The higher-order numerical scheme of nonlinear advection-diffusion equations is studied in this article, where the space fractional derivatives are evaluated by using weighted and shifted Grünwald difference oper...The higher-order numerical scheme of nonlinear advection-diffusion equations is studied in this article, where the space fractional derivatives are evaluated by using weighted and shifted Grünwald difference operators and combining the compact technique, in the time direction is discretized by the Crank-Nicolson method. Through the energy method, the stability and convergence of the numerical scheme in the sense of L<sub>2</sub>-norm are proved, and the convergence order is . Some examples are given to show that our numerical scheme is effective.展开更多
Intracellular diffusion is critical for molecule translocation in cytoplasm and mediates many important cellular processes.Meanwhile,the diffusion dynamics is affected by the heterogeneous cytoplasm.Previous studies o...Intracellular diffusion is critical for molecule translocation in cytoplasm and mediates many important cellular processes.Meanwhile,the diffusion dynamics is affected by the heterogeneous cytoplasm.Previous studies on intracellular diffusion are mainly based on two-dimensional(2 D)measurements under the assumption that the three-dimensional(3 D)diffusion is isotropic.However,the real behaviors of 3 D diffusion of molecules in cytoplasm are still unclear.Here,we have built a 3 D single-particle tracking(SPT)microscopy and studied the 3 D diffusion of quantum dots(QDs)in adherent A549 cells.Notably,we found that the intracellular diffusion of QDs is quasi-2 D,with the axial motion being severely confined.Further investigations demonstrated that disrupting the cytoskeleton component or endoplasmic reticulum(ER)does not alter the quasi-2 D diffusion pattern,although ER reduces the diffusion rates and slightly relieves the constraint in the axial diffusion.The preferred quasi-2 D diffusion is quite robust and attributed to the complex cytoarchitectures in the flat adherent cells.With the aid of 3 D SPT method,the quasi-2 D diffusion in cells was revealed,shedding new light on the physical nature of cytoplasm.展开更多
A new approach, is established to show that the semigroup {S(t)≥0 generated by a reaction-diffusion equation with supercritical exponent is uniformly quasi-differentiable in L^q(Ω) (2 ≤ q 〈 ∞) with respect ...A new approach, is established to show that the semigroup {S(t)≥0 generated by a reaction-diffusion equation with supercritical exponent is uniformly quasi-differentiable in L^q(Ω) (2 ≤ q 〈 ∞) with respect to the initial value. As an application, this proves the upper-bound of fractal dimension for its global attractor in the corresponding space.展开更多
In the present paper, based on the conservation law of mass and momentum for ion and electron, the distribution of velocity, density of ions and electrons along radial direction are solved numerically. Furthermore, th...In the present paper, based on the conservation law of mass and momentum for ion and electron, the distribution of velocity, density of ions and electrons along radial direction are solved numerically. Furthermore, the comparison between MHD properties of ambipolar and qua- si- ambipolar diffusion is made. The numerical calculation is carried out for argon plasma. The results show that the ion density, ratio of ion and electron velocity at the cathode sheath boundary surface in- crease with the intensity of magnetic induction, meanwhile, the distance between sheaths decreases as well as the radial velocity of ion and electron at the anode sheath boundary. The ion density varies in accord with experiment qualitatively. All parameters mentioned above are not sensitive to magnetic field in ambipolar diffusion.展开更多
This paper is devoted to the study of a three-dimensional delayed system with nonlocal diffusion and partial quasi-monotonicity. By developing a new definition of upper-lower solutions and a new cross iteration scheme...This paper is devoted to the study of a three-dimensional delayed system with nonlocal diffusion and partial quasi-monotonicity. By developing a new definition of upper-lower solutions and a new cross iteration scheme, we establish some existence results of traveling wave solutions. The results are applied to a nonlocal diffusion model which takes the three-species Lotka-Volterra model as its special case.展开更多
By using the approximate derivative-dependent functional variable separation approach, we study the quasi-linear diffusion equations with a weak source ut = (A(u)Ux)x + eB(u, Ux). A complete classification of t...By using the approximate derivative-dependent functional variable separation approach, we study the quasi-linear diffusion equations with a weak source ut = (A(u)Ux)x + eB(u, Ux). A complete classification of these perturbed equations which admit approximate derivative-dependent functional separable solutions is listed. As a consequence, some approxi- mate solutions to the resulting perturbed equations are constructed via examples.展开更多
In this paper,we consider nonnegative classical solutions of a Quasi-linear reaction-diffusion system with nonlinear boundary conditions.We prove the uniqueness of a nonnegative classical solution to this problem.
