The optimal current difference lattice hydrodynamic model is extended to investigate the traffic flow dynamics on a unidirectional single lane gradient highway. The effect of slope on uphill/downhill highway is examin...The optimal current difference lattice hydrodynamic model is extended to investigate the traffic flow dynamics on a unidirectional single lane gradient highway. The effect of slope on uphill/downhill highway is examined through linear stability analysis and shown that the slope significantly affects the stability region on the phase diagram.Using nonlinear stability analysis, the Burgers, Korteweg-deVries(KdV) and modified Korteweg-deVries(mKdV) equations are derived in stable, metastable and unstable region, respectively. The effect of reaction coefficient is examined and concluded that it plays an important role in suppressing the traffic jams on a gradient highway. The theoretical findings have been verified through numerical simulation which confirm that the slope on a gradient highway significantly influence the traffic dynamics and traffic jam can be suppressed efficiently by considering the optimal current difference effect in the new lattice model.展开更多
Gradient vector flow （GVF） is an effective external force for active contours, but its iso- tropic nature handicaps its performance. The recently proposed gradient vector flow in the normal direction （NGVF） is ani...Gradient vector flow （GVF） is an effective external force for active contours, but its iso- tropic nature handicaps its performance. The recently proposed gradient vector flow in the normal direction （NGVF） is anisotropic since it only keeps the diffusion along the normal direction of the isophotes; however, it has difficulties forcing a snake into long, thin boundary indentations. In this paper, a novel external force for active contours called normally generalized gradient vector flow （NGGVF） is proposed, which generalizes the NGVF formulation to include two spatially varying weighting functions. Consequently, the proposed NGGVF snake is anisotropic and would improve ac- tive contour convergence into long, thin boundary indentations while maintaining other desirable properties of the NGVF snake, such as enlarged capture range, initialization insensitivity and good convergence at concavities. The advantages on synthetic and real images are demonstrated.展开更多
This paper uses the Oseen transformation to solve the differential equations governing motion of the vertical linear gradient flow distribution close to a wall surface. The Navier-Stokes equations are used to consider...This paper uses the Oseen transformation to solve the differential equations governing motion of the vertical linear gradient flow distribution close to a wall surface. The Navier-Stokes equations are used to consider the inertia term along the flow direction. A novel contour integral method is used to solve the complex Airy function. The boundary conditions of linear gradient flow distribution for finite problems are determined. The vorticity function, the pressure function, and the turbulent velocity profiles are provided, and the stability of particle trajectories is studied. An Lx-function form of the third derivative circulation is used to to simplify the solution. Theoretical results are compared with the experimental measurements with satisfactory agreement.展开更多
Heavy ingots are widely used in many industrial fields. The coarse grains formed during the process of in- got solidification influence the properties and fracture behaviors of the final products. The coarse grain gro...Heavy ingots are widely used in many industrial fields. The coarse grains formed during the process of in- got solidification influence the properties and fracture behaviors of the final products. The coarse grain growth was simulated under different thermal gradients. A 30Cr2Ni4MoV steel ingot was melted in a cubic crucible with dimen-sions of 15 cm×10 cm×23 cm, and the cooling conditions on each side of the crucible were controlled by different thermal curves. The influences of thermal gradients and rotational flows on grain growth in heavy steel ingots were then investigated both numerically and experimentally. The results showed that when the amplitude of the rotation angle was 60°, the metal was solidified under a reciprocating horizontal rotational condition when the angular velocity was 10 （°）/s or 20 （°）/s. As the thermal gradient increased, the lengths of the primary columnar grains in- creased, and the diameters of equiaxed grains decreased. When the direction of flow rotation was perpendicular to the direction of grain growth, the columnar grain zone was nearly eliminated, and the average diameter of equiaxed grains was 0.5 mm.展开更多
In this paper, we propose a fast centerline extraction method to be used for gradient and direction vector flow of active contours. The gradient and direction vector flow is a recently reported active contour model ca...In this paper, we propose a fast centerline extraction method to be used for gradient and direction vector flow of active contours. The gradient and direction vector flow is a recently reported active contour model capable of significantly improving the image segmentation performance especially for complex object shape, by seamlessly integrating gradient vector flow and prior directional information. Since the prior directional information is provided by manual line drawing, it can be inconvenient for inexperienced users who might have difficulty in finding the best place to draw the directional lines to achieve the best segmentation performance. This paper describes a method to overcome this problem by automatically extracting centerlines to guide the users for providing the right directional information. Experimental results on synthetic and real images demonstrate the feasibility of the proposed method.展开更多
The accelerated method in solving optimization problems has always been an absorbing topic.Based on the fixedtime(FxT)stability of nonlinear dynamical systems,we provide a unified approach for designing FxT gradient f...The accelerated method in solving optimization problems has always been an absorbing topic.Based on the fixedtime(FxT)stability of nonlinear dynamical systems,we provide a unified approach for designing FxT gradient flows(FxTGFs).First,a general class of nonlinear functions in designing FxTGFs is provided.A unified method for designing first-order FxTGFs is shown under Polyak-Łjasiewicz inequality assumption,a weaker condition than strong convexity.When there exist both bounded and vanishing disturbances in the gradient flow,a specific class of nonsmooth robust FxTGFs with disturbance rejection is presented.Under the strict convexity assumption,Newton-based FxTGFs is given and further extended to solve time-varying optimization.Besides,the proposed FxTGFs are further used for solving equation-constrained optimization.Moreover,an FxT proximal gradient flow with a wide range of parameters is provided for solving nonsmooth composite optimization.To show the effectiveness of various FxTGFs,the static regret analyses for several typical FxTGFs are also provided in detail.Finally,the proposed FxTGFs are applied to solve two network problems,i.e.,the network consensus problem and solving a system linear equations,respectively,from the perspective of optimization.Particularly,by choosing component-wisely sign-preserving functions,these problems can be solved in a distributed way,which extends the existing results.The accelerated convergence and robustness of the proposed FxTGFs are validated in several numerical examples stemming from practical applications.展开更多
