Time-dependent diffusion coefficient and conventional diffusion constant are calculated and analyzed to study diffusion of nanoparticles in polymer melts. A generalized Langevin equa- tion is adopted to describe the d...Time-dependent diffusion coefficient and conventional diffusion constant are calculated and analyzed to study diffusion of nanoparticles in polymer melts. A generalized Langevin equa- tion is adopted to describe the diffusion dynamics. Mode-coupling theory is employed to calculate the memory kernel of friction. For simplicity, only microscopic terms arising from binary collision and coupling to the solvent density fluctuation are included in the formalism. The equilibrium structural information functions of the polymer nanocomposites required by mode-coupling theory are calculated on the basis of polymer reference interaction site model with Percus-Yevick closure. The effect of nanoparticle size and that of the polymer size are clarified explicitly. The structural functions, the friction kernel, as well as the diffusion coefficient show a rich variety with varying nanoparticle radius and polymer chain length. We find that for small nanoparticles or short chain polymers, the characteristic short time non-Markov diffusion dynamics becomes more prominent, and the diffusion coefficient takes longer time to approach asymptotically the conventional diffusion constant. This constant due to the microscopic contributions will decrease with the increase of nanoparticle size, while increase with polymer size. Furthermore, our result of diffusion constant from mode- coupling theory is compared with the value predicted from the Stokes-Einstein relation. It shows that the microscopic contributions to the diffusion constant are dominant for small nanoparticles or long chain polymers. Inversely, when nanonparticle is big, or polymer chain is short, the hydrodynamic contribution might play a significant role.展开更多
Increasingly,attention is being directed towards time-dependent diffusion magnetic resonance imaging(TDDMRI),a method that reveals time-related changes in the diffusional behavior of water molecules in biological tiss...Increasingly,attention is being directed towards time-dependent diffusion magnetic resonance imaging(TDDMRI),a method that reveals time-related changes in the diffusional behavior of water molecules in biological tissues,thereby enabling us to probe related microstructure events.With ongoing improvements in hardware and advanced pulse sequences,significant progress has been made in applying TDDMRI to clinical research.The development of accurate mathematical models and computational methods has bolstered theoretical support for TDDMRI and elevated our understanding of molecular diffusion.In this review,we introduce the concept and basic physics of TDDMRI,and then focus on the measurement strategies and modeling approaches in short-and long-diffusion-time domains.Finally,we discuss the challenges in this field,including the requirement for efficient scanning and data processing technologies,the development of more precise models depicting time-dependent molecular diffusion,and critical clinical applications.展开更多
The main result of this paper is that when the coefficients of the time-dependent divergence form operators are Hlder continuous in time with order not too much smaller than （1/2）,the distance of the semigroups of t...The main result of this paper is that when the coefficients of the time-dependent divergence form operators are Hlder continuous in time with order not too much smaller than （1/2）,the distance of the semigroups of two operators is bounded by the L<sub>2</sub> distance of the coefficients of their corresponding operators.展开更多
This study aims to develop a chloride diffusion simulation method that considers the hydration microstructure and pore solution properties during the hydration of tricalcium silicate(C3S).The method combines the hydra...This study aims to develop a chloride diffusion simulation method that considers the hydration microstructure and pore solution properties during the hydration of tricalcium silicate(C3S).The method combines the hydration simulation,thermodynamic calculation,and finite element analysis to examine the effects of pore solution,including effect of electrochemical potential,effect of chemical activity,and effect of mechanical interactions between ions,on the chloride effective diffusion coefficient of hydrated C3S paste.The results indicate that the effect of electrochemical potential on chloride diffusion becomes stronger with increasing hydration age due to the increase in the content of hydrated calcium silicate;as the hydration age increases,the effect of chemical activity on chloride diffusion weakens when the number of diffusible elements decreases;the effect of mechanical interactions between ions on chloride diffusion decreases with the increase of hydration age.展开更多
