Self-similar singular solution of fast diffusion equation with gradient absorption terms

The self-similar singular solution of the fast diffusion equation with nonlinear gradient absorption terms are studied. By a self-similar transformation, the self-similar solutions satisfy a boundary value problem of nonlinear ordinary differential equation （ODE）. Using the shooting arguments, the existence and uniqueness of the solution to the initial data problem of the nonlinear ODE are investigated, and the solutions are classified by the region of the initial data. The necessary and sufficient condition for the existence and uniqueness of self-similar very singular solutions is obtained by investigation of the classification of the solutions. In case of existence, the self-similar singular solution is very singular solution.

STREAMLINE DIFFUSION F.E.M. FOR SOBOLEV EQUATIONS WITH CONVECTION DOMINATED TERM

In this paper,a streamline diffusion F.E.M. for linear Sobolev equations with convection dominated term is given.According to the range of space time F.E mesh parameter h ,two choices for artifical diffusion parameter δ are presented,and for the corresponding computation schemes the stability and error estimates in suitable norms are estabilished.

Fast ion diffusion alloy layer facilitating 3D mesh substrate for dendrite-free zinc-ion hybrid capacitors

Although aqueous zinc ion hybrid capacitors have advantageous integration of batteries and supercapacitors,they still suffer from the inherent problems of dendrite growth and interfacial side reactions on Zn anodes.Herein,a universal fast zinc-ion diffusion layer on a three-dimensional(3 D)mesh structure model is demonstrated to effectively improve Zn plating/stripping reversibility.The fast ion diffusion alloy layer accelerates the Zn^(2+)migration in an orderly manner to homogenize Zn^(2+)flux and overcomes the defects of the commercial mesh substrate,effectively avoiding dendrite growth and side reactions.Consequently,the proof-of-concept silver-zinc alloy modified stainless steel mesh delivers superb reversibility with the high coulombic efficiency over 99.4%at 4 mA cm^(-2)after 1600 cycles and excellent reliability of over 830 h at 1 mA cm^(-2),Its feasibility is also evidenced in commercial zinc ion hybrid capacitors with activated carbon as the cathode.This work enriches the fundamental comprehension of fast zinc-ion diffusion layer combined with a 3 D substrate on the Zn deposition and opens a universal approach to design advanced host for Zn electrodes in zinc ion hybrid capacitors.

Exact Solution of Fractional Diffusion Model with Source Term used in Study of Concentration of Fission Product in Uranium Dioxide Particle

The exact solution of fractional diffusion model with a location-independent source term used in the study of the concentration of fission product in spherical uranium dioxide （U02） particle is built. The adsorption effect of the fission product on the surface of the U02 particle and the delayed decay effect are also considered. The solution is given in terms of Mittag-Leffler function with finite Hankel integral transformation and Laplace transformation. At last, the reduced forms of the solution under some special physical conditions, which is used in nuclear engineering, are obtained and corresponding remarks are given to provide significant exact results to the concentration analysis of nuclear fission products in nuclear reactor.

Exponential Attractors of the Nonclassical Diffusion Equations with Lower Regular Forcing Term

In this article, we prove the existence of exponential attractors of the nonclassical diffusion equation with critical nonlinearity and lower regular forcing term. As an additional product, we show that the fractal dimension of the global attractors of this problem is finite.

Towards extreme fast charging of 4.6 V LiCoO_(2) via mitigating high-voltage kinetic hindrance

High-voltage LiCoO_(2)(LCO) is an attractive cathode for ultra-high energy density lithium-ion batteries(LIBs) in the 3 C markets.However,the sluggish lithium-ion diffusion at high voltage significantly hampers its rate capability.Herein,combining experiments with density functional theory(DFT) calculations,we demonstrate that the kinetic limitations can be mitigated by a facial Mg^(2+)+Gd^(3+)co-doping method.The as-prepared LCO shows significantly enhanced Li-ion diffusion mobility at high voltage,making more homogenous Li-ion de/intercalation at a high-rate charge/discharge process.The homogeneity enables the structural stability of LCO at a high-rate current density,inhibiting stress accumulation and irreversible phase transition.When used in combination with a Li metal anode,the doped LCO shows an extreme fast charging(XFC) capability,with a superior high capacity of 193.1 mAh g^(-1)even at the current density of 20 C and high-rate capacity retention of 91.3% after 100 cycles at 5 C.This work provides a new insight to prepare XFC high-voltage LCO cathode materials.

