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A Fast Algorithm for Solving the Poisson Equations Based on the Discrete Cosine/Sine Transforms in the Finite Difference Method
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作者 LI Congcong WANG Danxia +1 位作者 JIA Hongen ZHANG Chenhui 《应用数学》 北大核心 2025年第3期651-669,共19页
To enhance the computational efficiency of spatio-temporally discretized phase-field models,we present a high-speed solver specifically designed for the Poisson equations,a component frequently used in the numerical c... To enhance the computational efficiency of spatio-temporally discretized phase-field models,we present a high-speed solver specifically designed for the Poisson equations,a component frequently used in the numerical computation of such models.This efficient solver employs algorithms based on discrete cosine transformations(DCT)or discrete sine transformations(DST)and is not restricted by any spatio-temporal schemes.Our proposed methodology is appropriate for a variety of phase-field models and is especially efficient when combined with flow field systems.Meanwhile,this study has conducted an extensive numerical comparison and found that employing DCT and DST techniques not only yields results comparable to those obtained via the Multigrid(MG)method,a conventional approach used in the resolution of the Poisson equations,but also enhances computational efficiency by over 90%. 展开更多
关键词 Phase-field model Finite difference method Fast Poisson solver(DC-T/DST) Explicit invariant energy quadratization Unconditional energy stability
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Effect of joint coalescence coefficient on rock bridge formation of slope based on finite difference method
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作者 Su LI Yi TANG Hang LIN 《Transactions of Nonferrous Metals Society of China》 2025年第10期3455-3467,共13页
A method combining finite difference method(FDM)and k-means clustering algorithm which can determine the threshold of rock bridge generation is proposed.Jointed slope models with different joint coalescence coefficien... A method combining finite difference method(FDM)and k-means clustering algorithm which can determine the threshold of rock bridge generation is proposed.Jointed slope models with different joint coalescence coefficients(k)are constructed based on FDM.The rock bridge area was divided through k-means algorithm and the optimal number of clusters was determined by sum of squared errors(SSE)and elbow method.The influence of maximum principal stress and stress change rate as clustering indexes on the clustering results of rock bridges was compared by using Euclidean distance.The results show that using stress change rate as clustering index is more effective.When the joint coalescence coefficient is less than 0.6,there is no significant stress concentration in the middle area of adjacent joints,that is,no generation of rock bridge.In addition,the range of rock bridge is affected by the coalescence coefficient(k),the relative position of joints and the parameters of weak interlayer. 展开更多
关键词 SLOPE rock bridge finite difference method k-means algorithm
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ASYMPTOTICS OF LARGE DEVIATIONS OF FINITE DIFFERENCE METHOD FOR STOCHASTIC CAHN-HILLIARD EQUATION
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作者 Diancong JIN Derui SHENG 《Acta Mathematica Scientia》 2025年第3期1078-1106,共29页
In this work, we first derive the one-point large deviations principle (LDP) for both the stochastic Cahn–Hilliard equation with small noise and its spatial finite difference method (FDM). Then, we focus on giving th... In this work, we first derive the one-point large deviations principle (LDP) for both the stochastic Cahn–Hilliard equation with small noise and its spatial finite difference method (FDM). Then, we focus on giving the convergence of the one-point large deviations rate function (LDRF) of the spatial FDM, which is about the asymptotical limit of a parametric variational problem. The main idea for proving the convergence of the LDRF of the spatial FDM is via the Γ-convergence of objective functions. This relies on the qualitative analysis of skeleton equations of the original equation and the numerical method. In order to overcome the difficulty that the drift coefficient is not one-sided Lipschitz continuous, we derive the equivalent characterization of the skeleton equation of the spatial FDM and the discrete interpolation inequality to obtain the uniform boundedness of the solution to the underlying skeleton equation. These play important roles in deriving the T-convergence of objective functions. 展开更多
关键词 large deviations rate function finite difference method convergence analysis F-convergence stochastic Cahn-Hilliard equation
