Direct numerical simulations have been conducted to investigate the evolution process of liquid metal laminar to turbulent flow in a rectangular duct under the influence of a non-uniform magnetic field.The Reynolds nu...Direct numerical simulations have been conducted to investigate the evolution process of liquid metal laminar to turbulent flow in a rectangular duct under the influence of a non-uniform magnetic field.The Reynolds number is Re=6299,and the inlet Hartmann number is Ha=2900,with the magnetic field strength decreasing along the flow direction.The results indicate that the dynamic reversal of the three-dimensional(3D)Lorentz force direction near the inflection point of the magnetic field dominates the flow reconstruction,driving the wall jet acceleration and forming an M-type velocity distribution.Moreover,the high-speed shear layer of the jet triggers Kelvin-Helmholtz instability,resulting in the generation of secondary vortex structures near the parallel layer in the non-uniform magnetic field region.In the cross-section perpendicular to the flow direction,the secondary flow gradually evolves into a four-vortex structure,while the velocity fluctuations and turbulent kinetic energy reach the peak.Based on the characteristics of the vortex rotation direction near the shear layer,the intrinsic mechanism behind the unique bimodal distribution of the root-mean-square of velocity fluctuations in the parallel layers is revealed.Furthermore,by comparing the evolution of turbulence under different magnetic field gradients,it is revealed that the distributions of shear stress,Reynolds stress,and turbulent kinetic energy exhibit significant parameter dependence.The strong 3D magnetohydrodynamic effects at the magnetic field gradientγ=0.6 have an immediate impact on the pressure distribution.The transverse Lorentz force LFz further promotes the fluid to accumulate at the wall,leading to a significant increase in the pressure drop and transverse pressure difference in the flow.展开更多
Growth of high-quality Nb_(3)Sn thin films for superconducting radiofrequency(SRF)applications using the vapor diffusion method requires a uniform distribution of tin nuclei on the niobium(Nb)surface.This study examin...Growth of high-quality Nb_(3)Sn thin films for superconducting radiofrequency(SRF)applications using the vapor diffusion method requires a uniform distribution of tin nuclei on the niobium(Nb)surface.This study examines the mechanism underlying the observed non-uniform distribution of tin nuclei with tin chloride SnCl_(2).Electron backscatter diffraction(EBSD)analysis was used to examine the correlation between the nucleation behavior and orientation of niobium grains in the substrate.The findings of the density functional theory(DFT)simulation are in good agreement with the experimental results,showing that the non-uniform distribution of tin nuclei is the result of the adsorption energy of SnCl_(2)molecules by varied niobium grain orientations.Further analysis indicated that the surface roughness and grain size of niobium also played significant roles in the nucleation behavior.This study provides valuable insights into enhancing the surface pretreatment of niobium substrates during the growth of Nb_(3)Sn thin films using the vapor diffusion method.展开更多
Cooling system design applicable to more than one photovoltaic(PV)unit may be challenging due to the arrangement and geometry of the modules.Different cooling techniques are provided in this study to regulate the temp...Cooling system design applicable to more than one photovoltaic(PV)unit may be challenging due to the arrangement and geometry of the modules.Different cooling techniques are provided in this study to regulate the temperature of conductive panels that are arranged perpendicular to each other.The model uses two vented cavity systems and one L-shaped channel with ternary nanofluid enhanced non-uniform magnetic field.Their cooling performances and comparative results between different systems are provided.The finite element method is used to conduct a numerical analysis for a range of values of the following:the strength of themagnetic field(Hartmann number(Ha)between 0 and 50),the inclination of the magnetic field(γbetween 0 and 90),and the loading of nanoparticles in the base fluid(ϕbetween 0 and 0.03),taking into account both uniformand non-uniformmagnetic fields.For the L-shaped channel and vented cavities,vortex size is controlled by imposing magnetic field and adjusting its strength.Whether uniform or non-uniform magnetic field is applied affects the cooling performances for different cooling configurations.Temperature drops of the horizontal panel with different magnetic field strengths by using channel cooling,vented cavity-1 and vented cavity-2 systems for uniformmagnetic are 11℃,21.5℃,and 3℃when the reference case of Ha=0 is considered for the same cooling systems.However,they become 9.5℃,13.5℃,and 12.5℃when nonuniform magnetic field is used.In the presence of uniform magnetic field effects and changing its magnitude,the use of cooling channel in vented cavity-1 and vented cavity-2 systems results in temperature drops of 4℃,10.8℃,and 3.8℃for vertical panels.On the other hand,when non-uniform magnetic field effects are present,they become 0.5℃,2.1℃,and 9℃.For L-channel cooling,the average Nu for the horizontal panel is more affected byγ,andNu rises asγrises.With increasing nanoparticle loading of ternary nanofluid,the average panel surface temperature shows a linear drop.For the horizontal panel,the temperature declines for nanofluid at the highest loading are 4℃,10℃,and 12℃as compared to using only base fluid.The values of 5℃,7℃,and 11℃are obtained for the vertical panel.Different cooling systems’performance is estimated using artificial neural networks.The method captures the combined impact of applying non-uniformmagnetic field and nanofluid together on the cooling performancewhile accounting for varied cooling strategies for both panels.展开更多
In low-light image enhancement,prevailing Retinex-based methods often struggle with precise illumina-tion estimation and brightness modulation.This can result in issues such as halo artifacts,blurred edges,and diminis...In low-light image enhancement,prevailing Retinex-based methods often struggle with precise illumina-tion estimation and brightness modulation.This can result in issues such as halo artifacts,blurred edges,and diminished details in bright regions,particularly under non-uniform illumination conditions.We propose an innovative approach that refines low-light images by leveraging an in-depth awareness of local content within the image.By introducing multi-scale effective guided filtering,our method surpasses the limitations of traditional isotropic filters,such as Gaussian filters,in handling non-uniform illumination.It dynamically adjusts regularization parameters in response to local image characteristics and significantly integrates edge perception across different scales.This balanced approach achieves a harmonious blend of smoothing and detail preservation,enabling more accurate illumination estimation.Additionally,we have designed an adaptive gamma correction function that dynamically adjusts the brightness value based on local pixel intensity,further balancing enhancement effects across different brightness levels in the image.Experimental results demonstrate the effectiveness of our proposed method for non-uniform illumination images across various scenarios.It exhibits superior quality and objective evaluation scores compared to existing methods.Our method effectively addresses potential issues that existing methods encounter when processing non-uniform illumination images,producing enhanced images with precise details and natural,vivid colors.展开更多