When a mass spreads in a turbulent flow, areas with obviously high concentration of the mass compared with surrounding areas are formed by organized structures of turbulence. In this study, we extract the high concent...When a mass spreads in a turbulent flow, areas with obviously high concentration of the mass compared with surrounding areas are formed by organized structures of turbulence. In this study, we extract the high concentration areas and investigate their diffusion process. For this purpose, a combination of Planar Laser Induced Fluorescence (PLIF) and Particle Image Velocimetry (PIV) techniques was employed to obtain simultaneously the two fields of the concentration of injected dye and of the velocity in a water turbulent channel flow. With focusing on a quasi-homogeneous turbulence in the channel central region, a series of PLIF and PIV images were acquired at several different downstream positions. We applied a conditional sampling technique to the PLIF images to extract the high concentration areas, or spikes, and calculated the conditional-averaged statistics of the extracted areas such as length scale, mean concentration, and turbulent diffusion coefficient. We found that the averaged length scale was constant with downstream distance from the diffusion source and was smaller than integral scale of the turbulent eddies. The spanwise distribution of the mean concentration was basically Gaussian, and the spanwise width of the spikes increased linearly with downstream distance from the diffusion source. Moreover, the turbulent diffusion coefficient was found to increase in proportion to the spanwise distance from the source. These results reveal aspects different from those of regular mass diffusion and let us conclude that the diffusion process of the spikes differs from that of regular mass diffusion.展开更多
Quasi-elastic neutron scattering(QENS) has many applications that are directly related to the development of highperformance functional materials and biological macromolecules, especially those containing some water. ...Quasi-elastic neutron scattering(QENS) has many applications that are directly related to the development of highperformance functional materials and biological macromolecules, especially those containing some water. The analysis method of QENS spectra data is important to obtain parameters that can explain the structure of materials and the dynamics of water. In this paper, we present a revised jump-diffusion and rotation-diffusion model(rJRM) used for QENS spectra data analysis. By the rJRM, the QENS spectra from a pure magnesium-silicate-hydrate(MSH) sample are fitted well for the Q range from 0.3 ^(-1) to 1.9 ^(-1) and temperatures from 210 K up to 280 K. The fitted parameters can be divided into two kinds. The first kind describes the structure of the MSH sample, including the ratio of immobile water(or bound water) C and the confining radius of mobile water a_0. The second kind describes the dynamics of confined water in pores contained in the MSH sample, including the translational diffusion coefficient Dt, the average translational residence timeτ0, the rotational diffusion coefficient D_r, and the mean squared displacement(MSD) u^2. The r JRM is a new practical method suitable to fit QENS spectra from porous materials, where hydrogen atoms appear in both solid and liquid phases.展开更多
Dimensional analysis and reduction are done to two existing schemes of 4th-order linear horizontal diffusion, and detailed control experiments between them are made using a topographyincluded mesoscale model. Horizon...Dimensional analysis and reduction are done to two existing schemes of 4th-order linear horizontal diffusion, and detailed control experiments between them are made using a topographyincluded mesoscale model. Horizontal diffusion is calculated on the or surface in one (known as Scheme A afterwards ), and on the p-surface in another (Scheme B ). Experiments show that differences are small in smooth-terrain areas and very large in steep mountain areas, with the 24h rainfall prediction deviating by 50 mm between forecasts of the two sChemes. The reason may be that temperature and humidity are falsely diffused in Scheme A, which causes abnormal temperature and humidity, and results in the anomalies of the unstable layer and convective processes. In addition, Scheme A could also bring about circulation anomalies which assumingly have direct link to the convective anomalies in the scheme. Furthermore, perturbation may also affect surrounding areas by wave-like propagation such that precipitation anomalies may occur in the area. The analysis indicate that Scheme B is necessary and feasible for it minimizes diffusion-involved forecast abnormality in steep mountains and areas around.展开更多
