In this paper,we study the eigenvalue problem of the Markov diffusion operator L^(2),and give generalized inequalities for eigenvalues of the operator L^(2)on a Markov diffusion triple.By applying these inequalities,w...In this paper,we study the eigenvalue problem of the Markov diffusion operator L^(2),and give generalized inequalities for eigenvalues of the operator L^(2)on a Markov diffusion triple.By applying these inequalities,we then get some new universal bounds for eigenvalues of a special Markov diffusion operator L^(2)on bounded domains in an Euclidean space.Moreover,our results can reveal the relationship between the(k+1)-th eigenvalue and the first k eigenvalues in a relatively straightforward manner.展开更多
With the growing demand for high-precision flow field simulations in computational science and engineering,the super-resolution reconstruction of physical fields has attracted considerable research interest.However,tr...With the growing demand for high-precision flow field simulations in computational science and engineering,the super-resolution reconstruction of physical fields has attracted considerable research interest.However,tradi-tional numerical methods often entail high computational costs,involve complex data processing,and struggle to capture fine-scale high-frequency details.To address these challenges,we propose an innovative super-resolution reconstruction framework that integrates a Fourier neural operator(FNO)with an enhanced diffusion model.The framework employs an adaptively weighted FNO to process low-resolution flow field inputs,effectively capturing global dependencies and high-frequency features.Furthermore,a residual-guided diffusion model is introduced to further improve reconstruction performance.This model uses a Markov chain for noise injection in phys-ical fields and integrates a reverse denoising procedure,efficiently solved by an adaptive time-step ordinary differential equation solver,thereby ensuring both stability and computational efficiency.Experimental results demonstrate that the proposed framework significantly outperforms existing methods in terms of accuracy and efficiency,offering a promising solution for fine-grained data reconstruction in scientific simulations.展开更多
In this article, we consider a backward problem in time of the diffusion equation with local and nonlocal operators. This inverse problem is ill-posed because the solution does not depend continuously on the measured ...In this article, we consider a backward problem in time of the diffusion equation with local and nonlocal operators. This inverse problem is ill-posed because the solution does not depend continuously on the measured data. Inspired by the classical Landweber iterative method and Fourier truncation technique, we develops a modified Landweber iterative regularization method to restore the continuous dependence of solution on the measurement data. Under the a-priori and a-posteriori choice rules for the regularized parameter, the convergence estimates for the regularization method are derived. Some results of numerical simulation are provided to verify the stability and feasibility of our method in dealing with the considered problem.展开更多
In this paper,we are concerned with the stability of traveling wavefronts of a Belousov-Zhabotinsky model with mixed nonlocal and degenerate diffusions.Such a system can be used to study the competition among nonlocal...In this paper,we are concerned with the stability of traveling wavefronts of a Belousov-Zhabotinsky model with mixed nonlocal and degenerate diffusions.Such a system can be used to study the competition among nonlocally diffusive species and degenerately diffusive species.We prove that the traveling wavefronts are exponentially stable,when the initial perturbation around the traveling waves decays exponentially as x→-∞,but in other locations,the initial data can be arbitrarily large.The adopted methods are the weighted energy with the comparison principle and squeezing technique.展开更多
In this note, we obtain the elliptic estimate for diffusion operator L = △＋△Ф·△ on complete, noncompact Riemannian manifolds, under the curvature condition CD（K, m）, which generalizes B. L. Kotschwar＇s wo...In this note, we obtain the elliptic estimate for diffusion operator L = △＋△Ф·△ on complete, noncompact Riemannian manifolds, under the curvature condition CD（K, m）, which generalizes B. L. Kotschwar＇s work [5]. As an application, we get estimate on the heat kernel. The Bernstein-type gradient estimate for SchrSdinger-type gradient is also derived.展开更多