To investigate the influence of non-uniform water distribution on the mechanical properties and failure behavior of red sandstone,we designed five immersion heights and durations to achieve varying non-uniform water d...To investigate the influence of non-uniform water distribution on the mechanical properties and failure behavior of red sandstone,we designed five immersion heights and durations to achieve varying non-uniform water distribution states.Uniaxial compression tests were conducted on red sandstone under these conditions.The effects of non-uniform water distribution on deformation,failure,strength,and energy characteristics of red sandstone were analyzed.The impact of non-uniform water distribution on the intensity of rock failure was discussed,and the failure mechanism under non-uniform water distribution was revealed.The hazards of low immersion heights on underground rock structures were analyzed.The results demonstrate that peak strength and elastic modulus of red sandstone exhibit high sensitivity to immersion height,with reductions of 38%and 23%respectively even at L=1/50H.Water immersion reduces both energy storage capacity and energy dissipation capability of red sandstone.The immersion height and duration influence the failure mode of red sandstone by controlling the migration and separation of dry-wet interfaces.Low immersion height poses significant risks to underground rock structures(e.g.,a 38%strength reduction when L=1/50H),and the concentration degree of water non-uniform distribution is the key factor in assessing the weakening effect of water on rocks.展开更多
The intrusion of obstacles onto railway tracks presents a significant threat to train safety,characterized by sudden and unpredictable occurrences.With China leading the world in high-speed rail mileage,ensuring railw...The intrusion of obstacles onto railway tracks presents a significant threat to train safety,characterized by sudden and unpredictable occurrences.With China leading the world in high-speed rail mileage,ensuring railway security is paramount.The current laser monitoring technologies suffer from high false alarm rates and unreliable intrusion identification.This study addresses these issues by investigating high-resolution laser monitoring technology for railway obstacles,focusing on key parameters such as monitoring range and resolution.We propose an enhanced non-uniform laser scanning method,developing a laser monitoring system that reduces the obstacle false alarm rate to 2.00%,significantly lower than the 20%standard(TJ/GW135-2015).This rate is the best record for laser monitoring systems on China Railway.Our system operates seamlessly in all weather conditions,providing superior accuracy,resolution,and identification efficiency.It is the only 3D LiDAR system certified by the China State Railway Group Co.,Ltd.(Certificate No.[2023]008).Over three years,our system has been deployed at numerous points along various lines managed by the China State Railway Group,accumulating a dataset of 300,000 observations.This extensive deployment has significantly enhanced railway safety.The development and implementation of our railway laser monitoring system represent a substantial advancement in railway safety technology.Its low false alarm rate(2.00%),high accuracy(20 cm×20 cm×20 cm),and robust performance in diverse conditions underscore its potential for widespread adoption,promising to enhance railway safety in China and internationally.展开更多
Seismic data regularization is an important preprocessing step in seismic signal processing. Traditional seismic acquisition methods follow the Shannon–Nyquist sampling theorem, whereas compressive sensing（CS） prov...Seismic data regularization is an important preprocessing step in seismic signal processing. Traditional seismic acquisition methods follow the Shannon–Nyquist sampling theorem, whereas compressive sensing（CS） provides a fundamentally new paradigm to overcome limitations in data acquisition. Besides the sparse representation of seismic signal in some transform domain and the 1-norm reconstruction algorithm, the seismic data regularization quality of CS-based techniques strongly depends on random undersampling schemes. For 2D seismic data, discrete uniform-based methods have been investigated, where some seismic traces are randomly sampled with an equal probability. However, in theory and practice, some seismic traces with different probability are required to be sampled for satisfying the assumptions in CS. Therefore, designing new undersampling schemes is imperative. We propose a Bernoulli-based random undersampling scheme and its jittered version to determine the regular traces that are randomly sampled with different probability, while both schemes comply with the Bernoulli process distribution. We performed experiments using the Fourier and curvelet transforms and the spectral projected gradient reconstruction algorithm for 1-norm（SPGL1）, and ten different random seeds. According to the signal-to-noise ratio（SNR） between the original and reconstructed seismic data, the detailed experimental results from 2D numerical and physical simulation data show that the proposed novel schemes perform overall better than the discrete uniform schemes.展开更多
Contrary to conventional design methods that assume uniform and slow temperature changes tied to atmospheric conditions,single-layer spherical reticulated shells undergo significant non-uniform and time-variant temper...Contrary to conventional design methods that assume uniform and slow temperature changes tied to atmospheric conditions,single-layer spherical reticulated shells undergo significant non-uniform and time-variant temperature variations due to dynamic environmental coupling.These differences can affect structural performance and pose safety risks.Here,a systematic numerical method was developed and applied to simulate long-term temperature variations in such a structure under real environmental conditions,revealing its non-uniform distribution characteristics and time-variant regularity.A simplified design method for non-uniform thermal loads,accounting for time-variant environmental factors,was theoretically derived and validated through experiments and simulations.The maximum deviation and mean error rate between calculated and tested results were 6.1℃ and 3.7%,respectively.Calculated temperature fields aligned with simulated ones,with deviations under 6.0℃.Using the design method,non-uniform thermal effects of the structure are analyzed.Maximum member stress and nodal displacement under non-uniform thermal loads reached 119.3 MPa and 19.7 mm,representing increases of 167.5%and 169.9%,respectively,compared to uniform thermal loads.The impacts of healing construction time on non-uniform thermal effects were evaluated,resulting in construction recommendations.The methodologies and conclusions presented here can serve as valuable references for the thermal design,construction,and control of single-layer spherical reticulated shells or similar structures.展开更多
Backfill mining is one of the most important technical means for controlling strata movement and reducing surface subsidence and environmental damage during exploitation of underground coal resources. Ensuring the sta...Backfill mining is one of the most important technical means for controlling strata movement and reducing surface subsidence and environmental damage during exploitation of underground coal resources. Ensuring the stability of the backfill bodies is the primary prerequisite for maintaining the safety of the backfilling working face, and the loading characteristics of backfill are closely related to the deformation and subsidence of the roof. Elastic thin plate model was used to explore the non-uniform subsidence law of the roof, and then the non-uniform distribution characteristics of backfill bodies’ load were revealed. Through a self-developed non-uniform loading device combined with acoustic emission (AE) and digital image correlation (DIC) monitoring technology, the synergistic dynamic evolution law of the bearing capacity, apparent crack, and internal fracture of cemented coal gangue backfills (CCGBs) under loads with different degrees of non-uniformity was deeply explored. The results showed that: 1) The uniaxial compressive strength (UCS) of CCGB increased and then decreased with an increase in the degree of non-uniformity of load (DNL). About 40% of DNL was the inflection point of DNL-UCS curve and when DNL exceeded 40%, the strength decreased in a cliff-like manner;2) A positive correlation was observed between the AE ringing count and UCS during the loading process of the specimen, which was manifested by a higher AE ringing count of the high-strength specimen. 3) Shear cracks gradually increased and failure mode of specimens gradually changed from “X” type dominated by tension cracks to inverted “Y” type dominated by shear cracks with an increase in DNL, and the crack opening displacement at the peak stress decreased and then increased. The crack opening displacement at 40% of the DNL was the smallest. This was consistent with the judgment of crack size based on the AE b-value, i. e., it showed the typical characteristics of “small b-value-large crack and large b-value-small crack”. The research results are of significance for preventing the instability and failure of backfill.展开更多