It has not been a simple matter to obtain a sound extension of the classical J2 flow theory of plasticity that incorporates a dependence on plastic strain gradients and that is capable of capturing size-dependent beha...It has not been a simple matter to obtain a sound extension of the classical J2 flow theory of plasticity that incorporates a dependence on plastic strain gradients and that is capable of capturing size-dependent behaviour of metals at the micron scale. Two classes of basic extensions of classical J2 theory have been proposed： one with increments in higher order stresses related to increments of strain gradients and the other characterized by the higher order stresses themselves expressed in terms of increments of strain gradients. The theories proposed by Muhlhans and Aifantis in 1991 and Fleck and Hutchinson in 2001 are in the first class, and, as formulated, these do not always satisfy thermodynamic requirements on plastic dissipation. On the other hand, theories of the second class proposed by Gudmundson in 2004 and Gurtin and Anand in 2009 have the physical deficiency that the higher order stress quantities can change discontinuously for bodies subject to arbitrarily small load changes. The present paper lays out this background to the quest for a sound phenomenological extension of the rateindependent J2 flow theory of plasticity to include a de- pendence on gradients of plastic strain. A modification of the Fleck-Hutchinson formulation that ensures its thermo- dynamic integrity is presented and contrasted with a comparable formulation of the second class where in the higher or- der stresses are expressed in terms of the plastic strain rate. Both versions are constructed to reduce to the classical J2 flow theory of plasticity when the gradients can be neglected and to coincide with the simpler and more readily formulated J2 deformation theory of gradient plasticity for deformation histories characterized by proportional straining.展开更多
Ramps and sloping roads appear everywhere in the built environment. It is obvious that the movement pattern of people in the sloping path may be different as compared with the pattern on level roads. Previously, most ...Ramps and sloping roads appear everywhere in the built environment. It is obvious that the movement pattern of people in the sloping path may be different as compared with the pattern on level roads. Previously, most of the studies, especially the mathematical and simulation models, on pedestrian movement consider the flow at level routes.This study proposes a new lattice model for bidirectional pedestrian flow on gradient road. The stability condition is obtained by using linear stability theory. The nonlinear analysis method is employed to derive the modified Korteweg-de Vries(mKdV) equation, and the space of pedestrian flow is divided into three regions: the stable region, the metastable region, and the unstable region respectively. Furthermore, the time-dependent Ginzburg–Landan(TDGL) equation is deduced and solved through the reductive perturbation method. Finally, we present detailed results obtained from the model, and it is found that the stability of the model is enhanced in uphill situation while reduced in downhill situation with increasing slope.展开更多
Subsurface water flow velocity influences the hydrodynamic characteristics of soil seepage and the interaction between subsurface water flow and surface runoff during soil erosion and sediment transport.A visualized m...Subsurface water flow velocity influences the hydrodynamic characteristics of soil seepage and the interaction between subsurface water flow and surface runoff during soil erosion and sediment transport.A visualized method and equipment was adopted in this study to observe the subsurface water flow.Quartz sand was used as the test material of subsurface water flow and fluorescent dye was used as the indicator for tracing subsurface water flow.Water was supplied at the same flow discharge to the three parts at the bottom of the test flume,and the subsurface water flow were determined with four slope gradients(4°,8°,10°,and 12°).The results showed that the seepage velocity gradually increased with increasing slope gradient.The pore water velocity at different depths of sand layer profile increased with increasing slope gradient,whereas the thickness of the flow front gradually decreased.For the same slope gradient,the pore water velocity in the lower layer was the largest,whereas the thickness of the flow front was the smallest.Comparative analysis of the relationship between seepage velocity and pore water velocity at different depths of sand layer profile showed that the maximum relative difference between the measured pore water velocity and the computational pore water velocity at different depths of sand profile in the experiment was 4.38%.Thus,the test method for measuring the subsurface water flow velocity of sand layer profile adopted in this study was effective and feasible.The development of this experiment and the exploration of research methods would lay a good test foundation for future studies on the variation law of subsurface water flow velocity and the determination of flow velocity in purple soils,thus contributing to the improvement of the hydrodynamic mechanism of purple soils.展开更多
As has been observed by Morse [1], any generic vector field v on a compact smooth manifold X with boundary gives rise to a stratification of the boundary by compact submanifolds , where . Our main observation is that ...As has been observed by Morse [1], any generic vector field v on a compact smooth manifold X with boundary gives rise to a stratification of the boundary by compact submanifolds , where . Our main observation is that this stratification re-flects the stratified convexity/concavity of the boundary ?with respect to the ?v-flow. We study the behavior of this stratification under deformations of the vector field v. We also investigate the restrictions that the existence of a convex/concave traversing ?v-flow imposes on the topology of X. Let be the orthogonal projection of on the tangent bundle of . We link the dynamics of theon the boundary with the property of in X being convex/concave. This linkage is an instance of more general phenomenon that we call “holography of traversing fields”—a subject of a different paper to follow.展开更多