PULMONARY VESSEL EXTRACTION BASED ON COHERENCE DIFFUSION AND FAST MARCHING

Objective To accurately extract pulmonary vessels on medical images. Methods An efficient vessel segmentation framework is presented, which includes a smoothing method and a extraction algorithm. The smoothing method is based on an improved coherence diffusion approach that integrates the second-order directional differential information. It can analyze weak edges such as narrow peak or ridge-like structures. Meanwhile, an improved extraction algorithm is proposed. It is based on a fast marching algorithm where a sorted sequence array and multi-initialization technique are applied. Results The improved coherence diffusion approach can precisely preserve important oriented patterns and remove noises on the images. Experimental results on several images show that the proposed method can effectively find the location of pulmonary vessels. Conclusion The segmentation method is accurate and fast that can be a useful tool for medical imaging applications.

Critical Exponents for Fast Diffusion Equations with Nonlinear Boundary Sources

In this paper,we study the large time behavior of solutions to a class of fast diffusion equations with nonlinear boundary sources on the exterior domain of the unit ball.We are interested in the critical global exponent q_o and the critical Fujita exponent q_c for the problem considered,and show that q_o=q_c for the multidimensional Non-Newtonian polytropic filtration equation with nonlinear boundary sources,which is quite different from the known results that q_o〈q_c for the onedimensional case;moreover,the value is different from the slow case.

Isolated diatomic Zn-Co metal–nitrogen/oxygen sites with synergistic effect on fast catalytic kinetics of sulfur species in Li-S battery

Lithium-sulfur batteries are severely restricted by low electronic conductivity of sulfur and Li_(2)S,shuttle effect,and slow conversion reaction of lithium polysulfides(LiPSs).Herein,we report a facile and highyield strategy for synthesizing dual-core single-atom catalyst(ZnCoN_(4)O_(2)/CN)with atomically dispersed nitrogen/oxygen-coordinated Zn-Co sites on carbon nanosheets.Based on density functional theory(DFT)calculations and LiPSs conversion catalytic ability,ZnCoN_(4)O_(2)/CN provides dual-atom sites of Zn and Co,which could facilitate Li^(+)transport and Li_(2)S diffusion,and catalyze LiPSs conversion more effectively than homonuclear bimetallic single-atom catalysts or their simple mixture and previously reported singleatom catalysts.Li-S cell with ZnCoN_(4)O_(2)/CN modified separator showed excellent rate performance(789.4 mA h g^(-1)at 5 C)and stable long cycle performance(0.05%capacity decay rate at 6C with 1000cycles,outperforming currently reported single atomic catalysts for LiPSs conversion.This work highlights the important role of metal active centers and provides a strategy for producing multifunctional dual-core single atom catalysts for high-performance Li-S cells.

TWO REGULARIZATION METHODS FOR IDENTIFYING THE SOURCE TERM PROBLEM ON THE TIME-FRACTIONAL DIFFUSION EQUATION WITH A HYPER-BESSEL OPERATOR

In this paper,we consider the inverse problem for identifying the source term of the time-fractional equation with a hyper-Bessel operator.First,we prove that this inverse problem is ill-posed,and give the conditional stability.Then,we give the optimal error bound for this inverse problem.Next,we use the fractional Tikhonov regularization method and the fractional Landweber iterative regularization method to restore the stability of the ill-posed problem,and give corresponding error estimates under different regularization parameter selection rules.Finally,we verify the effectiveness of the method through numerical examples.

Modeling Fast Diffusion Processes in Time Integration of Stiff Stochastic Differential Equations

Numerical algorithms for stiff stochastic differential equations are developed using lin-ear approximations of the fast diffusion processes,under the assumption of decoupling between fast and slow processes.Three numerical schemes are proposed,all of which are based on the linearized formulation albeit with different degrees of approximation.The schemes are of comparable complexity to the classical explicit Euler-Maruyama scheme but can achieve better accuracy at larger time steps in stiff systems.Convergence analysis is conducted for one of the schemes,that shows it to have a strong convergence order of 1/2 and a weak convergence order of 1.Approximations arriving at the other two schemes are discussed.Numerical experiments are carried out to examine the convergence of the schemes proposed on model problems.

