This paper deal with optimal control problems for a non-stationary Stokes system. We study a simultaneous distributed-boundary optimal control problem with distributed observation. We prove the existence and uniquenes...This paper deal with optimal control problems for a non-stationary Stokes system. We study a simultaneous distributed-boundary optimal control problem with distributed observation. We prove the existence and uniqueness of a simultaneous optimal control and we give the first order optimality condition for this problem. We also consider a distributed optimal control problem and a boundary optimal control problem and we obtain estimations between the simultaneous optimal control and the optimal controls of these last ones. Finally, some regularity results are presented.展开更多
Through the estimates for Greens function of linearized system, we obtain L p estimates of the asymptotic behavior of solutions of the Cauchy problem for the Navier Stokes systems of compressible flow in seve...Through the estimates for Greens function of linearized system, we obtain L p estimates of the asymptotic behavior of solutions of the Cauchy problem for the Navier Stokes systems of compressible flow in several space dimensions.展开更多
This paper focuses on the higher order fractional differentiability of weak solution pairs to the following nonlinear stationary Stokes system{div A(x-Du)-■π=divF,inΩdivu=0,inΩ.In terms of the difference quotient ...This paper focuses on the higher order fractional differentiability of weak solution pairs to the following nonlinear stationary Stokes system{div A(x-Du)-■π=divF,inΩdivu=0,inΩ.In terms of the difference quotient method,our first result reveals that if F∈B_(p,q.loc)^(β)(Ω,R^(n))for p=2 and 1≤q≤2n/n-2β,then such extra Besov regularity can transfer to the symmetric gradient Du and its pressureπwith no losses under a suitable fractional differentiability assumption on x■A(x,ξ).Furthermore,when the vector field A(x,Du)is simplified to the full gradient■u,we improve the aforementioned Besov regularity for all integrability exponents p and q by establishing a new Campanato-type decay estimates for(■u,π).展开更多
Pressure correction methods constitute the most widely used solvers for the timedependent Navier-Stokes equations.There are several different pressure correction methods,where each time step usually consists in a pred...Pressure correction methods constitute the most widely used solvers for the timedependent Navier-Stokes equations.There are several different pressure correction methods,where each time step usually consists in a predictor step for a non-divergence-free velocity,followed by a Poisson problem for the pressure(or pressure update),and a final velocity correction to obtain a divergence-free vector field.In some situations,the equations for the velocities are solved explicitly,so that the numerical most expensive step is the elliptic pressure problem.We here propose to solve this Poisson problem by a domain decomposition method which does not need any communication between the sub-regions.Hence,this system is perfectly adapted for parallel computation.We show under certain assumptions that this new scheme has the same order of convergence as the original pressure correction scheme(with global projection).Numerical examples for the Stokes system show the effectivity of this new pressure correction method.The convergence order O(k^2)for resulting velocity fields can be observed in the norm l^2(0,T;L^2(Ω)).展开更多
This paper builds a bridge between partial regularity theory and nonlinear potential theory for the following generalized stationary Stokes system with super-quadratic growth and continuous coefficients:-div A(x,Du)+...This paper builds a bridge between partial regularity theory and nonlinear potential theory for the following generalized stationary Stokes system with super-quadratic growth and continuous coefficients:-div A(x,Du)+■π=f,div u=0,where Du is the symmetric part of the gradient■u.We first establish anε-regularity criterion involving both the excess functional of the symmetric gradient Du and Wolff potentials of the nonhomogeneous term f to guarantee the local vanishing mean oscillation(VMO)-regularity of Du in an open subset Ω_(u) of Ω with full measure.Such anε-regularity criterion leads to a pointwise Wolff potential estimate of Du,which immediately infers that Du is partially C^(0)-regular under appropriate assumptions.Finally,we give a local continuous modulus estimate of Du.展开更多
