In this paper, we consider the global existence of classical solution to the 3-D compressible Navier-Stokes equations with a density-dependent viscosity coefficient λ(ρ)provided that the initial energy is small in s...In this paper, we consider the global existence of classical solution to the 3-D compressible Navier-Stokes equations with a density-dependent viscosity coefficient λ(ρ)provided that the initial energy is small in some sense. In our result, we give a relation between the initial energy and the viscosity coefficient μ, and it shows that the initial energy can be large if the coefficient of the viscosity μ is taken to be large, which implies that large viscosity μ means large solution.展开更多
We study the large-time behavior toward viscous shock waves to the Cauchy problem of the one-dimensional compressible isentropic Navier-Stokes equations with density- dependent viscosity. The nonlinear stability of th...We study the large-time behavior toward viscous shock waves to the Cauchy problem of the one-dimensional compressible isentropic Navier-Stokes equations with density- dependent viscosity. The nonlinear stability of the viscous shock waves is shown for certain class of large initial perturbation with integral zero which can allow the initial density to have large oscillation. Our analysis relies upon the technique developed by Kanel~ and the continuation argument.展开更多
This paper is concerned with the Navier-Stokes/Allen-Cahn system,which is used to model the dynamics of immiscible two-phase flows.We consider a 1D free boundary problem and assume that the viscosity coefficient depen...This paper is concerned with the Navier-Stokes/Allen-Cahn system,which is used to model the dynamics of immiscible two-phase flows.We consider a 1D free boundary problem and assume that the viscosity coefficient depends on the density in the form ofη(ρ)=ρ^(α).The existence of unique global H^(2m)-solutions(m∈N)to the free boundary problem is proven for when 0<α<1/4.Furthermore,we obtain the global C^(∞)-solutions if the initial data is smooth.展开更多
In this paper, we investigate the free boundary value problem （FBVP） for the cylindrically symmetric isentropic compressible Navier-Stokes equations （CNS） with density- dependent viscosity coefficients in the case...In this paper, we investigate the free boundary value problem （FBVP） for the cylindrically symmetric isentropic compressible Navier-Stokes equations （CNS） with density- dependent viscosity coefficients in the case that across the free surface stress tensor is balanced by a constant exterior pressure. Under certain assumptions imposed on the initial data, we prove that there exists a unique global strong solution which tends pointwise to a non-vacuum equilibrium state at an exponential time-rate as the time tends to infinity.展开更多
The global existence of solutions to the equations of one-dimensional compressible flow with density-dependent viscosity is proved. Specifically,the assumptions on initial data are that the modulo constant is stated a...The global existence of solutions to the equations of one-dimensional compressible flow with density-dependent viscosity is proved. Specifically,the assumptions on initial data are that the modulo constant is stated at x=∞ ＋and x=-∞ ,which may be different ,the density and velocity are in L^z ,and the density is bounded above and below away from zero. The results also show that even under these conditions, neither vacuum states nor concentration states can be formed in finite time.展开更多
In this paper,we prove the existence of general Cartesian vector solutions u=b(t)+A(t)x for the Ndimensional compressible Navier–Stokes equations with density-dependent viscosity,based on the matrix and curve integra...In this paper,we prove the existence of general Cartesian vector solutions u=b(t)+A(t)x for the Ndimensional compressible Navier–Stokes equations with density-dependent viscosity,based on the matrix and curve integration theory.Two exact solutions are obtained by solving the reduced systems.展开更多
This paper is devoted to studying the zero dissipation limit problem for the one-dimensional compressible Navier-Stokes equations with selected density-dependent viscosity.In particular,we focus our attention on the v...This paper is devoted to studying the zero dissipation limit problem for the one-dimensional compressible Navier-Stokes equations with selected density-dependent viscosity.In particular,we focus our attention on the viscosity taking the formμ(ρ)=ρ^(ϵ)(ϵ>0).For the selected density-dependent viscosity,it is proved that the solutions of the one-dimensional compressible Navier-Stokes equations with centered rarefaction wave initial data exist for all time,and converge to the centered rarefaction waves as the viscosity vanishes,uniformly away from the initial discontinuities.New and subtle analysis is developed to overcome difficulties due to the selected density-dependent viscosity to derive energy estimates,in addition to the scaling argument and elementary energy analysis.Moreover,our results extend the studies in[Xin Z P.Comm Pure Appl Math,1993,46(5):621-665].展开更多