During the production,the fluid in the vicinity of the directional well enters the wellbore with different rates,leading to non-uniform flux distribution along the directional well.However,in all existing studies,it i...During the production,the fluid in the vicinity of the directional well enters the wellbore with different rates,leading to non-uniform flux distribution along the directional well.However,in all existing studies,it is oversimplified to a uniform flux distribution,which can result in inaccurate results for field applications.Therefore,this paper proposes a semi-analytical model of a directional well based on the assumption of non-uniform flux distribution.Specifically,the direction well is discretized into a carefully chosen series of linear sources,such that the complex well trajectory can be captured and the nonuniform flux distribution along the wellbore can be considered to model the three-dimensional flow behavior.By using the finite difference method,we can obtain the numerical solutions of the transient flow within the wellbore.With the aid of Green's function method,we can obtain the analytical solutions of the transient flow from the matrix to the wellbore.The complete flow behavior of a directional well is perfectly represented by coupling the above two types of transient flow.Subsequently,on the basis of the proposed model,we conduct a comprehensive analysis of the pressure transient behavior of a directional well.The computation results show that the flux variation along the direction well has a significant effect on pressure responses.In addition,the directional well in an infinite reservoir may exhibit the following flow regimes:wellbore afterflow,transition flow,inclined radial flow,elliptical flow,horizontal linear flow,and horizontal radial flow.The horizontal linear flow can be observed only if the formation thickness is much smaller than the well length.Furthermore,a dip region that appears on the pressure derivative curve indicates the three-dimensional flow behavior near the wellbore.展开更多
In current dual porosity/permeability models,there exists a fundamental assumption that the adsorption-induced swelling is distributed uniformly within the representative elementary volume (REV),irrespective of its in...In current dual porosity/permeability models,there exists a fundamental assumption that the adsorption-induced swelling is distributed uniformly within the representative elementary volume (REV),irrespective of its internal structures and transient processes.However,both internal structures and transient processes can lead to the non-uniform swelling.In this study,we hypothesize that the non-uniform swelling is responsible for why coal permeability in experimental measurements is not only controlled by the effective stress but also is affected by the adsorption-induced swelling.We propose a concept of the swelling triangle composed of swelling paths to characterize the evolution of the non-uniform swelling and serve as a core link in coupled multiphysics.A swelling path is determined by a dimensionless volumetric ratio and a dimensionless swelling ratio.Different swelling paths have the same start and end point,and each swelling path represents a unique swelling case.The swelling path as the diagonal of the triangle represents the case of the uniform swelling while that as the two perpendicular boundaries represents the case of the localized swelling.The paths of all intermediate cases populate inside the triangle.The corresponding relations between the swelling path and the response of coal multiphysics are established by a non-uniform swelling coefficient.We define this method as the triangle approach and corresponding models as swelling path-based ones.The proposed concept and models are verified against a long-term experimental measurement of permeability and strains under constant effective stress.Our results demonstrate that during gas injection,coal multiphysics responses have a close dependence on the swelling path,and that in both future experiments and field predictions,this dependence must be considered.展开更多
Corner stall receives noticeable attention in the aeroengine field as an important phenomenon in highly-load compressors.Non-uniform leading-edge tubercles,as an effective method to delay stall,are introduced into the...Corner stall receives noticeable attention in the aeroengine field as an important phenomenon in highly-load compressors.Non-uniform leading-edge tubercles,as an effective method to delay stall,are introduced into the compressor.In this paper,the shape of leading-edge tubercles was controlled by a third-order Fourier function.To judge corner stall,a more precise stall indicator for compressor cascade with flow control methods was defined.Besides,the total kinetic energy of the secondary flow at large incidence was adopted as a parameter for stall evaluation to save computing resources.The results of multiobjective optimization reveal that the loss coefficient exhibited negligible variation at design incidence,while the total kinetic energy of secondary flow showed a significant reduction at large incidence,resulting in a substantial increase in stall incidence.In the optimal profiling cases,the stall incidencewas delayed from 7.9°to 11.6°.The major purpose of the research is to provide proper design guidelines for nonuniformleading-edge tubercles and uncover the flow controlmechanisms of leading-edge profiling.Hence,the geometric features that meet different optimization objectives were extracted through geometric analysis near the Pareto Front and through Self-OrganizingMap(SOM)dataminingmethods in the optimization database.Besides,flow field analysis reveals the flow control mechanism of leading-edge tubercles.The convex-concave-convex structure at the 0%-70%blade height region can form two branches of leading-edge vortex pairs that are opposite in the rotation direction to the passage vortex.The two branches of leading-edge vortex pairs mixed with the leading-edge separation vortex to form two stronger mixed vortices,which can effectively suppress the development of passage vortex and delay stall incidence.展开更多
Polymer flooding in fractured wells has been extensively applied in oilfields to enhance oil recovery.In contrast to water,polymer solution exhibits non-Newtonian and nonlinear behavior such as effects of shear thinni...Polymer flooding in fractured wells has been extensively applied in oilfields to enhance oil recovery.In contrast to water,polymer solution exhibits non-Newtonian and nonlinear behavior such as effects of shear thinning and shear thickening,polymer convection,diffusion,adsorption retention,inaccessible pore volume and reduced effective permeability.Meanwhile,the flux density and fracture conductivity along the hydraulic fracture are generally non-uniform due to the effects of pressure distribution,formation damage,and proppant breakage.In this paper,we present an oil-water two-phase flow model that captures these complex non-Newtonian and nonlinear behavior,and non-uniform fracture characteristics in fractured polymer flooding.The hydraulic fracture is firstly divided into two parts:high-conductivity fracture near the wellbore and low-conductivity fracture in the far-wellbore section.A hybrid grid system,including perpendicular bisection(PEBI)and Cartesian grid,is applied to discrete the partial differential flow equations,and the local grid refinement method is applied in the near-wellbore region to accurately calculate the pressure distribution and shear rate of polymer solution.The combination of polymer behavior characterizations and numerical flow simulations are applied,resulting in the calculation for the distribution of water saturation,polymer concentration and reservoir pressure.Compared with the polymer flooding well with uniform fracture conductivity,this non-uniform fracture conductivity model exhibits the larger pressure difference,and the shorter bilinear flow period due to the decrease of fracture flow ability in the far-wellbore section.The field case of the fall-off test demonstrates that the proposed method characterizes fracture characteristics more accurately,and yields fracture half-lengths that better match engineering reality,enabling a quantitative segmented characterization of the near-wellbore section with high fracture conductivity and the far-wellbore section with low fracture conductivity.The novelty of this paper is the analysis of pressure performances caused by the fracture dynamics and polymer rheology,as well as an analysis method that derives formation and fracture parameters based on the pressure and its derivative curves.展开更多