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Data matching and association based on the arc-segment difference method
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作者 Jiannan Sun Zhe Kang +1 位作者 Zhenwei Li Cunbo Fan 《Astronomical Techniques and Instruments》 2025年第5期299-309,共11页
In response to the issue of fuzzy matching and association when optical observation data are matched with the orbital elements in a catalog database,this paper proposes a matching and association strategy based on the... In response to the issue of fuzzy matching and association when optical observation data are matched with the orbital elements in a catalog database,this paper proposes a matching and association strategy based on the arcsegment difference method.First,a matching error threshold is set to match the observation data with the known catalog database.Second,the matching results for the same day are sorted on the basis of target identity and observation residuals.Different matching error thresholds and arc-segment dynamic association thresholds are then applied to categorize the observation residuals of the same target across different arc-segments,yielding matching results under various thresholds.Finally,the orbital residual is computed through orbit determination(OD),and the positional error is derived by comparing the OD results with the orbit track from the catalog database.The appropriate matching error threshold is then selected on the basis of these results,leading to the final matching and association of the fuzzy correlation data.Experimental results showed that the correct matching rate for data arc-segments is 92.34% when the matching error threshold is set to 720″,with the arc-segment difference method processing the results of an average matching rate of 97.62% within 8 days.The remaining 5.28% of the fuzzy correlation data are correctly matched and associated,enabling identification of orbital maneuver targets through further processing and analysis.This method substantially enhances the efficiency and accuracy of space target cataloging,offering robust technical support for dynamic maintenance of the space target database. 展开更多
关键词 Optical data processing Space target identification Fuzzy correlation Arc-segment difference method Orbit determination
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HIGH-ORDER COMPACT DIFFERENCE METHODS FOR 2D SOBOLEV EQUATIONS WITH PIECEWISE CONTINUOUS ARGUMENT
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作者 Chengjian ZHANG Bo HOU 《Acta Mathematica Scientia》 2025年第5期1855-1878,共24页
This paper deals with numerical computation and analysis for the initial boundary problems of two dimensional(2D)Sobolev equations with piecewise continuous argument.Firstly,a two-level high-order compact difference m... This paper deals with numerical computation and analysis for the initial boundary problems of two dimensional(2D)Sobolev equations with piecewise continuous argument.Firstly,a two-level high-order compact difference method(HOCDM)with computational accuracy O(τ^(2)+h_(x)^(4)+h_(y)^(4))is suggested,whereτ,h_(x),h_(y) denote the temporal and spatial stepsizes of the method,respectively.In order to improve the temporal computational accuracy of this method,the Richardson extrapolation technique is used and thus a new two-level HOCDMis derived,which is proved to be convergent of order four both in time and space.Although the new two-level HOCDM has the higher computational accuracy in time than the previous one,it will bring a larger computational cost.To overcome this deficiency,a three-level HOCDM with computational accuracy O(τ^(4)+h_(x)^(4)+h_(y)^(4))is constructed.Finally,with a series of numerical experiments,the theoretical accuracy and computational efficiency of the above methods are further verified. 展开更多
关键词 delay Sobolev equations piecewise continuous argument compact difference methods Richardson extrapolation error analysis
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Unravelling Temperature Profile through Bifacial PV Modules via Finite Difference Method:Effects of Heat Internal Generation Due to Spectral Absorption
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作者 Khadija Ibaararen Mhammed Zaimi +1 位作者 Khadija El Ainaoui El Mahdi Assaid 《Energy Engineering》 2025年第9期3487-3505,共19页