Catastrophic failure in engineering structures of island reefs would occur when the tertiary creep initiates in coral reef limestone with a transition from short-to long-term load.Due to the complexity of biological s...Catastrophic failure in engineering structures of island reefs would occur when the tertiary creep initiates in coral reef limestone with a transition from short-to long-term load.Due to the complexity of biological structures,the underlying micro-behaviors involving time-dependent deformation are poorly understood.For this,an abnormal phenomenon was observed where the axial and lateral creep deformations were mutually independent by a series of triaxial tests under constant stress and strain rate conditions.The significantly large lateral creep deformation implies that the creep process cannot be described in continuum mechanics regime.Herein,it is hypothesized that sliding mechanism of crystal cleavages dominates the lateral creep deformation in coral reef limestone.Then,approaches of polarizing microscope(PM)and scanning electronic microscope(SEM)are utilized to validate the hypothesis.It shows that the sliding behavior of crystal cleavages combats with conventional creep micro-mechanisms at certain condition.The former is sensitive to time and strain rate,and is merely activated in the creep regime.展开更多
In this article, a finite volume element algorithm is presented and discussed for the numerical solutions of a time-fractional nonlinear fourth-order diffusion equation with time delay. By choosing the second-order sp...In this article, a finite volume element algorithm is presented and discussed for the numerical solutions of a time-fractional nonlinear fourth-order diffusion equation with time delay. By choosing the second-order spatial derivative of the original unknown as an additional variable, the fourth-order problem is transformed into a second-order system. Then the fully discrete finite volume element scheme is formulated by using L1approximation for temporal Caputo derivative and finite volume element method in spatial direction. The unique solvability and stable result of the proposed scheme are proved. A priori estimate of L2-norm with optimal order of convergence O(h2+τ2−α)where τand hare time step length and space mesh parameter, respectively, is obtained. The efficiency of the scheme is supported by some numerical experiments.展开更多
Deep learning has achieved great progress in image recognition,segmentation,semantic recognition and game theory.In this study,a latest deep learning model,a conditional diffusion model was adopted as a surrogate mode...Deep learning has achieved great progress in image recognition,segmentation,semantic recognition and game theory.In this study,a latest deep learning model,a conditional diffusion model was adopted as a surrogate model to predict the heat transfer during the casting process instead of numerical simulation.The conditional diffusion model was established and trained with the geometry shapes,initial temperature fields and temperature fields at t_(i) as the condition and random noise sampled from standard normal distribution as the input.The output was the temperature field at t_(i+1).Therefore,the temperature field at t_(i+1)can be predicted as the temperature field at t_(i) is known,and the continuous temperature fields of all the time steps can be predicted based on the initial temperature field of an arbitrary 2D geometry.A training set with 3022D shapes and their simulated temperature fields at different time steps was established.The accuracy for the temperature field for a single time step reaches 97.7%,and that for continuous time steps reaches 69.1%with the main error actually existing in the sand mold.The effect of geometry shape and initial temperature field on the prediction accuracy was investigated,the former achieves better result than the latter because the former can identify casting,mold and chill by different colors in the input images.The diffusion model has proved the potential as a surrogate model for numerical simulation of the casting process.展开更多
Growth of high-quality Nb_(3)Sn thin films for superconducting radiofrequency(SRF)applications using the vapor diffusion method requires a uniform distribution of tin nuclei on the niobium(Nb)surface.This study examin...Growth of high-quality Nb_(3)Sn thin films for superconducting radiofrequency(SRF)applications using the vapor diffusion method requires a uniform distribution of tin nuclei on the niobium(Nb)surface.This study examines the mechanism underlying the observed non-uniform distribution of tin nuclei with tin chloride SnCl_(2).Electron backscatter diffraction(EBSD)analysis was used to examine the correlation between the nucleation behavior and orientation of niobium grains in the substrate.The findings of the density functional theory(DFT)simulation are in good agreement with the experimental results,showing that the non-uniform distribution of tin nuclei is the result of the adsorption energy of SnCl_(2)molecules by varied niobium grain orientations.Further analysis indicated that the surface roughness and grain size of niobium also played significant roles in the nucleation behavior.This study provides valuable insights into enhancing the surface pretreatment of niobium substrates during the growth of Nb_(3)Sn thin films using the vapor diffusion method.展开更多
With respect to oceanic fluid dynamics,certain models have appeared,e.g.,an extended time-dependent(3+1)-dimensional shallow water wave equation in an ocean or a river,which we investigate in this paper.Using symbolic...With respect to oceanic fluid dynamics,certain models have appeared,e.g.,an extended time-dependent(3+1)-dimensional shallow water wave equation in an ocean or a river,which we investigate in this paper.Using symbolic computation,we find out,on one hand,a set of bilinear auto-Backlund transformations,which could connect certain solutions of that equation with other solutions of that equation itself,and on the other hand,a set of similarity reductions,which could go from that equation to a known ordinary differential equation.The results in this paper depend on all the oceanic variable coefficients in that equation.展开更多