The magnetic field is one of the most important parameters in solar physics,and a polarimeter is the key device to measure the solar magnetic field.Liquid crystals based Stokes polarimeter is a novel technology,and wi...The magnetic field is one of the most important parameters in solar physics,and a polarimeter is the key device to measure the solar magnetic field.Liquid crystals based Stokes polarimeter is a novel technology,and will be applied for magnetic field measurement in the first space-based solar observatory satellite developed by China,Advanced Space-based Solar Observatory.However,the liquid crystals based Stokes polarimeter in space is not a mature technology.Therefore,it is of great scientific significance to study the control method and characteristics of the device.The retardation produced by a liquid crystal variable retarder is sensitive to the temperature,and the retardation changes 0.09°per 0.10℃.The error in polarization measurement caused by this change is 0.016,which affects the accuracy of magnetic field measurement.In order to ensure the stability of its performance,this paper proposes a high-precision temperature control system for liquid crystals based Stokes polarimeter in space.In order to optimize the structure design and temperature control system,the temperature field of liquid crystals based Stokes polarimeter is analyzed by the finite element method,and the influence of light on the temperature field of the liquid crystal variable retarder is analyzed theoretically.By analyzing the principle of highprecision temperature measurement in space,a high-precision temperature measurement circuit based on integrated operational amplifier,programmable amplifier and 12 bit A/D is designed,and a high-precision space temperature control system is developed by applying the integral separation PI temperature control algorithm and PWM driving heating films.The experimental results show that the effect of temperature control is accurate and stable,whenever the liquid crystals based Stokes polarimeter is either in the air or vacuum.The temperature stability is within±0.0150℃,which demonstrates greatly improved stability for the liquid crystals based Stokes polarimeter.展开更多
Given initial data(ρ0, u0) satisfying 0 < m ρ0≤ M, ρ0- 1 ∈ L2∩˙W1,r(R3) and u0 ∈˙H-2δ∩ H1(R3) for δ∈ ]1/4, 1/2[ and r ∈ ]6, 3/1- 2δ[, we prove that: there exists a small positive constant ε1,which d...Given initial data(ρ0, u0) satisfying 0 < m ρ0≤ M, ρ0- 1 ∈ L2∩˙W1,r(R3) and u0 ∈˙H-2δ∩ H1(R3) for δ∈ ]1/4, 1/2[ and r ∈ ]6, 3/1- 2δ[, we prove that: there exists a small positive constant ε1,which depends on the norm of the initial data, so that the 3-D incompressible inhomogeneous Navier-Stokes system with variable viscosity has a unique global strong solution(ρ, u) whenever‖ u0‖ L2 ‖▽u0 ‖L2 ≤ε1 and ‖μ(ρ0)- 1‖ L∞≤ε0 for some uniform small constant ε0. Furthermore, with smoother initial data and viscosity coefficient, we can prove the propagation of the regularities for such strong solution.展开更多
In this paper, a new analytical method of symplectic system, Hamiltonian system, is introduced for solving the problem of the Stokes flow in a two-dimensional rectangular domain. In the system, the fundamental problem...In this paper, a new analytical method of symplectic system, Hamiltonian system, is introduced for solving the problem of the Stokes flow in a two-dimensional rectangular domain. In the system, the fundamental problem is reduced to an eigenvalue and eigensolution problem. The solution and boundary conditions can be expanded by eigensolutions using adjoint relationships of the symplectic ortho-normalization between the eigensolutions. A closed method of the symplectic eigensolution is presented based on completeness of the symplectic eigensolution space. The results show that fundamental flows can be described by zero eigenvalue eigensolutions, and local effects by nonzero eigenvalue eigensolutions. Numerical examples give various flows in a rectangular domain and show effectiveness of the method for solving a variety of problems. Meanwhile, the method can be used in solving other problems.展开更多
We prove the asymptotic properties of the solutions to the 3D Navier–Stokes system with singular external force, by making use of Fourier localization method, the Littlewood–Paley theory and some subtle estimates in...We prove the asymptotic properties of the solutions to the 3D Navier–Stokes system with singular external force, by making use of Fourier localization method, the Littlewood–Paley theory and some subtle estimates in Fourier–Herz space. The main idea of the proof is motivated by that of Cannone et al. [J. Differential Equations, 314, 316–339(2022)]. We deal either with the nonstationary problem or with the stationary problem where solution may be singular due to singular external force. In this paper, the Fourier–Herz space includes the function space of pseudomeasure type used in Cannone et al. [J. Differential Equations, 314, 316–339(2022)]展开更多