Radioheliographs can obtain solar images at high temporal and spatial resolution,with a high dynamic range.These are among the most important instruments for studying solar radio bursts,understanding solar eruption ev...Radioheliographs can obtain solar images at high temporal and spatial resolution,with a high dynamic range.These are among the most important instruments for studying solar radio bursts,understanding solar eruption events,and conducting space weather forecasting.This study aims to explore the effective use of radioheliographs for solar observations,specifically for imaging coronal mass ejections(CME),to track their evolution and provide space weather warnings.We have developed an imaging simulation program based on the principle of aperture synthesis imaging,covering the entire data processing flow from antenna configuration to dirty map generation.For grid processing,we propose an improved non-uniform fast Fourier transform(NUFFT)method to provide superior image quality.Using simulated imaging of radio coronal mass ejections,we provide practical recommendations for the performance of radioheliographs.This study provides important support for the validation and calibration of radioheliograph data processing,and is expected to profoundly enhance our understanding of solar activities.展开更多
This paper is concerned with a study of wave propagation due to scattering of an obliquely incident wave by a porous vertical plate with nonuniform porosity which is completely submerged in water of finite depth.The p...This paper is concerned with a study of wave propagation due to scattering of an obliquely incident wave by a porous vertical plate with nonuniform porosity which is completely submerged in water of finite depth.The problem is formulated in terms of a Fredholm integral equation of the second kind in difference in potential across the barrier.The integral equation is then solved using two methods:the boundary element method and the collocation method.The reflection coefficients,transmission coefficient,and amount of energy dissipation are evaluated using the solution of the integral equation.It is observed that non-uniform porosity of a barrier has significant effect on the reflection of waves and energy dissipation compared to a barrier with uniform porosity.The dissipation of the wave energy by a non-uniform porous barrier can be enhanced and can be made larger than that of a barrier with uniform porosity,by suitable choice of non-uniform porosity distribution in the barrier.This has an important bearing on reducing the wave power and thereby protecting the shore line from coastal erosion.Also,an obliquely incident wave reduces reflection and dissipation while increasing transmission of wave energy as compared to a normally incident wave.展开更多
To analyze a multibody system composed of non-uniform beam and spring-mass subsystems, the model discretization is carried on by utilizing the finite element method（FEM）, the dynamic model of non-uniform beam is dev...To analyze a multibody system composed of non-uniform beam and spring-mass subsystems, the model discretization is carried on by utilizing the finite element method（FEM）, the dynamic model of non-uniform beam is developed by using the transfer matrix method of multibody system（MS-TMM）, the transfer matrix of non-u- niform beam is derived, and the natural frequencies are computed. Compared with the numerical assembly method （NAM）, the results by MS-TMM have good agreement with the results by FEM, and are better than the results by NAM. When using the high precision method, the global dynamic equations of the complex multibody system are not needed and the orders of involved system matrices are decreased greatly. For the investigation on the re- verse problem of the physical parameter identification of multibody system, MS-TMM and the optimization tech- nology based on genetic algorithms（GAs） are combined and extended. The identification problem is exchanged for an optimization problem, and it is formulated as a global minimum solution of the objective function with respect to natural frequencies of multibody system. At last, the numerical example of non-uniform beam with attach- ments is discussed, and the identification results indicate the feasibility and the effectivity of the proposed aop- proach.展开更多
Array configuration of multiple-input multiple-output （MIMO） radar with non-uniform linear array （NLA） is proposed. Unlike a standard phased-array radar where NLA is used to generate thinner beam patterns, in MIMO...Array configuration of multiple-input multiple-output （MIMO） radar with non-uniform linear array （NLA） is proposed. Unlike a standard phased-array radar where NLA is used to generate thinner beam patterns, in MIMO radar the property of NLA is exploited to get more distinct virtual array elements so as to improve pa- rameter identifiability, which means the maximum number of targets that can be uniquely identified by the radar. A class of NLA called minimum redundancy linear array （MRLA） is employed and a new method to construct large MRLAs is descrihed. The numerical results verify that compared to uniform linear array （ULA） MIMO radars, NLA MIMO radars can retain the same parameter identifiability with fewer physical antennas and achieve larger aperture length and lower Cramer-Rao bound with the same number of the physical antennas.展开更多
Aim To find an effective and fast algorithm to analyze undersampled signals. Methods\ The advantage of high order ambiguity function(HAF) algorithm is that it can analyze polynomial phase signals by phase rank reduct...Aim To find an effective and fast algorithm to analyze undersampled signals. Methods\ The advantage of high order ambiguity function(HAF) algorithm is that it can analyze polynomial phase signals by phase rank reduction. In this paper, it was first used to analyze the parameters of undersampled signals. When some conditions are satisfied, the problem of frequency confusion can be solved. Results and Conclusion\ As an example, we analyze undersampled linear frequency modulated signal. The simulation results verify the effectiveness of HAF algorithm. Compared with time frequency distribution, HAF algorithm reduces computation burden to a great extent, needs weak boundary conditions and doesn't have boundary effect.展开更多
基金supported by the Chinese Academy of Sciences Project for Young Scientists in Basic Research(Grant No.YSBR-087)and the National Key R&D Program of China(Grant No.2022YFA1204100)。
文摘Direct numerical simulations have been conducted to investigate the evolution process of liquid metal laminar to turbulent flow in a rectangular duct under the influence of a non-uniform magnetic field.The Reynolds number is Re=6299,and the inlet Hartmann number is Ha=2900,with the magnetic field strength decreasing along the flow direction.The results indicate that the dynamic reversal of the three-dimensional(3D)Lorentz force direction near the inflection point of the magnetic field dominates the flow reconstruction,driving the wall jet acceleration and forming an M-type velocity distribution.Moreover,the high-speed shear layer of the jet triggers Kelvin-Helmholtz instability,resulting in the generation of secondary vortex structures near the parallel layer in the non-uniform magnetic field region.In the cross-section perpendicular to the flow direction,the secondary flow gradually evolves into a four-vortex structure,while the velocity fluctuations and turbulent kinetic energy reach the peak.Based on the characteristics of the vortex rotation direction near the shear layer,the intrinsic mechanism behind the unique bimodal distribution of the root-mean-square of velocity fluctuations in the parallel layers is revealed.Furthermore,by comparing the evolution of turbulence under different magnetic field gradients,it is revealed that the distributions of shear stress,Reynolds stress,and turbulent kinetic energy exhibit significant parameter dependence.The strong 3D magnetohydrodynamic effects at the magnetic field gradientγ=0.6 have an immediate impact on the pressure distribution.The transverse Lorentz force LFz further promotes the fluid to accumulate at the wall,leading to a significant increase in the pressure drop and transverse pressure difference in the flow.