A Compact Finite Volume Scheme for the Multi-Term Time Fractional Sub-Diffusion Equation

In this paper, we introduce high-order finite volume methods for the multi-term time fractional sub-diffusion equation. The time fractional derivatives are described in Caputo’s sense. By using some operators, we obtain the compact finite volume scheme have high order accuracy. We use a compact operator to deal with spatial direction;then we can get the compact finite volume scheme. It is proved that the finite volume scheme is unconditionally stable and convergent in L∞-norm. The convergence order is O(τ2-α + h4). Finally, two numerical examples are given to confirm the theoretical results. Some tables listed also can explain the stability and convergence of the scheme.

融合多源异构气象数据的光伏功率预测模型

高精度光伏功率预测对提高电力系统运行效率具有重要意义。光伏功率受多种因素影响,其中云层的变化是最主要的不确定因素。传统光伏功率预测方法没有充分考虑云的3维结构和气象要素对光伏功率的影响。因此,该文提出一种融合多源异构气象数据的多源变量光伏功率预测模型(MPPM)。MPPM的核心包括时空条件扩散模型(STCDM)、注意力堆叠LSTM网络(ASLSTM)和多维特征融合模块(MFFM)。STCDM模型通过对2维卫星云图进行精确预测,消除了云层边界处的模糊现象。ASLSTM模型则提取了3维天气研究与预报模式(WRF)气象要素特征。MFFM模块将2维卫星云图特征和3维WRF气象要素特征进行融合,以得到未来1 h光伏功率预测结果。该文分别利用STCDM模型和MPPM模型开展卫星云图预测实验和光伏功率预测实验。实验结果显示,STCDM模型预测1 h内卫星云图的结构相似性指数(SSIM)达到0.914,MPPM模型预测1 h内光伏功率的相关系数(CORR)达到0.949,优于所有对比算法。

工业竖窑内低速高温物料流动换热模型研究

从气固两相流动传热控制方程出发,应用数量级分析方法,推导适用于工业竖窑内低速流动的高温物料冷却过程的一维气固换热数值模型。基于FLUENT 2021R2仿真平台与MATLAB R2021平台,分别采用完整的气固流动传热模型与上述简化的一维换热模型对某一工业石灰竖窑高温石灰冷却过程进行计算,对比不同冷却气流速度与换热高度下FLUENT仿真结果与一维气固换热模型计算结果。研究结果表明:气、固两相能量控制方程中扩散项的影响可以忽略;气流速度对气固相温度的影响远大于换热高度对气固相温度的影响;当气流速度较大时,这2种模型计算结果偏差主要出现在高温段,而当气流速度较小时,则主要出现在低温段;当冷却气流速度适中时,这2种模型计算得到的气相温度偏差均小于固相温度偏差,大部分区域气固相温度偏差小于20%。

采用局部-全局区域重检测机制的无人机长期跟踪算法

为解决基础跟踪器面对遮挡和移出视野等长期跟踪场景时易出现跟踪失败等问题,提出了一种基于局部-全局区域重检测的无人机长期跟踪算法。设计了基础滤波器,将高置信度样本与其结合,并融入自适应时空正则化,解决了滤波器退化问题,提高了模型鲁棒性以及复杂场景下的性能;优化了滤波器更新策略,通过评价跟踪结果进行自适应更新;设计快速尺度滤波器,解决了跟踪过程中的尺度变化问题;设计了局部-全局区域重检测机制,跟踪失败时启动重检测器恢复跟踪目标,先完成局部区域重检测,若恢复跟踪失败,再利用全局区域重检测器继续恢复目标跟踪状态。实验结果表明:所提算法在UAV20L数据集上的精确度和准确率分别可达0.724和0.621,与基于时空正则化相关滤波器的跟踪算法(STRCF)相比分别提升了25.9%和20.6%,与同类主流算法相比,跟踪效果得到提升,证明了算法的有效性。