Polarization filtering and atomic cell filtering are applied in the identification of Stokes signals in an atomic ensemble, and reduce the noise to a level of 10-5 and 10-4 respectively. Good Stokes signals are then o...Polarization filtering and atomic cell filtering are applied in the identification of Stokes signals in an atomic ensemble, and reduce the noise to a level of 10-5 and 10-4 respectively. Good Stokes signals are then obtained. In this article the two filtering systems and the final Stokes output are presented, and the optimization of the polarization filtering system is highlighted.展开更多
The aggressive nature and high mortality rate of lung cancer underscore the imperative need for early diagnosis of the disease.Thus,aminopeptidase N(APN),a potential biomarker for lung cancer,should be thoroughly inve...The aggressive nature and high mortality rate of lung cancer underscore the imperative need for early diagnosis of the disease.Thus,aminopeptidase N(APN),a potential biomarker for lung cancer,should be thoroughly investigated in this context.This report describes the development of HA-apn,a novel near-infrared fluorescent probe,specifically engineered for the sensitive detection of endogenous APN.Characterized by its high selectivity,straightforward molecular architecture,and suitable optical properties,including a long-wavelength emission at 835 nm and a large Stokes shift of 285 nm,HA-apn had high efficacy in identifying overexpressed APN in tumor cells,which shows its potential in pinpointing malignancies.To further validate its applicability and effectiveness in facilitating the direct and enhanced visualization of pulmonary alterations,an in situ lung cancer mouse model was employed.Notably,HAapn was applied for in vivo imaging of APN activity in the lung cancer mouse model receiving the probe through aerosol inhalation,and rapid and precise diagnostic results were achieved within 30min postadministration.Overall,HA-apn can be applied as an effective,non-intrusive tool for the rapid and accurate detection of pulmonary conditions.展开更多
Red fluorescent proteins with large Stokes shift(LSS-RFPs)are advantageous for multicolor imaging applications that allow simultaneous visualizations of multiple biological events.But it is difficult to develop LSS-RF...Red fluorescent proteins with large Stokes shift(LSS-RFPs)are advantageous for multicolor imaging applications that allow simultaneous visualizations of multiple biological events.But it is difficult to develop LSS-RFPs by extending the emission wavelength of RFPs to far-red region.Here,we employed Forster resonance energy transfer(FRET)strategy to engineer the far-red fluorescent proteins with large Stokes shift.LSS-m Apple and LSS-mCherry were constructed by fusing HaloTag to m Apple and mCherry,allowing the fluorophore TMSi R to be connected to these RFPs.FRET between RFPs and TMSi R enabled them to apply the excitation of donor RFPs to emit far-red fluorescence of acceptor TMSi R.The Stokes shifts of LSS-m Apple and LSS-mCherry were 97 nm and 75 nm,respectively.The high FRET efficiency of LSS-mCherry(E_(FRET)=83.7%)can greatly reduce the fluorescence from the donor channel,which did not affect co-imaging with mCherry.In addition,LSS-mCherry also showed excellent photostability(t_(1/2)=449.3 s),enabling stable confocal fluorescence imaging for 15 min under continuous strong excitation.Furthermore,LSS-mCherry was applied for fluorescence labeling and imaging of the nucleus,mitochondria,lysosomes,and endoplasmic reticulum in living cells.Finally,we applied LSS-mCherry to perform multi-color bioimaging of 2–4 channels,and there was no obvious crosstalk between these channels.展开更多
The Stokes–Einstein–Debye(SED) relation in TIP5P water is tested with the original formula and its variants within the temperature range 240–390 K. The results indicate that although the variants explicitly break d...The Stokes–Einstein–Debye(SED) relation in TIP5P water is tested with the original formula and its variants within the temperature range 240–390 K. The results indicate that although the variants explicitly break down, the original SED relation is almost valid. Compared with the Stokes–Einstein relation, no explicit decoupling is observed in translational and rotational motion. Variation of the effective hydrodynamic radius is critical to testing the validity of the SED relation.展开更多
基金partially supported by PIP No.0534 from CONICET-Univ.AustralPPI No.18C417 from SECy T-UNRCpartially supported by AVENTURES-ANR-12-BLAN-BS01-0001-01
文摘This paper deal with optimal control problems for a non-stationary Stokes system. We study a simultaneous distributed-boundary optimal control problem with distributed observation. We prove the existence and uniqueness of a simultaneous optimal control and we give the first order optimality condition for this problem. We also consider a distributed optimal control problem and a boundary optimal control problem and we obtain estimations between the simultaneous optimal control and the optimal controls of these last ones. Finally, some regularity results are presented.