This study investigates the complex heat transfer dynamics inmultilayer bifacial photovoltaic(bPV)solar modules under spectrally resolved solar irradiation.A novel numericalmodel is developed to incorporate internal h... This study investigates the complex heat transfer dynamics inmultilayer bifacial photovoltaic(bPV)solar modules under spectrally resolved solar irradiation.A novel numericalmodel is developed to incorporate internal heat generation resulting from optical absorption,grounded in the physical equations governing light-matter interactions within the module’smultilayer structure.The model accounts for reflection and transmission at each interface between adjacent layers,as well as absorption within individual layers,using the wavelength-dependent dielectric properties of constituent materials.These properties are used to calculate the spectral reflectance,transmittance,and absorption coefficients,enabling precise quantification of internal heat sources from irradiance incidents on both the front and rear surfaces of the module.The study further examines the influence of irradiance reflection on thermal behavior,evaluates the thermal impact of various supporting materials placed beneath the module,and analyzes the role of albedo in modifying heat distribution.By incorporating spectrally resolved heat generation across each layer often simplified or omitted in conventional models,the proposed approach enhances physical accuracy.The transient heat equation is solved using a one-dimensional finite difference(FD)method to produce detailed temperature profiles under multiple operating scenarios,including Standard Test Conditions(STC),Bifacial Standard Test Conditions(BSTC),Normal Operating Cell Temperature(NOCT),and Bifacial NOCT(BNOCT).The results offer valuable insights into the interplay between optical and thermal phenomena in bifacial systems,informing the design and optimization of more efficient photovoltaic technologies. 展开更多
关键词 Bifacial photovoltaic(bPV) solarmodule heat transfer optical absorption temperature profile ALBEDO finite difference method
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Path Planning of Oil Spill Recovery System With Double USVs Based on Artificial Potential Field Method
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作者 Yulei Liao Xiaoyu Tang +3 位作者 Congcong Chen Zijia Ren Shuo Pang Guocheng Zhang 《哈尔滨工程大学学报(英文版)》 2025年第3期606-618,共13页
Path planning for recovery is studied on the engineering background of double unmanned surface vehicles(USVs)towing oil booms for oil spill recovery.Given the influence of obstacles on the sea,the improved artificial ... Path planning for recovery is studied on the engineering background of double unmanned surface vehicles(USVs)towing oil booms for oil spill recovery.Given the influence of obstacles on the sea,the improved artificial potential field(APF)method is used for path planning.For addressing the two problems of unreachable target and local minimum in the APF,three improved algorithms are proposed by combining the motion performance constraints of the double USV system.These algorithms are then combined as the final APF-123 algorithm for oil spill recovery.Multiple sets of simulation tests are designed according to the flaws of the APF and the process of oil spill recovery.Results show that the proposed algorithms can ensure the system’s safety in tracking oil spills in a complex environment,and the speed is increased by more than 40%compared with the APF method. 展开更多
关键词 Oil spill recovery double unmanned surface vehicles Artificial potential field method Path planning Simulated annealing algorithm
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A new control method based on the lattice hydrodynamic model considering the double flux difference
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作者 Shunda Qin Hongxia Ge Rongjun Cheng 《Chinese Physics B》 SCIE EI CAS CSCD 2018年第5期131-136,共6页
A new feedback control method is derived based on the lattice hydrodynamic model in a single lane. A signal based on the double flux difference is designed in the lattice hydrodynamic model to suppress the traffic jam... A new feedback control method is derived based on the lattice hydrodynamic model in a single lane. A signal based on the double flux difference is designed in the lattice hydrodynamic model to suppress the traffic jam. The stability of the model is analyzed by using the new control method. The advantage of the new model with and without the effect of double flux difference is explored by the numerical simulation. The numerical simulations demonstrate that the traffic jam can be alleviated by the control signal. 展开更多
关键词 traffic flow lattice hydrodynamic model control method double flux difference
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Enhancing the crop yield through capacity building programs: Application of double difference method for evaluation of drip capacity building program in Tamil Nadu State, India
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作者 Kuppannan Palanisami Coimbatore RamaRao Ranganathan +1 位作者 Devarajulu Sureshkumar Ravinder Paul Singh Malik 《Agricultural Sciences》 2014年第1期33-42,共10页