Some patients with severe aortic stenosis (AS), due to restrictive cardiac physiology, paradoxically have relatively low flow and low gradients across stenotic aortic valves despite preserved left ventricular (LV) sys...Some patients with severe aortic stenosis (AS), due to restrictive cardiac physiology, paradoxically have relatively low flow and low gradients across stenotic aortic valves despite preserved left ventricular (LV) systolic function. It results in symptoms and reduced quality of life and carries a high mortality. Whilst this form of severe AS, termed paradoxical low flow low gradient (pLFLG), is well reported, patients with this diagnosis experience inappropriate barriers to aortic valve replacement (AVR), the only efficacious treatment. We present the case of an 88-year-old female with 12 months of exertional dyspnoea on a background of hypothyroidism and hypercholesterolemia. Transthoracic echocardiogram (TTE) revealed LV hypertrophy, with a small LV cavity size and reduced stroke volume, yet normal systolic function. A heavily calcified aortic valve was identified with severe aortic stenosis, based on valve area, yet with incongruous mean transvalvular gradient of 25 mmHg (severe ≥ 50 mmHg). Following exclusion of other differential diagnoses, her symptoms were attributed to paradoxical LFLG severe AS. She was however declined definitive transcatheter aortic valve implantation (TAVI) due to her paradoxically low mean aortic gradient. Following further deterioration in her symptoms and supportive quantification of poor exercise performance, she was ultimately re-referred, accepted, and underwent TAVI. Following her AVR, the patient experiences significant improvement in both symptoms and quality of life after only one month. Paradoxical LFLG severe AS remains a well-documented yet under recognized disease. It carries high morbidity and mortality if untreated, yet is significantly less likely to be referred and accepted for intervention. With its prevalence expected to rise with an ageing population, this case serves as a timely reminder for clinicians to address the under recognition of important pathology.展开更多
Analysis of high resolution of aeromagnetic data was carried out over Lamurde, Adamawa state north-eastern Nigeria to determine the Curie point depth (CPD), heat flow and geothermal gradient. The aeromagnetic data use...Analysis of high resolution of aeromagnetic data was carried out over Lamurde, Adamawa state north-eastern Nigeria to determine the Curie point depth (CPD), heat flow and geothermal gradient. The aeromagnetic data used for this work was obtained at Nigerian geological survey agency, the total magnetic intensity was processed to produce the residual magnetic map which was divided into 4 overlapping blocks, each block was subjected to spectral analyses to obtain depths to the top boundary and centroid, while depth to bottom of the magnetic sources was calculated using empirical formula. The depths values obtained were then used to assess the CPD, heat flow and geothermal gradient in the area. The result shows that the CPD varies between 9.62 and 10.92 km with an average of 10.45 k, the heat flow varies between 150.73 and 132.78 mWm−20⋅°C−1 with an average of 139.12 mWm−20⋅°C−1 and the geothermal gradient in the study area varies between 12.16 and 15.67 °C/km with an average of 13.39 °C/km. In view of the above results, the high heat flow may be responsible for maturation of hydrocarbon in Benue Trough as well as responsible for the lead Zinc Mineralization. Again by implication, Lamurde area can be a good area for geothermal reservoir exploration for an alternative source for power generation.展开更多
A local gradient estimate for positive solutions of porous medium equations on complete noncompact Riemannian manifolds under the Ricci flow is derived. Moreover, a global gradient estimate for such equations on compa...A local gradient estimate for positive solutions of porous medium equations on complete noncompact Riemannian manifolds under the Ricci flow is derived. Moreover, a global gradient estimate for such equations on compact Riemannian manifolds is also obtained.展开更多
Information on geothermal gradient and heat flow within the subsurface is critical in the quest for geothermal energy exploration. In a bid to ascertain the thermal potential of Nigeria sector of the Chad Basin for en...Information on geothermal gradient and heat flow within the subsurface is critical in the quest for geothermal energy exploration. In a bid to ascertain the thermal potential of Nigeria sector of the Chad Basin for energy generation, subsurface temperature information from 19 oil wells, 24 water boreholes drilled to depths beyond 100 metres and atmospheric temperature from the Chad basin were utilized in calculating geothermal gradient of the area. Selected ditch cuttings from the wells were subjected to thermal conductivity test using Thermal Conductivity Scanner (TCS) at the Polish Geological Institute Laboratory in Warsaw. The terrestrial heat flow was calculated according to the Fourier’s law as a simple product of the geothermal gradient and the mean thermal conductivity. Results obtained indicated geothermal gradient range of 2.81<sup> °</sup>C/100 m to 5.88<sup> °</sup>C/100 m with an average of 3.71<sup> °</sup>C/100 m. The thermal conductivity values from the different representative samples range from 0.58 W/m*K to 4.207 W/m*K with an average of 1.626 W/m*K. The work presented a heat flow value ranging from 45 mW/m<sup>2</sup> to about 90 mW/m<sup>2</sup> in the Nigerian sector of the Chad Basin.展开更多
Many in vitro studies focus on effects of wall shear stress (WSS) and wall shear stress gradient (WSSG) on endothelial cells, which are linked to the initiation and progression of atherosclerosis in the arterial syste...Many in vitro studies focus on effects of wall shear stress (WSS) and wall shear stress gradient (WSSG) on endothelial cells, which are linked to the initiation and progression of atherosclerosis in the arterial system. Limitation in available flow chambers with a constant WSSG in the testing region makes it difficult to quantify cellular responses to WSSG. The current study proposes and characterizes a type of converging parallel plate flow chamber (PPFC) featuring a constant gradient of WSS. A simple formula was derived for the curvature of side walls, which relates WSSG to flow rate (Q), height of the PPFC (h), length of the convergent section (L), its widths at the entrance (w0) and exit (w1). CFD simulation of flow in the chamber is carried out. Constant WSSG is observed in most regions of the top and bottom plates except those in close proximity of side walls. A change in Q or h induces equally proportional changes in WSS and WSSG whereas an alteration in the ratio between w0 and w1 results in a more significant change in WSSG than that in WSS. The current design makes possible an easy quantification of WSSG on endothelial cells in the flow chamber.展开更多
The present paper is concerned with the steady thin film flow of the Sisko fluid on a horizontal moving plate, where the surface tension gradient is a driving mechanism. The analytic solution for the resulting nonline...The present paper is concerned with the steady thin film flow of the Sisko fluid on a horizontal moving plate, where the surface tension gradient is a driving mechanism. The analytic solution for the resulting nonlinear ordinary differential equation is obtained by the Adomian decomposition method （ADM）. The physical quantities are derived including the pressure profile, the velocity profile, the maximum residue time, the stationary points, the volume flow rate, the average film velocity, the uniform film thickness, the shear stress, the surface tension profile~ and the vorticity vector. It is found that the velocity of the Sisko fluid film decreases when the fluid behavior index and the Sisko fluid parameter increase, whereas it increases with an increase in the inverse capillary number. An increase in the inverse capillary number results in an increase in the surface tension which in turn results in an increase in the surface tension gradient on the Sisko fluid film. The locations of the stationary points are shifted towards the moving plate with the increase in the inverse capillary number, and vice versa locations for the stationary points are found with the increasing Sisko fluid parameter. Furthermore, shear thinning and shear thickening characteristics of the Sisko fluid are discussed. A comparison is made between the Sisko fluid film and the Newtonian fluid film.展开更多