In this paper, two finite difference streamline diffusion (FDSD) schemes for solving two-dimensional time-dependent convection-diffusion equations are constructed. Stability and optimal order error estimati-ions for c...In this paper, two finite difference streamline diffusion (FDSD) schemes for solving two-dimensional time-dependent convection-diffusion equations are constructed. Stability and optimal order error estimati-ions for considered schemes are derived in the norm stronger than L^2-norm.展开更多
A nonconforming finite element method of finite difference streamline diffusion type is proposed to solve the time-dependent linearized Navier-Stokes equations. The backward Euler scheme is used for time discretizatio...A nonconforming finite element method of finite difference streamline diffusion type is proposed to solve the time-dependent linearized Navier-Stokes equations. The backward Euler scheme is used for time discretization. Crouzeix-Raviart nonconforming finite element approximation, namely, nonconforming （P1）2 - P0 element, is used for the velocity and pressure fields with the streamline diffusion technique to cope with usual instabilities caused by the convection and time terms. Stability and error estimates are derived with suitable norms.展开更多
In this paper, we establish an SIR reaction-diffusion infectious disease model with saturated incidence rate and vaccination. Firstly, we prove the uniform boundedness of the solution of this model. Secondly, we estab...In this paper, we establish an SIR reaction-diffusion infectious disease model with saturated incidence rate and vaccination. Firstly, we prove the uniform boundedness of the solution of this model. Secondly, we establish the threshold dynamic behavior of the model based on the basic reproduction number R0, specifically, we prove the globally asymptotic stability of the disease-free equilibrium and the uniform persistence of the model. Thirdly, we show the existence and stability of the endemic equilibrium of the homogeneous system and obtain different cases of positive solution. Fourthly, we investigate the effects of vaccination rate and saturated incidence rate on the basic reproduction number. The results indicate that increasing vaccination rate and saturation rate can effectively control the transmission of the disease. Finally, we conduct numerical simulations to verify the aforementioned conclusions.展开更多
This paper proposes a new nonconforming finite difference streamline diffusion method to solve incompressible time-dependent Navier-Stokes equations with a high Reynolds number. The backwards difference in time and th...This paper proposes a new nonconforming finite difference streamline diffusion method to solve incompressible time-dependent Navier-Stokes equations with a high Reynolds number. The backwards difference in time and the Crouzeix-Raviart （CR） element combined with the P0 element in space are used. The result shows that this scheme has good stabilities and error estimates independent of the viscosity coefficient.展开更多
In this paper,we are concerned with the asymptotic behavior of L^(∞) weak-entropy solutions to the compressible Euler equations with a vacuum and time-dependent damping-m/(1+t)^(λ).As λ∈(0,l/7],we prove tht the L^...In this paper,we are concerned with the asymptotic behavior of L^(∞) weak-entropy solutions to the compressible Euler equations with a vacuum and time-dependent damping-m/(1+t)^(λ).As λ∈(0,l/7],we prove tht the L^(∞) weak-entropy solution converges to the nonlinear diffusion wave of the generalized porous media equation(GPME)in L^(2)(R).As λ∈(1/7,1),we prove that the L^(∞) weak-entropy solution converges to an expansion around the nonlinear diffusion wave in L^(2)(R),which is the best asymptotic profile.The proof is based on intensive entropy analysis and an energy method.展开更多
A comparison between a non-Gaussian puff model and an advanced time-dependent model to simulate the pollutant dispersion in the Planetary Boundary Layer is presented. The puff model is based on a general technique for...A comparison between a non-Gaussian puff model and an advanced time-dependent model to simulate the pollutant dispersion in the Planetary Boundary Layer is presented. The puff model is based on a general technique for solving the K-equation, using the truncated Gram-Charlier expansion (type A) of the concentration field and finite set equations for the corresponding moments. The other model (named ADMM: Analytical Dispersion Multilayers Model) is an semi- analytical solution to the time-dependent two-dimensional advection-diffusion equation based on a discretization of the PBL in N sub-layers;in each sub-layers the advection-diffusion equation is solved by the Laplace transform technique, considering an average value for eddy diffusivity and the wind speed. A preliminary performance evaluation is shown in the case of continuous emission from an elevated source in a variable boundary layer. Both models were able to correctly reproduce the concentration field measured and so to be used as operative air pollution models.展开更多
基金This work was supported by the National Natural Science Foundation of China （No.21173152）, the Ministry of Education of China （No.NCET-11-0359 and No.2011SCU04B31）, and the Science and Technology Department of Sichuan Province （No.2011HH0005）.
