In this study,we systematically investigated the effect of proton concentration on the kinetics of the oxygen reduction reaction(ORR)on Pt(111)in acidic solutions.Experimental results demonstrate a rectangular hyperbo...In this study,we systematically investigated the effect of proton concentration on the kinetics of the oxygen reduction reaction(ORR)on Pt(111)in acidic solutions.Experimental results demonstrate a rectangular hyperbolic relationship,i.e.,the ORR current excluding the effect of other variables increases with proton concentration and then tends to a constant value.We consider that this is caused by the limitation of ORR kinetics by the trace oxygen concentration in the solution,which determines the upper limit of ORR kinetics.A model of effective concentration is further proposed for rectangular hyperbolic relationships:when the reactant concentration is high enough to reach a critical saturation concentration,the effective reactant concentration will become a constant value.This could be due to the limited concentration of a certain reactant for reactions involving more than one reactant or the limited number of active sites available on the catalyst.Our study provides new insights into the kinetics of electrocatalytic reactions,and it is important for the proper evaluation of catalyst activity and the study of structureperformance relationships.展开更多
The prediction of bathymetry has advanced significantly with the development of satellite altimetry.However,the majority of its data originate from marine gravity anomaly.In this study,based on the expression of verti...The prediction of bathymetry has advanced significantly with the development of satellite altimetry.However,the majority of its data originate from marine gravity anomaly.In this study,based on the expression of vertical gravity gradient(VGG)of a rectangular prism,the governing equations for determining sea depths to invert bathymetry.The governing equation is solved by linearization through an iterative process,and numerical simulations verify its algorithm and its stability.We also study the processing methods of different interference errors.The regularization method improves the stability of the inversion process for errors.A piecewise bilinear interpolation function roughly replaces the low-frequency error,and numerical simulations show that the accuracy can be improved by 41.2%after this treatment.For variable ocean crust density,simulation simulations verify that the root-mean-square(RMS)error of prediction is approximately 5 m for the sea depth of 6 km if density is chosen as the average one.Finally,two test regions in the South China Sea are predicted and compared with ship soundings data,RMS errors of predictions are 71.1 m and 91.4 m,respectively.展开更多
The boundary value problem plays a crucial role in the analytical investigation of continuum dynamics. In this paper, an analytical method based on the Dirac operator to solve the nonlinear and non-homogeneous boundar...The boundary value problem plays a crucial role in the analytical investigation of continuum dynamics. In this paper, an analytical method based on the Dirac operator to solve the nonlinear and non-homogeneous boundary value problem of rectangular plates is proposed. The key concept behind this method is to transform the nonlinear or non-homogeneous part on the boundary into a lateral force within the governing function by the Dirac operator, which linearizes and homogenizes the original boundary, allowing one to employ the modal superposition method for obtaining solutions to reconstructive governing equations. Once projected into the modal space, the harmonic balance method(HBM) is utilized to solve coupled ordinary differential equations(ODEs)of truncated systems with nonlinearity. To validate the convergence and accuracy of the proposed Dirac method, the results of typical examples, involving nonlinearly restricted boundaries, moment excitation, and displacement excitation, are compared with those of the differential quadrature element method(DQEM). The results demonstrate that when dealing with nonlinear boundaries, the Dirac method exhibits more excellent accuracy and convergence compared with the DQEM. However, when facing displacement excitation, there exist some discrepancies between the proposed approach and simulations;nevertheless, the proposed method still accurately predicts resonant frequencies while being uniquely capable of handling nonuniform displacement excitations. Overall, this methodology offers a convenient way for addressing nonlinear and non-homogenous plate boundaries.展开更多
This study proposes a novel open-type rectangular breakwater combined with horizontal perforated plates on both sides to enhance the sheltering effect of the rectangular box-type breakwaters against longer waves.The h...This study proposes a novel open-type rectangular breakwater combined with horizontal perforated plates on both sides to enhance the sheltering effect of the rectangular box-type breakwaters against longer waves.The hydrodynamic characteristics of this breakwater are analyzed through analytical potential solutions and experimental tests.The quadratic pressure drop conditions are exerted on the horizontal perforated plates to facilitate assessing the effect of wave height on the dissipated wave energy of breakwater through the analytical solution.The hydrodynamic quantities of the breakwater,including the reflection,transmission,and energyloss coefficients,together with vertical and horizontal wave forces,are calculated using the velocity potential decomposition method as well as an iterative algorithm.Furthermore,the reflection and transmission coefficients of the breakwater are measured by conducting experimental tests at various wave periods,wave heights,and both porosities and widths of the horizontal perforated plates.The analytical predicted results demonstrate good agreement with the iterative boundary element method solution and measured data.The influences of variable incident waves and structure parameters on the hydrodynamic characteristics of the breakwater are investigated through further calculations based on analytical solutions.Results indicate that horizontal perforated plates placed on the water surface for both sides of the rectangular breakwater can enhance the wave dissipation ability of the breakwater while effectively decreasing the transmission and reflection coefficients.展开更多