基金supported by the National Natural Science Foundation of China(No.12175283)Youth Innovation Promotion Association of Chinese Academy of Sciences(2020410)Advanced Energy Science and Technology Guangdong Laboratory(HND20TDSPCD,HND22PTDZD).
文摘Growth of high-quality Nb_(3)Sn thin films for superconducting radiofrequency(SRF)applications using the vapor diffusion method requires a uniform distribution of tin nuclei on the niobium(Nb)surface.This study examines the mechanism underlying the observed non-uniform distribution of tin nuclei with tin chloride SnCl_(2).Electron backscatter diffraction(EBSD)analysis was used to examine the correlation between the nucleation behavior and orientation of niobium grains in the substrate.The findings of the density functional theory(DFT)simulation are in good agreement with the experimental results,showing that the non-uniform distribution of tin nuclei is the result of the adsorption energy of SnCl_(2)molecules by varied niobium grain orientations.Further analysis indicated that the surface roughness and grain size of niobium also played significant roles in the nucleation behavior.This study provides valuable insights into enhancing the surface pretreatment of niobium substrates during the growth of Nb_(3)Sn thin films using the vapor diffusion method.
基金funded by the Deanship of Scientific Research and Libraries,Princess Nourah bint Abdulrahman University,through the Program of Research Project Funding after Publication,grant No.(RPFAP-88-1445).
文摘Cooling system design applicable to more than one photovoltaic(PV)unit may be challenging due to the arrangement and geometry of the modules.Different cooling techniques are provided in this study to regulate the temperature of conductive panels that are arranged perpendicular to each other.The model uses two vented cavity systems and one L-shaped channel with ternary nanofluid enhanced non-uniform magnetic field.Their cooling performances and comparative results between different systems are provided.The finite element method is used to conduct a numerical analysis for a range of values of the following:the strength of themagnetic field(Hartmann number(Ha)between 0 and 50),the inclination of the magnetic field(γbetween 0 and 90),and the loading of nanoparticles in the base fluid(ϕbetween 0 and 0.03),taking into account both uniformand non-uniformmagnetic fields.For the L-shaped channel and vented cavities,vortex size is controlled by imposing magnetic field and adjusting its strength.Whether uniform or non-uniform magnetic field is applied affects the cooling performances for different cooling configurations.Temperature drops of the horizontal panel with different magnetic field strengths by using channel cooling,vented cavity-1 and vented cavity-2 systems for uniformmagnetic are 11℃,21.5℃,and 3℃when the reference case of Ha=0 is considered for the same cooling systems.However,they become 9.5℃,13.5℃,and 12.5℃when nonuniform magnetic field is used.In the presence of uniform magnetic field effects and changing its magnitude,the use of cooling channel in vented cavity-1 and vented cavity-2 systems results in temperature drops of 4℃,10.8℃,and 3.8℃for vertical panels.On the other hand,when non-uniform magnetic field effects are present,they become 0.5℃,2.1℃,and 9℃.For L-channel cooling,the average Nu for the horizontal panel is more affected byγ,andNu rises asγrises.With increasing nanoparticle loading of ternary nanofluid,the average panel surface temperature shows a linear drop.For the horizontal panel,the temperature declines for nanofluid at the highest loading are 4℃,10℃,and 12℃as compared to using only base fluid.The values of 5℃,7℃,and 11℃are obtained for the vertical panel.Different cooling systems’performance is estimated using artificial neural networks.The method captures the combined impact of applying non-uniformmagnetic field and nanofluid together on the cooling performancewhile accounting for varied cooling strategies for both panels.
文摘In low-light image enhancement,prevailing Retinex-based methods often struggle with precise illumina-tion estimation and brightness modulation.This can result in issues such as halo artifacts,blurred edges,and diminished details in bright regions,particularly under non-uniform illumination conditions.We propose an innovative approach that refines low-light images by leveraging an in-depth awareness of local content within the image.By introducing multi-scale effective guided filtering,our method surpasses the limitations of traditional isotropic filters,such as Gaussian filters,in handling non-uniform illumination.It dynamically adjusts regularization parameters in response to local image characteristics and significantly integrates edge perception across different scales.This balanced approach achieves a harmonious blend of smoothing and detail preservation,enabling more accurate illumination estimation.Additionally,we have designed an adaptive gamma correction function that dynamically adjusts the brightness value based on local pixel intensity,further balancing enhancement effects across different brightness levels in the image.Experimental results demonstrate the effectiveness of our proposed method for non-uniform illumination images across various scenarios.It exhibits superior quality and objective evaluation scores compared to existing methods.Our method effectively addresses potential issues that existing methods encounter when processing non-uniform illumination images,producing enhanced images with precise details and natural,vivid colors.