We consider the Cauchy problem, free boundary problem and piston problem for one-dimensional compressible Navier-Stokes equations with density-dependent viscosity. Using the reduction to absurdity method, we prove tha...We consider the Cauchy problem, free boundary problem and piston problem for one-dimensional compressible Navier-Stokes equations with density-dependent viscosity. Using the reduction to absurdity method, we prove that the weak solutions to these systems do not exhibit vacuum states, provided that no vacuum states are present initially. The essential re- quirements on the solutions are that the mass and energy of the fluid are locally integrable at each time, and the Lloc1-norm of the velocity gradient is locally integrable in time.展开更多
This paper studies the existence and uniqueness of local strong solutions to an Oldroyd-B model with density-dependent viscosity in a bounded domain Ω ⊂ R<sup>d</sup>, d = 2 or 3 via incompressible limit,...This paper studies the existence and uniqueness of local strong solutions to an Oldroyd-B model with density-dependent viscosity in a bounded domain Ω ⊂ R<sup>d</sup>, d = 2 or 3 via incompressible limit, in which the initial data is “well-prepared” and the velocity field enjoys the slip boundary conditions. The main idea is to derive the uniform energy estimates for nonlinear systems and corresponding incompressible limit.展开更多
In this article, we prove the local existence and uniqueness of the classical solution to the Cauchy problem of the 3-D compressible Navier-Stokes equations with large initial data and vacuum, if the shear viscosity ...In this article, we prove the local existence and uniqueness of the classical solution to the Cauchy problem of the 3-D compressible Navier-Stokes equations with large initial data and vacuum, if the shear viscosity μ is a positive constant and the bulk viscosity λ（ρ） = ρ^β with β≥0. Note that the initial data can be arbitrarily large to contain vacuum states.展开更多
In this paper,we consider the 3D compressible isentropic Navier-Stokes equations when the shear viscosityμis a positive constant and the bulk viscosity is λ(ρ)=ρ^(β) with β>2,which is a situation that was fir...In this paper,we consider the 3D compressible isentropic Navier-Stokes equations when the shear viscosityμis a positive constant and the bulk viscosity is λ(ρ)=ρ^(β) with β>2,which is a situation that was first introduced by Vaigant and Kazhikhov in[1].The global axisymmetric classical solution with arbitrarily large initial data in a periodic domain Ω={(r,z)|r=√x^(2)+y^(2),(x,y,z)∈R^(3),r∈I⊂(0,+∞),-∞<z<+∞} is obtained.Here the initial density keeps a non-vacuum state ρ>0 when z→±∞.Our results also show that the solution will not develop the vacuum state in any finite time,provided that the initial density is uniformly away from the vacuum.展开更多
The Navier-Stokes system for one-dimensional compressible fluids with density-dependent viscosities when the initial density connects to vacuum continuously is considered in the present paper. When the viscosity coeff...The Navier-Stokes system for one-dimensional compressible fluids with density-dependent viscosities when the initial density connects to vacuum continuously is considered in the present paper. When the viscosity coefficient u is proportional to pθ with 0 〈 θ 〈 1, the global existence and the uniqueness of weak solutions are proved which improves the previous results in [Vong, S. W., Yang, T., Zhu, C. J.： Compressible Navier-Stokes equations with degenerate viscosity coefficient and vacuum II. J. Differential Equations, 192（2）, 475-501 （2003）]. Here p is the density. Moreover, a stabilization rate estimate for the density as t → ＋∞ for any θ 〉 0 is also given.展开更多
We consider the Cauchy problem for one-dimensional compressible isentropic Navier-Stokes equations with density-dependent viscosity μ（ρ） = Aρα, where α〉 0 and A 〉0. The global existence of strong solutions is...We consider the Cauchy problem for one-dimensional compressible isentropic Navier-Stokes equations with density-dependent viscosity μ（ρ） = Aρα, where α〉 0 and A 〉0. The global existence of strong solutions is obtained, which improves the previous results by enlarging the interval of α. Moreover, our result shows that no vacuum is developed in a finite time provided the initial data does not contain vacuum.展开更多