The aim of this study is to numerically investigate the impact of boundary slip on electroosmotic flow(EOF) in curved rectangular microchannels. Navier slip boundary conditions were employed at the curved microchannel...The aim of this study is to numerically investigate the impact of boundary slip on electroosmotic flow(EOF) in curved rectangular microchannels. Navier slip boundary conditions were employed at the curved microchannel walls. The electric potential distribution was governed by the Poisson–Boltzmann equation, whereas the velocity distribution was determined by the Navier–Stokes equation. The finite-difference method was employed to solve these two equations. The detailed discussion focuses on the impact of the curvature ratio, electrokinetic width, aspect ratio and slip length on the velocity. The results indicate that the present problem is strongly dependent on these parameters. The results demonstrate that by varying the dimensionless slip length from 0.001 to 0.01 while maintaining a curvature ratio of 0.5 there is a twofold increase in the maximum velocity. Moreover, this increase becomes more pronounced at higher curvature ratios. In addition, the velocity difference between the inner and outer radial regions increases with increasing slip length. Therefore, the incorporation of the slip boundary condition results in an augmented velocity and a more non-uniform velocity distribution. The findings presented here offer valuable insights into the design and optimization of EOF performance in curved hydrophobic microchannels featuring rectangular cross-sections.展开更多
The effect of porosity on surface wave scattering by a vertical porous barrier over a rectangular trench is studied here under the assumption of linearized theory of water waves.The fluid region is divided into four s...The effect of porosity on surface wave scattering by a vertical porous barrier over a rectangular trench is studied here under the assumption of linearized theory of water waves.The fluid region is divided into four subregions depending on the position of the barrier and the trench.Using the Havelock’s expansion of water wave potential in different regions along with suitable matching conditions at the interface of different regions,the problem is formulated in terms of three integral equations.Considering the edge conditions at the submerged end of the barrier and at the edges of the trench,these integral equations are solved using multi-term Galerkin approximation technique taking orthogonal Chebyshev’s polynomials and ultra-spherical Gegenbauer polynomial as its basis function and also simple polynomial as basis function.Using the solutions of the integral equations,the reflection coefficient,transmission coefficient,energy dissipation coefficient and horizontal wave force are determined and depicted graphically.It was observed that the rate of convergence of the Galerkin method in computing the reflection coefficient,considering special functions as basis function is more than the simple polynomial as basis function.The change of porous parameter of the barrier and variation of trench width and height significantly contribute to the change in the scattering coefficients and the hydrodynamic force.The present results are likely to play a crucial role in the analysis of surface wave propagation in oceans involving porous barrier over submarine trench.展开更多
Tunnel heading stability in two dimensions(2D)has been extensively investigated by numerous scholars in the past decade.One significant limitation of 2D analysis is the absence of actual tunnel geometry modeling with ...Tunnel heading stability in two dimensions(2D)has been extensively investigated by numerous scholars in the past decade.One significant limitation of 2D analysis is the absence of actual tunnel geometry modeling with a considerable degree of idealization.Nevertheless,it is possible to study the stability of tunnels in three dimensions(3D)with a rectangular shape using finite element limit analysis(FELA)and a nonlinear programming technique.This paper employs 3D FELA to generate rigorous solutions for stability numbers,failure mechanisms,and safety factors for rectangular-shaped tunnels.To further explore the usefulness of the produced results,multivariate adaptive regression spline(MARS)is used for machine learning of big dataset and development of design equations for practical design applications.The study should be of great benefit to tunnel design practices using the developed equations provided in the paper.展开更多
The bending of rectangular plate is divided into the generalized statically determinate bending and the generalized statically indeterminate bending based on the analysis of the completeness of calculating condition a...The bending of rectangular plate is divided into the generalized statically determinate bending and the generalized statically indeterminate bending based on the analysis of the completeness of calculating condition at the corner point. The former can be solved directly by the equilibrium differential equation and the boundary conditions of four edges of the plate. The latter can be solved by using the superposition principle. Making use of the recommended method, the bending of the plate with all kinds of...展开更多
In order to study the effects of the process parameters on springback and section deformation, a sensitivity analysis model was established based on the combination use of the multi-parameter sensitivity analysis meth...In order to study the effects of the process parameters on springback and section deformation, a sensitivity analysis model was established based on the combination use of the multi-parameter sensitivity analysis method and the springback/section deformation prediction finite element model, and by using this model the sensitivities of the springback and the section deformation to process parameters were analyzed and compared. The results show that the most sensitive process conditions for springback angle are the boost speed and the pressure of pressure die, and the most sensitive process condition for section deformation is the number of cores. When the clamp force, the boost speed and the pressure of pressure die are utilized to control section deformation, the effect of these process parameters on springback should be considered. When the process parameters are mainly used to control springback, the effect of these process parameters on the section deformation should be always considered.展开更多
Experimental results of new type joints between the column and the. steel beam of concrete-filled rectangular steel tubular (CFRT) under reversed cyclic loads are presented. The earthquake resistant capacity of the ...Experimental results of new type joints between the column and the. steel beam of concrete-filled rectangular steel tubular (CFRT) under reversed cyclic loads are presented. The earthquake resistant capacity of the joint is influenced by infilled concrete, stiffener length and relative dimensions of column and beam. It is found that the hysteresis curves obtained in the experiment are full and the joints have a good energy dissipation capacity. The nonlinear finite element models are also used to analyze the hysteresis behavior of the joints under reversed cyclic loads using ANSYS 8.0. The influences of the stiffener length and the infilled concrete are analyzed. Analytical results show that the stiffener length and the infilled concrete are critical for the joints. Furthermore, the skeleton curves of the finite element models are in good agreement with those of experiments.展开更多
