLM patients,with an area under the curve of 0.873.Furthermore,parameters from SEM showed substantial repeatability.CONCLUSION The developed nomogram,incorporating the pre-treatment DDC and the short axis of the largest lymph node,can be used to predict the presence of hepatic LNM in CRLM patients undergoing chemotherapy before surgery.This nomogram was proven to be more valuable,exhibiting superior diagnostic performance compared to quantitative parameters derived from multiple b values of DWI.The nomogram can serve as a preoperative assessment tool for determining the status of hepatic lymph nodes and aiding in the decision-making process for surgical treatment in CRLM patients.

A high Li-ion diffusion kinetics in multidimensional and compact-structured electrodes via vacuum filtration casting

Manufacturing process,diffusion co-efficient and areal capacity are the three main criteria for regulating thick electrodes for lithium-ion batteries(LIBs).However,simultaneously regulating these criteria for LIBs is desirable but remains a significant challenge.In this work,niobium pentoxide(Nb_(2)O_(5))anode and lithium iron phosphate(LiFePO_(4))cathode materials were chosen as the model materials and demonstrate that these three parameters can be simultaneously modulated by incorporation of micro-carbon fibers(MCF)and carbon nanotubes(CNT)with both Nb_(2)O_(5) and LFP via vacuum filtration approach.Both as-prepared MNC-20 anode and MLC-20 cathode achieves high reversible areal capacity of≈5.4 m A h cm^(-2)@0.1 C and outstanding Li-ion diffusion coefficients of≈10~(-8)cm~2 s~(-1)in the half-cell configuration.The assembled MNC-20‖MLC-20 full cell LIB delivers maximum energy and power densities of244.04 W h kg^(-1)and 108.86 W kg^(-1),respectively.The excellent electrochemical properties of the asprepared thick electrodes can be attributed to the highly conductive,mechanical compactness and multidimensional mutual effects of the MCF,CNT and active materials that facilitates rapid Li-ion diffusion kinetics.Furthermore,electrochemical impedance spectroscopy(EIS),symmetric cells analysis,and insitu Raman techniques clearly validates the enhanced Li-ion diffusion kinetics in the present architecture.

Calculation and prediction of divertor detachment via impurity seeding by using one-dimensional model

Achieving the detachment of divertor can help to alleviate excessive heat load and sputtering problems on the target plates,thereby extending the lifetime of divertor components for fusion devices.In order to provide a fast but relatively reliable prediction of plasma parameters along the flux tube for future device design,a one-dimensional(1D)modeling code for the operating point of impurity seeded detached divertor is developed based on Python language,which is a fluid model based on previous work(Plasma Phys.Control.Fusion 58045013(2016)).The experimental observation of the onset of divertor detachment by neon(Ne)and argon(Ar)seeding in EAST is well reproduced by using the 1D modeling code.The comparison between the 1D modeling and two-dimensional(2D)simulation by the SOLPS-ITER code for CFETR detachment operation with Ne and Ar seeding also shows that they are in good agreement.We also predict the radiative power loss and corresponding impurity concentration requirement for achieving divertor detachment via different impurity seeding under high heating power conditions in EAST and CFETR phase II by using the 1D model.Based on the predictions,the optimized parameter space for divertor detachment operation on EAST and CFETR is also determined.Such a simple but reliable 1D model can provide a reasonable parameter input for a detailed and accurate analysis by 2D or three-dimensional(3D)modeling tools through rapid parameter scanning.

Research on the correlation between the dual diffusion behavior of zinc in InGaAs/InP single-photon avalanche photodiodes and device performance

The development of InGaAs/InP single-photon avalanche photodiodes(SPADs)necessitates the utiliza-tion of a two-element diffusion technique to achieve accurate manipulation of the multiplication width and the dis-tribution of its electric field.Regarding the issue of accurately predicting the depth of diffusion in InGaAs/InP SPAD,simulation analysis and device development were carried out,focusing on the dual diffusion behavior of zinc atoms.A formula of X_(j)=k√t-t_(0)+c to quantitatively predict the diffusion depth is obtained by fitting the simulated twice-diffusion depths based on a two-dimensional(2D)model.The 2D impurity morphologies and the one-dimensional impurity profiles for the dual-diffused region are characterized by using scanning electron micros-copy and secondary ion mass spectrometry as a function of the diffusion depth,respectively.InGaAs/InP SPAD devices with different dual-diffusion conditions are also fabricated,which show breakdown behaviors well consis-tent with the simulated results under the same junction geometries.The dark count rate(DCR)of the device de-creased as the multiplication width increased,as indicated by the results.DCRs of 2×10^(6),1×10^(5),4×10^(4),and 2×10^(4) were achieved at temperatures of 300 K,273 K,263 K,and 253 K,respectively,with a bias voltage of 3 V,when the multiplication width was 1.5µm.These results demonstrate an effective prediction route for accu-rately controlling the dual-diffused zinc junction geometry in InP-based planar device processing.

Similarities and differences in inherent mechanism and characteristic frequency between the one-dimensional poroelastic model and the layered White model

The similarities and differences in inherent mechanism and characteristic frequency between the onedimensional(1D)poroelastic model and the layered White model were investigated.This investigation was conducted under the assumption that the rock was homogenous and isotropic at the mesoscopic scale.For the inherent mechanism,both models resulted from quasi-static flow in a slow P-wave diffusion mode,and the differences between them originated from saturated fluids and boundary conditions.On the other hand,for the characteristic frequencies of the models,the characteristic frequency of the 1D poroelastic model was first modified because the elastic constant and formula for calculating it were misused and then compared to that of the layered White model.Both of them moved towards higher frequencies with increasing permeability and decreasing viscosity and diffusion length.The differences between them were due to the diffusion length.The diffusion length for the 1D poroelastic model was determined by the sample length,whereas that for the layered White model was determined by the length of the representative elementary volume(REV).Subsequently,a numerical example was presented to demonstrate the similarities and differences between the models.Finally,published experimental data were interpreted using the 1D poroelastic model combined with the Cole-Cole model.The prediction of the combined model was in good agreement with the experimental data,thereby validating the effectiveness of the 1D poroelastic model.Furthermore,the modified characteristic frequency in our study was much closer to the experimental data than the previous prediction,validating the effectiveness of our modification of the characteristic frequency of the 1D poroelastic model.The investigation provided insight into the internal relationship between wave-induced fluid flow(WIFF)models at macroscopic and mesoscopic scales and can aid in a better understanding of the elastic modulus dispersion and attenuation caused by the WIFF at different scales.