In this paper,we study the one-dimensional motion of viscous gas with a general pres- sure law and a general density-dependent viscosity coefficient when the initial density connects to the vacuum state with a jump.We...In this paper,we study the one-dimensional motion of viscous gas with a general pres- sure law and a general density-dependent viscosity coefficient when the initial density connects to the vacuum state with a jump.We prove the global existence and the uniqueness of weak solutions to the compressible Navier-Stokes equations by using the line method.For this,some new a priori estimates are obtained to take care of the general viscosity coefficientμ(ρ)instead ofρ~θ.展开更多
In this paper, we consider the initial-boundary problem for a 1D two-fluid model with densitydependent viscosity and vacuum. The pressure depends on two variables but the viscosity only depends on one of the densities...In this paper, we consider the initial-boundary problem for a 1D two-fluid model with densitydependent viscosity and vacuum. The pressure depends on two variables but the viscosity only depends on one of the densities. We prove the global existence and uniqueness of the classical solution in the one-dimensional space with large initial data and vacuum. We use a new Helmholtz free energy function and the material derivative of the velocity field to deal with the general pressure with two variables, without the equivalence condition. We also develop a new argument to handle the general viscosity.展开更多
This paper is concerned with the Cauchy problems of one-dimensional compressible Navier-Stokes equations with density-dependent viscosity coefcients.By assumingρ0∈L1（R）,we will prove the existence of weak solution...This paper is concerned with the Cauchy problems of one-dimensional compressible Navier-Stokes equations with density-dependent viscosity coefcients.By assumingρ0∈L1（R）,we will prove the existence of weak solutions to the Cauchy problems forθ〉0.This will improve results in Jiu and Xin’s paper（Kinet.Relat.Models,1（2）：313–330（2008））in whichθ〉12is required.In addition,We will study the large time asymptotic behavior of such weak solutions.展开更多
The viscosity of refining slags plays a critical role in metallurgical processes.However,obtaining accurate viscosity data remains challenging due to the complexities of high-temperature experiments,often relying on e...The viscosity of refining slags plays a critical role in metallurgical processes.However,obtaining accurate viscosity data remains challenging due to the complexities of high-temperature experiments,often relying on empirical models with limited predictive capabilities.This study focuses on the influence of optical basicity on viscosity in CaO-Al_(2)O_(3)-based refining slags,leveraging machine learning to address data scarcity and improve prediction accuracy.An automated framework for algorithm integration,parameter tuning,and evaluation ranking framework(Auto-APE)is employed to develop customized data-driven models for various slag systems,including CaO-Al_(2)O_(3)-SiO_(2),CaO-Al_(2)O_(3)-CaF_(2),CaO-Al_(2)O_(3)-SiO_(2)-MgO,and CaO-Al_(2)O_(3)-SiO_(2)-MgO-CaF_(2).By incorporating optical basicity as a key feature,the models achieve an average validation error of 8.0%to 15.1%,significantly outperforming traditional empirical models.Additionally,symbolic regression is introduced to rapidly construct domain-specific features,such as optical basicity-like descriptors,offering a potential breakthrough in performance prediction for small datasets.This work highlights the critical role of domain-specific knowledge in understanding and predicting viscosity,providing a robust machine learning-based approach for optimizing refining slag properties.展开更多
Currently,the Al_(2)O_(3)content in the high-alumina slag systems within blast furnaces is generally limited to 16wt%–18.5wt%,making it challenging to overcome this limitation.Unlike most studies that concentrated on...Currently,the Al_(2)O_(3)content in the high-alumina slag systems within blast furnaces is generally limited to 16wt%–18.5wt%,making it challenging to overcome this limitation.Unlike most studies that concentrated on managing the MgO/Al_(2)O_(3)ratio or basicity,this paper explored the effect of equimolar substitution of MgO for CaO on the viscosity and structure of a high-alumina CaO-MgO-Al_(2)O_(3)-SiO_(2)slag system,providing theoretical guidance and data to facilitate the application of high-alumina ores.The results