This study is devoted to the analysis of a one-dimensional time-dependent double-diffusive flow over a semi-infinite vertical plate, under a convective surface boundary condition. Using similarity variable, the govern...This study is devoted to the analysis of a one-dimensional time-dependent double-diffusive flow over a semi-infinite vertical plate, under a convective surface boundary condition. Using similarity variable, the governing nonlinear partial differential equations have been transformed into a set of coupled nonlinear ordinary differential equations, which are solved numerically by using shooting method alongside with Runge-Kutta integration scheme as embedded in Maple software programme. The numerical results of the skin-friction coefficient, the Nusselt and Sherwood numbers are discussed and depicted graphically.展开更多
The application of mathematical modeling to biological fluids is of utmost importance, as it has diverse applicationsin medicine. The peristaltic mechanism plays a crucial role in understanding numerous biological flo...The application of mathematical modeling to biological fluids is of utmost importance, as it has diverse applicationsin medicine. The peristaltic mechanism plays a crucial role in understanding numerous biological flows. In thispaper, we present a theoretical investigation of the double diffusion convection in the peristaltic transport of aPrandtl nanofluid through an asymmetric tapered channel under the combined action of thermal radiation andan induced magnetic field. The equations for the current flow scenario are developed, incorporating relevantassumptions, and considering the effect of viscous dissipation. The impact of thermal radiation and doublediffusion on public health is of particular interest. For instance, infrared radiation techniques have been used totreat various skin-related diseases and can also be employed as a measure of thermotherapy for some bones toenhance blood circulation, with radiation increasing blood flow by approximately 80%. To solve the governingequations, we employ a numerical method with the aid of symbolic software such as Mathematica and MATLAB.The velocity, magnetic force function, pressure rise, temperature, solute (species) concentration, and nanoparticlevolume fraction profiles are analytically derived and graphically displayed. The results outcomes are compared withthe findings of limiting situations for verification.展开更多
Particle-fluid two-phase flows in rock fractures and fracture networks play a pivotal role in determining the efficiency and effectiveness of hydraulic fracturing operations,a vital component in unconventional oil and...Particle-fluid two-phase flows in rock fractures and fracture networks play a pivotal role in determining the efficiency and effectiveness of hydraulic fracturing operations,a vital component in unconventional oil and gas extraction.Central to this phenomenon is the transport of proppants,tiny solid particles injected into the fractures to prevent them from closing once the injection is stopped.However,effective transport and deposition of proppant is critical in keeping fracture pathways open,especially in lowpermeability reservoirs.This review explores,then quantifies,the important role of fluid inertia and turbulent flows in governing proppant transport.While traditional models predominantly assume and then characterise flow as laminar,this may not accurately capture the complexities inherent in realworld hydraulic fracturing and proppant emplacement.Recent investigations highlight the paramount importance of fluid inertia,especially at the high Reynolds numbers typically associated with fracturing operations.Fluid inertia,often overlooked,introduces crucial forces that influence particle settling velocities,particle-particle interactions,and the eventual deposition of proppants within fractures.With their inherent eddies and transient and chaotic nature,turbulent flows introduce additional complexities to proppant transport,crucially altering proppant settling velocities and dispersion patterns.The following comprehensive survey of experimental,numerical,and analytical studies elucidates controls on the intricate dynamics of proppant transport under fluid inertia and turbulence-towards providing a holistic understanding of the current state-of-the-art,guiding future research directions,and optimising hydraulic fracturing practices.展开更多