The dynamic behaviors of water contained in calcium-silicate-hydrate(C-S-H) gel with different water content values from 10%to 30%(by weight),are studied by using an empirical diffusion model(EDM) to analyze the...The dynamic behaviors of water contained in calcium-silicate-hydrate(C-S-H) gel with different water content values from 10%to 30%(by weight),are studied by using an empirical diffusion model(EDM) to analyze the experimental data of quasi-elastic neutron scattering(QENS) spectra at measured temperatures ranging from 230 K to 280 K.In the study,the experimental QENS spectra with the whole Q-range are considered.Several important parameters including the bound/immobile water elastic coefficient A,the bound water index BWI,the Lorentzian with a half-width at half-maximum(HWHM) Γ;(Q) and Γ;(Q),the self-diffusion coefficients D;and D;of water molecules,the average residence times τ;and τ;,and the proton mean squared displacement(MSD)(u;) are obtained.The results show that the QENS spectra can be fitted very well not only for small Q(≤1 A;) but also for large Q.The bound/immobile water fraction in a C-S-H gel sample can be shown by the fitted BWI.The distinction between bound/immobile and mobile water,which includes confined water and ultra-confined water,can be seen by the fitted MSD.All the MSD tend to be the smallest value below 0.25 A;(the MSD of bound/immobile water) as the Q increases to 1.9 A;no matter what the temperature and water content are.Furthermore,by the abrupt changes of the fitted values of D;,τ;,and Γ;(Q),a crossover temperature at 250 K,namely the liquid-to-crystal-like transition temperature,can be identified for confined water in large gel pores(LGPs) and/or small gel pores(SGPs) contained in the C-S-H gel sample with 30% water content.展开更多
In this piece of work, using three spatial grid points, we discuss a new two-level implicit cubic spline method of O(k2 + kh2 + h4) for the solution of quasi-linear parabolic equation , 0 0 subject to appropriate init...In this piece of work, using three spatial grid points, we discuss a new two-level implicit cubic spline method of O(k2 + kh2 + h4) for the solution of quasi-linear parabolic equation , 0 0 subject to appropriate initial and Dirichlet boundary conditions, where h > 0, k > 0 are grid sizes in space and time-directions, respectively. The cubic spline approximation produces at each time level a spline function which may be used to obtain the solution at any point in the range of the space variable. The proposed cubic spline method is applicable to parabolic equations having singularity. The stability analysis for diffusion- convection equation shows the unconditionally stable character of the cubic spline method. The numerical tests are performed and comparative results are provided to illustrate the usefulness of the proposed method.展开更多
The quasi-neutral limit of time-dependent drift diffusion model with general sign-changing doping profile is justified rigorously in super-norm (i.e., uniformly in space). This improves the spatial square norm limit b...The quasi-neutral limit of time-dependent drift diffusion model with general sign-changing doping profile is justified rigorously in super-norm (i.e., uniformly in space). This improves the spatial square norm limit by Wang, Xin and Markowich.展开更多
We study quasi-stationarity for one-dimensional diffusions killed at 0, when 0 is a regular boundary and +∞ is an entrance boundary. We give a necessary and sufficient condition for the existence of exactly one quas...We study quasi-stationarity for one-dimensional diffusions killed at 0, when 0 is a regular boundary and +∞ is an entrance boundary. We give a necessary and sufficient condition for the existence of exactly one quasistationary distribution, and we also show that this distribution attracts all initial distributions.展开更多
文摘The higher-order numerical scheme of nonlinear advection-diffusion equations is studied in this article, where the space fractional derivatives are evaluated by using weighted and shifted Grünwald difference operators and combining the compact technique, in the time direction is discretized by the Crank-Nicolson method. Through the energy method, the stability and convergence of the numerical scheme in the sense of L<sub>2</sub>-norm are proved, and the convergence order is . Some examples are given to show that our numerical scheme is effective.
基金supported by the National Natural Science Foundation of China(Grant Nos.11674383,11874415,21991133,11774407)the National Key Research and Development Program(Grant No.2016YFA0301500)+1 种基金the Youth Innovation Promotion Association of CAS(Grant No.2019006)the Fundamental Research Funds for the Central Universities(Grant No.2019NTST26)。
文摘Intracellular diffusion is critical for molecule translocation in cytoplasm and mediates many important cellular processes.Meanwhile,the diffusion dynamics is affected by the heterogeneous cytoplasm.Previous studies on intracellular diffusion are mainly based on two-dimensional(2 D)measurements under the assumption that the three-dimensional(3 D)diffusion is isotropic.However,the real behaviors of 3 D diffusion of molecules in cytoplasm are still unclear.Here,we have built a 3 D single-particle tracking(SPT)microscopy and studied the 3 D diffusion of quantum dots(QDs)in adherent A549 cells.Notably,we found that the intracellular diffusion of QDs is quasi-2 D,with the axial motion being severely confined.Further investigations demonstrated that disrupting the cytoskeleton component or endoplasmic reticulum(ER)does not alter the quasi-2 D diffusion pattern,although ER reduces the diffusion rates and slightly relieves the constraint in the axial diffusion.The preferred quasi-2 D diffusion is quite robust and attributed to the complex cytoarchitectures in the flat adherent cells.With the aid of 3 D SPT method,the quasi-2 D diffusion in cells was revealed,shedding new light on the physical nature of cytoplasm.