In this paper, the mechanism for fluid flow at low velocity in a porous medium is analyzed based on plastic flow of oil in a reservoir and the fractal approach. The analytical expressions for flow rate and velocity of...In this paper, the mechanism for fluid flow at low velocity in a porous medium is analyzed based on plastic flow of oil in a reservoir and the fractal approach. The analytical expressions for flow rate and velocity of non-Newtonian fluid flow in the low permeability porous medium are derived, and the threshold pressure gradient （TPG） is also obtained. It is notable that the TPG （J） and permeability （K） of the porous medium analytically exhibit the scaling behavior J ~ K-D＇r/（l＋Or）, where DT is the fractal dimension for tortuous capillaries. The fractal characteristics of tortuosity for capillaries should be considered in analysis of non-Darcy flow in a low permeability porous medium. The model predictions of TPG show good agreement with those obtained by the available expression and experimental data. The proposed model may be conducible to a better understanding of the mechanism for nonlinear flow in the low permeability porous medium.展开更多
Rainfall intensity and slope gradient are two of the most important factors affecting the variations of runoff nitrogen(N).However,the effects of slope gradient and rainfall intensity on N loss via surface flow and in...Rainfall intensity and slope gradient are two of the most important factors affecting the variations of runoff nitrogen(N).However,the effects of slope gradient and rainfall intensity on N loss via surface flow and interflow on weathered granite slopes are poorly understood.In this study,12 artificial rainfalls(three rainfall intensities and four slope gradients)were simulated to investigate the coupling loss characteristics of surface flow–interflow–total nitrogen(TN),nitrate nitrogen(NO_3^--N)and ammonia nitrogen(NH_4^+-N)on weathered granite slopes.The results show that slope gradient has a greater impact on the surface flow when the rainfall intensity is relatively large.The effect gradually weakens with the decrement of rainfall intensity.The interflow yield increases firstly with the prolongation of rainfall duration,then tends to be stable and finally decreases.The total surface flow percentage increases with rainfall intensity while it decreases with increasing slope gradient with a range of 10.88%-71.47%.The TN loss concentration of the surface flow continually decreases with rainfall duration while that of the interflow shows different fluctuations.However,the TN loss loads of both surface flow and interflow increase with increasing rainfall intensity and slope gradient.The NO_3^--N concentration of interflow is much higher than that of the surface flow.The NH_4^+-N concentration is always less than that of NO_3^--N with no significant difference between surface flow and interflow.The percentages of the TN,NO_3^--N,and NH_4^+-N total loss load and concentration of surface flow and interflow were analyzed.The results show that N loss via both surface flow and interflow occurs mainly in the form of NO_3^--N.Most of the N loss is caused by interflow which is the preferential path of runoff nutrient loss.These findings provide data support and underlying insights for the control of runoff and N loss on the weathered granite slopes.展开更多
Siltation gradient and siltation length are important parameters for designing gravity check dams for debris flows,which directly affect the accuracy of estimates of interception capacity.At present,siltation gradient...Siltation gradient and siltation length are important parameters for designing gravity check dams for debris flows,which directly affect the accuracy of estimates of interception capacity.At present,siltation gradient calculations are based primarily on empirical values,and range from 0.4 to 0.95 times the channel slope coefficient.The middle reaches of the Bailong River are one of the four areas in China that are most severely affected by debris flow hazards.Gravity dams are widely employed in this mountainous area.However,field studies of their capacity are lacking.In this paper,the operations of check dams were investigated.Based on field investigation results and theoretical analysis,calculations for siltation gradient,siltation length,and dam storage capacity are established.The impact of debris flow density,channel slope,and particle size weight percentages are discussed.The calculations show that the theoretical values for siltation gradient are consistent with measured values with 83.6% accuracy;and theoretical values of siltation length are consistent with measured values with 91.6% accuracy.The results of this research are an important reference for optimal height and spacing of dams,estimation of dam storage capacity,and disaster prevention.展开更多
The main factors influencing soil erosion include the net rain excess, the water depth, the velocity, the shear stress of overland flows, and the erosion-resisting capacity of soil. The laws of these factors varying w...The main factors influencing soil erosion include the net rain excess, the water depth, the velocity, the shear stress of overland flows, and the erosion-resisting capacity of soil. The laws of these factors varying with the slope gradient were investigated by using the kinematic wave theory. Furthermore, the critical slope gradient of erosion was driven. The analysis shows that the critical slope gradient of soil erosion is dependent on grain size, soil bulk density, surface roughness, runoff length, net rain excess, and the friction coefficient of soil, etc. The critical slope gradient has been estimated theoretically with its range between 41.5 degrees similar to 50 degrees.展开更多
基金Council of Scientific and Industrial Research (CSIR), India for providing financial assistancesupported by Chinese Universities Scientific Fund under Grant No.WK0010000032
文摘The optimal current difference lattice hydrodynamic model is extended to investigate the traffic flow dynamics on a unidirectional single lane gradient highway. The effect of slope on uphill/downhill highway is examined through linear stability analysis and shown that the slope significantly affects the stability region on the phase diagram.Using nonlinear stability analysis, the Burgers, Korteweg-deVries(KdV) and modified Korteweg-deVries(mKdV) equations are derived in stable, metastable and unstable region, respectively. The effect of reaction coefficient is examined and concluded that it plays an important role in suppressing the traffic jams on a gradient highway. The theoretical findings have been verified through numerical simulation which confirm that the slope on a gradient highway significantly influence the traffic dynamics and traffic jam can be suppressed efficiently by considering the optimal current difference effect in the new lattice model.