This paper aims to numerically explore the characteristics of unsteady cavitating flow around a NACA0015 hydrofoil,with a focus on vorticity attributes.The simulation utilizes a homogeneous mixture model coupled with ...This paper aims to numerically explore the characteristics of unsteady cavitating flow around a NACA0015 hydrofoil,with a focus on vorticity attributes.The simulation utilizes a homogeneous mixture model coupled with a filter-based density correction turbulence model and a modified Zwart cavitation model.The study investigates the dynamic cavitation features of the thermal fluid around the hydrofoil at various incoming flow velocities.It systematically elucidates the evolution of cavitation and vortex dynamics corresponding to each velocity condition.The results indicate that with increasing incoming flow velocity,distinct cavitation processes take place in the flow field.展开更多
Large size titanium alloy parts are widely used in aerospace.However,they are difficult to manufacture using mechanical cutting technology because of severe tool wear.Electrochemical jet machining is a promising techn...Large size titanium alloy parts are widely used in aerospace.However,they are difficult to manufacture using mechanical cutting technology because of severe tool wear.Electrochemical jet machining is a promising technology to achieve high efficiency,because it has high machining flexibility and no machining tool wear.However,reports on the macro electrochemical jet machining of large size titanium alloy parts are very scarce,because it is difficult to achieve effective constraint of the flow field in macro electrochemical jet machining.In addition,titanium alloy is very sensitive to fluctuation of the flow field,and a turbulent flow field would lead to serious stray corrosion.This paper reports a series of investigations of the electrochemical jet machining of titanium alloy parts.Based on the flow analysis and experiments,the machining flow field was effectively constrained.TB6 titanium alloy part with a perimeter of one meter was machined.The machined surface was smooth with no obvious machining defects.The machining process was particularly stable with no obvious spark discharge.The research provides a reference for the application of electrochemical jet machining technology to achieve large allowance material removal in the machining of large titanium alloy parts.展开更多
A numerical analysis has been carried out to study the problem of plane stagnation double-diffusive MHD convective flow with convective boundary condition in a porous media. The governing nonlinear partial differentia...A numerical analysis has been carried out to study the problem of plane stagnation double-diffusive MHD convective flow with convective boundary condition in a porous media. The governing nonlinear partial differential equations have been reduced to systems of nonlinear ordinary differential equations by the similarity transformations. The transformed equations are solved numerically by using the classical fourth order Runge-Kutta method together with the shooting technique implemented on a computer program. The effects of the physical parameters are examined on the velocity, temperature and concentration profiles. Numerical data for the skin-friction coefficients, Nusselt and Sherwood numbers have been tabulated for various parametric conditions and are also shown graphically and discussed.展开更多
All-vanadium flow batteries(VFBs)are one of the most promising large-scale energy storage technologies.Conducting an operando quantitative analysis of the polarizations in VFBs under different conditions is essential ...All-vanadium flow batteries(VFBs)are one of the most promising large-scale energy storage technologies.Conducting an operando quantitative analysis of the polarizations in VFBs under different conditions is essential for developing high power density batteries.Here,we employ an operando decoupling method to quantitatively analyze the polarizations in each electrochemical and chemical reaction of VFBs under different catalytic conditions.Results show that the reduction reaction of V^(3+)presents the largest activation polarization,while the reduction reaction of VO_(2)^(+)primarily contributes to concentration polarizations due to the formation of the intermediate product V_(2)O_(3)^(3+).Additionally,it is found that the widely used electrode catalytic methods,incorporating oxygen functional groups and electrodepositing Bi,not only enhance the reaction kinetics but also exacerbate concentration polarizations simultaneously,especially during the discharge process.Specifically,in the battery with the high oxygen-containing electrodes,the negative side still accounts for the majority of activation loss(75.3%)at 200 mA cm^(-2),but it comes down to 36,9% after catalyzing the negative reactions with bismuth.This work provides an effective way to probe the limiting steps in flow batteries under various working conditions and offers insights for effectively enhancing battery performance for future developments.展开更多
