An efficient and accurate exponential wave integrator Fourier pseudospectral （EWI-FP） method is proposed and analyzed for solving the symmetric regularized-long-wave （SRLW） equation, which is used for modeling the...An efficient and accurate exponential wave integrator Fourier pseudospectral （EWI-FP） method is proposed and analyzed for solving the symmetric regularized-long-wave （SRLW） equation, which is used for modeling the weakly nonlinear ion acoustic and space-charge waves. The numerical method here is based on a Gautschi-type exponential wave integrator for temporal approximation and the Fourier pseudospectral method for spatial discretization. The scheme is fully explicit and efficient due to the fast Fourier transform. Numerical analysis of the proposed EWI-FP method is carried out and rigorous error estimates are established without CFL-type condition by means of the mathematical induction. The error bound shows that EWI-FP has second order accuracy in time and spectral accuracy in space. Numerical results are reported to confirm the theoretical studies and indicate that the error bound here is optimal.展开更多
The objective of this paper is to introduce elementary discrete reflected backward equations and to give a simple method to discretize in time a （continuous） reflected backward equation. A presentation of numerical ...The objective of this paper is to introduce elementary discrete reflected backward equations and to give a simple method to discretize in time a （continuous） reflected backward equation. A presentation of numerical simulations is also described.展开更多
In what follows, we consider the relation between Aldous's extended convergence and weak convergence of nitrations. We prove that, for a sequence (Xn) of J_t^n)-special semimartingales, with canonical decompositio...In what follows, we consider the relation between Aldous's extended convergence and weak convergence of nitrations. We prove that, for a sequence (Xn) of J_t^n)-special semimartingales, with canonical decomposition Xn = Mn + An, if the extended convergence (Xn.Jrn)→ (X,F.) holds with a quasi-left continuous (Ft)-special semimartingale X = M + A, then, under an additional assumption of uniform integrability,we get the convergence in probability under the Skorokhod topology: Mn→M and An→A.展开更多
We consider the empirical spectral distribution （ESD） of a random matrix from the Gaussian Unitary Ensemble. Based on the Plancherel-Rotaeh approximation formula for Hermite polynomials, we prove that the expected e...We consider the empirical spectral distribution （ESD） of a random matrix from the Gaussian Unitary Ensemble. Based on the Plancherel-Rotaeh approximation formula for Hermite polynomials, we prove that the expected empirical spectral distribution converges at the rate of O（n^-1） to the Wigner distribution function uniformly on every compact intervals [u,v] within the limiting support （-1, 1）. Furthermore, the variance of the ESD for such an interval is proved to be （πn）^-2 logn asymptotically which surprisingly enough, does not depend on the details （e.g. length or location） of the interval, This property allows us to determine completely the covariance function between the values of the ESD on two intervals.展开更多
The author shows the existence of long-time averages to turbulent solutions of the Navier-Stokes equations and determines the equations satisfied by them, involving a Reynolds stress that is shown to be dissipative.
In this paper the authors present a derivation of a back-scatter rotational Large Eddy Simulation model,which is the extension of the Baldwin&Lomax model to nonequilibrium problems.The model is particularly design...In this paper the authors present a derivation of a back-scatter rotational Large Eddy Simulation model,which is the extension of the Baldwin&Lomax model to nonequilibrium problems.The model is particularly designed to mathematically describe a fluid filling a domain with solid walls and consequently the differential operators appearing in the smoothing terms are degenerate at the boundary.After the derivation of the model,the authors prove some of the mathematical properties coming from the weighted energy estimates,which allow to prove existence and uniqueness of a class of regular weak solutions.展开更多
Background Extreme rainfall and flooding events are projected to increase in frequency and disturb biogeochemical cycles such as the nitrogen(N)cycle.By combining trees and grasses,silvopastoral agroforestry is expect...Background Extreme rainfall and flooding events are projected to increase in frequency and disturb biogeochemical cycles such as the nitrogen(N)cycle.By combining trees and grasses,silvopastoral agroforestry is expected to increase the stability of this cycle in response to flooding.However,little is known about the response of nitrification to flooding in silvopastoral systems.Aim of this study was to assess nitrification stability in response to flooding and identify the main causal relations that drive it in temperate silvopastures.Methods The nitrification stability(i.e.,resistance and resilience)was assessed in two