revealed that the viscosity first decreased and then increased with higher MgO substitution,reaching a minimum at 15mol%MgO concentration.Fourier transform infrared spectroscopy(FTIR)results found that the depths of the troughs representing[SiO_(4)]tetrahedra,[AlO_(4)]tetrahedra,and Si-O-Al bending became progressively deeper with increased MgO substitution.Deconvolution of the Raman spectra showed that the average number of bridging oxygens per Si atom and the X_(Q^(3))/X_(Q^(2))(X_(Q^(i))is the molar fraction of Q^(i) unit,and i is the number of bridging oxygens in a[SiO_(4)]tetrahedral unit)ratio increased from 2.30 and 1.02 to 2.52 and 2.14,respectively,indicating a progressive polymerization of the silicate structure.X-ray photoelectron spectroscopy(XPS)results highlighted that non-bridging oxygen content decreased from 77.97mol% to 63.41mol% with increasing MgO concentration,whereas bridging oxygen and free oxygen contents increased.Structural analysis demonstrated a gradual increase in the polymerization degree of the tetrahedral structure with the increase in MgO substitution.However,bond strength is another important factor affecting the slag viscosity.The occurrence of a viscosity minimum can be attributed to the complex evolution of bond strengths of non-bridging oxygens generated during depolymerization of the[SiO_(4)]and[AlO_(4)]tetrahedral structures by CaO and MgO.展开更多
PBQ[1-(4-chlorophenyl)-3-(pyridin-3-yl)urea],an enormous potent molluscicide,showed excellent Pomacea canaliculata(P.canaliculata)control activity and low toxicity for other aquatic organisms,but its snail-killing mec...PBQ[1-(4-chlorophenyl)-3-(pyridin-3-yl)urea],an enormous potent molluscicide,showed excellent Pomacea canaliculata(P.canaliculata)control activity and low toxicity for other aquatic organisms,but its snail-killing mechanisms are still not fully understood.We employed an optical method to elucidate PBQ action via a novel fluorescent viscosity probe,NCV.As the viscosity in the test solutions increased,compared with that in pure ethanol,a 54-fold fluorescence intensity enhancement of NCV was observed in 310 cP of 90%glycerol.Furthermore,NCV successfully exhibited a selective fluorescence response towards monensin-induced cellular viscosity changes in HepG2 cells.The liver,stomach,and foot plantar of the tested snails were frozen and sectioned for fluorescent imaging experiments after the treatment with different PBQ concentrations over various times.A significant fluorescent increase in the snail's liver was observed upon exposure to 0.75 mg/L PBQ for 72 h,which highlighted an increase in viscosity.Hematoxylin and eosin(HE)staining further supported PBQ-induced liver damage with a viscosity increase in P.canaliculata.Our study provides a new rapid optical visualization method to study the killing mechanisms of PBQ and may help discover new chemicals that control snail populations.展开更多
Colorectal cancer(CRC)is one of the most prevalent malignant tumors worldwide,exhibiting high morbidity and mortality.Lack of efficient tools for early diagnosis and surgical resection guidance of CRC have been a seri...Colorectal cancer(CRC)is one of the most prevalent malignant tumors worldwide,exhibiting high morbidity and mortality.Lack of efficient tools for early diagnosis and surgical resection guidance of CRC have been a serious threat to the long-term survival rate of the CRC patients.Recent studies have shown that relative higher viscosity was presented in tumor cells compared to that in normal cells,leading to viscosity as a potential biomarker for CRC.Herein,we reported the development of a series of novel viscosity-sensitive and mitochondria-specific fluorescent probes(HTB,HTI,and HTP)for CRC detection.Among them,HTB showed high sensitivity,minimal background interference,low cytotoxicity,and significant viscous response capability,making it an ideal tool for distinguishing colorectal tumor cells from normal cells.Importantly,we have successfully utilized HTB to visualize in a CRC-cells-derived xenograft(CDX)model,enriching its medical imaging capacity,which laid a foundation for further clinical translational application.展开更多
文摘In this paper, we consider the global existence of classical solution to the 3-D compressible Navier-Stokes equations with a density-dependent viscosity coefficient λ(ρ)provided that the initial energy is small in some sense. In our result, we give a relation between the initial energy and the viscosity coefficient μ, and it shows that the initial energy can be large if the coefficient of the viscosity μ is taken to be large, which implies that large viscosity μ means large solution.