In this paper, the classical and weak derivatives with respect to spatial variable of a class of hysteresis functional are discussed. Some conclusions about solutions of a class of reaction-diffusion equations with hy...In this paper, the classical and weak derivatives with respect to spatial variable of a class of hysteresis functional are discussed. Some conclusions about solutions of a class of reaction-diffusion equations with hysteresis differential operator are given.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
After discretization by the finite volume method,the numerical solution of fractional diffusion equations leads to a linear system with the Toeplitz-like structure.The theoretical analysis gives sufficient conditions ...After discretization by the finite volume method,the numerical solution of fractional diffusion equations leads to a linear system with the Toeplitz-like structure.The theoretical analysis gives sufficient conditions to guarantee the positive-definite property of the discretized matrix.Moreover,we develop a class of positive-definite operator splitting iteration methods for the numerical solution of fractional diffusion equations,which is unconditionally convergent for any positive constant.Meanwhile,the iteration methods introduce a new preconditioner for Krylov subspace methods.Numerical experiments verify the convergence of the positive-definite operator splitting iteration methods and show the efficiency of the proposed preconditioner,compared with the existing approaches.展开更多
Missing values in radionuclide diffusion datasets can undermine the predictive accuracy and robustness of the machine learning(ML)models.In this study,regression-based missing data imputation method using a light grad...Missing values in radionuclide diffusion datasets can undermine the predictive accuracy and robustness of the machine learning(ML)models.In this study,regression-based missing data imputation method using a light gradient boosting machine(LGBM)algorithm was employed to impute more than 60%of the missing data,establishing a radionuclide diffusion dataset containing 16 input features and 813 instances.The effective diffusion coefficient(D_(e))was predicted using ten ML models.The predictive accuracy of the ensemble meta-models,namely LGBM-extreme gradient boosting(XGB)and LGBM-categorical boosting(CatB),surpassed that of the other ML models,with R^(2)values of 0.94.The models were applied to predict the D_(e)values of EuEDTA^(−)and HCrO_(4)^(−)in saturated compacted bentonites at compactions ranging from 1200 to 1800 kg/m^(3),which were measured using a through-diffusion method.The generalization ability of the LGBM-XGB model surpassed that of LGB-CatB in predicting the D_(e)of HCrO_(4)^(−).Shapley additive explanations identified total porosity as the most significant influencing factor.Additionally,the partial dependence plot analysis technique yielded clearer results in the univariate correlation analysis.This study provides a regression imputation technique to refine radionuclide diffusion datasets,offering deeper insights into analyzing the diffusion mechanism of radionuclides and supporting the safety assessment of the geological disposal of high-level radioactive waste.展开更多
A medical image encryption is proposed based on the Fisher-Yates scrambling,filter diffusion and S-box substitution.First,chaotic sequence associated with the plaintext is generated by logistic-sine-cosine system,whic...A medical image encryption is proposed based on the Fisher-Yates scrambling,filter diffusion and S-box substitution.First,chaotic sequence associated with the plaintext is generated by logistic-sine-cosine system,which is used for the scrambling,substitution and diffusion processes.The three-dimensional Fisher-Yates scrambling,S-box substitution and diffusion are employed for the first round of encryption.The chaotic sequence is adopted for secondary encryption to scramble the ciphertext obtained in the first round.Then,three-dimensional filter is applied to diffusion for further useful information hiding.The key to the algorithm is generated by the combination of hash value of plaintext image and the input parameters.It improves resisting ability of plaintext attacks.The security analysis shows that the algorithm is effective and efficient.It can resist common attacks.In addition,the good diffusion effect shows that the scheme can solve the differential attacks encountered in the transmission of medical images and has positive implications for future research.展开更多