基金Supported by the National Natural Science Foundation of China(60805004)the State Key Lab of Space Medicine Fundamen-tals and Application(SMFA09A16)
文摘Gradient vector flow （GVF） is an effective external force for active contours, but its iso- tropic nature handicaps its performance. The recently proposed gradient vector flow in the normal direction （NGVF） is anisotropic since it only keeps the diffusion along the normal direction of the isophotes; however, it has difficulties forcing a snake into long, thin boundary indentations. In this paper, a novel external force for active contours called normally generalized gradient vector flow （NGGVF） is proposed, which generalizes the NGVF formulation to include two spatially varying weighting functions. Consequently, the proposed NGGVF snake is anisotropic and would improve ac- tive contour convergence into long, thin boundary indentations while maintaining other desirable properties of the NGVF snake, such as enlarged capture range, initialization insensitivity and good convergence at concavities. The advantages on synthetic and real images are demonstrated.
基金Project supported by the National Natural Science foundation of China(No.51079095)the Science Fund for Creative Research Groups of the National Natural Science Foundation of China(No.51021004)
文摘This paper uses the Oseen transformation to solve the differential equations governing motion of the vertical linear gradient flow distribution close to a wall surface. The Navier-Stokes equations are used to consider the inertia term along the flow direction. A novel contour integral method is used to solve the complex Airy function. The boundary conditions of linear gradient flow distribution for finite problems are determined. The vorticity function, the pressure function, and the turbulent velocity profiles are provided, and the stability of particle trajectories is studied. An Lx-function form of the third derivative circulation is used to to simplify the solution. Theoretical results are compared with the experimental measurements with satisfactory agreement.
基金Sponsored by National Basic Research Program of China(2011CB012900)
文摘Heavy ingots are widely used in many industrial fields. The coarse grains formed during the process of in- got solidification influence the properties and fracture behaviors of the final products. The coarse grain growth was simulated under different thermal gradients. A 30Cr2Ni4MoV steel ingot was melted in a cubic crucible with dimen-sions of 15 cm×10 cm×23 cm, and the cooling conditions on each side of the crucible were controlled by different thermal curves. The influences of thermal gradients and rotational flows on grain growth in heavy steel ingots were then investigated both numerically and experimentally. The results showed that when the amplitude of the rotation angle was 60°, the metal was solidified under a reciprocating horizontal rotational condition when the angular velocity was 10 （°）/s or 20 （°）/s. As the thermal gradient increased, the lengths of the primary columnar grains in- creased, and the diameters of equiaxed grains decreased. When the direction of flow rotation was perpendicular to the direction of grain growth, the columnar grain zone was nearly eliminated, and the average diameter of equiaxed grains was 0.5 mm.
文摘In this paper, we propose a fast centerline extraction method to be used for gradient and direction vector flow of active contours. The gradient and direction vector flow is a recently reported active contour model capable of significantly improving the image segmentation performance especially for complex object shape, by seamlessly integrating gradient vector flow and prior directional information. Since the prior directional information is provided by manual line drawing, it can be inconvenient for inexperienced users who might have difficulty in finding the best place to draw the directional lines to achieve the best segmentation performance. This paper describes a method to overcome this problem by automatically extracting centerlines to guide the users for providing the right directional information. Experimental results on synthetic and real images demonstrate the feasibility of the proposed method.
基金supported by the National Key Research and Development Program of China(2020YFA0714300)the National Natural Science Foundation of China(62003084,62203108,62073079)+3 种基金the Natural Science Foundation of Jiangsu Province of China(BK20200355)the General Joint Fund of the Equipment Advance Research Program of Ministry of Education(8091B022114)Jiangsu Province Excellent Postdoctoral Program(2022ZB131)China Postdoctoral Science Foundation(2022M720720,2023T160105).