基金supported by"the Fundamental Research Funds for the Central Universities"
文摘We study the large-time behavior toward viscous shock waves to the Cauchy problem of the one-dimensional compressible isentropic Navier-Stokes equations with density- dependent viscosity. The nonlinear stability of the viscous shock waves is shown for certain class of large initial perturbation with integral zero which can allow the initial density to have large oscillation. Our analysis relies upon the technique developed by Kanel~ and the continuation argument.
基金supported by the Key Project of the NSFC(12131010)the NSFC(11771155,12271032)+1 种基金the NSF of Guangdong Province(2021A1515010249,2021A1515010303)supported by the NSFC(11971179,12371205)。
文摘This paper is concerned with the Navier-Stokes/Allen-Cahn system,which is used to model the dynamics of immiscible two-phase flows.We consider a 1D free boundary problem and assume that the viscosity coefficient depends on the density in the form ofη(ρ)=ρ^(α).The existence of unique global H^(2m)-solutions(m∈N)to the free boundary problem is proven for when 0<α<1/4.Furthermore,we obtain the global C^(∞)-solutions if the initial data is smooth.
基金supported by NNSFC(11101145),supported by NNSFC(11326140 and11501323)China Postdoctoral Science Foundation(2012M520360)+1 种基金Doctoral Foundation of North China University of Water Sources and Electric Power(201032),Innovation Scientists and Technicians Troop Construction Projects of Henan Provincethe Doctoral Starting up Foundation of Quzhou University(BSYJ201314 and XNZQN201313)
文摘In this paper, we investigate the free boundary value problem （FBVP） for the cylindrically symmetric isentropic compressible Navier-Stokes equations （CNS） with density- dependent viscosity coefficients in the case that across the free surface stress tensor is balanced by a constant exterior pressure. Under certain assumptions imposed on the initial data, we prove that there exists a unique global strong solution which tends pointwise to a non-vacuum equilibrium state at an exponential time-rate as the time tends to infinity.
文摘The global existence of solutions to the equations of one-dimensional compressible flow with density-dependent viscosity is proved. Specifically,the assumptions on initial data are that the modulo constant is stated at x=∞ ＋and x=-∞ ,which may be different ,the density and velocity are in L^z ,and the density is bounded above and below away from zero. The results also show that even under these conditions, neither vacuum states nor concentration states can be formed in finite time.
基金This research is partially supported by the National Science Foundation of China(Grant No.11271079,10671095)RG 11/2015-2016R from the Education University of Hong Kong。
文摘In this paper,we prove the existence of general Cartesian vector solutions u=b(t)+A(t)x for the Ndimensional compressible Navier–Stokes equations with density-dependent viscosity,based on the matrix and curve integration theory.Two exact solutions are obtained by solving the reduced systems.
基金supported by the National Natural Science Foundation of China(11671319,11931013).
文摘This paper is devoted to studying the zero dissipation limit problem for the one-dimensional compressible Navier-Stokes equations with selected density-dependent viscosity.In particular,we focus our attention on the viscosity taking the formμ(ρ)=ρ^(ϵ)(ϵ>0).For the selected density-dependent viscosity,it is proved that the solutions of the one-dimensional compressible Navier-Stokes equations with centered rarefaction wave initial data exist for all time,and converge to the centered rarefaction waves as the viscosity vanishes,uniformly away from the initial discontinuities.New and subtle analysis is developed to overcome difficulties due to the selected density-dependent viscosity to derive energy estimates,in addition to the scaling argument and elementary energy analysis.Moreover,our results extend the studies in[Xin Z P.Comm Pure Appl Math,1993,46(5):621-665].