silvopastoral systems(i.e.,hedgerows and alley cropping)at three positions relative to the trees.The resistance and resilience of nitrification potential were measured in the laboratory after four weeks of flooding stress and four weeks after the end of the stress,respectively.For the first time,we used multigroup latent structural equation modeling(ML-SEM)to explore the spatial structure of causal relations between nitrification stability and soil properties across all positions of the two silvopastoral systems.Results Tree rows of both systems favored nitrification resistance,while the mean nitrification potential under flooded conditions was on average 27%and 35%higher as compared to non-stressed soils at the two positions assessed in the grass alleys.ML-SEM revealed that the causal relations that explained these results differed between the two systems.The ML-SEM models tested were unable to explain the causal relations in the hedgerow system.However,the model that considered a covariance between soil physical properties and soil resources availability(model A)was able to explain them in the alley-cropping system.It revealed that causal relations explaining nitrification stability varied according to the position relative to the trees:in the tree rows nitrification stability was associated with higher soil organic carbon concentration and earthworm abundance;in the grass alleys it was associated with higher soil organic carbon concentration and soil bulk density.Conclusions This study indicates that silvopastoral systems help regulate the N cycle near the trees.The results further imply that improvements in soil organic carbon concentration and soil bulk density favor the regulation of N-related processes in grasslands.展开更多
In this paper, we present a mathematical model that describes tumor-normal cells inter- action dynamics focusing on role of drugs in treatment of brain tumors. The goal is to predict distribution and necessary quantit...In this paper, we present a mathematical model that describes tumor-normal cells inter- action dynamics focusing on role of drugs in treatment of brain tumors. The goal is to predict distribution and necessary quantity of drugs delivered in drug-therapy by using optimal control framework. The model describes interactions of tumor and normal cells using a system of reactions^diffusion equations involving the drug concentration, tumor cells and normal tissues. The control estimates simultaneously blood perfusion rate, reabsorption rate of drug and drug dosage administered, which affect the effects of brain tumor chemotherapy. First, we develop mathematical framework which mod- els the competition between tumor and normal cells under chemotherapy constraints. Then, existence, uniqueness and regularity of solution of state equations are proved as well as stability results. Afterwards, optimal control problems are formulated in order to minimize the drug delivery and tumor cell burden in different situations. We show existence and uniqueness of optimal solution, and we derive necessary conditions for optimality. Finally, to solve numerically optimal control and optimization problems, we propose and investigate an adjoint multiple-relaxation-time lattice Boltzmann method for a general nonlinear coupled anisotropic convection-diffusion system （which includes the developed model for brain tumor targeted drug delivery system）.展开更多
文摘An efficient and accurate exponential wave integrator Fourier pseudospectral （EWI-FP） method is proposed and analyzed for solving the symmetric regularized-long-wave （SRLW） equation, which is used for modeling the weakly nonlinear ion acoustic and space-charge waves. The numerical method here is based on a Gautschi-type exponential wave integrator for temporal approximation and the Fourier pseudospectral method for spatial discretization. The scheme is fully explicit and efficient due to the fast Fourier transform. Numerical analysis of the proposed EWI-FP method is carried out and rigorous error estimates are established without CFL-type condition by means of the mathematical induction. The error bound shows that EWI-FP has second order accuracy in time and spectral accuracy in space. Numerical results are reported to confirm the theoretical studies and indicate that the error bound here is optimal.
基金Supported by the National Basic Research Programme (No.2007CB814902).
文摘The objective of this paper is to introduce elementary discrete reflected backward equations and to give a simple method to discretize in time a （continuous） reflected backward equation. A presentation of numerical simulations is also described.
文摘In what follows, we consider the relation between Aldous's extended convergence and weak convergence of nitrations. We prove that, for a sequence (Xn) of J_t^n)-special semimartingales, with canonical decomposition Xn = Mn + An, if the extended convergence (Xn.Jrn)→ (X,F.) holds with a quasi-left continuous (Ft)-special semimartingale X = M + A, then, under an additional assumption of uniform integrability,we get the convergence in probability under the Skorokhod topology: Mn→M and An→A.