A capacity building program on drip irrigation (TNDRIP) was undertaken in certain regions of the Indian State of Tamil Nadu during 2009-2010. An assessment of the impact of the program in terms of effective use of dri... A capacity building program on drip irrigation (TNDRIP) was undertaken in certain regions of the Indian State of Tamil Nadu during 2009-2010. An assessment of the impact of the program in terms of effective use of drip irrigation and increased crop yields was made in 2011 by applying double difference method (a combination of both with and without and before and after approaches). The results had indicated that the drip capacity building program resulted in a yield increase of 2.5 t/ha for Banana 1, 1.9 t/ha for Banana 2, 3.3 t/ha for sugarcane and 0.3 t/ha for turmeric. The conventional method using the before and after situations had shown a yield increase of 4.3 t/ha for Banana 1, 12.1 t/ha for Banana 2, 40.6 t/ha for sugarcane and 2.6 t/ha for turmeric. The conventional approach is highly upward biased in estimating the impact of the drip capacity building program and thus the double difference method will be an appropriate method to evaluate the impact of the programs that involve both with and without as well as before and after situations. 展开更多
关键词 DRIP IRRIGATION double difference method Impact EVALUATION
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Gain adaptive tuning method for fiber Raman amplifier based on two-stage neural networks and double weights updates
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作者 MU Kuanlin WU Yue 《Optoelectronics Letters》 2025年第5期284-289,共6页
We present a gain adaptive tuning method for fiber Raman amplifier(FRA) using two-stage neural networks(NNs) and double weights updates. After training the connection weights of two-stage NNs separately in training ph... We present a gain adaptive tuning method for fiber Raman amplifier(FRA) using two-stage neural networks(NNs) and double weights updates. After training the connection weights of two-stage NNs separately in training phase, the connection weights of the unified NN are updated again in verification phase according to error between the predicted and target gains to eliminate the inherent error of the NNs. The simulation results show that the mean of root mean square error(RMSE) and maximum error of gains are 0.131 d B and 0.281 d B, respectively. It shows that the method can realize adaptive adjustment function of FRA gain with high accuracy. 展开更多
关键词 gain adaptive tuning connection weights error predicted target gains training connection weights unified nn gain adaptive tuning method double weights updates fiber raman amplifier fra
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Application of the Double-difference Relocation Method Combined with Waveform Cross-correlation on the Three Gorges Reservoir Seismicity
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作者 Luo Jiahong Ma Wentao Li Chunzheng 《Earthquake Research in China》 CSCD 2017年第3期368-380,共13页
In this paper,we use the double difference location method based on waveform crosscorrelation algorithm for precise positioning of the Three Gorges Reservoir( TGR)earthquakes and analysis of seismic activity. First,we... In this paper,we use the double difference location method based on waveform crosscorrelation algorithm for precise positioning of the Three Gorges Reservoir( TGR)earthquakes and analysis of seismic activity. First,we use the bi-spectrum cross-correlation method to analyze the seismic waveform data of TGR encrypted networks from March,2009 to December,2010,and evaluate the quality of waveform cross-correlation analysis.Combined with the waveform cross-correlation of data obtained, we use the double difference method to relocate the earthquake position. The results show that location precision using bi-spectrum verified waveform cross-correlation data is higher than that by using other types of data,and the mean 2 sig-error in EW,NS and UD are 3.2 m,3.9 m and 6.2 m,respectively. For the relocation of the Three Gorges Reservoir earthquakes,the results show that the micro-earthquakes along the Shenlongxi river in the Badong reservoir area obviously show the characteristics of three linear zones with nearly east-west direction,which is in accordance with the small faults and carbonate strata line of the neotectonic period,revealing the reservoir water main along the underground rivers or caves permeated and induced seismic activity. The stronger earthquakes may have resulted from small earthquakes through the active layers. 展开更多
关键词 Bi-spectrum verification WAVEFORM CROSS-CORRELATION double-difference LOCATION The Three Gorges RESERVOIR
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Dynamic Analysis of Contact Bounce of Aerospace Relay Based on Finite Difference Method 被引量:4