基金Project supported by the National Natural Science Foundation of China (No. 10571158) and the DFG
文摘We consider the Cauchy problem, free boundary problem and piston problem for one-dimensional compressible Navier-Stokes equations with density-dependent viscosity. Using the reduction to absurdity method, we prove that the weak solutions to these systems do not exhibit vacuum states, provided that no vacuum states are present initially. The essential re- quirements on the solutions are that the mass and energy of the fluid are locally integrable at each time, and the Lloc1-norm of the velocity gradient is locally integrable in time.
文摘This paper studies the existence and uniqueness of local strong solutions to an Oldroyd-B model with density-dependent viscosity in a bounded domain Ω ⊂ R<sup>d</sup>, d = 2 or 3 via incompressible limit, in which the initial data is “well-prepared” and the velocity field enjoys the slip boundary conditions. The main idea is to derive the uniform energy estimates for nonlinear systems and corresponding incompressible limit.
基金supported by China Postdoctoral Science Foundation(2012M520205)supported by National Natural SciencesFoundation of China(11171229,11231006)Project of Beijing Chang Cheng Xue Zhe
文摘In this article, we prove the local existence and uniqueness of the classical solution to the Cauchy problem of the 3-D compressible Navier-Stokes equations with large initial data and vacuum, if the shear viscosity μ is a positive constant and the bulk viscosity λ（ρ） = ρ^β with β≥0. Note that the initial data can be arbitrarily large to contain vacuum states.
基金supported by NNSFC(11701443,11901444,11931013)Natural Science Basic Research Plan in Shaanxi Province of China(2019JQ-870)。
文摘In this paper,we consider the 3D compressible isentropic Navier-Stokes equations when the shear viscosityμis a positive constant and the bulk viscosity is λ(ρ)=ρ^(β) with β>2,which is a situation that was first introduced by Vaigant and Kazhikhov in[1].The global axisymmetric classical solution with arbitrarily large initial data in a periodic domain Ω={(r,z)|r=√x^(2)+y^(2),(x,y,z)∈R^(3),r∈I⊂(0,+∞),-∞<z<+∞} is obtained.Here the initial density keeps a non-vacuum state ρ>0 when z→±∞.Our results also show that the solution will not develop the vacuum state in any finite time,provided that the initial density is uniformly away from the vacuum.
基金supported by National Natural Science Foundation of China (Grant Nos. 10401012, 10771170)supported by (#10625105)the Key Laboratory of Mathematical Physics of Hubei Province
文摘The Navier-Stokes system for one-dimensional compressible fluids with density-dependent viscosities when the initial density connects to vacuum continuously is considered in the present paper. When the viscosity coefficient u is proportional to pθ with 0 〈 θ 〈 1, the global existence and the uniqueness of weak solutions are proved which improves the previous results in [Vong, S. W., Yang, T., Zhu, C. J.： Compressible Navier-Stokes equations with degenerate viscosity coefficient and vacuum II. J. Differential Equations, 192（2）, 475-501 （2003）]. Here p is the density. Moreover, a stabilization rate estimate for the density as t → ＋∞ for any θ 〉 0 is also given.
基金supported by the National Natural Science Foundation of China under Grant No.11301244the Foundation of Education Department of Liaoning Province of China under Grant L2013006+1 种基金the Doctor Startup Foundation of Liaoning Province of China Grant 20131040supported by the National Natural Science Foundation of China under Grant No.11371297
文摘We consider the Cauchy problem for one-dimensional compressible isentropic Navier-Stokes equations with density-dependent viscosity μ（ρ） = Aρα, where α〉 0 and A 〉0. The global existence of strong solutions is obtained, which improves the previous results by enlarging the interval of α. Moreover, our result shows that no vacuum is developed in a finite time provided the initial data does not contain vacuum.
基金the National Natural Science Foundation of China(Grant Nos.10625105 and 10431060)the Program for New Century Excellent Talents in University(Grant No.NCET-04-0745)
文摘In this paper,we study the one-dimensional motion of viscous gas with a general pres- sure law and a general density-dependent viscosity coefficient when the initial density connects to the vacuum state with a jump.We prove the global existence and the uniqueness of weak solutions to the compressible Navier-Stokes equations by using the line method.For this,some new a priori estimates are obtained to take care of the general viscosity coefficientμ(ρ)instead ofρ~θ.