In integrated circuits, the defects associated with photolithography are assumed to be in the shape of circular discs in order to perform the estimation of yield and fault analysis. However,real defects exhibit a grea...In integrated circuits, the defects associated with photolithography are assumed to be in the shape of circular discs in order to perform the estimation of yield and fault analysis. However,real defects exhibit a great variety of shapes. In this paper,a novel yield model is presented and the critical area model of short circuit is correspondingly provided. In comparison with the circular model corrently available, the new model takes the similarity shape to an original defect, the two-dimensional distributional characteristic of defects, the feature of a layout routing and the character of yield estimation into account. As for the aspect of prediction of yield, the experimental results show that the new model may predict the yield caused by real defects more accurately than the circular model does. It is significant that the yield is accurately estimated and improved using the proposed model.展开更多
An idealized numerical wave flume has been established by finite element method on the bases of Navier Stokes equations through prescribing the appropriate boundary conditions for the open boundary,incident boundary,...An idealized numerical wave flume has been established by finite element method on the bases of Navier Stokes equations through prescribing the appropriate boundary conditions for the open boundary,incident boundary,free surface and solid boundary in this paper.The characteristics of waves propagating over a step have been investigated by this numerical model.The breaker wave height is determined depending on the kinetic criterion.The numerical model is verified by laboratory experiments,and the empirical formula for the damping of wave height due to breaking is also given by experiments.展开更多
The environment modeling algorithm named rectangular decomposition, which is composed of cellular nodes and interleaving networks, is proposed. The principle of environment modeling is to divide the environment into i...The environment modeling algorithm named rectangular decomposition, which is composed of cellular nodes and interleaving networks, is proposed. The principle of environment modeling is to divide the environment into individual square sub-areas. Each sub-area is orientated by the central point of the sub-areas called a node. The rectangular map based on the square map can enlarge the square area side size to increase the coverage efficiency in the case of there being an adjacent obstacle. Based on this algorithm, a new coverage algorithm, which includes global path planning and local path planning, is introduced. In the global path planning, uncovered subspaces are found by using a special rule. A one-dimensional array P, which is used to obtain the searching priority of node in every direction, is defined as the search rule. The array P includes the condition of coverage towards the adjacent cells, the condition of connectivity and the priorities defined by the user in all eight directions. In the local path planning, every sub-area is covered by using template models according to the shape of the environment. The simulation experiments show that the coverage algorithm is simple, efficient and adapted for complex two- dimensional environments.展开更多
The two-phase detection method for directional discrimination in laser Doppler measurements is discussed.The diffraction efficiency of a sin- gle period rectangular phase grating is analysed and a kind of back-scatter...The two-phase detection method for directional discrimination in laser Doppler measurements is discussed.The diffraction efficiency of a sin- gle period rectangular phase grating is analysed and a kind of back-scattered laser Doppler vibrometer without directional ambiguity using the single peri- od rectangular phase grating as the beam-combiner described.The principles of this kind of vibrometer are explained in detail,and some experimental re- sults are given.In this kind of vibrometer,the rectangular phase grating, without the zero diffracted order and even orders,is used to eliminate use- less stray light and to combine the useful signal light.Differential electronics is employed to reject signal noise.Therefore,the signal-to-noise ratio of Doppler signals and the measurement accuracy of the instrument are im- proved and the range of application is expanded.展开更多
The wave propagation behavior in an elastic wedge-shaped medium with an arbitrary shaped cylindrical canyon at its vertex has been studied.Numerical computation of the wave displacement field is carried out on and nea...The wave propagation behavior in an elastic wedge-shaped medium with an arbitrary shaped cylindrical canyon at its vertex has been studied.Numerical computation of the wave displacement field is carried out on and near the canyon surfaces using weighted-residuals(moment method).The wave displacement fields are computed by the residual method for the cases of elliptic,circular,rounded-rectangular and flat-elliptic canyons,The analysis demonstrates that the resulting surface displacement depends,as in similar previous analyses,on several factors including,but not limited,to the angle of the wedge,the geometry of the vertex,the frequencies of the incident waves,the angles of incidence,and the material properties of the media.The analysis provides intriguing results that help to explain geophysical observations regarding the amplification of seismic energy as a function of site conditions.展开更多
The pressure drop of gas-liquid two-phase flow in microchannel is of fundamental importance in heat and mass transfer processes. In this work,the pressure drop of gas-liquid two-phase flow in horizontal rectangular cr...The pressure drop of gas-liquid two-phase flow in microchannel is of fundamental importance in heat and mass transfer processes. In this work,the pressure drop of gas-liquid two-phase flow in horizontal rectangular cross-section microchannels was measured by a pressure differential transducer system. Water,ethanol and n-propanol were used as liquid phase to study the effects of capillary number on pressure drop;air was used as the gas phase. Four microchannels with various dimensions of 100 μm× 200 μm,100 μm× 400 μm,100 μm× 800 μm and 100 μm× 2000 μm(depth × width) were used for determining the influence of configuration on the pressure drop. Experimental results showed that in micro-scale,the capillary number also affected the pressure drop remarkably,and in spite of only one-fold difference in aspect ratio,the variation of pressure drop reached up to near three times under the same experimental conditions. Taking the effects of aspect ratio and surface tension into account,a modi-fied correlation for Chisholm parameter C in the Chisholm model was proposed for predicting the frictional multi-plier,and the predicted values by the proposed correlation showed a satisfactory agreement with experimental data.展开更多