文摘Through the estimates for Greens function of linearized system, we obtain L p estimates of the asymptotic behavior of solutions of the Cauchy problem for the Navier Stokes systems of compressible flow in several space dimensions.
基金Supported by the National Natural Science Foundation of China(Grant Nos.12071229,12101452)Tianjin Normal University Doctoral Research Project(Grant No.52XB2110)。
文摘This paper focuses on the higher order fractional differentiability of weak solution pairs to the following nonlinear stationary Stokes system{div A(x-Du)-■π=divF,inΩdivu=0,inΩ.In terms of the difference quotient method,our first result reveals that if F∈B_(p,q.loc)^(β)(Ω,R^(n))for p=2 and 1≤q≤2n/n-2β,then such extra Besov regularity can transfer to the symmetric gradient Du and its pressureπwith no losses under a suitable fractional differentiability assumption on x■A(x,ξ).Furthermore,when the vector field A(x,Du)is simplified to the full gradient■u,we improve the aforementioned Besov regularity for all integrability exponents p and q by establishing a new Campanato-type decay estimates for(■u,π).
文摘Pressure correction methods constitute the most widely used solvers for the timedependent Navier-Stokes equations.There are several different pressure correction methods,where each time step usually consists in a predictor step for a non-divergence-free velocity,followed by a Poisson problem for the pressure(or pressure update),and a final velocity correction to obtain a divergence-free vector field.In some situations,the equations for the velocities are solved explicitly,so that the numerical most expensive step is the elliptic pressure problem.We here propose to solve this Poisson problem by a domain decomposition method which does not need any communication between the sub-regions.Hence,this system is perfectly adapted for parallel computation.We show under certain assumptions that this new scheme has the same order of convergence as the original pressure correction scheme(with global projection).Numerical examples for the Stokes system show the effectivity of this new pressure correction method.The convergence order O(k^2)for resulting velocity fields can be observed in the norm l^2(0,T;L^2(Ω)).
基金supported by National Natural Science Foundation of China (Grant Nos. 12101452 and 12071229)。
文摘This paper builds a bridge between partial regularity theory and nonlinear potential theory for the following generalized stationary Stokes system with super-quadratic growth and continuous coefficients:-div A(x,Du)+■π=f,div u=0,where Du is the symmetric part of the gradient■u.We first establish anε-regularity criterion involving both the excess functional of the symmetric gradient Du and Wolff potentials of the nonhomogeneous term f to guarantee the local vanishing mean oscillation(VMO)-regularity of Du in an open subset Ω_(u) of Ω with full measure.Such anε-regularity criterion leads to a pointwise Wolff potential estimate of Du,which immediately infers that Du is partially C^(0)-regular under appropriate assumptions.Finally,we give a local continuous modulus estimate of Du.
