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百里香精油在果胶甲酯酶响应型抗菌薄膜中的扩散性能及其迁移行为
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作者 杨晨浩 辛颖 +2 位作者 刘珍珍 闫潇柯 刘昆仑 《食品研究与开发》 CAS 2024年第5期8-14,共7页
抗菌薄膜因其优异的保鲜性能在果蔬保鲜中应用广泛。然而果蔬储藏过程中内源果胶甲酯酶活性的升高及外源微生物的侵染会干扰抗菌薄膜中抗菌剂的迁移扩散,但抗菌剂在薄膜中的传质迁移决定了抗菌薄膜是否能够发挥预期作用。因此,该文对百... 抗菌薄膜因其优异的保鲜性能在果蔬保鲜中应用广泛。然而果蔬储藏过程中内源果胶甲酯酶活性的升高及外源微生物的侵染会干扰抗菌薄膜中抗菌剂的迁移扩散,但抗菌剂在薄膜中的传质迁移决定了抗菌薄膜是否能够发挥预期作用。因此,该文对百里香精油在纳米复合抗菌薄膜中的酶响应迁移行为进行研究,建立释放动力学模型。纳米复合抗菌薄膜溶胀率和扫描电镜结果表明,抗菌薄膜在果胶甲酯酶活为0~2.5 U/mL的食品模拟液中均具有明显的溶胀行为,随着酶活的增强,薄膜横截面微观结构由致密逐渐变为疏松,甚至出现孔洞或缝隙;百里香精油释放动力学结果显示,当释放初期扩散比率Mt/M∞<2/3时,精油释放曲线趋于线性,利用短时释放模型和幂律模型对其进行模拟分析,发现随着酶活的升高,百里香精油的释放机制呈现出由不规则扩散向Fick定律转变的趋势;百里香精油扩散释放的全过程属于扩散⁃溶胀叠加机制,符合自拟的负指数生长回归模型(R2>0.95)。 展开更多
关键词 响应型抗菌薄膜 百里香精油 果胶甲酯酶 扩散⁃溶胀 自拟模型
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大气边界层湍流积分尺度的分析方法 被引量:35
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作者 庞加斌 葛耀君 陆烨 《同济大学学报(自然科学版)》 EI CAS CSCD 北大核心 2002年第5期622-626,共5页
分析了大气边界层风洞中模拟湍流和实测大气湍流的积分尺度 ,通过风洞中的模拟湍流积分尺度分析 ,检验了Taylor假设的合理性 ,并比较了五种常用方法的计算结果 ,确定出合适的分析方法 ;利用自相关函数直接积分和自拟合模型 (AR模型 )的... 分析了大气边界层风洞中模拟湍流和实测大气湍流的积分尺度 ,通过风洞中的模拟湍流积分尺度分析 ,检验了Taylor假设的合理性 ,并比较了五种常用方法的计算结果 ,确定出合适的分析方法 ;利用自相关函数直接积分和自拟合模型 (AR模型 )的方法分析了实际大气湍流的积分尺度 ,结果证明自相关函数直接积分的方法最为简便合理 . 展开更多
关键词 Taylor假设 自相关函数 自拟模型 大气边界层 湍流 积分尺度
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Photolithography Process Simulation for Integrated Circuits and Microelectromechanical System Fabrication 被引量:1
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作者 周再发 黄庆安 李伟华 《Journal of Semiconductors》 EI CAS CSCD 北大核心 2006年第4期705-711,共7页
Simulations of photoresist etching,aerial image,exposure,and post-bake processes are integrated to obtain a photolithography process simulation for microelectromechanical system(MEMS) and integrated circuit(IC) fa... Simulations of photoresist etching,aerial image,exposure,and post-bake processes are integrated to obtain a photolithography process simulation for microelectromechanical system(MEMS) and integrated circuit(IC) fabrication based on three-dimensional (3D) cellular automata(CA). The simulation results agree well with available experimental results. This indicates that the 3D dynamic CA model for the photoresist etching simulation and the 3D CA model for the post-bake simulation could be useful for the monolithic simulation of various lithography processes. This is determined to be useful for the device-sized fabrication process simulation of IC and MEMS. 展开更多
关键词 cellular automata process simulation photolithography simulation MODEL TCAD
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SDG-based Model Validation in Chemical Process Simulation 被引量:7
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作者 张贝克 许欣 +1 位作者 马昕 吴重光 《Chinese Journal of Chemical Engineering》 SCIE EI CAS CSCD 2013年第8期876-885,共10页
Signed direct graph (SDG) theory provides algorithms and methods that can be applied directly to chemical process modeling and analysis to validate simulation models, and is a basis for the development of a software e... Signed direct graph (SDG) theory provides algorithms and methods that can be applied directly to chemical process modeling and analysis to validate simulation models, and is a basis for the development of a software environment that can automate the validation activity. This paper is concentrated on the pretreatment of the model validation. We use the validation scenarios and standard sequences generated by well-established SDG model to validate the trends fitted from the simulation model. The results are helpful to find potential problems, assess possible bugs in the simulation model and solve the problem effectively. A case study on a simulation model of boiler is presented to demonstrate the effectiveness of this method. 展开更多
关键词 model validation signed direct graph chemical process qualitative trend
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Microscopic simulation of multi-lane traffic under dynamic tolling and information feedback 被引量:4
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作者 刘天亮 黄海军 田丽君 《Journal of Central South University》 SCIE EI CAS 2009年第5期865-870,共6页