文摘Time-dependent diffusion coefficient and conventional diffusion constant are calculated and analyzed to study diffusion of nanoparticles in polymer melts. A generalized Langevin equa- tion is adopted to describe the diffusion dynamics. Mode-coupling theory is employed to calculate the memory kernel of friction. For simplicity, only microscopic terms arising from binary collision and coupling to the solvent density fluctuation are included in the formalism. The equilibrium structural information functions of the polymer nanocomposites required by mode-coupling theory are calculated on the basis of polymer reference interaction site model with Percus-Yevick closure. The effect of nanoparticle size and that of the polymer size are clarified explicitly. The structural functions, the friction kernel, as well as the diffusion coefficient show a rich variety with varying nanoparticle radius and polymer chain length. We find that for small nanoparticles or short chain polymers, the characteristic short time non-Markov diffusion dynamics becomes more prominent, and the diffusion coefficient takes longer time to approach asymptotically the conventional diffusion constant. This constant due to the microscopic contributions will decrease with the increase of nanoparticle size, while increase with polymer size. Furthermore, our result of diffusion constant from mode- coupling theory is compared with the value predicted from the Stokes-Einstein relation. It shows that the microscopic contributions to the diffusion constant are dominant for small nanoparticles or long chain polymers. Inversely, when nanonparticle is big, or polymer chain is short, the hydrodynamic contribution might play a significant role.
基金supported by the Ministry of Science and Technology of the People’s Republic of China(No.2021ZD0200202)the National Natural Science Foundation of China(No.82122032)the Science and Technology Department of Zhejiang Province(Nos.202006140 and 2022C03057).
文摘Increasingly,attention is being directed towards time-dependent diffusion magnetic resonance imaging(TDDMRI),a method that reveals time-related changes in the diffusional behavior of water molecules in biological tissues,thereby enabling us to probe related microstructure events.With ongoing improvements in hardware and advanced pulse sequences,significant progress has been made in applying TDDMRI to clinical research.The development of accurate mathematical models and computational methods has bolstered theoretical support for TDDMRI and elevated our understanding of molecular diffusion.In this review,we introduce the concept and basic physics of TDDMRI,and then focus on the measurement strategies and modeling approaches in short-and long-diffusion-time domains.Finally,we discuss the challenges in this field,including the requirement for efficient scanning and data processing technologies,the development of more precise models depicting time-dependent molecular diffusion,and critical clinical applications.
基金Research partially supported by N.S.F.Grants DMS-9625642
文摘The main result of this paper is that when the coefficients of the time-dependent divergence form operators are Hlder continuous in time with order not too much smaller than （1/2）,the distance of the semigroups of two operators is bounded by the L<sub>2</sub> distance of the coefficients of their corresponding operators.
基金Funded by the Natural Science Foundation of Jiangsu Province(No.BK20241529)China Postdoctoral Science Foundation(No.2024M750736)。
文摘This study aims to develop a chloride diffusion simulation method that considers the hydration microstructure and pore solution properties during the hydration of tricalcium silicate(C3S).The method combines the hydration simulation,thermodynamic calculation,and finite element analysis to examine the effects of pore solution,including effect of electrochemical potential,effect of chemical activity,and effect of mechanical interactions between ions,on the chloride effective diffusion coefficient of hydrated C3S paste.The results indicate that the effect of electrochemical potential on chloride diffusion becomes stronger with increasing hydration age due to the increase in the content of hydrated calcium silicate;as the hydration age increases,the effect of chemical activity on chloride diffusion weakens when the number of diffusible elements decreases;the effect of mechanical interactions between ions on chloride diffusion decreases with the increase of hydration age.
