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 ...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.展开更多
As an important sustainable energy source,Li-ion batteries have been widely used in mobile phones,electric vehicles,large-scale energy storage and aerospace.However,due to the inevitable safety risks of traditional li...As an important sustainable energy source,Li-ion batteries have been widely used in mobile phones,electric vehicles,large-scale energy storage and aerospace.However,due to the inevitable safety risks of traditional liquid Li-ion batteries,the use of all-solid-state batteries to replace organic liquid electrolytes has become one of the most effective ways to solve safety problem.Solid-state electrolyte(SSE)is the core part of allsolid-state Li-ion battery,and ideal SSE has the characteristics of high ionic conductivity,wide enough electrochemical stability window,suitable mechanical strength and excellent chemical stability,the first among which is particularly an essential prerequisite.While,so far only a few SSEs exhibit the Li ionic conductivities higher than 10^(-4) S/cm at room temperature.展开更多
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 par...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.展开更多
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.He...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.展开更多
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...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.展开更多
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 di...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.展开更多
In this paper,a class of slow reaction-diffusion equations with nonlocal source and inner absorption terms are studied.By using the technique of improved differential inequality,the lower bounds of blow up time for th...In this paper,a class of slow reaction-diffusion equations with nonlocal source and inner absorption terms are studied.By using the technique of improved differential inequality,the lower bounds of blow up time for the system under either homogeneous Dirichlet or nonhomogeneous Neumann boundary conditions are obtained.展开更多
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 ...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.展开更多
This paper considers a fast diffusion equation with potential ut= um V （x）um＋upin Rn×（0,T）, where 1 2αm＋n m ≤ 1, p 1, n ≥ 2, V （x） ～ω｜x｜2with ω ≥ 0 as ｜x｜ → ∞,and α is the positive root of ...This paper considers a fast diffusion equation with potential ut= um V （x）um＋upin Rn×（0,T）, where 1 2αm＋n m ≤ 1, p 1, n ≥ 2, V （x） ～ω｜x｜2with ω ≥ 0 as ｜x｜ → ∞,and α is the positive root of αm（αm ＋ n 2） ω = 0. The critical Fujita exponent was determined as pc= m ＋2αm＋nin a previous paper of the authors. In the present paper,we establish the second critical exponent to identify the global and non-global solutions in their co-existence parameter region p pcvia the critical decay rates of the initial data.With u0（x） ～ ｜x｜ aas ｜x｜ → ∞, it is shown that the second critical exponent a =2p m,independent of the potential parameter ω, is quite different from the situation for the critical exponent pc.展开更多
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 expon...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.展开更多
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...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.展开更多
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 nume...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.展开更多
Lithium(Li)dendrite issue,which is usually caused by inhomogeneous Li nucleation and fragile solid electrolyte interphase(SEI),impedes the further development of high-energy Li metal batteries.However,the integrated c...Lithium(Li)dendrite issue,which is usually caused by inhomogeneous Li nucleation and fragile solid electrolyte interphase(SEI),impedes the further development of high-energy Li metal batteries.However,the integrated construction of a high-stable SEI layer that can regulate uniform nucleation and facilitate fast Li-ion diffusion kinetics for Li metal anode still falls short.Herein,we designed an artificial SEI with hybrid ionic/electronic interphase to regulate Li deposition by in-situ constructing metal Co clusters embedded in LiF matrix.The generated Co and LiF both enable fast Li-ion diffusion kinetics,meanwhile,the lithiophilic properties of Co clusters can serve as Li-ion nucleation sites,thereby contributing to uniform Li nucleation and non-dendritic growth.As a result,a dendrite-free Li deposition with a low overpotential(16.1 mV)is achieved,which enables an extended lifespan over 750 h under strict conditions.The full cells with high-mass-loading LiFePO_(4)(11.5 mg/cm^(2))as cathodes exhibit a remarkable rate capacity of 84.1 mAh/g at 5 C and an improved cycling performance with a capacity retention of 96.4%after undergoing 180 cycles.展开更多
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 obt...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<sub>∞</sub>-norm. The convergence order is O(τ<sup>2-α</sup> + h<sup>4</sup>). Finally, two numerical examples are given to confirm the theoretical results. Some tables listed also can explain the stability and convergence of the scheme.展开更多
基金Project supported by the National Natural Science Foundation of China (No. 10471022)the Science and Technology Foundation of Ministry of Education of China (Major Projects) (No.104090)
文摘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.