The investigations of physical attributes of oceans,including parameters such as heat flow and bathymetry,have garnered substantial attention and are particularly valuable for examining Earth’s thermal structures and...The investigations of physical attributes of oceans,including parameters such as heat flow and bathymetry,have garnered substantial attention and are particularly valuable for examining Earth’s thermal structures and dynamic processes.Nevertheless,classical plate cooling models exhibit disparities when predicting observed heat flow and seafloor depth for extremely young and old lithospheres.Furthermore,a comprehensive analysis of global heat flow predictions and regional ocean heat flow or bathymetry data with physical models has been lacking.In this study,we employed power-law models derived from the singularity theory of fractal density to meticulously fit the latest ocean heat flow and bathymetry.Notably,power-law models offer distinct advantages over traditional plate cooling models,showcasing robust self-similarity,scale invariance,or scaling properties,and providing a better fit to observed data.The outcomes of our singularity analysis concerning heat flow and bathymetry across diverse oceanic regions exhibit a degree of consistency with the global ocean spreading rate model.In addition,we applied the similarity method to predict a higher resolution(0.1°×0.1°)global heat flow map based on the most recent heat flow data and geological/geophysical observables refined through linear correlation analysis.Regions displaying significant disparities between predicted and observed heat flow are closely linked to hydrothermal vent fields and active structures.Finally,combining the actual bathymetry and predicted heat flow with the power-law models allows for the quantitative and comprehensive detection of anomalous regions of ocean subsidence and heat flow,which deviate from traditional plate cooling models.The anomalous regions of subsidence and heat flow show different degrees of anisotropy,providing new ideas and clues for further analysis of ocean topography or hydrothermal circulation of mid-ocean ridges.展开更多
The core-surface flow is crucial for understanding the dynamics of the Earth's outer core and geomagnetic secular variations.Conventional core flow models often use a single set of spherical harmonic coefficients ...The core-surface flow is crucial for understanding the dynamics of the Earth's outer core and geomagnetic secular variations.Conventional core flow models often use a single set of spherical harmonic coefficients to represent the flow both inside and outside the tangent cylinder,inherently imposing continuity across the tangent cylinder around the solid inner core.To address this limitation,we present a core-surface flow inversion framework based on physics-informed neural networks.This framework employs distinct neural network representations for the flow inside and outside the tangent cylinder,allowing for discontinuities as the flow crosses the tangent cylinder.Additionally,it incorporates secular acceleration data to constrain the temporal evolution of the core flow.Using this inversion framework,we derive a new core-surface flow model spanning 2001 to 2024 from a geomagnetic model,incorporating the latest magnetic data from Swarm satellites and Macao Science Satellite-1.The recovered model reveals persistent large-scale circulation linked to westward drift,significant temporal variations in the equatorial Pacific,and distinct jet-like structures at the poles.The inversion also reveals a large-scale wave pattern in equatorial azimuthal flow acceleration,corresponding to observed geomagnetic jerks and likely resulting from quasi-geostrophic magneto-Coriolis waves.Additionally,the framework infers small-scale magnetic fields at the core-mantle boundary,highlighting split flux concentrations and localized high-latitude patches.展开更多