文摘The accelerated method in solving optimization problems has always been an absorbing topic.Based on the fixedtime(FxT)stability of nonlinear dynamical systems,we provide a unified approach for designing FxT gradient flows(FxTGFs).First,a general class of nonlinear functions in designing FxTGFs is provided.A unified method for designing first-order FxTGFs is shown under Polyak-Łjasiewicz inequality assumption,a weaker condition than strong convexity.When there exist both bounded and vanishing disturbances in the gradient flow,a specific class of nonsmooth robust FxTGFs with disturbance rejection is presented.Under the strict convexity assumption,Newton-based FxTGFs is given and further extended to solve time-varying optimization.Besides,the proposed FxTGFs are further used for solving equation-constrained optimization.Moreover,an FxT proximal gradient flow with a wide range of parameters is provided for solving nonsmooth composite optimization.To show the effectiveness of various FxTGFs,the static regret analyses for several typical FxTGFs are also provided in detail.Finally,the proposed FxTGFs are applied to solve two network problems,i.e.,the network consensus problem and solving a system linear equations,respectively,from the perspective of optimization.Particularly,by choosing component-wisely sign-preserving functions,these problems can be solved in a distributed way,which extends the existing results.The accelerated convergence and robustness of the proposed FxTGFs are validated in several numerical examples stemming from practical applications.
文摘It has not been a simple matter to obtain a sound extension of the classical J2 flow theory of plasticity that incorporates a dependence on plastic strain gradients and that is capable of capturing size-dependent behaviour of metals at the micron scale. Two classes of basic extensions of classical J2 theory have been proposed： one with increments in higher order stresses related to increments of strain gradients and the other characterized by the higher order stresses themselves expressed in terms of increments of strain gradients. The theories proposed by Muhlhans and Aifantis in 1991 and Fleck and Hutchinson in 2001 are in the first class, and, as formulated, these do not always satisfy thermodynamic requirements on plastic dissipation. On the other hand, theories of the second class proposed by Gudmundson in 2004 and Gurtin and Anand in 2009 have the physical deficiency that the higher order stress quantities can change discontinuously for bodies subject to arbitrarily small load changes. The present paper lays out this background to the quest for a sound phenomenological extension of the rateindependent J2 flow theory of plasticity to include a de- pendence on gradients of plastic strain. A modification of the Fleck-Hutchinson formulation that ensures its thermo- dynamic integrity is presented and contrasted with a comparable formulation of the second class where in the higher or- der stresses are expressed in terms of the plastic strain rate. Both versions are constructed to reduce to the classical J2 flow theory of plasticity when the gradients can be neglected and to coincide with the simpler and more readily formulated J2 deformation theory of gradient plasticity for deformation histories characterized by proportional straining.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11372166,11262005,11262003the Scientific Research Fund of Zhejiang Provincial under Grant No.LQ13D050002the K.C.Wong Magna Fund in Ningbo University,China,Government of the Hong Kong Administrative Region,China No.119011
文摘Ramps and sloping roads appear everywhere in the built environment. It is obvious that the movement pattern of people in the sloping path may be different as compared with the pattern on level roads. Previously, most of the studies, especially the mathematical and simulation models, on pedestrian movement consider the flow at level routes.This study proposes a new lattice model for bidirectional pedestrian flow on gradient road. The stability condition is obtained by using linear stability theory. The nonlinear analysis method is employed to derive the modified Korteweg-de Vries(mKdV) equation, and the space of pedestrian flow is divided into three regions: the stable region, the metastable region, and the unstable region respectively. Furthermore, the time-dependent Ginzburg–Landan(TDGL) equation is deduced and solved through the reductive perturbation method. Finally, we present detailed results obtained from the model, and it is found that the stability of the model is enhanced in uphill situation while reduced in downhill situation with increasing slope.
基金This work was supported by the Fundamental Research Funds for the National Natural Science Foundation of China(No.41571265,41971244)the Key Research and Development Project of Social Livelihood in Chongqing(cstc2018jscxmszdX0061)the Foundation of Graduate Research and Innovation in Chongqing under project CYB18089.
文摘Subsurface water flow velocity influences the hydrodynamic characteristics of soil seepage and the interaction between subsurface water flow and surface runoff during soil erosion and sediment transport.A visualized method and equipment was adopted in this study to observe the subsurface water flow.Quartz sand was used as the test material of subsurface water flow and fluorescent dye was used as the indicator for tracing subsurface water flow.Water was supplied at the same flow discharge to the three parts at the bottom of the test flume,and the subsurface water flow were determined with four slope gradients(4°,8°,10°,and 12°).The results showed that the seepage velocity gradually increased with increasing slope gradient.The pore water velocity at different depths of sand layer profile increased with increasing slope gradient,whereas the thickness of the flow front gradually decreased.For the same slope gradient,the pore water velocity in the lower layer was the largest,whereas the thickness of the flow front was the smallest.Comparative analysis of the relationship between seepage velocity and pore water velocity at different depths of sand layer profile showed that the maximum relative difference between the measured pore water velocity and the computational pore water velocity at different depths of sand profile in the experiment was 4.38%.Thus,the test method for measuring the subsurface water flow velocity of sand layer profile adopted in this study was effective and feasible.The development of this experiment and the exploration of research methods would lay a good test foundation for future studies on the variation law of subsurface water flow velocity and the determination of flow velocity in purple soils,thus contributing to the improvement of the hydrodynamic mechanism of purple soils.
文摘As has been observed by Morse [1], any generic vector field v on a compact smooth manifold X with boundary gives rise to a stratification of the boundary by compact submanifolds , where . Our main observation is that this stratification re-flects the stratified convexity/concavity of the boundary ?with respect to the ?v-flow. We study the behavior of this stratification under deformations of the vector field v. We also investigate the restrictions that the existence of a convex/concave traversing ?v-flow imposes on the topology of X. Let be the orthogonal projection of on the tangent bundle of . We link the dynamics of theon the boundary with the property of in X being convex/concave. This linkage is an instance of more general phenomenon that we call “holography of traversing fields”—a subject of a different paper to follow.