The dynamics of phase separation in H–He binary systems within gas giants such as Jupiter and Saturn exhibit remarkable complexity, yet lack systematic investigation. Through large-scale machine-learning-accelerated ...The dynamics of phase separation in H–He binary systems within gas giants such as Jupiter and Saturn exhibit remarkable complexity, yet lack systematic investigation. Through large-scale machine-learning-accelerated molecular dynamics simulations spanning broad temperature-pressure-composition(2000–10000 K, 1–7 Mbar,pure H to pure He) regimes, we systematically determine self and mutual diffusion coefficients in H–He systems and establish a six-dimensional framework correlating temperature, pressure, helium abundance, phase separation degree, diffusion coefficients, and anisotropy. Key findings reveal that hydrogen exhibits active directional migration with pronounced diffusion anisotropy, whereas helium passively aggregates in response. While the conventional mixing rule underestimates mutual diffusion coefficients by neglecting velocity cross-correlations,the assumption of an ideal thermodynamic factor(Q = 1) overestimates them due to unaccounted non-ideal thermodynamic effects—both particularly pronounced in strongly phase-separated regimes. Notably, hydrogen's dual role, anisotropic diffusion and bond stabilization via helium doping, modulates demixing kinetics. Large-scale simulations(216,000 atoms) propose novel phase-separation paradigms, such as “hydrogen bubble/wisp” formation, challenging the classical “helium rain” scenario, striving to bridge atomic-scale dynamics to planetary-scale phase evolution.展开更多
The interdiffusion coefficients in Al_(0.2)CoCrFeNi,CoCrCu_(0.2)FeNi,and CoCrFeMn_(0.2)Ni high-entropy alloys were efficiently determined by combining diffusion couple experiments and high-throughput determination of ...The interdiffusion coefficients in Al_(0.2)CoCrFeNi,CoCrCu_(0.2)FeNi,and CoCrFeMn_(0.2)Ni high-entropy alloys were efficiently determined by combining diffusion couple experiments and high-throughput determination of interdiffusion coefficients(HitDIC)software at 1273−1373 K.The results show that the addition of Al,Cu,and Mn to CoCrFeNi high-entropy alloys promotes the diffusion of Co,Cr,and Fe atoms.The comparison of tracer diffusion coefficients indicates that there is no sluggish diffusion in tracer diffusion on the thermodynamic temperature scale for the present Al_(0.2)CoCrFeNi,CoCrCu_(0.2)FeNi,and CoCrFeMn_(0.2)Ni high-entropy alloys.The linear relationship between diffusion entropy and activation energy reveals that the diffusion process of atoms is unaffected by an increase in the number of components as long as the crystal structure remains unchanged.展开更多
基金Supported by the Open Research Fund of Key Laboratory of Nonlinear Analysis and Applications(Central China Normal University),Ministry of Education,P.R.China(Grant No.NAA2025ORG011)Science and Technology Plan Project of Jingmen(Grant No.2024YFZD076)+3 种基金Research Team Project of Jingchu University of Technology(Grant No.TD202006)Research Project of Jingchu University of Technology(Grant Nos.HX20240049HX20240200)the Teaching Reform Research Project of Hubei Province(Grant No.2024496)。
文摘In this paper,we study the eigenvalue problem of the Markov diffusion operator L^(2),and give generalized inequalities for eigenvalues of the operator L^(2)on a Markov diffusion triple.By applying these inequalities,we then get some new universal bounds for eigenvalues of a special Markov diffusion operator L^(2)on bounded domains in an Euclidean space.Moreover,our results can reveal the relationship between the(k+1)-th eigenvalue and the first k eigenvalues in a relatively straightforward manner.
基金supported by the National Natural Science Foundation of China(Grant Nos.42005003 and 41475094)National Key R&D Program of China(Grant No.2018YFC1506704).
文摘With the growing demand for high-precision flow field simulations in computational science and engineering,the super-resolution reconstruction of physical fields has attracted considerable research interest.However,tradi-tional numerical methods often entail high computational costs,involve complex data processing,and struggle to capture fine-scale high-frequency details.To address these challenges,we propose an innovative super-resolution reconstruction framework that integrates a Fourier neural operator(FNO)with an enhanced diffusion model.The framework employs an adaptively weighted FNO to process low-resolution flow field inputs,effectively capturing global dependencies and high-frequency features.Furthermore,a residual-guided diffusion model is introduced to further improve reconstruction performance.This model uses a Markov chain for noise injection in phys-ical fields and integrates a reverse denoising procedure,efficiently solved by an adaptive time-step ordinary differential equation solver,thereby ensuring both stability and computational efficiency.Experimental results demonstrate that the proposed framework significantly outperforms existing methods in terms of accuracy and efficiency,offering a promising solution for fine-grained data reconstruction in scientific simulations.