肝硬化是慢性肝病的常见终末期表现,门静脉高压症是肝硬化患者最常见、最致命的并发症,门静脉高压症及其并发症是肝硬化患者死亡的主要原因。肝硬化患者在门静脉高压症发展过程中,血流会发生剧烈变化。因此门静脉系统血流动力学的评价...肝硬化是慢性肝病的常见终末期表现,门静脉高压症是肝硬化患者最常见、最致命的并发症,门静脉高压症及其并发症是肝硬化患者死亡的主要原因。肝硬化患者在门静脉高压症发展过程中,血流会发生剧烈变化。因此门静脉系统血流动力学的评价在肝硬化病变的诊断与评估起着重要作用。4D Flow MRI是一种能无创性定量评估血流动力学的技术,本文将对目前4D Flow MRI在肝硬化门静脉高压中的应用进行综述。Cirrhosis is a common end-stage manifestation of chronic liver disease, and portal hypertension is the most common and fatal complication in patients with cirrhosis. Portal hypertension and its complications are the main cause of death in patients with cirrhosis. During the development of portal hypertension, patients with cirrhosis may experience significant changes in blood flow. Therefore, the evaluation of portal vein hemodynamics plays an important role in the diagnosis and assessment of liver cirrhosis lesions. 4D Flow MRI is a non-invasive quantitative assessment technique for hemodynamics. In this review, we will summarize the current research progress of 4D Flow MRI in portal hypertension in liver cirrhosis.展开更多
This paper mainly studies the well-posedness of steady incompressible impinging jet flow problem through a 3D axisymmetric finitely long nozzle.This problem originates from the physical phenomena encountered in practi...This paper mainly studies the well-posedness of steady incompressible impinging jet flow problem through a 3D axisymmetric finitely long nozzle.This problem originates from the physical phenomena encountered in practical engineering fields,such as in short take-off and vertical landing(STOVL)aircraft.Nowadays many intricate phenomena associated with impinging jet flows remain inadequately elucidated,which limits the ability to optimize aircraft design.Given a boundary condition in the inlet,the impinging jet problem is transformed into a Bernoulli-type free boundary problem according to the stream function.Then the variational method is used to study the corresponding variational problem with one parameter,thereby the wellposedness is established.The main conclusion is as follows.For a 3D axisymmetric finitely long nozzle and an infinitely long vertical wall,given an axial velocity in the inlet of nozzle,there exists a unique smooth incom‑pressible impinging jet flow such that the free boundary initiates smoothly at the endpoint of the nozzle and extends to infinity along the vertical wall at far fields.The key point is to investigate the regularity of the corner where the nozzle and the vertical axis intersect.展开更多
文摘This study is devoted to the analysis of a one-dimensional time-dependent double-diffusive flow over a semi-infinite vertical plate, under a convective surface boundary condition. Using similarity variable, the governing nonlinear partial differential equations have been transformed into a set of coupled nonlinear ordinary differential equations, which are solved numerically by using shooting method alongside with Runge-Kutta integration scheme as embedded in Maple software programme. The numerical results of the skin-friction coefficient, the Nusselt and Sherwood numbers are discussed and depicted graphically.
基金Institutional Fund Projects under No.(IFP-A-2022-2-5-24)by Ministry of Education and University of Hafr Al Batin,Saudi Arabia.
文摘The application of mathematical modeling to biological fluids is of utmost importance, as it has diverse applicationsin medicine. The peristaltic mechanism plays a crucial role in understanding numerous biological flows. In thispaper, we present a theoretical investigation of the double diffusion convection in the peristaltic transport of aPrandtl nanofluid through an asymmetric tapered channel under the combined action of thermal radiation andan induced magnetic field. The equations for the current flow scenario are developed, incorporating relevantassumptions, and considering the effect of viscous dissipation. The impact of thermal radiation and doublediffusion on public health is of particular interest. For instance, infrared radiation techniques have been used totreat various skin-related diseases and can also be employed as a measure of thermotherapy for some bones toenhance blood circulation, with radiation increasing blood flow by approximately 80%. To solve the governingequations, we employ a numerical method with the aid of symbolic software such as Mathematica and MATLAB.The velocity, magnetic force function, pressure rise, temperature, solute (species) concentration, and nanoparticlevolume fraction profiles are analytically derived and graphically displayed. The results outcomes are compared withthe findings of limiting situations for verification.