文摘Some patients with severe aortic stenosis (AS), due to restrictive cardiac physiology, paradoxically have relatively low flow and low gradients across stenotic aortic valves despite preserved left ventricular (LV) systolic function. It results in symptoms and reduced quality of life and carries a high mortality. Whilst this form of severe AS, termed paradoxical low flow low gradient (pLFLG), is well reported, patients with this diagnosis experience inappropriate barriers to aortic valve replacement (AVR), the only efficacious treatment. We present the case of an 88-year-old female with 12 months of exertional dyspnoea on a background of hypothyroidism and hypercholesterolemia. Transthoracic echocardiogram (TTE) revealed LV hypertrophy, with a small LV cavity size and reduced stroke volume, yet normal systolic function. A heavily calcified aortic valve was identified with severe aortic stenosis, based on valve area, yet with incongruous mean transvalvular gradient of 25 mmHg (severe ≥ 50 mmHg). Following exclusion of other differential diagnoses, her symptoms were attributed to paradoxical LFLG severe AS. She was however declined definitive transcatheter aortic valve implantation (TAVI) due to her paradoxically low mean aortic gradient. Following further deterioration in her symptoms and supportive quantification of poor exercise performance, she was ultimately re-referred, accepted, and underwent TAVI. Following her AVR, the patient experiences significant improvement in both symptoms and quality of life after only one month. Paradoxical LFLG severe AS remains a well-documented yet under recognized disease. It carries high morbidity and mortality if untreated, yet is significantly less likely to be referred and accepted for intervention. With its prevalence expected to rise with an ageing population, this case serves as a timely reminder for clinicians to address the under recognition of important pathology.
文摘Analysis of high resolution of aeromagnetic data was carried out over Lamurde, Adamawa state north-eastern Nigeria to determine the Curie point depth (CPD), heat flow and geothermal gradient. The aeromagnetic data used for this work was obtained at Nigerian geological survey agency, the total magnetic intensity was processed to produce the residual magnetic map which was divided into 4 overlapping blocks, each block was subjected to spectral analyses to obtain depths to the top boundary and centroid, while depth to bottom of the magnetic sources was calculated using empirical formula. The depths values obtained were then used to assess the CPD, heat flow and geothermal gradient in the area. The result shows that the CPD varies between 9.62 and 10.92 km with an average of 10.45 k, the heat flow varies between 150.73 and 132.78 mWm−20⋅°C−1 with an average of 139.12 mWm−20⋅°C−1 and the geothermal gradient in the study area varies between 12.16 and 15.67 °C/km with an average of 13.39 °C/km. In view of the above results, the high heat flow may be responsible for maturation of hydrocarbon in Benue Trough as well as responsible for the lead Zinc Mineralization. Again by implication, Lamurde area can be a good area for geothermal reservoir exploration for an alternative source for power generation.
基金Supported by the National Natural Science Foundation of China(11571361)China Scholarship Council
文摘A local gradient estimate for positive solutions of porous medium equations on complete noncompact Riemannian manifolds under the Ricci flow is derived. Moreover, a global gradient estimate for such equations on compact Riemannian manifolds is also obtained.
文摘Information on geothermal gradient and heat flow within the subsurface is critical in the quest for geothermal energy exploration. In a bid to ascertain the thermal potential of Nigeria sector of the Chad Basin for energy generation, subsurface temperature information from 19 oil wells, 24 water boreholes drilled to depths beyond 100 metres and atmospheric temperature from the Chad basin were utilized in calculating geothermal gradient of the area. Selected ditch cuttings from the wells were subjected to thermal conductivity test using Thermal Conductivity Scanner (TCS) at the Polish Geological Institute Laboratory in Warsaw. The terrestrial heat flow was calculated according to the Fourier’s law as a simple product of the geothermal gradient and the mean thermal conductivity. Results obtained indicated geothermal gradient range of 2.81<sup> °</sup>C/100 m to 5.88<sup> °</sup>C/100 m with an average of 3.71<sup> °</sup>C/100 m. The thermal conductivity values from the different representative samples range from 0.58 W/m*K to 4.207 W/m*K with an average of 1.626 W/m*K. The work presented a heat flow value ranging from 45 mW/m<sup>2</sup> to about 90 mW/m<sup>2</sup> in the Nigerian sector of the Chad Basin.
文摘Many in vitro studies focus on effects of wall shear stress (WSS) and wall shear stress gradient (WSSG) on endothelial cells, which are linked to the initiation and progression of atherosclerosis in the arterial system. Limitation in available flow chambers with a constant WSSG in the testing region makes it difficult to quantify cellular responses to WSSG. The current study proposes and characterizes a type of converging parallel plate flow chamber (PPFC) featuring a constant gradient of WSS. A simple formula was derived for the curvature of side walls, which relates WSSG to flow rate (Q), height of the PPFC (h), length of the convergent section (L), its widths at the entrance (w0) and exit (w1). CFD simulation of flow in the chamber is carried out. Constant WSSG is observed in most regions of the top and bottom plates except those in close proximity of side walls. A change in Q or h induces equally proportional changes in WSS and WSSG whereas an alteration in the ratio between w0 and w1 results in a more significant change in WSSG than that in WSS. The current design makes possible an easy quantification of WSSG on endothelial cells in the flow chamber.