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作者 熊军 何俊佳 臧春艳 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2009年第3期262-267,共6页
Contact bounce of relay, which is the main cause of electric abrasion and material erosion, is inevitable. By using the mode expansion form, the dynamic behavior of two different reed systems for aerospace relays is a... Contact bounce of relay, which is the main cause of electric abrasion and material erosion, is inevitable. By using the mode expansion form, the dynamic behavior of two different reed systems for aerospace relays is analyzed. The dynamic model uses Euler-Bernoulli beam theory for cantilever beam, in which the driving force (or driving moment) of the electromagnetic system is taken into account, and the contact force between moving contact and stationary contact is simulated by the Kelvin-Voigt vis-coelastic... 展开更多
关键词 aerospace relay dynamic analysis finite difference method contact bounce reed system
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Improved finite difference method for pressure distribution of aerostatic bearing 被引量:4
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作者 郑书飞 蒋书运 《Journal of Southeast University(English Edition)》 EI CAS 2009年第4期501-505,共5页
An improved finite difference method (FDM)is described to solve existing problems such as low efficiency and poor convergence performance in the traditional method adopted to derive the pressure distribution of aero... An improved finite difference method (FDM)is described to solve existing problems such as low efficiency and poor convergence performance in the traditional method adopted to derive the pressure distribution of aerostatic bearings. A detailed theoretical analysis of the pressure distribution of the orifice-compensated aerostatic journal bearing is presented. The nonlinear dimensionless Reynolds equation of the aerostatic journal bearing is solved by the finite difference method. Based on the principle of flow equilibrium, a new iterative algorithm named the variable step size successive approximation method is presented to adjust the pressure at the orifice in the iterative process and enhance the efficiency and convergence performance of the algorithm. A general program is developed to analyze the pressure distribution of the aerostatic journal bearing by Matlab tool. The results show that the improved finite difference method is highly effective, reliable, stable, and convergent. Even when very thin gas film thicknesses (less than 2 Win)are considered, the improved calculation method still yields a result and converges fast. 展开更多
关键词 aerostatic bearing: pressure distribution: Reynolds equation: finite difference method variable step size
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A new double reduction method for slope stability analysis 被引量:16
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作者 白冰 袁维 李小春 《Journal of Central South University》 SCIE EI CAS 2014年第3期1158-1164,共7页
The core of strength reduction method(SRM) involves finding a critical strength curve that happens to make the slope globally fail and a definition of factor of safety(FOS). A new double reduction method, including a ... The core of strength reduction method(SRM) involves finding a critical strength curve that happens to make the slope globally fail and a definition of factor of safety(FOS). A new double reduction method, including a detailed calculation procedure and a definition of FOS for slope stability was developed based on the understanding of SRM. When constructing the new definition of FOS, efforts were made to make sure that it has concise physical meanings and fully reflects the shear strength of the slope. Two examples, slopes A and B with the slope angles of 63° and 34° respectively, were given to verify the method presented. It is found that, for these two slopes, the FOSs from original strength reduction method are respectively 1.5% and 38% higher than those from double reduction method. It is also found that the double reduction method predicts a deeper potential slide line and a larger slide mass. These results show that on one hand, the double reduction method is comparative to the traditional methods and is reasonable, and on the other hand, the original strength reduction method may overestimate the safety of a slope. The method presented is advised to be considered as an additional option in the practical slope stability evaluations although more useful experience is required. 展开更多
关键词 slope stability strength reduction method double strength reduction method factor of safety limit equilibrium method
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A strength reduction method based on double reduction parameters and its application 被引量:45