文摘目的基于4D Flow MRI技术探究急性心肌梗死患者左心室(left ventricular,LV)腔内局部血流动能(kinetic energy,KE)改变。方法纳入30名急性心肌梗死(acute myocardial infarction,AMI)患者和20名对照者。应用4D Flow MRI技术定量评价左心室腔内血流动能,包括左心室平均动能、最小动能、收缩期动能、舒张期动能以及平面内动能(in-plane kinetic energy,In-plane KE)百分比。比较心肌梗死组和对照组之间以及梗死节段与非梗死节段之间血流动能参数的差异。结果与对照组相比,急性心肌梗死组左心室整体平均动能(10.7μJ/mL±3.3 vs 14.7μJ/mL±3.6,P<0.001)、收缩期动能(14.6μJ/mL±5.1 vs 18.9μJ/mL±3.9,P=0.003)及舒张期动能(7.9μJ/mL±2.5 vs 10.6μJ/mL±3.8,P=0.018)均显著降低,其中梗死节段较非梗死节段邻近心腔血流的平均动能降低而收缩期平面内动能百分比增加(49.5μJ/mL±18.7 vs 126.3μJ/mL±50.7,P<0.001;61.8%±11.5 vs 42.9%±14.4,P=0.001)。结论4D Flow MRI技术可定量评价左心室腔内局部血流动能参数。急性心肌梗死后整体心腔血流动能减低,而梗死节段邻近心腔局部血流平面内动能百分比增加。
基金the Australian Research Council Discovery Project(ARC DP 220100851)scheme and would acknowledge that.
文摘Particle-fluid two-phase flows in rock fractures and fracture networks play a pivotal role in determining the efficiency and effectiveness of hydraulic fracturing operations,a vital component in unconventional oil and gas extraction.Central to this phenomenon is the transport of proppants,tiny solid particles injected into the fractures to prevent them from closing once the injection is stopped.However,effective transport and deposition of proppant is critical in keeping fracture pathways open,especially in lowpermeability reservoirs.This review explores,then quantifies,the important role of fluid inertia and turbulent flows in governing proppant transport.While traditional models predominantly assume and then characterise flow as laminar,this may not accurately capture the complexities inherent in realworld hydraulic fracturing and proppant emplacement.Recent investigations highlight the paramount importance of fluid inertia,especially at the high Reynolds numbers typically associated with fracturing operations.Fluid inertia,often overlooked,introduces crucial forces that influence particle settling velocities,particle-particle interactions,and the eventual deposition of proppants within fractures.With their inherent eddies and transient and chaotic nature,turbulent flows introduce additional complexities to proppant transport,crucially altering proppant settling velocities and dispersion patterns.The following comprehensive survey of experimental,numerical,and analytical studies elucidates controls on the intricate dynamics of proppant transport under fluid inertia and turbulence-towards providing a holistic understanding of the current state-of-the-art,guiding future research directions,and optimising hydraulic fracturing practices.
文摘This paper aims to numerically explore the characteristics of unsteady cavitating flow around a NACA0015 hydrofoil,with a focus on vorticity attributes.The simulation utilizes a homogeneous mixture model coupled with a filter-based density correction turbulence model and a modified Zwart cavitation model.The study investigates the dynamic cavitation features of the thermal fluid around the hydrofoil at various incoming flow velocities.It systematically elucidates the evolution of cavitation and vortex dynamics corresponding to each velocity condition.The results indicate that with increasing incoming flow velocity,distinct cavitation processes take place in the flow field.
基金the National Natural Science Foundation of China(No.52205468)China Postdoctoral Science Foundation(No.2022M710061 and No.2023T160277)Natural Science Foundation of Jiangsu Province(No.BK20210755)。
文摘Large size titanium alloy parts are widely used in aerospace.However,they are difficult to manufacture using mechanical cutting technology because of severe tool wear.Electrochemical jet machining is a promising technology to achieve high efficiency,because it has high machining flexibility and no machining tool wear.However,reports on the macro electrochemical jet machining of large size titanium alloy parts are very scarce,because it is difficult to achieve effective constraint of the flow field in macro electrochemical jet machining.In addition,titanium alloy is very sensitive to fluctuation of the flow field,and a turbulent flow field would lead to serious stray corrosion.This paper reports a series of investigations of the electrochemical jet machining of titanium alloy parts.Based on the flow analysis and experiments,the machining flow field was effectively constrained.TB6 titanium alloy part with a perimeter of one meter was machined.The machined surface was smooth with no obvious machining defects.The machining process was particularly stable with no obvious spark discharge.The research provides a reference for the application of electrochemical jet machining technology to achieve large allowance material removal in the machining of large titanium alloy parts.
