In this paper,we propose a new non-local diffusion equation for noise removal,which is derived from the classical Perona-Malik equation(PM equation)and the regularized PM equation.Using the convolution of the image gr...In this paper,we propose a new non-local diffusion equation for noise removal,which is derived from the classical Perona-Malik equation(PM equation)and the regularized PM equation.Using the convolution of the image gradient and the gradient,we propose a new diffusion coefficient.Due to the use of the convolution,the diffusion coefficient is non-local.However,the solution of the new diffusion equation may be discontinuous and belong to the bounded variation space(BV space).By virtue of Young measure method,the existence of a BV solution to the new non-local diffusion equation is established.Experimental results illustrate that the new method has some non-local performance and performs better than the original PM and other methods.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 paper, the global blowup properties of solutions for a class of nonlinear non-local reaction-diffusion problems are investigated by the methods of the prior estimates. Moreover, the blowup rate estimate of the...In this paper, the global blowup properties of solutions for a class of nonlinear non-local reaction-diffusion problems are investigated by the methods of the prior estimates. Moreover, the blowup rate estimate of the solution is given.展开更多
For the development of the fast charging technology of lithium-ion batteries,describing the rapid transient mass diffusion process accurately is the premise to avert the mechanical degradation caused by the diffusion-...For the development of the fast charging technology of lithium-ion batteries,describing the rapid transient mass diffusion process accurately is the premise to avert the mechanical degradation caused by the diffusion-induced stress.In this paper,we present a diffusion-elasticity model based on the finite deformation theory with the consideration of nonlocal effects of mass transfer.The proposed model is then applied to analyze the evolution and distribution of stress and lithium concentration in a silicon electrode during the rapid charging process under potentiostatic operation.The cases with and without the contribution of non-local diffusion effects are both calculated for comparative analysis.The dependence of the influence of non-local effects on diffusion relaxation time r〇is discussed.The results show that a diffusive wave appears when the value of r〇is sufficiently large,and it moves inside gradually during the rapid charging process,which is qualitatively consistent with the results from literature.展开更多
The problem of two small parameters in ordinary differential equations were extended to that in partial differential equations. The initial boundary problem for the singularly perturbed non-local reaction-diffusion eq...The problem of two small parameters in ordinary differential equations were extended to that in partial differential equations. The initial boundary problem for the singularly perturbed non-local reaction-diffusion equation was solved. Under suitable conditions, the formal asymptotic solutions were constructed using the method of two-step expansions and the uniform validity of the solutions was proved using the differential inequality.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
Grain boundary diffusion technology is pivotal in the preparation of high-performance NdFeB magnets.This study investigates the factors that affect the efficiency of grain boundary diffusion,starting from the properti...Grain boundary diffusion technology is pivotal in the preparation of high-performance NdFeB magnets.This study investigates the factors that affect the efficiency of grain boundary diffusion,starting from the properties of the diffusion matrix.Through the adjustment of the sintering process,we effectively prepared magnets with varied densities that serve as the matrix for grain boundary diffusion with TbH,diffusion.The mobility characteristics of the Nd-rich phase during the densification stage are leveraged to ensure a more extensive distribution of heavy rare earth elements within the magnets.According to the experimental results,the increase in coercivity of low-density magnets after diffusion is significantly greater than that of relatively high-density magnets.The coercivity values measured are 805.32 kA/m for low-density magnets and 470.3 kA/m for high-density magnets.Additionally,grain boundary diffusion notably enhances the density of initial low-density magnets,addressing the issue of low density during the sintering stage.Before the diffusion treatment,the Nd-rich phases primarily concentrate at the triangular grain boundaries,resulting in an increased number of cavity defects in the magnets.These cavity defects contain atoms in a higher energy state,making them more prone to transition.Consequently,the diffusion activation energy at the void defects is lower than the intracrystalline diffusion activation energy,accelerating atom diffusion.The presence of larger cavities also provides more space for atom migration,thereby promoting the diffusion process.After the diffusion treatment,the proportion of bulk Nd-rich phases significantly decreases,and they infiltrate between the grains to fill the cavity defects,forming continuous fine grain boundaries.Based on these observations,the study aims to explore how to utilize this information to develop an efficient technique for grain boundary diffusion.展开更多
Imputation of missing data has long been an important topic and an essential application for intelligent transportation systems(ITS)in the real world.As a state-of-the-art generative model,the diffusion model has prov...Imputation of missing data has long been an important topic and an essential application for intelligent transportation systems(ITS)in the real world.As a state-of-the-art generative model,the diffusion model has proven highly successful in image generation,speech generation,time series modelling etc.and now opens a new avenue for traffic data imputation.In this paper,we propose a conditional diffusion model,called the implicit-explicit diffusion model,for traffic data imputation.This model exploits both the implicit and explicit feature of the data simultaneously.More specifically,we design two types of feature extraction modules,one to capture the implicit dependencies hidden in the raw data at multiple time scales and the other to obtain the long-term temporal dependencies of the time series.This approach not only inherits the advantages of the diffusion model for estimating missing data,but also takes into account the multiscale correlation inherent in traffic data.To illustrate the performance of the model,extensive experiments are conducted on three real-world time series datasets using different missing rates.The experimental results demonstrate that the model improves imputation accuracy and generalization capability.展开更多
基金partially supported by the National Natural Science Foundation of China(11971131,12171123,11871133,11671111,U1637208,61873071,51476047)the Guangdong Basic and Applied Basic Research Foundation(2020B1515310006)+1 种基金the Natural Sciences Foundation of Heilongjiang Province(LH2021A011)China Postdoctoral Science Foundation(2020M670893).