基金Supported by NSFC Grant(11401100,10601021)the foundation of Fujian Education Department(JB14021)the innovation foundation of Fujian Normal University(IRTL1206)
文摘A new approach, is established to show that the semigroup {S(t)≥0 generated by a reaction-diffusion equation with supercritical exponent is uniformly quasi-differentiable in L^q(Ω) (2 ≤ q 〈 ∞) with respect to the initial value. As an application, this proves the upper-bound of fractal dimension for its global attractor in the corresponding space.
文摘In the present paper, based on the conservation law of mass and momentum for ion and electron, the distribution of velocity, density of ions and electrons along radial direction are solved numerically. Furthermore, the comparison between MHD properties of ambipolar and qua- si- ambipolar diffusion is made. The numerical calculation is carried out for argon plasma. The results show that the ion density, ratio of ion and electron velocity at the cathode sheath boundary surface in- crease with the intensity of magnetic induction, meanwhile, the distance between sheaths decreases as well as the radial velocity of ion and electron at the anode sheath boundary. The ion density varies in accord with experiment qualitatively. All parameters mentioned above are not sensitive to magnetic field in ambipolar diffusion.
基金Supported by the Natural Science Foundation of China (11171120)the Doctoral Program of Higher Education of China (20094407110001)Natural Science Foundation of Guangdong Province (10151063101000003)
文摘This paper is devoted to the study of a three-dimensional delayed system with nonlocal diffusion and partial quasi-monotonicity. By developing a new definition of upper-lower solutions and a new cross iteration scheme, we establish some existence results of traveling wave solutions. The results are applied to a nonlocal diffusion model which takes the three-species Lotka-Volterra model as its special case.
基金Project supported by the National Natural Science Foundation of China(Grant No.10671156)the Natural Science Foundation of Shaanxi Province of China(Grant No.SJ08A05)
文摘By using the approximate derivative-dependent functional variable separation approach, we study the quasi-linear diffusion equations with a weak source ut = (A(u)Ux)x + eB(u, Ux). A complete classification of these perturbed equations which admit approximate derivative-dependent functional separable solutions is listed. As a consequence, some approxi- mate solutions to the resulting perturbed equations are constructed via examples.
基金Supported by the National Natural Science Foundation of China(90410011)
文摘In this paper,we consider nonnegative classical solutions of a Quasi-linear reaction-diffusion system with nonlinear boundary conditions.We prove the uniqueness of a nonnegative classical solution to this problem.
文摘When a mass spreads in a turbulent flow, areas with obviously high concentration of the mass compared with surrounding areas are formed by organized structures of turbulence. In this study, we extract the high concentration areas and investigate their diffusion process. For this purpose, a combination of Planar Laser Induced Fluorescence (PLIF) and Particle Image Velocimetry (PIV) techniques was employed to obtain simultaneously the two fields of the concentration of injected dye and of the velocity in a water turbulent channel flow. With focusing on a quasi-homogeneous turbulence in the channel central region, a series of PLIF and PIV images were acquired at several different downstream positions. We applied a conditional sampling technique to the PLIF images to extract the high concentration areas, or spikes, and calculated the conditional-averaged statistics of the extracted areas such as length scale, mean concentration, and turbulent diffusion coefficient. We found that the averaged length scale was constant with downstream distance from the diffusion source and was smaller than integral scale of the turbulent eddies. The spanwise distribution of the mean concentration was basically Gaussian, and the spanwise width of the spikes increased linearly with downstream distance from the diffusion source. Moreover, the turbulent diffusion coefficient was found to increase in proportion to the spanwise distance from the source. These results reveal aspects different from those of regular mass diffusion and let us conclude that the diffusion process of the spikes differs from that of regular mass diffusion.
文摘Quasi-elastic neutron scattering(QENS) has many applications that are directly related to the development of highperformance functional materials and biological macromolecules, especially those containing some water. The analysis method of QENS spectra data is important to obtain parameters that can explain the structure of materials and the dynamics of water. In this paper, we present a revised jump-diffusion and rotation-diffusion model(rJRM) used for QENS spectra data analysis. By the rJRM, the QENS spectra from a pure magnesium-silicate-hydrate(MSH) sample are fitted well for the Q range from 0.3 ^(-1) to 1.9 ^(-1) and temperatures from 210 K up to 280 K. The fitted parameters can be divided into two kinds. The first kind describes the structure of the MSH sample, including the ratio of immobile water(or bound water) C and the confining radius of mobile water a_0. The second kind describes the dynamics of confined water in pores contained in the MSH sample, including the translational diffusion coefficient Dt, the average translational residence timeτ0, the rotational diffusion coefficient D_r, and the mean squared displacement(MSD) u^2. The r JRM is a new practical method suitable to fit QENS spectra from porous materials, where hydrogen atoms appear in both solid and liquid phases.