文摘We consider the empirical spectral distribution （ESD） of a random matrix from the Gaussian Unitary Ensemble. Based on the Plancherel-Rotaeh approximation formula for Hermite polynomials, we prove that the expected empirical spectral distribution converges at the rate of O（n^-1） to the Wigner distribution function uniformly on every compact intervals [u,v] within the limiting support （-1, 1）. Furthermore, the variance of the ESD for such an interval is proved to be （πn）^-2 logn asymptotically which surprisingly enough, does not depend on the details （e.g. length or location） of the interval, This property allows us to determine completely the covariance function between the values of the ESD on two intervals.
基金supported by ISFMA,Fudan University,China and CNRS,France
文摘The author shows the existence of long-time averages to turbulent solutions of the Navier-Stokes equations and determines the equations satisfied by them, involving a Reynolds stress that is shown to be dissipative.
基金supported by the group GNAMPA of INd AM and the University of Pisa,under grantPRA 201852 UNIPI。
文摘In this paper the authors present a derivation of a back-scatter rotational Large Eddy Simulation model,which is the extension of the Baldwin&Lomax model to nonequilibrium problems.The model is particularly designed to mathematically describe a fluid filling a domain with solid walls and consequently the differential operators appearing in the smoothing terms are degenerate at the boundary.After the derivation of the model,the authors prove some of the mathematical properties coming from the weighted energy estimates,which allow to prove existence and uniqueness of a class of regular weak solutions.
基金financially supported by La Fondation de France(grant no.00117721/WB-2021-35937).
文摘Background Extreme rainfall and flooding events are projected to increase in frequency and disturb biogeochemical cycles such as the nitrogen(N)cycle.By combining trees and grasses,silvopastoral agroforestry is expected to increase the stability of this cycle in response to flooding.However,little is known about the response of nitrification to flooding in silvopastoral systems.Aim of this study was to assess nitrification stability in response to flooding and identify the main causal relations that drive it in temperate silvopastures.Methods The nitrification stability(i.e.,resistance and resilience)was assessed in two silvopastoral systems(i.e.,hedgerows and alley cropping)at three positions relative to the trees.The resistance and resilience of nitrification potential were measured in the laboratory after four weeks of flooding stress and four weeks after the end of the stress,respectively.For the first time,we used multigroup latent structural equation modeling(ML-SEM)to explore the spatial structure of causal relations between nitrification stability and soil properties across all positions of the two silvopastoral systems.Results Tree rows of both systems favored nitrification resistance,while the mean nitrification potential under flooded conditions was on average 27%and 35%higher as compared to non-stressed soils at the two positions assessed in the grass alleys.ML-SEM revealed that the causal relations that explained these results differed between the two systems.The ML-SEM models tested were unable to explain the causal relations in the hedgerow system.However,the model that considered a covariance between soil physical properties and soil resources availability(model A)was able to explain them in the alley-cropping system.It revealed that causal relations explaining nitrification stability varied according to the position relative to the trees:in the tree rows nitrification stability was associated with higher soil organic carbon concentration and earthworm abundance;in the grass alleys it was associated with higher soil organic carbon concentration and soil bulk density.Conclusions This study indicates that silvopastoral systems help regulate the N cycle near the trees.The results further imply that improvements in soil organic carbon concentration and soil bulk density favor the regulation of N-related processes in grasslands.
文摘In this paper, we present a mathematical model that describes tumor-normal cells inter- action dynamics focusing on role of drugs in treatment of brain tumors. The goal is to predict distribution and necessary quantity of drugs delivered in drug-therapy by using optimal control framework. The model describes interactions of tumor and normal cells using a system of reactions^diffusion equations involving the drug concentration, tumor cells and normal tissues. The control estimates simultaneously blood perfusion rate, reabsorption rate of drug and drug dosage administered, which affect the effects of brain tumor chemotherapy. First, we develop mathematical framework which mod- els the competition between tumor and normal cells under chemotherapy constraints. Then, existence, uniqueness and regularity of solution of state equations are proved as well as stability results. Afterwards, optimal control problems are formulated in order to minimize the drug delivery and tumor cell burden in different situations. We show existence and uniqueness of optimal solution, and we derive necessary conditions for optimality. Finally, to solve numerically optimal control and optimization problems, we propose and investigate an adjoint multiple-relaxation-time lattice Boltzmann method for a general nonlinear coupled anisotropic convection-diffusion system （which includes the developed model for brain tumor targeted drug delivery system）.