基金supported by the Natural Science Foundation of Shandong Province(No.ZR2020MB049)the Shandong Laboratory of Advanced Materials and Green Manufacturing at Yantai(No.AMGM2023A07)。
文摘As an important sustainable energy source,Li-ion batteries have been widely used in mobile phones,electric vehicles,large-scale energy storage and aerospace.However,due to the inevitable safety risks of traditional liquid Li-ion batteries,the use of all-solid-state batteries to replace organic liquid electrolytes has become one of the most effective ways to solve safety problem.Solid-state electrolyte(SSE)is the core part of allsolid-state Li-ion battery,and ideal SSE has the characteristics of high ionic conductivity,wide enough electrochemical stability window,suitable mechanical strength and excellent chemical stability,the first among which is particularly an essential prerequisite.While,so far only a few SSEs exhibit the Li ionic conductivities higher than 10^(-4) S/cm at room temperature.
基金Supported by the National Natural Sciences Foundation of China(1 8971 0 51 )
文摘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.
基金financially supported by the National Natural Science Foundation of China(51901249,U1904216)。
文摘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.
基金Supported by the National S&T Major Project under Grant No.ZX06901
文摘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.
文摘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.
基金Supported by the Natural Science Foundation of Shaanxi Province(2019JM-534)the Youth Innovation Team of Shaanxi Universities+7 种基金the 14th Five Year Plan for Educational Science in Shaanxi Province(SGH21Y0308)Key Topic of China Higher Education Association(21DFD04)Higher Education Teaching Reform Project of Xi’an International University(2023B03)2022 Annual Planning Project of China Association of Private Education(School Development)(CANFZG22222)Project of Department of Education of Shaanxi Provincethe 2022 Annual Topic of the"14th Five-Year Plan"of Shaanxi Provincial Educational Science(SGH22Y1885)Project of Qi Fang Education Research Institute of Xi’an International University(23mjy10)Special Project of the Shaanxi Provincial Social Science Found in 2023(2023SJ12,2023LS04)。
文摘In this paper,a class of slow reaction-diffusion equations with nonlocal source and inner absorption terms are studied.By using the technique of improved differential inequality,the lower bounds of blow up time for the system under either homogeneous Dirichlet or nonhomogeneous Neumann boundary conditions are obtained.
文摘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.
基金Supported by the National Natural Science Foundation of China (Grant No. 11171048)
文摘This paper considers a fast diffusion equation with potential ut= um V （x）um＋upin Rn×（0,T）, where 1 2αm＋n m ≤ 1, p 1, n ≥ 2, V （x） ～ω｜x｜2with ω ≥ 0 as ｜x｜ → ∞,and α is the positive root of αm（αm ＋ n 2） ω = 0. The critical Fujita exponent was determined as pc= m ＋2αm＋nin a previous paper of the authors. In the present paper,we establish the second critical exponent to identify the global and non-global solutions in their co-existence parameter region p pcvia the critical decay rates of the initial data.With u0（x） ～ ｜x｜ aas ｜x｜ → ∞, it is shown that the second critical exponent a =2p m,independent of the potential parameter ω, is quite different from the situation for the critical exponent pc.
基金The Fundamental Research Funds for the Central Universities and the NSF(11071100) of China
文摘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.
基金supported by the National Natural Science Foundation of China(11961044)the Doctor Fund of Lan Zhou University of Technologythe Natural Science Foundation of Gansu Provice(21JR7RA214)。
文摘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.
文摘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.
基金financially supported by the National Natural Science Foundation of China(Nos.22279097,52172217)Natural Science Foundation of Guangdong Province(No.2021A1515010144)Shenzhen Science and Technology Program(No.JCYJ20210324120400002).
文摘Lithium(Li)dendrite issue,which is usually caused by inhomogeneous Li nucleation and fragile solid electrolyte interphase(SEI),impedes the further development of high-energy Li metal batteries.However,the integrated construction of a high-stable SEI layer that can regulate uniform nucleation and facilitate fast Li-ion diffusion kinetics for Li metal anode still falls short.Herein,we designed an artificial SEI with hybrid ionic/electronic interphase to regulate Li deposition by in-situ constructing metal Co clusters embedded in LiF matrix.The generated Co and LiF both enable fast Li-ion diffusion kinetics,meanwhile,the lithiophilic properties of Co clusters can serve as Li-ion nucleation sites,thereby contributing to uniform Li nucleation and non-dendritic growth.As a result,a dendrite-free Li deposition with a low overpotential(16.1 mV)is achieved,which enables an extended lifespan over 750 h under strict conditions.The full cells with high-mass-loading LiFePO_(4)(11.5 mg/cm^(2))as cathodes exhibit a remarkable rate capacity of 84.1 mAh/g at 5 C and an improved cycling performance with a capacity retention of 96.4%after undergoing 180 cycles.
文摘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<sub>∞</sub>-norm. The convergence order is O(τ<sup>2-α</sup> + h<sup>4</sup>). Finally, two numerical examples are given to confirm the theoretical results. Some tables listed also can explain the stability and convergence of the scheme.