文摘Dimensional analysis and reduction are done to two existing schemes of 4th-order linear horizontal diffusion, and detailed control experiments between them are made using a topographyincluded mesoscale model. Horizontal diffusion is calculated on the or surface in one (known as Scheme A afterwards ), and on the p-surface in another (Scheme B ). Experiments show that differences are small in smooth-terrain areas and very large in steep mountain areas, with the 24h rainfall prediction deviating by 50 mm between forecasts of the two sChemes. The reason may be that temperature and humidity are falsely diffused in Scheme A, which causes abnormal temperature and humidity, and results in the anomalies of the unstable layer and convective processes. In addition, Scheme A could also bring about circulation anomalies which assumingly have direct link to the convective anomalies in the scheme. Furthermore, perturbation may also affect surrounding areas by wave-like propagation such that precipitation anomalies may occur in the area. The analysis indicate that Scheme B is necessary and feasible for it minimizes diffusion-involved forecast abnormality in steep mountains and areas around.
文摘The dynamic behaviors of water contained in calcium-silicate-hydrate(C-S-H) gel with different water content values from 10%to 30%(by weight),are studied by using an empirical diffusion model(EDM) to analyze the experimental data of quasi-elastic neutron scattering(QENS) spectra at measured temperatures ranging from 230 K to 280 K.In the study,the experimental QENS spectra with the whole Q-range are considered.Several important parameters including the bound/immobile water elastic coefficient A,the bound water index BWI,the Lorentzian with a half-width at half-maximum(HWHM) Γ;(Q) and Γ;(Q),the self-diffusion coefficients D;and D;of water molecules,the average residence times τ;and τ;,and the proton mean squared displacement(MSD)(u;) are obtained.The results show that the QENS spectra can be fitted very well not only for small Q(≤1 A;) but also for large Q.The bound/immobile water fraction in a C-S-H gel sample can be shown by the fitted BWI.The distinction between bound/immobile and mobile water,which includes confined water and ultra-confined water,can be seen by the fitted MSD.All the MSD tend to be the smallest value below 0.25 A;(the MSD of bound/immobile water) as the Q increases to 1.9 A;no matter what the temperature and water content are.Furthermore,by the abrupt changes of the fitted values of D;,τ;,and Γ;(Q),a crossover temperature at 250 K,namely the liquid-to-crystal-like transition temperature,can be identified for confined water in large gel pores(LGPs) and/or small gel pores(SGPs) contained in the C-S-H gel sample with 30% water content.
文摘In this piece of work, using three spatial grid points, we discuss a new two-level implicit cubic spline method of O(k2 + kh2 + h4) for the solution of quasi-linear parabolic equation , 0 0 subject to appropriate initial and Dirichlet boundary conditions, where h > 0, k > 0 are grid sizes in space and time-directions, respectively. The cubic spline approximation produces at each time level a spline function which may be used to obtain the solution at any point in the range of the space variable. The proposed cubic spline method is applicable to parabolic equations having singularity. The stability analysis for diffusion- convection equation shows the unconditionally stable character of the cubic spline method. The numerical tests are performed and comparative results are provided to illustrate the usefulness of the proposed method.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10431060, 10701011,10771009)Beijing Science Foundation of China (Grant No. 1082001)
文摘The quasi-neutral limit of time-dependent drift diffusion model with general sign-changing doping profile is justified rigorously in super-norm (i.e., uniformly in space). This improves the spatial square norm limit by Wang, Xin and Markowich.
基金The first author would 5ke to thank Prof. Server Martfnez for his kind hospitality during a visit to the CMM of Universidad de Chile, where part of this work was done. The authors also sincerely thank the referees for helpful comments. This work was supported by the National Natural Science Foundation of China (Grant No. 11371301) and Hunan Provincial Innovation Foundation For Postgraduate (Grant No. CX2015B203).
文摘We study quasi-stationarity for one-dimensional diffusions killed at 0, when 0 is a regular boundary and +∞ is an entrance boundary. We give a necessary and sufficient condition for the existence of exactly one quasistationary distribution, and we also show that this distribution attracts all initial distributions.