基金supported by the National Natural Science Foundation of China(Nos.52474133,52304227,52304091,and 52374095)the Natural Science Foundation of Hunan Province(Nos.2025JJ50316 and 2023JJ40548).
文摘To investigate the influence of non-uniform water distribution on the mechanical properties and failure behavior of red sandstone,we designed five immersion heights and durations to achieve varying non-uniform water distribution states.Uniaxial compression tests were conducted on red sandstone under these conditions.The effects of non-uniform water distribution on deformation,failure,strength,and energy characteristics of red sandstone were analyzed.The impact of non-uniform water distribution on the intensity of rock failure was discussed,and the failure mechanism under non-uniform water distribution was revealed.The hazards of low immersion heights on underground rock structures were analyzed.The results demonstrate that peak strength and elastic modulus of red sandstone exhibit high sensitivity to immersion height,with reductions of 38%and 23%respectively even at L=1/50H.Water immersion reduces both energy storage capacity and energy dissipation capability of red sandstone.The immersion height and duration influence the failure mode of red sandstone by controlling the migration and separation of dry-wet interfaces.Low immersion height poses significant risks to underground rock structures(e.g.,a 38%strength reduction when L=1/50H),and the concentration degree of water non-uniform distribution is the key factor in assessing the weakening effect of water on rocks.
基金financially supported by the National Natural Science Foundation of China(Nos.62275244,62375258,62225507,U2033211,62175230,and 62175232)the CAS Project for Young Scientists in Basic Research(No.YSBR-065)+2 种基金Scientific Instrument Developing Project of the Chinese Academy of Sciences(No.YJKYYQ20200001)National Key R&D Program of China(No.2022YFB3607800,No.2022YFB3605800,and No.2022YFB4601501)Key Program of the Chinese Academy of Sciences(ZDBS-ZRKJZ-TLC018)。
文摘The intrusion of obstacles onto railway tracks presents a significant threat to train safety,characterized by sudden and unpredictable occurrences.With China leading the world in high-speed rail mileage,ensuring railway security is paramount.The current laser monitoring technologies suffer from high false alarm rates and unreliable intrusion identification.This study addresses these issues by investigating high-resolution laser monitoring technology for railway obstacles,focusing on key parameters such as monitoring range and resolution.We propose an enhanced non-uniform laser scanning method,developing a laser monitoring system that reduces the obstacle false alarm rate to 2.00%,significantly lower than the 20%standard(TJ/GW135-2015).This rate is the best record for laser monitoring systems on China Railway.Our system operates seamlessly in all weather conditions,providing superior accuracy,resolution,and identification efficiency.It is the only 3D LiDAR system certified by the China State Railway Group Co.,Ltd.(Certificate No.[2023]008).Over three years,our system has been deployed at numerous points along various lines managed by the China State Railway Group,accumulating a dataset of 300,000 observations.This extensive deployment has significantly enhanced railway safety.The development and implementation of our railway laser monitoring system represent a substantial advancement in railway safety technology.Its low false alarm rate(2.00%),high accuracy(20 cm×20 cm×20 cm),and robust performance in diverse conditions underscore its potential for widespread adoption,promising to enhance railway safety in China and internationally.
基金financially supported by The 2011 Prospective Research Project of SINOPEC(P11096)
文摘Seismic data regularization is an important preprocessing step in seismic signal processing. Traditional seismic acquisition methods follow the Shannon–Nyquist sampling theorem, whereas compressive sensing（CS） provides a fundamentally new paradigm to overcome limitations in data acquisition. Besides the sparse representation of seismic signal in some transform domain and the 1-norm reconstruction algorithm, the seismic data regularization quality of CS-based techniques strongly depends on random undersampling schemes. For 2D seismic data, discrete uniform-based methods have been investigated, where some seismic traces are randomly sampled with an equal probability. However, in theory and practice, some seismic traces with different probability are required to be sampled for satisfying the assumptions in CS. Therefore, designing new undersampling schemes is imperative. We propose a Bernoulli-based random undersampling scheme and its jittered version to determine the regular traces that are randomly sampled with different probability, while both schemes comply with the Bernoulli process distribution. We performed experiments using the Fourier and curvelet transforms and the spectral projected gradient reconstruction algorithm for 1-norm（SPGL1）, and ten different random seeds. According to the signal-to-noise ratio（SNR） between the original and reconstructed seismic data, the detailed experimental results from 2D numerical and physical simulation data show that the proposed novel schemes perform overall better than the discrete uniform schemes.
基金This work is supported by the National Natural Science Foundation of China(Nos.51578491 and 52238001).
文摘Contrary to conventional design methods that assume uniform and slow temperature changes tied to atmospheric conditions,single-layer spherical reticulated shells undergo significant non-uniform and time-variant temperature variations due to dynamic environmental coupling.These differences can affect structural performance and pose safety risks.Here,a systematic numerical method was developed and applied to simulate long-term temperature variations in such a structure under real environmental conditions,revealing its non-uniform distribution characteristics and time-variant regularity.A simplified design method for non-uniform thermal loads,accounting for time-variant environmental factors,was theoretically derived and validated through experiments and simulations.The maximum deviation and mean error rate between calculated and tested results were 6.1℃ and 3.7%,respectively.Calculated temperature fields aligned with simulated ones,with deviations under 6.0℃.Using the design method,non-uniform thermal effects of the structure are analyzed.Maximum member stress and nodal displacement under non-uniform thermal loads reached 119.3 MPa and 19.7 mm,representing increases of 167.5%and 169.9%,respectively,compared to uniform thermal loads.The impacts of healing construction time on non-uniform thermal effects were evaluated,resulting in construction recommendations.The methodologies and conclusions presented here can serve as valuable references for the thermal design,construction,and control of single-layer spherical reticulated shells or similar structures.