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作者 袁维 白冰 +1 位作者 李小春 汪海滨 《Journal of Central South University》 SCIE EI CAS 2013年第9期2555-2562,共8页
In the traditional strength reduction method,the cohesion and the friction angle adopt the same reduction parameter,resulting in equivalent proportional reduction.This method does not consider the different effects of... In the traditional strength reduction method,the cohesion and the friction angle adopt the same reduction parameter,resulting in equivalent proportional reduction.This method does not consider the different effects of the cohesion and friction angle on the stability of the same slope and is defective to some extent.Regarding this defect,a strength reduction method based on double reduction parameters,which adopts different reduction parameters,is proposed.The core of the double-parameter reduction method is the matching reduction principle of the slope with different angles.This principle is represented by the ratio of the reduction parameter of the cohesion to that of the friction angle,described as η.With the increase in the slopeangle,ηincreases; in particular,when the slope angle is 45°,tηis 1.0.Through the matching reduction principle,different safety margin factors can be calculated for the cohesion and friction angle.In combination with these two safety margin factors,a formula for calculating the overall safety factor of the slope is proposed,reflecting the different contributions of the cohesion and friction angle to the slope stability.Finally,it is shown that the strength reduction method based on double reduction parameters acquires a larger safety factor than the classic limit equilibrium method,but the calculation results are very close to those obtained by the limit equilibrium method. 展开更多
关键词 double reduction parameter strength reduction method matching reduction principle slope stability
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COMPACT FINITE DIFFERENCE-FOURIER SPECTRAL METHOD FOR THREE-DIMENSIONAL INCOMPRESSIBLE NAVIER-STOKES EQUATIONS 被引量:5
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作者 熊忠民 凌国灿 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 1996年第4期296-306,共11页
A new compact finite difference-Fourier spectral hybrid method for solving the three dimensional incompressible Navier-Stokes equations is developed in the present paper. The fifth-order upwind compact finite differen... A new compact finite difference-Fourier spectral hybrid method for solving the three dimensional incompressible Navier-Stokes equations is developed in the present paper. The fifth-order upwind compact finite difference schemes for the nonlinear convection terms in the physical space, and the sixth-order center compact schemes for the derivatives in spectral space are described, respectively. The fourth-order compact schemes in a single nine-point cell for solving the Helmholtz equations satisfied by the velocities and pressure in spectral space is derived and its preconditioned conjugate gradient iteration method is studied. The treatment of pressure boundary conditions and the three dimensional non-reflecting outflow boundary conditions are presented. Application to the vortex dislocation evolution in a three dimensional wake is also reported. 展开更多
关键词 compact finite difference Fourier spectral method numerical simulation vortex dislocation
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Characterization of amphiphilic dendrimer modified PEG-PLA nanoparticles prepared by a double emulsion-solvent evaporation method
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作者 李欣 庞宁 +1 位作者 李骥 齐宪荣 《Journal of Chinese Pharmaceutical Sciences》 CAS CSCD 2017年第7期521-527,共7页
Drug delivery by nanocarriers requires characterizations of suitable particle size, high drug loading and safety. In this work, we prepared an amphiphilic dendrimer modified PEG-PLA mixed nanoparticles(NPs) by a dou... Drug delivery by nanocarriers requires characterizations of suitable particle size, high drug loading and safety. In this work, we prepared an amphiphilic dendrimer modified PEG-PLA mixed nanoparticles(NPs) by a double emulsion-solvent evaporation(DESE) method. The particle size and drug encapsulation efficacy(EE) were compared to evaluate and optimize the preparation parameters. The mixed NPs had average size ranging from(102±1) nm to(137±5) nm, and the zeta potential turned to positive with incorporation of the amphiphilic dendrimer. The NPs showed different EE of docetaxel(DTX) and paclitaxel(PTX) with higher affinity to more lipophilic PTX. The blank mixed NPs showed little cytotoxicity, and the DTX-loaded NPs could effectively facilitate the antiproliferation activity on PC-3 cells. The NPs could be used as an effective drug delivery system, and its anti-tumor effect is worthy of further study. 展开更多