Nonlinear parametric vibration and stability is investigated for an axially accelerating rectangular thin plate subjected to parametric excitations resulting from the axial time-varying tension and axial time-varying ...Nonlinear parametric vibration and stability is investigated for an axially accelerating rectangular thin plate subjected to parametric excitations resulting from the axial time-varying tension and axial time-varying speed in the magnetic field. Consid- ering geometric nonlinearity, based on the expressions of total kinetic energy, potential energy, and electromagnetic force, the nonlinear magneto-elastic vibration equations of axially moving rectangular thin plate are derived by using the Hamilton principle. Based on displacement mode hypothesis, by using the Galerkin method, the nonlinear para- metric oscillation equation of the axially moving rectangular thin plate with four simply supported edges in the transverse magnetic field is obtained. The nonlinear principal parametric resonance amplitude-frequency equation is further derived by means of the multiple-scale method. The stability of the steady-state solution is also discussed, and the critical condition of stability is determined. As numerical examples for an axially moving rectangular thin plate, the influences of the detuning parameter, axial speed, axial tension, and magnetic induction intensity on the principal parametric resonance behavior are investigated.展开更多
A rectangular m × n resistor network with an arbitrary boundary is investigated, and a general resistance formula between two nodes on an arbitrary axis is derived by the Recursion-Transform(RT) method, a probl...A rectangular m × n resistor network with an arbitrary boundary is investigated, and a general resistance formula between two nodes on an arbitrary axis is derived by the Recursion-Transform(RT) method, a problem that has never been resolved before, for the Green's function technique and the Laplacian matrix approach are inapplicable to it. To have the exact solution of resistance is important but it is difficult to obtain under the condition of arbitrary boundary. Our result is directly expressed in a single summation and mainly composed of characteristic roots, which contain both finite and infinite cases. Further, the current distribution is given explicitly as a byproduct of the method. Our framework can be effectively applied to RLC networks. As an application to the LC network, we find that our formulation leads to the occurrence of resonances at h_1= 1-cosφ_i-sinφ_icotnφ_i. This somewhat curious result suggests the possibility of practical applications of our formulae to resonant circuits.展开更多
The aim of this study is to apply process mineralogy as a practical tool for further understanding and predicting the flotation kinetics of the copper sulfide minerals. The minerals' composition and association, g...The aim of this study is to apply process mineralogy as a practical tool for further understanding and predicting the flotation kinetics of the copper sulfide minerals. The minerals' composition and association, grain distribution, and liberation within the ore samples were analyzed in the feed, concentrate, and the tailings of the flotation processes with two pulp densities of 25 wt% and 30 wt%. The major copper-bearing minerals identified by microscopic analysis of the concentrate samples included chalcopyrite(56.2 wt%), chalcocite(29.1 wt%),covellite(6.4 wt%), and bornite(4.7 wt%). Pyrite was the main sulfide gangue mineral(3.6 wt%) in the concentrates. A 95% degree of liberation with d_(80) > 80 μm was obtained for chalcopyrite as the main copper mineral in the ore sample. The recovery rate and the grade in the concentrates were enhanced with increasing chalcopyrite particle size. Chalcopyrite particles with a d_(80) of approximately 100 μm were recovered at the early stages of the flotation process. The kinetic studies showed that the kinetic second-order rectangular distribution model perfectly fit the flotation test data. Characterization of the kinetic parameters indicated that the optimum granulation distribution range for achieving a maximum flotation rate for chalcopyrite particles was between the sizes 50 and 55 μm.展开更多
A liquid sloshing experimental rig driven by a wave-maker is designed and built to study liquid sloshing problems in a rectangular liquid tank with perforated baffle. A series of experiments are conducted in this expe...A liquid sloshing experimental rig driven by a wave-maker is designed and built to study liquid sloshing problems in a rectangular liquid tank with perforated baffle. A series of experiments are conducted in this experimental rig to estimate the free surface fluctuation and pressure distribution by changing external excitation frequency of the shaking table. An in-house CFD code is also used in this study to simulate the liquid sloshing in three-dimensional (3D) rectangular tank with perforated baffle. Good agreements of free surface elevation and pressure between the numerical results and the experimental data are obtained and presented. Spectral analysis of the time history of free surface elevation is conducted by using the fast Fourier transformation.展开更多
基金supported by the National Natural Science Foundation of China(21972131)。
文摘In this study,we systematically investigated the effect of proton concentration on the kinetics of the oxygen reduction reaction(ORR)on Pt(111)in acidic solutions.Experimental results demonstrate a rectangular hyperbolic relationship,i.e.,the ORR current excluding the effect of other variables increases with proton concentration and then tends to a constant value.We consider that this is caused by the limitation of ORR kinetics by the trace oxygen concentration in the solution,which determines the upper limit of ORR kinetics.A model of effective concentration is further proposed for rectangular hyperbolic relationships:when the reactant concentration is high enough to reach a critical saturation concentration,the effective reactant concentration will become a constant value.This could be due to the limited concentration of a certain reactant for reactions involving more than one reactant or the limited number of active sites available on the catalyst.Our study provides new insights into the kinetics of electrocatalytic reactions,and it is important for the proper evaluation of catalyst activity and the study of structureperformance relationships.