基金supported by the Shantou University funding(Grant No.NTF20025)National Natural Science Foundation of China(Grant No.12101386)+1 种基金supported by National Natural Science Foundation of China(Grant Nos.12171160,11771150 and 11831003)Guangdong Basic and Applied Basic Research Foundation(Grant No.2020B1515310015)。
文摘In this paper, we consider the initial-boundary problem for a 1D two-fluid model with densitydependent viscosity and vacuum. The pressure depends on two variables but the viscosity only depends on one of the densities. We prove the global existence and uniqueness of the classical solution in the one-dimensional space with large initial data and vacuum. We use a new Helmholtz free energy function and the material derivative of the velocity field to deal with the general pressure with two variables, without the equivalence condition. We also develop a new argument to handle the general viscosity.
基金Supported by the National Natural Science Foundation of China(No.10771170)
文摘This paper is concerned with the Cauchy problems of one-dimensional compressible Navier-Stokes equations with density-dependent viscosity coefcients.By assumingρ0∈L1（R）,we will prove the existence of weak solutions to the Cauchy problems forθ〉0.This will improve results in Jiu and Xin’s paper（Kinet.Relat.Models,1（2）：313–330（2008））in whichθ〉12is required.In addition,We will study the large time asymptotic behavior of such weak solutions.
基金supported by the National Key Research and Development Program of China(No.2023YFB3712401),the National Natural Science Foundation of China(No.52274301)the Aeronautical Science Foundation of China(No.2023Z0530S6005)the Ningbo Yongjiang Talent-Introduction Programme(No.2022A-023-C).
文摘The viscosity of refining slags plays a critical role in metallurgical processes.However,obtaining accurate viscosity data remains challenging due to the complexities of high-temperature experiments,often relying on empirical models with limited predictive capabilities.This study focuses on the influence of optical basicity on viscosity in CaO-Al_(2)O_(3)-based refining slags,leveraging machine learning to address data scarcity and improve prediction accuracy.An automated framework for algorithm integration,parameter tuning,and evaluation ranking framework(Auto-APE)is employed to develop customized data-driven models for various slag systems,including CaO-Al_(2)O_(3)-SiO_(2),CaO-Al_(2)O_(3)-CaF_(2),CaO-Al_(2)O_(3)-SiO_(2)-MgO,and CaO-Al_(2)O_(3)-SiO_(2)-MgO-CaF_(2).By incorporating optical basicity as a key feature,the models achieve an average validation error of 8.0%to 15.1%,significantly outperforming traditional empirical models.Additionally,symbolic regression is introduced to rapidly construct domain-specific features,such as optical basicity-like descriptors,offering a potential breakthrough in performance prediction for small datasets.This work highlights the critical role of domain-specific knowledge in understanding and predicting viscosity,providing a robust machine learning-based approach for optimizing refining slag properties.
基金financially supported by the National Natural Science Foundation of China(Nos.52425408 and 52304345)the Fundamental Research Funds for the Central Universities,China(No.2023CDJXY-016)the Postdoctoral Science Foundation of Chongqing(No.CSTB2023NSCQ-BHX0174)。
文摘Currently,the Al_(2)O_(3)content in the high-alumina slag systems within blast furnaces is generally limited to 16wt%–18.5wt%,making it challenging to overcome this limitation.Unlike most studies that concentrated on managing the MgO/Al_(2)O_(3)ratio or basicity,this paper explored the effect of equimolar substitution of MgO for CaO on the viscosity and structure of a high-alumina CaO-MgO-Al_(2)O_(3)-SiO_(2)slag system,providing theoretical guidance and data to facilitate the application of high-alumina ores.The results revealed that the viscosity first decreased and then increased with higher MgO substitution,reaching a minimum at 15mol%MgO concentration.Fourier transform infrared spectroscopy(FTIR)results found that the depths of the troughs representing[SiO_(4)]tetrahedra,[AlO_(4)]tetrahedra,and Si-O-Al bending became progressively deeper with increased MgO substitution.Deconvolution of the Raman spectra showed that the average number of bridging oxygens per Si atom and the X_(Q^(3))/X_(Q^(2))(X_(Q^(i))is the molar fraction of Q^(i) unit,and i is the number of bridging oxygens in a[SiO_(4)]tetrahedral unit)ratio increased from 2.30 and 1.02 to 2.52 and 2.14,respectively,indicating a progressive polymerization of the silicate structure.X-ray photoelectron spectroscopy(XPS)results highlighted that non-bridging oxygen content decreased from 77.97mol% to 63.41mol% with increasing MgO concentration,whereas bridging oxygen and free oxygen contents increased.Structural analysis demonstrated a gradual increase in the polymerization degree of the tetrahedral structure with the increase in MgO substitution.However,bond strength is another important factor affecting the slag viscosity.The occurrence of a viscosity minimum can be attributed to the complex evolution of bond strengths of non-bridging oxygens generated during depolymerization of the[SiO_(4)]and[AlO_(4)]tetrahedral structures by CaO and MgO.