高分辨率磁共振成像对臂丛神经损伤的预测价值

目的探析高分辨率磁共振(MRI)成像对臂丛神经损伤(brachial plexus injury,BPI)的预测价值。方法对59例临床拟诊BPI的病例行高分辨MRI检查。根据年龄,将年龄≥65岁者纳入老年组,18~64岁者纳入青中年组。观察两组臂丛神经显像效果,计算臂丛神经成像评分、臂丛神经信噪比(signal-to-noise ratio,SNR)、对比度噪声比(contrast-to-noise ratio,CNR)和背景抑制评分,分析高分辨率MRI成像对不同年龄段BPI的预测价值。结果59例临床拟诊BPI病例中,MRI诊断为BPI 20例,其余正常。20例经MRI确诊BPI中,老年组7例和青中年组13例。老年组节前损伤2例(28.57%),节后损伤5例(71.43%);青中年组节前损伤5例(38.46%),节后损伤8例(61.54%)。两组病人臂丛神经成像评分由低到高依次为三维双回波稳态(3D-DESS)序列增强扫描、三维短时反转恢复快速自旋回波(3D SPACE)序列平扫、DESS序列平扫和SPACE序列增强扫描,且在干3、支5 DESS序列平扫、股6 DESS序列增强扫描及支5 SPACE序列增强扫描上,老年组臂丛神经成像评分明显低于青中年组(P<0.05)。两组SNR、CNR由低到高依次为DESS增强、SPACE平扫、DESS平扫和SPACE增强(P<0.05),两组背景组织抑制评分比较,SPACE增强最高,其次为DESS平扫,DESS增强和SPACE平扫最低(P<0.05)。老年组DESS序列增强扫描的SNR、CNR以及SPACE序列平扫、增强扫描的SNR、CNR均明显低于青中年组(P<0.05)。结论与青中年BPI病人相比,老年BPI病人臂丛神经成像评分、SNR与CNR更低,MRI 3D SPACE序列可清晰显示臂丛神经内部信号改变,同时降低神经周围背景组织信号干扰,对于显示神经损伤优势明显,值得临床优先选择。

多项时间分数阶混合扩散-波动方程ADI有限差分法

用交替方向隐式(ADI)有限差分法研究多项时间分数阶混合扩散-波动方程的数值解,在时间方向上,采用降阶的方法,将扩散项和波动项转化为RL积分项和扩散项,分别使用L2-1_(σ)和L1公式逼近;空间方向结合二阶中心差商离散,并通过数值算例验证差分格式的有效性.

应用于人脑胶质淋巴系统的磁共振成像技术研究进展

胶质淋巴系统是神经科学领域近期发现的解剖结构,具有调节间质液运动、废物清除和潜在的大脑免疫等功能,在中枢神经系统的生理及病理中发挥重要作用。随着影像学技术的发展,越来越多的磁共振成像(MRI)技术被应用于人脑胶质淋巴系统的研究,目前常用的MRI技术有动态对比增强磁共振成像技术、沿血管周围间隙扩散张量成像分析技术及新型多模态超快速磁共振技术等,本文就这些技术在脑胶质淋巴系统的应用现状进行汇总综述,以期为胶质淋巴系统的影像学研究提供参考。

非定常自由面流动模拟的反扩散VOF算法研究

VOF(Volume of Fluid)方法由于其良好的守恒性和网格适应性,且具有计算资源需求相对较小等优点,成为船舶水动力学领域自由面流动CFD(Computational Fluid Dynamics)模拟的主流方法。但原始的VOF方法存在较为严重的界面扩散问题,导致模拟的界面厚度过大、空间分辨率不够,进而影响流场相关变量的计算精度,这一问题在非定常自由面流动模拟中尤为明显。本文针对上述问题,通过在VOF控制方程中引入人工对流项以达到抑制界面扩散、压缩界面厚度的目的,并采用隐式离散人工对流项的方式提高计算稳定性,形成了反扩散VOF算法。经Zalesak和剪切场等经典算例在不同数量网格下的测试验证,表明反扩散VOF算法能够大幅压缩界面厚度,同时明显减小质量误差。随后的三维无障碍溃坝算例和破舱进水算例,进一步证明了反扩散VOF算法在实际非定常流动模拟中能够更好地捕捉自由面并提高计算精度。

基于Transformer和关系图卷积网络的信息传播预测模型

针对在信息传播动态演化中,结构特征和时序特征以及两者间的交互表达难以有效捕获的问题,提出一种基于Transformer和关系图卷积网络的信息传播预测模型(TRGCN)。首先,构建由社交关系图和传播级联图组合而成的异构图,使用关系图卷积网络(RGCN)提取图中各节点的结构特征;其次,使用双向长短期记忆(Bi-LSTM)网络对各节点的时间嵌入重新编码,引入时间衰减项以不同的权重赋予不同时间位置的节点,获得节点的时序特征;最后,将结构特征和时序特征输入Transformer进行融合,得到时空特征以预测信息传播。在Twitter、Douban和Memetracker这3个真实数据集上的实验结果表明,相较于对比实验中的最优模型,TRGCN的Hits@100指标分别提升3.18%,5.96%和3.34%,Map@100指标分别提升11.60%,19.72%和8.47%,验证了所提模型的有效性和合理性。