基金funded jointly by the National Nature Science Funds of China(No.42274010)the Fundamental Research Funds for the Central Universities(Nos.2023000540,2023000407).
文摘The prediction of bathymetry has advanced significantly with the development of satellite altimetry.However,the majority of its data originate from marine gravity anomaly.In this study,based on the expression of vertical gravity gradient(VGG)of a rectangular prism,the governing equations for determining sea depths to invert bathymetry.The governing equation is solved by linearization through an iterative process,and numerical simulations verify its algorithm and its stability.We also study the processing methods of different interference errors.The regularization method improves the stability of the inversion process for errors.A piecewise bilinear interpolation function roughly replaces the low-frequency error,and numerical simulations show that the accuracy can be improved by 41.2%after this treatment.For variable ocean crust density,simulation simulations verify that the root-mean-square(RMS)error of prediction is approximately 5 m for the sea depth of 6 km if density is chosen as the average one.Finally,two test regions in the South China Sea are predicted and compared with ship soundings data,RMS errors of predictions are 71.1 m and 91.4 m,respectively.
基金Project supported by the National Natural Science Foundation of China (No. 12002195)the National Science Fund for Distinguished Young Scholars (No. 12025204)the Program of Shanghai Municipal Education Commission (No. 2019-01-07-00-09-E00018)。
文摘The boundary value problem plays a crucial role in the analytical investigation of continuum dynamics. In this paper, an analytical method based on the Dirac operator to solve the nonlinear and non-homogeneous boundary value problem of rectangular plates is proposed. The key concept behind this method is to transform the nonlinear or non-homogeneous part on the boundary into a lateral force within the governing function by the Dirac operator, which linearizes and homogenizes the original boundary, allowing one to employ the modal superposition method for obtaining solutions to reconstructive governing equations. Once projected into the modal space, the harmonic balance method(HBM) is utilized to solve coupled ordinary differential equations(ODEs)of truncated systems with nonlinearity. To validate the convergence and accuracy of the proposed Dirac method, the results of typical examples, involving nonlinearly restricted boundaries, moment excitation, and displacement excitation, are compared with those of the differential quadrature element method(DQEM). The results demonstrate that when dealing with nonlinear boundaries, the Dirac method exhibits more excellent accuracy and convergence compared with the DQEM. However, when facing displacement excitation, there exist some discrepancies between the proposed approach and simulations;nevertheless, the proposed method still accurately predicts resonant frequencies while being uniquely capable of handling nonuniform displacement excitations. Overall, this methodology offers a convenient way for addressing nonlinear and non-homogenous plate boundaries.
基金supported by the National Natural Sci-ence Foundation of China(Nos.52201345,and 52001293)the New Cornerstone Science Foundation through the XPLORER PRIZE.
文摘This study proposes a novel open-type rectangular breakwater combined with horizontal perforated plates on both sides to enhance the sheltering effect of the rectangular box-type breakwaters against longer waves.The hydrodynamic characteristics of this breakwater are analyzed through analytical potential solutions and experimental tests.The quadratic pressure drop conditions are exerted on the horizontal perforated plates to facilitate assessing the effect of wave height on the dissipated wave energy of breakwater through the analytical solution.The hydrodynamic quantities of the breakwater,including the reflection,transmission,and energyloss coefficients,together with vertical and horizontal wave forces,are calculated using the velocity potential decomposition method as well as an iterative algorithm.Furthermore,the reflection and transmission coefficients of the breakwater are measured by conducting experimental tests at various wave periods,wave heights,and both porosities and widths of the horizontal perforated plates.The analytical predicted results demonstrate good agreement with the iterative boundary element method solution and measured data.The influences of variable incident waves and structure parameters on the hydrodynamic characteristics of the breakwater are investigated through further calculations based on analytical solutions.Results indicate that horizontal perforated plates placed on the water surface for both sides of the rectangular breakwater can enhance the wave dissipation ability of the breakwater while effectively decreasing the transmission and reflection coefficients.