基金supported by the National Natural Science Foundation of China(Grant Nos.41877267,41877260)the Priority Research Program of the Chinese Academy of Science(Grant No.XDA13010201).
文摘Catastrophic failure in engineering structures of island reefs would occur when the tertiary creep initiates in coral reef limestone with a transition from short-to long-term load.Due to the complexity of biological structures,the underlying micro-behaviors involving time-dependent deformation are poorly understood.For this,an abnormal phenomenon was observed where the axial and lateral creep deformations were mutually independent by a series of triaxial tests under constant stress and strain rate conditions.The significantly large lateral creep deformation implies that the creep process cannot be described in continuum mechanics regime.Herein,it is hypothesized that sliding mechanism of crystal cleavages dominates the lateral creep deformation in coral reef limestone.Then,approaches of polarizing microscope(PM)and scanning electronic microscope(SEM)are utilized to validate the hypothesis.It shows that the sliding behavior of crystal cleavages combats with conventional creep micro-mechanisms at certain condition.The former is sensitive to time and strain rate,and is merely activated in the creep regime.
文摘In this article, a finite volume element algorithm is presented and discussed for the numerical solutions of a time-fractional nonlinear fourth-order diffusion equation with time delay. By choosing the second-order spatial derivative of the original unknown as an additional variable, the fourth-order problem is transformed into a second-order system. Then the fully discrete finite volume element scheme is formulated by using L1approximation for temporal Caputo derivative and finite volume element method in spatial direction. The unique solvability and stable result of the proposed scheme are proved. A priori estimate of L2-norm with optimal order of convergence O(h2+τ2−α)where τand hare time step length and space mesh parameter, respectively, is obtained. The efficiency of the scheme is supported by some numerical experiments.
文摘Deep learning has achieved great progress in image recognition,segmentation,semantic recognition and game theory.In this study,a latest deep learning model,a conditional diffusion model was adopted as a surrogate model to predict the heat transfer during the casting process instead of numerical simulation.The conditional diffusion model was established and trained with the geometry shapes,initial temperature fields and temperature fields at t_(i) as the condition and random noise sampled from standard normal distribution as the input.The output was the temperature field at t_(i+1).Therefore,the temperature field at t_(i+1)can be predicted as the temperature field at t_(i) is known,and the continuous temperature fields of all the time steps can be predicted based on the initial temperature field of an arbitrary 2D geometry.A training set with 3022D shapes and their simulated temperature fields at different time steps was established.The accuracy for the temperature field for a single time step reaches 97.7%,and that for continuous time steps reaches 69.1%with the main error actually existing in the sand mold.The effect of geometry shape and initial temperature field on the prediction accuracy was investigated,the former achieves better result than the latter because the former can identify casting,mold and chill by different colors in the input images.The diffusion model has proved the potential as a surrogate model for numerical simulation of the casting process.
基金supported by the National Natural Science Foundation of China(No.12175283)Youth Innovation Promotion Association of Chinese Academy of Sciences(2020410)Advanced Energy Science and Technology Guangdong Laboratory(HND20TDSPCD,HND22PTDZD).
文摘Growth of high-quality Nb_(3)Sn thin films for superconducting radiofrequency(SRF)applications using the vapor diffusion method requires a uniform distribution of tin nuclei on the niobium(Nb)surface.This study examines the mechanism underlying the observed non-uniform distribution of tin nuclei with tin chloride SnCl_(2).Electron backscatter diffraction(EBSD)analysis was used to examine the correlation between the nucleation behavior and orientation of niobium grains in the substrate.The findings of the density functional theory(DFT)simulation are in good agreement with the experimental results,showing that the non-uniform distribution of tin nuclei is the result of the adsorption energy of SnCl_(2)molecules by varied niobium grain orientations.Further analysis indicated that the surface roughness and grain size of niobium also played significant roles in the nucleation behavior.This study provides valuable insights into enhancing the surface pretreatment of niobium substrates during the growth of Nb_(3)Sn thin films using the vapor diffusion method.
基金financially supported by the Scientific Research Foundation of North China University of Technology(Grant Nos.11005136024XN147-87 and 110051360024XN151-86).