文摘A numerical analysis has been carried out to study the problem of plane stagnation double-diffusive MHD convective flow with convective boundary condition in a porous media. The governing nonlinear partial differential equations have been reduced to systems of nonlinear ordinary differential equations by the similarity transformations. The transformed equations are solved numerically by using the classical fourth order Runge-Kutta method together with the shooting technique implemented on a computer program. The effects of the physical parameters are examined on the velocity, temperature and concentration profiles. Numerical data for the skin-friction coefficients, Nusselt and Sherwood numbers have been tabulated for various parametric conditions and are also shown graphically and discussed.
基金supported by the Guangdong Major Project of Basic and Applied Basic Research(2023B0303000002)the National Natural Science Foundation of China(No.52206089)+3 种基金the Guangdong Basic and Applied Basic Research Foundation(2024A1515010288,2023B1515120005)the Natural Science Foundation of Shenzhen(JCYJ20230807093315033)the Shenzhen Engineering Research Center,Southern University of Science and Technology(No.XMHT20230208003)high level of special funds(G03034K001)。
文摘All-vanadium flow batteries(VFBs)are one of the most promising large-scale energy storage technologies.Conducting an operando quantitative analysis of the polarizations in VFBs under different conditions is essential for developing high power density batteries.Here,we employ an operando decoupling method to quantitatively analyze the polarizations in each electrochemical and chemical reaction of VFBs under different catalytic conditions.Results show that the reduction reaction of V^(3+)presents the largest activation polarization,while the reduction reaction of VO_(2)^(+)primarily contributes to concentration polarizations due to the formation of the intermediate product V_(2)O_(3)^(3+).Additionally,it is found that the widely used electrode catalytic methods,incorporating oxygen functional groups and electrodepositing Bi,not only enhance the reaction kinetics but also exacerbate concentration polarizations simultaneously,especially during the discharge process.Specifically,in the battery with the high oxygen-containing electrodes,the negative side still accounts for the majority of activation loss(75.3%)at 200 mA cm^(-2),but it comes down to 36,9% after catalyzing the negative reactions with bismuth.This work provides an effective way to probe the limiting steps in flow batteries under various working conditions and offers insights for effectively enhancing battery performance for future developments.
基金supported by the Guangdong Province Introduced Innovative R&D Team of Big Data-Mathematical Earth Sciences and Extreme Geological Events Team(grant number 2021ZT09H399)the National Natural Science Foundation of China(grant number 42430111,42050103).
文摘The investigations of physical attributes of oceans,including parameters such as heat flow and bathymetry,have garnered substantial attention and are particularly valuable for examining Earth’s thermal structures and dynamic processes.Nevertheless,classical plate cooling models exhibit disparities when predicting observed heat flow and seafloor depth for extremely young and old lithospheres.Furthermore,a comprehensive analysis of global heat flow predictions and regional ocean heat flow or bathymetry data with physical models has been lacking.In this study,we employed power-law models derived from the singularity theory of fractal density to meticulously fit the latest ocean heat flow and bathymetry.Notably,power-law models offer distinct advantages over traditional plate cooling models,showcasing robust self-similarity,scale invariance,or scaling properties,and providing a better fit to observed data.The outcomes of our singularity analysis concerning heat flow and bathymetry across diverse oceanic regions exhibit a degree of consistency with the global ocean spreading rate model.In addition,we applied the similarity method to predict a higher resolution(0.1°×0.1°)global heat flow map based on the most recent heat flow data and geological/geophysical observables refined through linear correlation analysis.Regions displaying significant disparities between predicted and observed heat flow are closely linked to hydrothermal vent fields and active structures.Finally,combining the actual bathymetry and predicted heat flow with the power-law models allows for the quantitative and comprehensive detection of anomalous regions of ocean subsidence and heat flow,which deviate from traditional plate cooling models.The anomalous regions of subsidence and heat flow show different degrees of anisotropy,providing new ideas and clues for further analysis of ocean topography or hydrothermal circulation of mid-ocean ridges.