基金Project supported by the Natural Science Foundation of Inner Mongolia of China(Grant No.2021BS01008)the Program for Innovative Research Team in Universities of Inner Mongolia Autonomous Region(Grant No.NMGIRT2323)the Scientific Research Funding Project for introduced high level talents of IMNU(Grant No.2020YJRC014)。
文摘The aim of this study is to numerically investigate the impact of boundary slip on electroosmotic flow(EOF) in curved rectangular microchannels. Navier slip boundary conditions were employed at the curved microchannel walls. The electric potential distribution was governed by the Poisson–Boltzmann equation, whereas the velocity distribution was determined by the Navier–Stokes equation. The finite-difference method was employed to solve these two equations. The detailed discussion focuses on the impact of the curvature ratio, electrokinetic width, aspect ratio and slip length on the velocity. The results indicate that the present problem is strongly dependent on these parameters. The results demonstrate that by varying the dimensionless slip length from 0.001 to 0.01 while maintaining a curvature ratio of 0.5 there is a twofold increase in the maximum velocity. Moreover, this increase becomes more pronounced at higher curvature ratios. In addition, the velocity difference between the inner and outer radial regions increases with increasing slip length. Therefore, the incorporation of the slip boundary condition results in an augmented velocity and a more non-uniform velocity distribution. The findings presented here offer valuable insights into the design and optimization of EOF performance in curved hydrophobic microchannels featuring rectangular cross-sections.
文摘The effect of porosity on surface wave scattering by a vertical porous barrier over a rectangular trench is studied here under the assumption of linearized theory of water waves.The fluid region is divided into four subregions depending on the position of the barrier and the trench.Using the Havelock’s expansion of water wave potential in different regions along with suitable matching conditions at the interface of different regions,the problem is formulated in terms of three integral equations.Considering the edge conditions at the submerged end of the barrier and at the edges of the trench,these integral equations are solved using multi-term Galerkin approximation technique taking orthogonal Chebyshev’s polynomials and ultra-spherical Gegenbauer polynomial as its basis function and also simple polynomial as basis function.Using the solutions of the integral equations,the reflection coefficient,transmission coefficient,energy dissipation coefficient and horizontal wave force are determined and depicted graphically.It was observed that the rate of convergence of the Galerkin method in computing the reflection coefficient,considering special functions as basis function is more than the simple polynomial as basis function.The change of porous parameter of the barrier and variation of trench width and height significantly contribute to the change in the scattering coefficients and the hydrodynamic force.The present results are likely to play a crucial role in the analysis of surface wave propagation in oceans involving porous barrier over submarine trench.
基金supported by the Thailand Science Research and Innovation Fundamental Fund fiscal year 2023The fifth author (V.Kamchoom)acknowledges the financial support from the National Science,Research and Innovation Fund (NSRF)at King Mongkut's Institute of Technology Ladkrabang (KMITL),Thailand (Grant No.FRB66065/0258-RE-KRIS/FF66/53)+1 种基金the Climate Change and Climate Variability Research in Monsoon Asia (CMON3)from the National Research Council of Thailand (NRCT) (Grant No.N10A650844)the National Natural Science Foundation of China (NSFC).
文摘Tunnel heading stability in two dimensions(2D)has been extensively investigated by numerous scholars in the past decade.One significant limitation of 2D analysis is the absence of actual tunnel geometry modeling with a considerable degree of idealization.Nevertheless,it is possible to study the stability of tunnels in three dimensions(3D)with a rectangular shape using finite element limit analysis(FELA)and a nonlinear programming technique.This paper employs 3D FELA to generate rigorous solutions for stability numbers,failure mechanisms,and safety factors for rectangular-shaped tunnels.To further explore the usefulness of the produced results,multivariate adaptive regression spline(MARS)is used for machine learning of big dataset and development of design equations for practical design applications.The study should be of great benefit to tunnel design practices using the developed equations provided in the paper.
文摘The bending of rectangular plate is divided into the generalized statically determinate bending and the generalized statically indeterminate bending based on the analysis of the completeness of calculating condition at the corner point. The former can be solved directly by the equilibrium differential equation and the boundary conditions of four edges of the plate. The latter can be solved by using the superposition principle. Making use of the recommended method, the bending of the plate with all kinds of...
基金Project (50975235) supported by the National Natural Science Foundation of ChinaProject (B08040) supported by the 111 Project
文摘In order to study the effects of the process parameters on springback and section deformation, a sensitivity analysis model was established based on the combination use of the multi-parameter sensitivity analysis method and the springback/section deformation prediction finite element model, and by using this model the sensitivities of the springback and the section deformation to process parameters were analyzed and compared. The results show that the most sensitive process conditions for springback angle are the boost speed and the pressure of pressure die, and the most sensitive process condition for section deformation is the number of cores. When the clamp force, the boost speed and the pressure of pressure die are utilized to control section deformation, the effect of these process parameters on springback should be considered. When the process parameters are mainly used to control springback, the effect of these process parameters on the section deformation should be always considered.