基金supported by the NSF of Ningxia(2022AAC03234)the NSF of China(11761004),the Construction Project of First-Class Disciplines in Ningxia Higher Education(NXYLXK2017B09)the Postgraduate Innovation Project of North Minzu University(YCX23074).
文摘In this article, we consider a backward problem in time of the diffusion equation with local and nonlocal operators. This inverse problem is ill-posed because the solution does not depend continuously on the measured data. Inspired by the classical Landweber iterative method and Fourier truncation technique, we develops a modified Landweber iterative regularization method to restore the continuous dependence of solution on the measurement data. Under the a-priori and a-posteriori choice rules for the regularized parameter, the convergence estimates for the regularization method are derived. Some results of numerical simulation are provided to verify the stability and feasibility of our method in dealing with the considered problem.
基金Supported by the National Natural Science Foundation of China(Grant No.12261081).
文摘In this paper,we are concerned with the stability of traveling wavefronts of a Belousov-Zhabotinsky model with mixed nonlocal and degenerate diffusions.Such a system can be used to study the competition among nonlocally diffusive species and degenerately diffusive species.We prove that the traveling wavefronts are exponentially stable,when the initial perturbation around the traveling waves decays exponentially as x→-∞,but in other locations,the initial data can be arbitrarily large.The adopted methods are the weighted energy with the comparison principle and squeezing technique.
基金China Scholarship Council for financial support(2007U13020)
文摘In this note, we obtain the elliptic estimate for diffusion operator L = △＋△Ф·△ on complete, noncompact Riemannian manifolds, under the curvature condition CD（K, m）, which generalizes B. L. Kotschwar＇s work [5]. As an application, we get estimate on the heat kernel. The Bernstein-type gradient estimate for SchrSdinger-type gradient is also derived.
基金the Natural Science Foundation of the Education Committee of Anhui Provinc
文摘In this paper, the classical and weak derivatives with respect to spatial variable of a class of hysteresis functional are discussed. Some conclusions about solutions of a class of reaction-diffusion equations with hysteresis differential operator are given.
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.
基金This work was supported by the National Natural Science Foundation of China(No.11971354)The author Yi-Shu Du acknowledges the financial support from the China Scholarship Council(File No.201906260146).
文摘After discretization by the finite volume method,the numerical solution of fractional diffusion equations leads to a linear system with the Toeplitz-like structure.The theoretical analysis gives sufficient conditions to guarantee the positive-definite property of the discretized matrix.Moreover,we develop a class of positive-definite operator splitting iteration methods for the numerical solution of fractional diffusion equations,which is unconditionally convergent for any positive constant.Meanwhile,the iteration methods introduce a new preconditioner for Krylov subspace methods.Numerical experiments verify the convergence of the positive-definite operator splitting iteration methods and show the efficiency of the proposed preconditioner,compared with the existing approaches.
基金supported by the National Natural Science Foundation of China(No.12475340 and 12375350)Special Branch project of South Taihu Lakethe Scientific Research Fund of Zhejiang Provincial Education Department(No.Y202456326).
文摘Missing values in radionuclide diffusion datasets can undermine the predictive accuracy and robustness of the machine learning(ML)models.In this study,regression-based missing data imputation method using a light gradient boosting machine(LGBM)algorithm was employed to impute more than 60%of the missing data,establishing a radionuclide diffusion dataset containing 16 input features and 813 instances.The effective diffusion coefficient(D_(e))was predicted using ten ML models.The predictive accuracy of the ensemble meta-models,namely LGBM-extreme gradient boosting(XGB)and LGBM-categorical boosting(CatB),surpassed that of the other ML models,with R^(2)values of 0.94.The models were applied to predict the D_(e)values of EuEDTA^(−)and HCrO_(4)^(−)in saturated compacted bentonites at compactions ranging from 1200 to 1800 kg/m^(3),which were measured using a through-diffusion method.The generalization ability of the LGBM-XGB model surpassed that of LGB-CatB in predicting the D_(e)of HCrO_(4)^(−).Shapley additive explanations identified total porosity as the most significant influencing factor.Additionally,the partial dependence plot analysis technique yielded clearer results in the univariate correlation analysis.This study provides a regression imputation technique to refine radionuclide diffusion datasets,offering deeper insights into analyzing the diffusion mechanism of radionuclides and supporting the safety assessment of the geological disposal of high-level radioactive waste.