基金the financial support of this work by the National Natural Science Foundation of China(Nos.82072309,22067019 and 22367023)the Major Science and Technology Projects in Yunnan Province(No.202402AE090006)+3 种基金the Project of Yunnan Characteristic Plant Screening and R&D Service CXO Platform(No.2022YKZY001)Yunnan Provincial Science and Technology Department Yunnan University Joint Special Project(No.202201BF070001-001)the Postgraduate Research Innovation Foundation of Yunnan University(No.KC-23234403)the Scientific Research Foundation Project of Yunnan Provincial Department of Education(No.2023Y0240)。
文摘PBQ[1-(4-chlorophenyl)-3-(pyridin-3-yl)urea],an enormous potent molluscicide,showed excellent Pomacea canaliculata(P.canaliculata)control activity and low toxicity for other aquatic organisms,but its snail-killing mechanisms are still not fully understood.We employed an optical method to elucidate PBQ action via a novel fluorescent viscosity probe,NCV.As the viscosity in the test solutions increased,compared with that in pure ethanol,a 54-fold fluorescence intensity enhancement of NCV was observed in 310 cP of 90%glycerol.Furthermore,NCV successfully exhibited a selective fluorescence response towards monensin-induced cellular viscosity changes in HepG2 cells.The liver,stomach,and foot plantar of the tested snails were frozen and sectioned for fluorescent imaging experiments after the treatment with different PBQ concentrations over various times.A significant fluorescent increase in the snail's liver was observed upon exposure to 0.75 mg/L PBQ for 72 h,which highlighted an increase in viscosity.Hematoxylin and eosin(HE)staining further supported PBQ-induced liver damage with a viscosity increase in P.canaliculata.Our study provides a new rapid optical visualization method to study the killing mechanisms of PBQ and may help discover new chemicals that control snail populations.
基金supported by the National Natural Science Foundation of China(Nos.82272067,81974386,M-0696,and 82273486)Natural Science Foundation of Hunan Province(Nos.2022JJ80052,2024JJ6596)the Innovation Fund for Postgraduate Students of Central South University(No.2023ZZTS0841)。
文摘Colorectal cancer(CRC)is one of the most prevalent malignant tumors worldwide,exhibiting high morbidity and mortality.Lack of efficient tools for early diagnosis and surgical resection guidance of CRC have been a serious threat to the long-term survival rate of the CRC patients.Recent studies have shown that relative higher viscosity was presented in tumor cells compared to that in normal cells,leading to viscosity as a potential biomarker for CRC.Herein,we reported the development of a series of novel viscosity-sensitive and mitochondria-specific fluorescent probes(HTB,HTI,and HTP)for CRC detection.Among them,HTB showed high sensitivity,minimal background interference,low cytotoxicity,and significant viscous response capability,making it an ideal tool for distinguishing colorectal tumor cells from normal cells.Importantly,we have successfully utilized HTB to visualize in a CRC-cells-derived xenograft(CDX)model,enriching its medical imaging capacity,which laid a foundation for further clinical translational application.