基金Supprorted by the Science and Technology Foundation of Jiangsu Construction Committee(JS200214)the Science Research Foundation of Nanjing Institute of Technology(KXJ08122)~~
文摘Experimental results of new type joints between the column and the. steel beam of concrete-filled rectangular steel tubular (CFRT) under reversed cyclic loads are presented. The earthquake resistant capacity of the joint is influenced by infilled concrete, stiffener length and relative dimensions of column and beam. It is found that the hysteresis curves obtained in the experiment are full and the joints have a good energy dissipation capacity. The nonlinear finite element models are also used to analyze the hysteresis behavior of the joints under reversed cyclic loads using ANSYS 8.0. The influences of the stiffener length and the infilled concrete are analyzed. Analytical results show that the stiffener length and the infilled concrete are critical for the joints. Furthermore, the skeleton curves of the finite element models are in good agreement with those of experiments.
文摘In integrated circuits, the defects associated with photolithography are assumed to be in the shape of circular discs in order to perform the estimation of yield and fault analysis. However,real defects exhibit a great variety of shapes. In this paper,a novel yield model is presented and the critical area model of short circuit is correspondingly provided. In comparison with the circular model corrently available, the new model takes the similarity shape to an original defect, the two-dimensional distributional characteristic of defects, the feature of a layout routing and the character of yield estimation into account. As for the aspect of prediction of yield, the experimental results show that the new model may predict the yield caused by real defects more accurately than the circular model does. It is significant that the yield is accurately estimated and improved using the proposed model.
文摘An idealized numerical wave flume has been established by finite element method on the bases of Navier Stokes equations through prescribing the appropriate boundary conditions for the open boundary,incident boundary,free surface and solid boundary in this paper.The characteristics of waves propagating over a step have been investigated by this numerical model.The breaker wave height is determined depending on the kinetic criterion.The numerical model is verified by laboratory experiments,and the empirical formula for the damping of wave height due to breaking is also given by experiments.
基金The National Natural Science Foundation of China(No.50475076)the National High Technology Research and Development Pro-gram of China(863Program)(No.2006AA04Z234)
文摘The environment modeling algorithm named rectangular decomposition, which is composed of cellular nodes and interleaving networks, is proposed. The principle of environment modeling is to divide the environment into individual square sub-areas. Each sub-area is orientated by the central point of the sub-areas called a node. The rectangular map based on the square map can enlarge the square area side size to increase the coverage efficiency in the case of there being an adjacent obstacle. Based on this algorithm, a new coverage algorithm, which includes global path planning and local path planning, is introduced. In the global path planning, uncovered subspaces are found by using a special rule. A one-dimensional array P, which is used to obtain the searching priority of node in every direction, is defined as the search rule. The array P includes the condition of coverage towards the adjacent cells, the condition of connectivity and the priorities defined by the user in all eight directions. In the local path planning, every sub-area is covered by using template models according to the shape of the environment. The simulation experiments show that the coverage algorithm is simple, efficient and adapted for complex two- dimensional environments.
文摘The two-phase detection method for directional discrimination in laser Doppler measurements is discussed.The diffraction efficiency of a sin- gle period rectangular phase grating is analysed and a kind of back-scattered laser Doppler vibrometer without directional ambiguity using the single peri- od rectangular phase grating as the beam-combiner described.The principles of this kind of vibrometer are explained in detail,and some experimental re- sults are given.In this kind of vibrometer,the rectangular phase grating, without the zero diffracted order and even orders,is used to eliminate use- less stray light and to combine the useful signal light.Differential electronics is employed to reject signal noise.Therefore,the signal-to-noise ratio of Doppler signals and the measurement accuracy of the instrument are im- proved and the range of application is expanded.
文摘The wave propagation behavior in an elastic wedge-shaped medium with an arbitrary shaped cylindrical canyon at its vertex has been studied.Numerical computation of the wave displacement field is carried out on and near the canyon surfaces using weighted-residuals(moment method).The wave displacement fields are computed by the residual method for the cases of elliptic,circular,rounded-rectangular and flat-elliptic canyons,The analysis demonstrates that the resulting surface displacement depends,as in similar previous analyses,on several factors including,but not limited,to the angle of the wedge,the geometry of the vertex,the frequencies of the incident waves,the angles of incidence,and the material properties of the media.The analysis provides intriguing results that help to explain geophysical observations regarding the amplification of seismic energy as a function of site conditions.
基金Supported by the National Natural Science Foundation of China (20876107) the Opening Project of State Key Laboratory of Chemical Engineering (SKL-ChE-08B06)
文摘The pressure drop of gas-liquid two-phase flow in microchannel is of fundamental importance in heat and mass transfer processes. In this work,the pressure drop of gas-liquid two-phase flow in horizontal rectangular cross-section microchannels was measured by a pressure differential transducer system. Water,ethanol and n-propanol were used as liquid phase to study the effects of capillary number on pressure drop;air was used as the gas phase. Four microchannels with various dimensions of 100 μm× 200 μm,100 μm× 400 μm,100 μm× 800 μm and 100 μm× 2000 μm(depth × width) were used for determining the influence of configuration on the pressure drop. Experimental results showed that in micro-scale,the capillary number also affected the pressure drop remarkably,and in spite of only one-fold difference in aspect ratio,the variation of pressure drop reached up to near three times under the same experimental conditions. Taking the effects of aspect ratio and surface tension into account,a modi-fied correlation for Chisholm parameter C in the Chisholm model was proposed for predicting the frictional multi-plier,and the predicted values by the proposed correlation showed a satisfactory agreement with experimental data.