基金supported by the National Natural Science Foundation of China (12250012,42250101)the Macao Foundation。
文摘The core-surface flow is crucial for understanding the dynamics of the Earth's outer core and geomagnetic secular variations.Conventional core flow models often use a single set of spherical harmonic coefficients to represent the flow both inside and outside the tangent cylinder,inherently imposing continuity across the tangent cylinder around the solid inner core.To address this limitation,we present a core-surface flow inversion framework based on physics-informed neural networks.This framework employs distinct neural network representations for the flow inside and outside the tangent cylinder,allowing for discontinuities as the flow crosses the tangent cylinder.Additionally,it incorporates secular acceleration data to constrain the temporal evolution of the core flow.Using this inversion framework,we derive a new core-surface flow model spanning 2001 to 2024 from a geomagnetic model,incorporating the latest magnetic data from Swarm satellites and Macao Science Satellite-1.The recovered model reveals persistent large-scale circulation linked to westward drift,significant temporal variations in the equatorial Pacific,and distinct jet-like structures at the poles.The inversion also reveals a large-scale wave pattern in equatorial azimuthal flow acceleration,corresponding to observed geomagnetic jerks and likely resulting from quasi-geostrophic magneto-Coriolis waves.Additionally,the framework infers small-scale magnetic fields at the core-mantle boundary,highlighting split flux concentrations and localized high-latitude patches.
文摘肝硬化是慢性肝病的常见终末期表现,门静脉高压症是肝硬化患者最常见、最致命的并发症,门静脉高压症及其并发症是肝硬化患者死亡的主要原因。肝硬化患者在门静脉高压症发展过程中,血流会发生剧烈变化。因此门静脉系统血流动力学的评价在肝硬化病变的诊断与评估起着重要作用。4D Flow MRI是一种能无创性定量评估血流动力学的技术,本文将对目前4D Flow MRI在肝硬化门静脉高压中的应用进行综述。Cirrhosis is a common end-stage manifestation of chronic liver disease, and portal hypertension is the most common and fatal complication in patients with cirrhosis. Portal hypertension and its complications are the main cause of death in patients with cirrhosis. During the development of portal hypertension, patients with cirrhosis may experience significant changes in blood flow. Therefore, the evaluation of portal vein hemodynamics plays an important role in the diagnosis and assessment of liver cirrhosis lesions. 4D Flow MRI is a non-invasive quantitative assessment technique for hemodynamics. In this review, we will summarize the current research progress of 4D Flow MRI in portal hypertension in liver cirrhosis.
文摘This paper mainly studies the well-posedness of steady incompressible impinging jet flow problem through a 3D axisymmetric finitely long nozzle.This problem originates from the physical phenomena encountered in practical engineering fields,such as in short take-off and vertical landing(STOVL)aircraft.Nowadays many intricate phenomena associated with impinging jet flows remain inadequately elucidated,which limits the ability to optimize aircraft design.Given a boundary condition in the inlet,the impinging jet problem is transformed into a Bernoulli-type free boundary problem according to the stream function.Then the variational method is used to study the corresponding variational problem with one parameter,thereby the wellposedness is established.The main conclusion is as follows.For a 3D axisymmetric finitely long nozzle and an infinitely long vertical wall,given an axial velocity in the inlet of nozzle,there exists a unique smooth incom‑pressible impinging jet flow such that the free boundary initiates smoothly at the endpoint of the nozzle and extends to infinity along the vertical wall at far fields.The key point is to investigate the regularity of the corner where the nozzle and the vertical axis intersect.