文摘In this paper,we propose a new non-local diffusion equation for noise removal,which is derived from the classical Perona-Malik equation(PM equation)and the regularized PM equation.Using the convolution of the image gradient and the gradient,we propose a new diffusion coefficient.Due to the use of the convolution,the diffusion coefficient is non-local.However,the solution of the new diffusion equation may be discontinuous and belong to the bounded variation space(BV space).By virtue of Young measure method,the existence of a BV solution to the new non-local diffusion equation is established.Experimental results illustrate that the new method has some non-local performance and performs better than the original PM and other methods.
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.
文摘In this paper, the global blowup properties of solutions for a class of nonlinear non-local reaction-diffusion problems are investigated by the methods of the prior estimates. Moreover, the blowup rate estimate of the solution is given.
基金the National Natural Science Foundation of China under Grant Nos.11902222 and 11672210the National Key Research and Development Program of China under Grant No.2016YFC0300600.
文摘For the development of the fast charging technology of lithium-ion batteries,describing the rapid transient mass diffusion process accurately is the premise to avert the mechanical degradation caused by the diffusion-induced stress.In this paper,we present a diffusion-elasticity model based on the finite deformation theory with the consideration of nonlocal effects of mass transfer.The proposed model is then applied to analyze the evolution and distribution of stress and lithium concentration in a silicon electrode during the rapid charging process under potentiostatic operation.The cases with and without the contribution of non-local diffusion effects are both calculated for comparative analysis.The dependence of the influence of non-local effects on diffusion relaxation time r〇is discussed.The results show that a diffusive wave appears when the value of r〇is sufficiently large,and it moves inside gradually during the rapid charging process,which is qualitatively consistent with the results from literature.
基金Project supported by National Natural Science Foundation ofChina(Grant No .10071048)
文摘The problem of two small parameters in ordinary differential equations were extended to that in partial differential equations. The initial boundary problem for the singularly perturbed non-local reaction-diffusion equation was solved. Under suitable conditions, the formal asymptotic solutions were constructed using the method of two-step expansions and the uniform validity of the solutions was proved using the differential inequality.
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.
基金Project supported by the National Natural Science Foundation of China(52361033)National Key Research and Development Program(2022YFB3505400)+3 种基金Ministry of Industry and Information Technology Heavy Rare Earth Special Use of Sintered NdFeB Project(TC220H06J)Academic and Technical Leaders in Major Disciplines in Jiangxi Province(2022BCJ23007)Jiangxi Province Science and Technology Cooperation Key Project(20212BDH80007)Jiangxi Graduate Student Innovation Special Fund Project(YC2023-B213)。
文摘Grain boundary diffusion technology is pivotal in the preparation of high-performance NdFeB magnets.This study investigates the factors that affect the efficiency of grain boundary diffusion,starting from the properties of the diffusion matrix.Through the adjustment of the sintering process,we effectively prepared magnets with varied densities that serve as the matrix for grain boundary diffusion with TbH,diffusion.The mobility characteristics of the Nd-rich phase during the densification stage are leveraged to ensure a more extensive distribution of heavy rare earth elements within the magnets.According to the experimental results,the increase in coercivity of low-density magnets after diffusion is significantly greater than that of relatively high-density magnets.The coercivity values measured are 805.32 kA/m for low-density magnets and 470.3 kA/m for high-density magnets.Additionally,grain boundary diffusion notably enhances the density of initial low-density magnets,addressing the issue of low density during the sintering stage.Before the diffusion treatment,the Nd-rich phases primarily concentrate at the triangular grain boundaries,resulting in an increased number of cavity defects in the magnets.These cavity defects contain atoms in a higher energy state,making them more prone to transition.Consequently,the diffusion activation energy at the void defects is lower than the intracrystalline diffusion activation energy,accelerating atom diffusion.The presence of larger cavities also provides more space for atom migration,thereby promoting the diffusion process.After the diffusion treatment,the proportion of bulk Nd-rich phases significantly decreases,and they infiltrate between the grains to fill the cavity defects,forming continuous fine grain boundaries.Based on these observations,the study aims to explore how to utilize this information to develop an efficient technique for grain boundary diffusion.
基金partially supported by the National Natural Science Foundation of China(62271485)the SDHS Science and Technology Project(HS2023B044)
文摘Imputation of missing data has long been an important topic and an essential application for intelligent transportation systems(ITS)in the real world.As a state-of-the-art generative model,the diffusion model has proven highly successful in image generation,speech generation,time series modelling etc.and now opens a new avenue for traffic data imputation.In this paper,we propose a conditional diffusion model,called the implicit-explicit diffusion model,for traffic data imputation.This model exploits both the implicit and explicit feature of the data simultaneously.More specifically,we design two types of feature extraction modules,one to capture the implicit dependencies hidden in the raw data at multiple time scales and the other to obtain the long-term temporal dependencies of the time series.This approach not only inherits the advantages of the diffusion model for estimating missing data,but also takes into account the multiscale correlation inherent in traffic data.To illustrate the performance of the model,extensive experiments are conducted on three real-world time series datasets using different missing rates.The experimental results demonstrate that the model improves imputation accuracy and generalization capability.