文摘A medical image encryption is proposed based on the Fisher-Yates scrambling,filter diffusion and S-box substitution.First,chaotic sequence associated with the plaintext is generated by logistic-sine-cosine system,which is used for the scrambling,substitution and diffusion processes.The three-dimensional Fisher-Yates scrambling,S-box substitution and diffusion are employed for the first round of encryption.The chaotic sequence is adopted for secondary encryption to scramble the ciphertext obtained in the first round.Then,three-dimensional filter is applied to diffusion for further useful information hiding.The key to the algorithm is generated by the combination of hash value of plaintext image and the input parameters.It improves resisting ability of plaintext attacks.The security analysis shows that the algorithm is effective and efficient.It can resist common attacks.In addition,the good diffusion effect shows that the scheme can solve the differential attacks encountered in the transmission of medical images and has positive implications for future research.
基金supported by the National University of Defense Technology Research Fund Projectthe National Natural Science Foundation of China under Grant Nos. 12047561 and 12104507+1 种基金the NSAF under Grant No. U1830206the Science and Technology Innovation Program of Hunan Province under Grant No. 2021RC4026。
文摘The dynamics of phase separation in H–He binary systems within gas giants such as Jupiter and Saturn exhibit remarkable complexity, yet lack systematic investigation. Through large-scale machine-learning-accelerated molecular dynamics simulations spanning broad temperature-pressure-composition(2000–10000 K, 1–7 Mbar,pure H to pure He) regimes, we systematically determine self and mutual diffusion coefficients in H–He systems and establish a six-dimensional framework correlating temperature, pressure, helium abundance, phase separation degree, diffusion coefficients, and anisotropy. Key findings reveal that hydrogen exhibits active directional migration with pronounced diffusion anisotropy, whereas helium passively aggregates in response. While the conventional mixing rule underestimates mutual diffusion coefficients by neglecting velocity cross-correlations,the assumption of an ideal thermodynamic factor(Q = 1) overestimates them due to unaccounted non-ideal thermodynamic effects—both particularly pronounced in strongly phase-separated regimes. Notably, hydrogen's dual role, anisotropic diffusion and bond stabilization via helium doping, modulates demixing kinetics. Large-scale simulations(216,000 atoms) propose novel phase-separation paradigms, such as “hydrogen bubble/wisp” formation, challenging the classical “helium rain” scenario, striving to bridge atomic-scale dynamics to planetary-scale phase evolution.
基金supported by the National Natural Science Foundation of China(No.52374372)the Natural Science Foundation of the Jiangsu Higher Education Institutions of China(No.23KJB430042)+3 种基金the Jiangsu Province Large Scientific Instruments Open Sharing Autonomous Research Filing Project,China(No.TC2023A037)the Yangzhou City−Yangzhou University Cooperation Foundation,China(No.YZ2022183)High-end Talent Support Program of Yangzhou University,China,Qinglan Project of Yangzhou University,ChinaLvyangjinfeng Talent program of Yangzhou,China.
文摘The interdiffusion coefficients in Al_(0.2)CoCrFeNi,CoCrCu_(0.2)FeNi,and CoCrFeMn_(0.2)Ni high-entropy alloys were efficiently determined by combining diffusion couple experiments and high-throughput determination of interdiffusion coefficients(HitDIC)software at 1273−1373 K.The results show that the addition of Al,Cu,and Mn to CoCrFeNi high-entropy alloys promotes the diffusion of Co,Cr,and Fe atoms.The comparison of tracer diffusion coefficients indicates that there is no sluggish diffusion in tracer diffusion on the thermodynamic temperature scale for the present Al_(0.2)CoCrFeNi,CoCrCu_(0.2)FeNi,and CoCrFeMn_(0.2)Ni high-entropy alloys.The linear relationship between diffusion entropy and activation energy reveals that the diffusion process of atoms is unaffected by an increase in the number of components as long as the crystal structure remains unchanged.