基金the National Natural Science Foundation of China(Grant Nos.11427803,11427901 and 11773040)the Strategic Pioneer Program on Space Science,Chinese Academy of Sciences(CAS)(XDA04061002 and XDA15010800)the Public Technology Service Center,National Astronomical Observatories of CAS(829011V01)。
文摘The magnetic field is one of the most important parameters in solar physics,and a polarimeter is the key device to measure the solar magnetic field.Liquid crystals based Stokes polarimeter is a novel technology,and will be applied for magnetic field measurement in the first space-based solar observatory satellite developed by China,Advanced Space-based Solar Observatory.However,the liquid crystals based Stokes polarimeter in space is not a mature technology.Therefore,it is of great scientific significance to study the control method and characteristics of the device.The retardation produced by a liquid crystal variable retarder is sensitive to the temperature,and the retardation changes 0.09°per 0.10℃.The error in polarization measurement caused by this change is 0.016,which affects the accuracy of magnetic field measurement.In order to ensure the stability of its performance,this paper proposes a high-precision temperature control system for liquid crystals based Stokes polarimeter in space.In order to optimize the structure design and temperature control system,the temperature field of liquid crystals based Stokes polarimeter is analyzed by the finite element method,and the influence of light on the temperature field of the liquid crystal variable retarder is analyzed theoretically.By analyzing the principle of highprecision temperature measurement in space,a high-precision temperature measurement circuit based on integrated operational amplifier,programmable amplifier and 12 bit A/D is designed,and a high-precision space temperature control system is developed by applying the integral separation PI temperature control algorithm and PWM driving heating films.The experimental results show that the effect of temperature control is accurate and stable,whenever the liquid crystals based Stokes polarimeter is either in the air or vacuum.The temperature stability is within±0.0150℃,which demonstrates greatly improved stability for the liquid crystals based Stokes polarimeter.
基金supported by National Natural Science Foundation of China(Grant Nos.10421101 and 10931007)the Fellowship from Chinese Academy of Sciences and Innovation Grant from National Center for Mathematics and Interdisciplinary Sciences
文摘Given initial data(ρ0, u0) satisfying 0 < m ρ0≤ M, ρ0- 1 ∈ L2∩˙W1,r(R3) and u0 ∈˙H-2δ∩ H1(R3) for δ∈ ]1/4, 1/2[ and r ∈ ]6, 3/1- 2δ[, we prove that: there exists a small positive constant ε1,which depends on the norm of the initial data, so that the 3-D incompressible inhomogeneous Navier-Stokes system with variable viscosity has a unique global strong solution(ρ, u) whenever‖ u0‖ L2 ‖▽u0 ‖L2 ≤ε1 and ‖μ(ρ0)- 1‖ L∞≤ε0 for some uniform small constant ε0. Furthermore, with smoother initial data and viscosity coefficient, we can prove the propagation of the regularities for such strong solution.
文摘In this paper, a new analytical method of symplectic system, Hamiltonian system, is introduced for solving the problem of the Stokes flow in a two-dimensional rectangular domain. In the system, the fundamental problem is reduced to an eigenvalue and eigensolution problem. The solution and boundary conditions can be expanded by eigensolutions using adjoint relationships of the symplectic ortho-normalization between the eigensolutions. A closed method of the symplectic eigensolution is presented based on completeness of the symplectic eigensolution space. The results show that fundamental flows can be described by zero eigenvalue eigensolutions, and local effects by nonzero eigenvalue eigensolutions. Numerical examples give various flows in a rectangular domain and show effectiveness of the method for solving a variety of problems. Meanwhile, the method can be used in solving other problems.
基金Supported by the National Natural Science Foundation of China (Grant No. 11771423)。
文摘We prove the asymptotic properties of the solutions to the 3D Navier–Stokes system with singular external force, by making use of Fourier localization method, the Littlewood–Paley theory and some subtle estimates in Fourier–Herz space. The main idea of the proof is motivated by that of Cannone et al. [J. Differential Equations, 314, 316–339(2022)]. We deal either with the nonstationary problem or with the stationary problem where solution may be singular due to singular external force. In this paper, the Fourier–Herz space includes the function space of pseudomeasure type used in Cannone et al. [J. Differential Equations, 314, 316–339(2022)]
基金Project supported by the National Natural Science Foundation of China (Grant Nos 10474053 and 10574162)Tsinghua University 985 (Grant No 051110001)
文摘Polarization filtering and atomic cell filtering are applied in the identification of Stokes signals in an atomic ensemble, and reduce the noise to a level of 10-5 and 10-4 respectively. Good Stokes signals are then obtained. In this article the two filtering systems and the final Stokes output are presented, and the optimization of the polarization filtering system is highlighted.