基金supported by the Natural Science Foundation of Hebei Province of China(No.E2010001254)
文摘Nonlinear parametric vibration and stability is investigated for an axially accelerating rectangular thin plate subjected to parametric excitations resulting from the axial time-varying tension and axial time-varying speed in the magnetic field. Consid- ering geometric nonlinearity, based on the expressions of total kinetic energy, potential energy, and electromagnetic force, the nonlinear magneto-elastic vibration equations of axially moving rectangular thin plate are derived by using the Hamilton principle. Based on displacement mode hypothesis, by using the Galerkin method, the nonlinear para- metric oscillation equation of the axially moving rectangular thin plate with four simply supported edges in the transverse magnetic field is obtained. The nonlinear principal parametric resonance amplitude-frequency equation is further derived by means of the multiple-scale method. The stability of the steady-state solution is also discussed, and the critical condition of stability is determined. As numerical examples for an axially moving rectangular thin plate, the influences of the detuning parameter, axial speed, axial tension, and magnetic induction intensity on the principal parametric resonance behavior are investigated.
基金Project supported by the Prophase Preparatory Project of Natural Science Foundation of Nantong University,China(Grant No.15ZY16)
文摘A rectangular m × n resistor network with an arbitrary boundary is investigated, and a general resistance formula between two nodes on an arbitrary axis is derived by the Recursion-Transform(RT) method, a problem that has never been resolved before, for the Green's function technique and the Laplacian matrix approach are inapplicable to it. To have the exact solution of resistance is important but it is difficult to obtain under the condition of arbitrary boundary. Our result is directly expressed in a single summation and mainly composed of characteristic roots, which contain both finite and infinite cases. Further, the current distribution is given explicitly as a byproduct of the method. Our framework can be effectively applied to RLC networks. As an application to the LC network, we find that our formulation leads to the occurrence of resonances at h_1= 1-cosφ_i-sinφ_icotnφ_i. This somewhat curious result suggests the possibility of practical applications of our formulae to resonant circuits.
文摘The aim of this study is to apply process mineralogy as a practical tool for further understanding and predicting the flotation kinetics of the copper sulfide minerals. The minerals' composition and association, grain distribution, and liberation within the ore samples were analyzed in the feed, concentrate, and the tailings of the flotation processes with two pulp densities of 25 wt% and 30 wt%. The major copper-bearing minerals identified by microscopic analysis of the concentrate samples included chalcopyrite(56.2 wt%), chalcocite(29.1 wt%),covellite(6.4 wt%), and bornite(4.7 wt%). Pyrite was the main sulfide gangue mineral(3.6 wt%) in the concentrates. A 95% degree of liberation with d_(80) > 80 μm was obtained for chalcopyrite as the main copper mineral in the ore sample. The recovery rate and the grade in the concentrates were enhanced with increasing chalcopyrite particle size. Chalcopyrite particles with a d_(80) of approximately 100 μm were recovered at the early stages of the flotation process. The kinetic studies showed that the kinetic second-order rectangular distribution model perfectly fit the flotation test data. Characterization of the kinetic parameters indicated that the optimum granulation distribution range for achieving a maximum flotation rate for chalcopyrite particles was between the sizes 50 and 55 μm.
基金supported by the China Postdoctoral Science Foundation(Grant No.2012M511192)the National Natural Science Foundation of China(Grant Nos.51209080 and 51061130547+5 种基金Open Fund of State Key Laboratory of Coastaland Off shore Engineering(Grant No.LP1207the Open Fund of State Key Laboratory of Hydraulics and Mountain River Engineering(Grant No.1213)Qing Lan Project and 333 Project of Jiangsu Province(Grant No.BRA2012130)the Fundamental Research Funds for the Central Universities(Hohai University,Grant No.2012B06514the 111 Project(Grant No.B12032)Research Fund for the Doctoral Program of Higher Education of China(Grant No.20120181110084)
文摘A liquid sloshing experimental rig driven by a wave-maker is designed and built to study liquid sloshing problems in a rectangular liquid tank with perforated baffle. A series of experiments are conducted in this experimental rig to estimate the free surface fluctuation and pressure distribution by changing external excitation frequency of the shaking table. An in-house CFD code is also used in this study to simulate the liquid sloshing in three-dimensional (3D) rectangular tank with perforated baffle. Good agreements of free surface elevation and pressure between the numerical results and the experimental data are obtained and presented. Spectral analysis of the time history of free surface elevation is conducted by using the fast Fourier transformation.