文摘The present paper is concerned with the steady thin film flow of the Sisko fluid on a horizontal moving plate, where the surface tension gradient is a driving mechanism. The analytic solution for the resulting nonlinear ordinary differential equation is obtained by the Adomian decomposition method （ADM）. The physical quantities are derived including the pressure profile, the velocity profile, the maximum residue time, the stationary points, the volume flow rate, the average film velocity, the uniform film thickness, the shear stress, the surface tension profile~ and the vorticity vector. It is found that the velocity of the Sisko fluid film decreases when the fluid behavior index and the Sisko fluid parameter increase, whereas it increases with an increase in the inverse capillary number. An increase in the inverse capillary number results in an increase in the surface tension which in turn results in an increase in the surface tension gradient on the Sisko fluid film. The locations of the stationary points are shifted towards the moving plate with the increase in the inverse capillary number, and vice versa locations for the stationary points are found with the increasing Sisko fluid parameter. Furthermore, shear thinning and shear thickening characteristics of the Sisko fluid are discussed. A comparison is made between the Sisko fluid film and the Newtonian fluid film.
基金Project supported by the National Natural Science Foundation of China(Grant No.41102080)the Fundamental Research Funds for the Central Universities,China(Grant Nos.CUG130404 and CUG130103)the Fund from the Key Laboratory of Tectonics and Petroleum Resources of Ministry of Education,China University of Geosciences(Wuhan),China(Grant No.TPR-2013-18)
文摘In this paper, the mechanism for fluid flow at low velocity in a porous medium is analyzed based on plastic flow of oil in a reservoir and the fractal approach. The analytical expressions for flow rate and velocity of non-Newtonian fluid flow in the low permeability porous medium are derived, and the threshold pressure gradient （TPG） is also obtained. It is notable that the TPG （J） and permeability （K） of the porous medium analytically exhibit the scaling behavior J ~ K-D＇r/（l＋Or）, where DT is the fractal dimension for tortuous capillaries. The fractal characteristics of tortuosity for capillaries should be considered in analysis of non-Darcy flow in a low permeability porous medium. The model predictions of TPG show good agreement with those obtained by the available expression and experimental data. The proposed model may be conducible to a better understanding of the mechanism for nonlinear flow in the low permeability porous medium.
基金supported by the National Natural Science Foundation of China (4187706541471221)
文摘Rainfall intensity and slope gradient are two of the most important factors affecting the variations of runoff nitrogen(N).However,the effects of slope gradient and rainfall intensity on N loss via surface flow and interflow on weathered granite slopes are poorly understood.In this study,12 artificial rainfalls(three rainfall intensities and four slope gradients)were simulated to investigate the coupling loss characteristics of surface flow–interflow–total nitrogen(TN),nitrate nitrogen(NO_3^--N)and ammonia nitrogen(NH_4^+-N)on weathered granite slopes.The results show that slope gradient has a greater impact on the surface flow when the rainfall intensity is relatively large.The effect gradually weakens with the decrement of rainfall intensity.The interflow yield increases firstly with the prolongation of rainfall duration,then tends to be stable and finally decreases.The total surface flow percentage increases with rainfall intensity while it decreases with increasing slope gradient with a range of 10.88%-71.47%.The TN loss concentration of the surface flow continually decreases with rainfall duration while that of the interflow shows different fluctuations.However,the TN loss loads of both surface flow and interflow increase with increasing rainfall intensity and slope gradient.The NO_3^--N concentration of interflow is much higher than that of the surface flow.The NH_4^+-N concentration is always less than that of NO_3^--N with no significant difference between surface flow and interflow.The percentages of the TN,NO_3^--N,and NH_4^+-N total loss load and concentration of surface flow and interflow were analyzed.The results show that N loss via both surface flow and interflow occurs mainly in the form of NO_3^--N.Most of the N loss is caused by interflow which is the preferential path of runoff nutrient loss.These findings provide data support and underlying insights for the control of runoff and N loss on the weathered granite slopes.
基金sponsored by the National Science and Technology Support Program (2014BAL05B01)STS Project of the Chinese Academy of Science (KFJ-EW-STS-094)Scientific Project of Department of land and resources of Sichuan Province (KJ-2015-18)
文摘Siltation gradient and siltation length are important parameters for designing gravity check dams for debris flows,which directly affect the accuracy of estimates of interception capacity.At present,siltation gradient calculations are based primarily on empirical values,and range from 0.4 to 0.95 times the channel slope coefficient.The middle reaches of the Bailong River are one of the four areas in China that are most severely affected by debris flow hazards.Gravity dams are widely employed in this mountainous area.However,field studies of their capacity are lacking.In this paper,the operations of check dams were investigated.Based on field investigation results and theoretical analysis,calculations for siltation gradient,siltation length,and dam storage capacity are established.The impact of debris flow density,channel slope,and particle size weight percentages are discussed.The calculations show that the theoretical values for siltation gradient are consistent with measured values with 83.6% accuracy;and theoretical values of siltation length are consistent with measured values with 91.6% accuracy.The results of this research are an important reference for optimal height and spacing of dams,estimation of dam storage capacity,and disaster prevention.
文摘The main factors influencing soil erosion include the net rain excess, the water depth, the velocity, the shear stress of overland flows, and the erosion-resisting capacity of soil. The laws of these factors varying with the slope gradient were investigated by using the kinematic wave theory. Furthermore, the critical slope gradient of erosion was driven. The analysis shows that the critical slope gradient of soil erosion is dependent on grain size, soil bulk density, surface roughness, runoff length, net rain excess, and the friction coefficient of soil, etc. The critical slope gradient has been estimated theoretically with its range between 41.5 degrees similar to 50 degrees.