基金supported by the National Natural Science Foundation of China(Nos.22004046 and 22074052)the Science and Technology Developing Foundation of Jilin Province of China(Nos.20240404044ZP,20230101033JC and 20220505015ZP).
文摘The aggressive nature and high mortality rate of lung cancer underscore the imperative need for early diagnosis of the disease.Thus,aminopeptidase N(APN),a potential biomarker for lung cancer,should be thoroughly investigated in this context.This report describes the development of HA-apn,a novel near-infrared fluorescent probe,specifically engineered for the sensitive detection of endogenous APN.Characterized by its high selectivity,straightforward molecular architecture,and suitable optical properties,including a long-wavelength emission at 835 nm and a large Stokes shift of 285 nm,HA-apn had high efficacy in identifying overexpressed APN in tumor cells,which shows its potential in pinpointing malignancies.To further validate its applicability and effectiveness in facilitating the direct and enhanced visualization of pulmonary alterations,an in situ lung cancer mouse model was employed.Notably,HAapn was applied for in vivo imaging of APN activity in the lung cancer mouse model receiving the probe through aerosol inhalation,and rapid and precise diagnostic results were achieved within 30min postadministration.Overall,HA-apn can be applied as an effective,non-intrusive tool for the rapid and accurate detection of pulmonary conditions.
基金supported by the National Natural Science Foundation of China(Nos.22225806,22078314,22278394,22378385)Dalian Institute of Chemical Physics(Nos.DICPI202142,DICPI202436)。
文摘Red fluorescent proteins with large Stokes shift(LSS-RFPs)are advantageous for multicolor imaging applications that allow simultaneous visualizations of multiple biological events.But it is difficult to develop LSS-RFPs by extending the emission wavelength of RFPs to far-red region.Here,we employed Forster resonance energy transfer(FRET)strategy to engineer the far-red fluorescent proteins with large Stokes shift.LSS-m Apple and LSS-mCherry were constructed by fusing HaloTag to m Apple and mCherry,allowing the fluorophore TMSi R to be connected to these RFPs.FRET between RFPs and TMSi R enabled them to apply the excitation of donor RFPs to emit far-red fluorescence of acceptor TMSi R.The Stokes shifts of LSS-m Apple and LSS-mCherry were 97 nm and 75 nm,respectively.The high FRET efficiency of LSS-mCherry(E_(FRET)=83.7%)can greatly reduce the fluorescence from the donor channel,which did not affect co-imaging with mCherry.In addition,LSS-mCherry also showed excellent photostability(t_(1/2)=449.3 s),enabling stable confocal fluorescence imaging for 15 min under continuous strong excitation.Furthermore,LSS-mCherry was applied for fluorescence labeling and imaging of the nucleus,mitochondria,lysosomes,and endoplasmic reticulum in living cells.Finally,we applied LSS-mCherry to perform multi-color bioimaging of 2–4 channels,and there was no obvious crosstalk between these channels.
基金Project supported by the National Natural Science Foundation of China (Grant No. 12104502)the Natural Science Foundation of Sichuan Province (Grant No. 2023YFG0308)the Fundamental Research Funds for the Central Universities (Grant No. 24CAFUC03057)。
文摘The Stokes–Einstein–Debye(SED) relation in TIP5P water is tested with the original formula and its variants within the temperature range 240–390 K. The results indicate that although the variants explicitly break down, the original SED relation is almost valid. Compared with the Stokes–Einstein relation, no explicit decoupling is observed in translational and rotational motion. Variation of the effective hydrodynamic radius is critical to testing the validity of the SED relation.