基金Project(51925402) supported by the National Natural Science Foundation for Distinguished Young Scholars of ChinaProject(202303021211060) supported by the Natural Science Research General Program for Shanxi Provincial Basic Research Program,China+1 种基金Project(U22A20169) supported by the Joint Fund Project of National Natural Science Foundation of ChinaProjects(2021SX-TD001, 2021SX-TD002) supported by the Shanxi-Zheda Institute of Advanced Materials and Chemical Engineering,China。
文摘Backfill mining is one of the most important technical means for controlling strata movement and reducing surface subsidence and environmental damage during exploitation of underground coal resources. Ensuring the stability of the backfill bodies is the primary prerequisite for maintaining the safety of the backfilling working face, and the loading characteristics of backfill are closely related to the deformation and subsidence of the roof. Elastic thin plate model was used to explore the non-uniform subsidence law of the roof, and then the non-uniform distribution characteristics of backfill bodies’ load were revealed. Through a self-developed non-uniform loading device combined with acoustic emission (AE) and digital image correlation (DIC) monitoring technology, the synergistic dynamic evolution law of the bearing capacity, apparent crack, and internal fracture of cemented coal gangue backfills (CCGBs) under loads with different degrees of non-uniformity was deeply explored. The results showed that: 1) The uniaxial compressive strength (UCS) of CCGB increased and then decreased with an increase in the degree of non-uniformity of load (DNL). About 40% of DNL was the inflection point of DNL-UCS curve and when DNL exceeded 40%, the strength decreased in a cliff-like manner;2) A positive correlation was observed between the AE ringing count and UCS during the loading process of the specimen, which was manifested by a higher AE ringing count of the high-strength specimen. 3) Shear cracks gradually increased and failure mode of specimens gradually changed from “X” type dominated by tension cracks to inverted “Y” type dominated by shear cracks with an increase in DNL, and the crack opening displacement at the peak stress decreased and then increased. The crack opening displacement at 40% of the DNL was the smallest. This was consistent with the judgment of crack size based on the AE b-value, i. e., it showed the typical characteristics of “small b-value-large crack and large b-value-small crack”. The research results are of significance for preventing the instability and failure of backfill.
基金the financial support provided by the National Natural Science Foundation of China(No.52104043)。
文摘During the production,the fluid in the vicinity of the directional well enters the wellbore with different rates,leading to non-uniform flux distribution along the directional well.However,in all existing studies,it is oversimplified to a uniform flux distribution,which can result in inaccurate results for field applications.Therefore,this paper proposes a semi-analytical model of a directional well based on the assumption of non-uniform flux distribution.Specifically,the direction well is discretized into a carefully chosen series of linear sources,such that the complex well trajectory can be captured and the nonuniform flux distribution along the wellbore can be considered to model the three-dimensional flow behavior.By using the finite difference method,we can obtain the numerical solutions of the transient flow within the wellbore.With the aid of Green's function method,we can obtain the analytical solutions of the transient flow from the matrix to the wellbore.The complete flow behavior of a directional well is perfectly represented by coupling the above two types of transient flow.Subsequently,on the basis of the proposed model,we conduct a comprehensive analysis of the pressure transient behavior of a directional well.The computation results show that the flux variation along the direction well has a significant effect on pressure responses.In addition,the directional well in an infinite reservoir may exhibit the following flow regimes:wellbore afterflow,transition flow,inclined radial flow,elliptical flow,horizontal linear flow,and horizontal radial flow.The horizontal linear flow can be observed only if the formation thickness is much smaller than the well length.Furthermore,a dip region that appears on the pressure derivative curve indicates the three-dimensional flow behavior near the wellbore.
基金supported by the Australian Research Council(Grant No.DP200101293)supported by the UWA-China Joint Scholarships(201906430030).
文摘In current dual porosity/permeability models,there exists a fundamental assumption that the adsorption-induced swelling is distributed uniformly within the representative elementary volume (REV),irrespective of its internal structures and transient processes.However,both internal structures and transient processes can lead to the non-uniform swelling.In this study,we hypothesize that the non-uniform swelling is responsible for why coal permeability in experimental measurements is not only controlled by the effective stress but also is affected by the adsorption-induced swelling.We propose a concept of the swelling triangle composed of swelling paths to characterize the evolution of the non-uniform swelling and serve as a core link in coupled multiphysics.A swelling path is determined by a dimensionless volumetric ratio and a dimensionless swelling ratio.Different swelling paths have the same start and end point,and each swelling path represents a unique swelling case.The swelling path as the diagonal of the triangle represents the case of the uniform swelling while that as the two perpendicular boundaries represents the case of the localized swelling.The paths of all intermediate cases populate inside the triangle.The corresponding relations between the swelling path and the response of coal multiphysics are established by a non-uniform swelling coefficient.We define this method as the triangle approach and corresponding models as swelling path-based ones.The proposed concept and models are verified against a long-term experimental measurement of permeability and strains under constant effective stress.Our results demonstrate that during gas injection,coal multiphysics responses have a close dependence on the swelling path,and that in both future experiments and field predictions,this dependence must be considered.
基金support by the National Natural Science Foundation of China(No.52076179).
文摘Corner stall receives noticeable attention in the aeroengine field as an important phenomenon in highly-load compressors.Non-uniform leading-edge tubercles,as an effective method to delay stall,are introduced into the compressor.In this paper,the shape of leading-edge tubercles was controlled by a third-order Fourier function.To judge corner stall,a more precise stall indicator for compressor cascade with flow control methods was defined.Besides,the total kinetic energy of the secondary flow at large incidence was adopted as a parameter for stall evaluation to save computing resources.The results of multiobjective optimization reveal that the loss coefficient exhibited negligible variation at design incidence,while the total kinetic energy of secondary flow showed a significant reduction at large incidence,resulting in a substantial increase in stall incidence.In the optimal profiling cases,the stall incidencewas delayed from 7.9°to 11.6°.The major purpose of the research is to provide proper design guidelines for nonuniformleading-edge tubercles and uncover the flow controlmechanisms of leading-edge profiling.Hence,the geometric features that meet different optimization objectives were extracted through geometric analysis near the Pareto Front and through Self-OrganizingMap(SOM)dataminingmethods in the optimization database.Besides,flow field analysis reveals the flow control mechanism of leading-edge tubercles.The convex-concave-convex structure at the 0%-70%blade height region can form two branches of leading-edge vortex pairs that are opposite in the rotation direction to the passage vortex.The two branches of leading-edge vortex pairs mixed with the leading-edge separation vortex to form two stronger mixed vortices,which can effectively suppress the development of passage vortex and delay stall incidence.
基金This work is supported by the National Natural Science Foundation of China(No.52104049)the Young Elite Scientist Sponsorship Program by Beijing Association for Science and Technology(No.BYESS2023262)Science Foundation of China University of Petroleum,Beijing(No.2462022BJRC004).