文摘With respect to oceanic fluid dynamics,certain models have appeared,e.g.,an extended time-dependent(3+1)-dimensional shallow water wave equation in an ocean or a river,which we investigate in this paper.Using symbolic computation,we find out,on one hand,a set of bilinear auto-Backlund transformations,which could connect certain solutions of that equation with other solutions of that equation itself,and on the other hand,a set of similarity reductions,which could go from that equation to a known ordinary differential equation.The results in this paper depend on all the oceanic variable coefficients in that equation.
基金Project supported by National Natural Science Foundation of China and China State Key project for Basic Researchcs.
文摘In this paper, two finite difference streamline diffusion (FDSD) schemes for solving two-dimensional time-dependent convection-diffusion equations are constructed. Stability and optimal order error estimati-ions for considered schemes are derived in the norm stronger than L^2-norm.
基金supported by the National Natural Science Foundation of China(No.10771150)the National Basic Research Program of China(No.2005CB321701)+1 种基金the Program for New Century Excellent Talents in University(No.NCET-07-0584)the Natural Science Foundation of Sichuan Province(No.07ZB087)
文摘A nonconforming finite element method of finite difference streamline diffusion type is proposed to solve the time-dependent linearized Navier-Stokes equations. The backward Euler scheme is used for time discretization. Crouzeix-Raviart nonconforming finite element approximation, namely, nonconforming （P1）2 - P0 element, is used for the velocity and pressure fields with the streamline diffusion technique to cope with usual instabilities caused by the convection and time terms. Stability and error estimates are derived with suitable norms.
文摘In this paper, we establish an SIR reaction-diffusion infectious disease model with saturated incidence rate and vaccination. Firstly, we prove the uniform boundedness of the solution of this model. Secondly, we establish the threshold dynamic behavior of the model based on the basic reproduction number R0, specifically, we prove the globally asymptotic stability of the disease-free equilibrium and the uniform persistence of the model. Thirdly, we show the existence and stability of the endemic equilibrium of the homogeneous system and obtain different cases of positive solution. Fourthly, we investigate the effects of vaccination rate and saturated incidence rate on the basic reproduction number. The results indicate that increasing vaccination rate and saturation rate can effectively control the transmission of the disease. Finally, we conduct numerical simulations to verify the aforementioned conclusions.
基金supported by the National Natural Science Foundation of China(Nos.11271273 and 11271298)
文摘This paper proposes a new nonconforming finite difference streamline diffusion method to solve incompressible time-dependent Navier-Stokes equations with a high Reynolds number. The backwards difference in time and the Crouzeix-Raviart （CR） element combined with the P0 element in space are used. The result shows that this scheme has good stabilities and error estimates independent of the viscosity coefficient.
基金S.Geng's research was supported in part by the National Natural Science Foundation of China(12071397)Excellent Youth Project of Hunan Education Department(21B0165)+1 种基金F.Huang's research was supported in part by the National Key R&D Program of China 2021YFA1000800the National Natural Science Foundation of China(12288201).
文摘In this paper,we are concerned with the asymptotic behavior of L^(∞) weak-entropy solutions to the compressible Euler equations with a vacuum and time-dependent damping-m/(1+t)^(λ).As λ∈(0,l/7],we prove tht the L^(∞) weak-entropy solution converges to the nonlinear diffusion wave of the generalized porous media equation(GPME)in L^(2)(R).As λ∈(1/7,1),we prove that the L^(∞) weak-entropy solution converges to an expansion around the nonlinear diffusion wave in L^(2)(R),which is the best asymptotic profile.The proof is based on intensive entropy analysis and an energy method.
文摘A comparison between a non-Gaussian puff model and an advanced time-dependent model to simulate the pollutant dispersion in the Planetary Boundary Layer is presented. The puff model is based on a general technique for solving the K-equation, using the truncated Gram-Charlier expansion (type A) of the concentration field and finite set equations for the corresponding moments. The other model (named ADMM: Analytical Dispersion Multilayers Model) is an semi- analytical solution to the time-dependent two-dimensional advection-diffusion equation based on a discretization of the PBL in N sub-layers;in each sub-layers the advection-diffusion equation is solved by the Laplace transform technique, considering an average value for eddy diffusivity and the wind speed. A preliminary performance evaluation is shown in the case of continuous emission from an elevated source in a variable boundary layer. Both models were able to correctly reproduce the concentration field measured and so to be used as operative air pollution models.