关键词 PEG-PLA nanoparticles DOCETAXEL PACLITAXEL double emulsion-solvent evaporation method Amphiphilic dendrimer
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An explicit finite element-finite difference method for analyzing the effect of visco-elastic local topography on the earthquake motion 被引量:7
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作者 李小军 廖振鹏 关慧敏 《Acta Seismologica Sinica(English Edition)》 CSCD 1995年第3期447-456,共10页
An explicit finite element-finite difference method for analyzing the effects of two-dimensional visco-elastic localtopography on earthquake ground motion is prOPosed in this paper. In the method, at first, the finite... An explicit finite element-finite difference method for analyzing the effects of two-dimensional visco-elastic localtopography on earthquake ground motion is prOPosed in this paper. In the method, at first, the finite elementdiscrete model is formed by using the artificial boundary and finite element method, and the dynamic equationsof local nodes in the discrete model are obtained according to the theory of the special finite element method similar to the finite difference method, and then the explicit step-by-step integration formulas are presented by usingthe explicit difference method for solving the visco-elastic dynamic equation and Generalized Multi-transmittingBoundary. The method has the advantages of saving computing time and computer memory space, and it is suitable for any case of topography and has high computing accuracy and good computing stability. 展开更多
关键词 VISCO-ELASTIC seismic response finite difference method explicit finite element artificial boundary
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A method of solving the stiffness problem in Biot's poroelastic equations using a staggered high-order finite-difference 被引量:3
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作者 赵海波 王秀明 陈浩 《Chinese Physics B》 SCIE EI CAS CSCD 2006年第12期2819-2827,共9页
In modelling elastic wave propagation in a porous medium, when the ratio between the fluid viscosity and the medium permeability is comparatively large, the stiffness problem of Blot's poroelastic equations will be e... In modelling elastic wave propagation in a porous medium, when the ratio between the fluid viscosity and the medium permeability is comparatively large, the stiffness problem of Blot's poroelastic equations will be encountered. In the paper, a partition method is developed to solve the stiffness problem with a staggered high-order finite-difference. The method splits the Biot equations into two systems. One is stiff, and solved analytically, the other is nonstiff, and solved numerically by using a high-order staggered-grid finite-difference scheme. The time step is determined by the staggered finite-difference algorithm in solving the nonstiff equations, thus a coarse time step may be employed. Therefore, the computation efficiency and computational stability are improved greatly. Also a perfect by matched layer technology is used in the split method as absorbing boundary conditions. The numerical results are compared with the analytical results and those obtained from the conventional staggered-grid finite-difference method in a homogeneous model, respectively. They are in good agreement with each other. Finally, a slightly more complex model is investigated and compared with related equivalent model to illustrate the good performance of the staggered-grid finite-difference scheme in the partition method. 展开更多
关键词 porous media STIFFNESS partition method staggered grid finite difference
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Implicit finite difference method for fractional percolation equation with Dirichlet and fractional boundary conditions 被引量:5
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作者 Boling GUO Qiang XU Zhe YIN 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2016年第3期403-416,共14页
An implicit finite difference method is developed for a one-dimensional frac- tional percolation equation (FPE) with the Dirichlet and fractional boundary conditions. The stability and convergence are discussed for ... An implicit finite difference method is developed for a one-dimensional frac- tional percolation equation (FPE) with the Dirichlet and fractional boundary conditions. The stability and convergence are discussed for two special cases, i.e., a continued seep- age flow with a monotone percolation coefficient and a seepage flow with the fractional Neumann boundary condition. The accuracy and efficiency of the method are checked with two numerical examples. 展开更多
关键词 fractional percolation equation (FPE) Riemann-Liouville derivative frac-tional boundary condition finite difference method stability and convergence Toeplitzmatrix
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