文摘Polymer flooding in fractured wells has been extensively applied in oilfields to enhance oil recovery.In contrast to water,polymer solution exhibits non-Newtonian and nonlinear behavior such as effects of shear thinning and shear thickening,polymer convection,diffusion,adsorption retention,inaccessible pore volume and reduced effective permeability.Meanwhile,the flux density and fracture conductivity along the hydraulic fracture are generally non-uniform due to the effects of pressure distribution,formation damage,and proppant breakage.In this paper,we present an oil-water two-phase flow model that captures these complex non-Newtonian and nonlinear behavior,and non-uniform fracture characteristics in fractured polymer flooding.The hydraulic fracture is firstly divided into two parts:high-conductivity fracture near the wellbore and low-conductivity fracture in the far-wellbore section.A hybrid grid system,including perpendicular bisection(PEBI)and Cartesian grid,is applied to discrete the partial differential flow equations,and the local grid refinement method is applied in the near-wellbore region to accurately calculate the pressure distribution and shear rate of polymer solution.The combination of polymer behavior characterizations and numerical flow simulations are applied,resulting in the calculation for the distribution of water saturation,polymer concentration and reservoir pressure.Compared with the polymer flooding well with uniform fracture conductivity,this non-uniform fracture conductivity model exhibits the larger pressure difference,and the shorter bilinear flow period due to the decrease of fracture flow ability in the far-wellbore section.The field case of the fall-off test demonstrates that the proposed method characterizes fracture characteristics more accurately,and yields fracture half-lengths that better match engineering reality,enabling a quantitative segmented characterization of the near-wellbore section with high fracture conductivity and the far-wellbore section with low fracture conductivity.The novelty of this paper is the analysis of pressure performances caused by the fracture dynamics and polymer rheology,as well as an analysis method that derives formation and fracture parameters based on the pressure and its derivative curves.
基金supported by the grants of National Natural Science Foundation of China(42374219,42127804)the Qilu Young Researcher Project of Shandong University.
文摘Radioheliographs can obtain solar images at high temporal and spatial resolution,with a high dynamic range.These are among the most important instruments for studying solar radio bursts,understanding solar eruption events,and conducting space weather forecasting.This study aims to explore the effective use of radioheliographs for solar observations,specifically for imaging coronal mass ejections(CME),to track their evolution and provide space weather warnings.We have developed an imaging simulation program based on the principle of aperture synthesis imaging,covering the entire data processing flow from antenna configuration to dirty map generation.For grid processing,we propose an improved non-uniform fast Fourier transform(NUFFT)method to provide superior image quality.Using simulated imaging of radio coronal mass ejections,we provide practical recommendations for the performance of radioheliographs.This study provides important support for the validation and calibration of radioheliograph data processing,and is expected to profoundly enhance our understanding of solar activities.
基金partially supported by SVMCM scholarship No.WBP211645525952 by Government of West Bengal,India,through Shreya Banerjee.
文摘This paper is concerned with a study of wave propagation due to scattering of an obliquely incident wave by a porous vertical plate with nonuniform porosity which is completely submerged in water of finite depth.The problem is formulated in terms of a Fredholm integral equation of the second kind in difference in potential across the barrier.The integral equation is then solved using two methods:the boundary element method and the collocation method.The reflection coefficients,transmission coefficient,and amount of energy dissipation are evaluated using the solution of the integral equation.It is observed that non-uniform porosity of a barrier has significant effect on the reflection of waves and energy dissipation compared to a barrier with uniform porosity.The dissipation of the wave energy by a non-uniform porous barrier can be enhanced and can be made larger than that of a barrier with uniform porosity,by suitable choice of non-uniform porosity distribution in the barrier.This has an important bearing on reducing the wave power and thereby protecting the shore line from coastal erosion.Also,an obliquely incident wave reduces reflection and dissipation while increasing transmission of wave energy as compared to a normally incident wave.
基金Supported by the National Natural Science Foundation of China(10902051)the Natural Science Foundation of Jiangsu Province(BK2008046)~~
文摘To analyze a multibody system composed of non-uniform beam and spring-mass subsystems, the model discretization is carried on by utilizing the finite element method（FEM）, the dynamic model of non-uniform beam is developed by using the transfer matrix method of multibody system（MS-TMM）, the transfer matrix of non-u- niform beam is derived, and the natural frequencies are computed. Compared with the numerical assembly method （NAM）, the results by MS-TMM have good agreement with the results by FEM, and are better than the results by NAM. When using the high precision method, the global dynamic equations of the complex multibody system are not needed and the orders of involved system matrices are decreased greatly. For the investigation on the re- verse problem of the physical parameter identification of multibody system, MS-TMM and the optimization tech- nology based on genetic algorithms（GAs） are combined and extended. The identification problem is exchanged for an optimization problem, and it is formulated as a global minimum solution of the objective function with respect to natural frequencies of multibody system. At last, the numerical example of non-uniform beam with attach- ments is discussed, and the identification results indicate the feasibility and the effectivity of the proposed aop- proach.
基金Supported by the Aeronautic Science Foundation of China(2008ZC52026)the Innovation Foundation of Nanjing University of Aeronautics and Astronautics~~
文摘Array configuration of multiple-input multiple-output （MIMO） radar with non-uniform linear array （NLA） is proposed. Unlike a standard phased-array radar where NLA is used to generate thinner beam patterns, in MIMO radar the property of NLA is exploited to get more distinct virtual array elements so as to improve pa- rameter identifiability, which means the maximum number of targets that can be uniquely identified by the radar. A class of NLA called minimum redundancy linear array （MRLA） is employed and a new method to construct large MRLAs is descrihed. The numerical results verify that compared to uniform linear array （ULA） MIMO radars, NLA MIMO radars can retain the same parameter identifiability with fewer physical antennas and achieve larger aperture length and lower Cramer-Rao bound with the same number of the physical antennas.
文摘Aim To find an effective and fast algorithm to analyze undersampled signals. Methods\ The advantage of high order ambiguity function(HAF) algorithm is that it can analyze polynomial phase signals by phase rank reduction. In this paper, it was first used to analyze the parameters of undersampled signals. When some conditions are satisfied, the problem of frequency confusion can be solved. Results and Conclusion\ As an example, we analyze undersampled linear frequency modulated signal. The simulation results verify the effectiveness of HAF algorithm. Compared with time frequency distribution, HAF algorithm reduces computation burden to a great extent, needs weak boundary conditions and doesn't have boundary effect.