To investigate drivers' lane-changing behavior under different information feedback strategies,a microscopic traffic simulation based on the cellular automaton model was made on the typical freeway with a regular ... To investigate drivers' lane-changing behavior under different information feedback strategies,a microscopic traffic simulation based on the cellular automaton model was made on the typical freeway with a regular lane and a high-occupancy one. A new dynamic tolling scheme in terms of the real-time traffic condition on the high-occupancy lane was further designed to enhance the whole freeway's flow throughput. The results show that the mean velocity feedback strategy is generally more efficient than the travel time feedback strategy in correctly guiding drivers' lane choice behavior. Specifically,the toll level,lane-changing rate and freeway's throughput and congestion coefficient induced by the travel time feedback strategy oscillate with larger amplitude and longer period. In addition,the dynamic tolling scheme can make the high-occupancy lane less congested and maximize the freeway's throughput when the regular-lane inflow rate is larger than 0.45. 展开更多
关键词 information feedback strategy dynamic tolling scheme cellular automaton model high-occupancy lane
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Modeling of Hillslope Runoff and Soil Erosion at Rainfall Events Using Cellular Automata Approach 被引量:13
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作者 MA Ting ZHOU Cheng-Hu CAI Qiang-Guo 《Pedosphere》 SCIE CAS CSCD 2009年第6期711-718,共8页
A novel quantitative cellular automata (CA) model that simulates and predicts hillslope runoff and soil erosion caused by rainfall events was developed by integrating the local interaction rules and the hillslope surf... A novel quantitative cellular automata (CA) model that simulates and predicts hillslope runoff and soil erosion caused by rainfall events was developed by integrating the local interaction rules and the hillslope surface hydraulic processes. In this CA model, the hillslope surface was subdivided into a series of discrete spatial cells with the same geometric features. At each time step, water and sediment were transported between two adjacent spatial cells. The flow direction was determined by a combination of water surface slope and stochastic assignment. The amounts of interchanged water and sediment were computed using the Chezy-Manning formula and the empirical sediment transport equation. The water and sediment discharged from the open boundary cells were considered as the runoff and the sediment yields over the entire hillslope surface. Two hillslope soil erosion experiments under simulated rainfall events were carried out. Cumulative runoff and sediment yields were measured, respectively. Then, the CA model was applied to simulate the water and soil erosion for these two experiments. Analysis of simulation results indicated that the size of the spatial cell, hydraulic parameters, and the setting of time step and iteration times had a large impact on the model accuracy. The comparison of the simulated and measured data suggested that the CA model was an applicable alternate for simulating the hillslope water flow and soil erosion. 展开更多
关键词 hillslope surface hydraulic parameters SEDIMENT simulation water
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A Vector-based Cellular Automata Model for Simulating Urban Land Use Change 被引量:3
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作者 LU Yi CAO Min ZHANG Lei 《Chinese Geographical Science》 SCIE CSCD 2015年第1期74-84,共11页
Cellular Automata(CA) is widely used for the simulation of land use changes. This study applied a vector-based CA model to simulate land use change in order to minimize or eliminate the scale sensitivity in traditiona... Cellular Automata(CA) is widely used for the simulation of land use changes. This study applied a vector-based CA model to simulate land use change in order to minimize or eliminate the scale sensitivity in traditional raster-based CA model. The cells of vector-based CA model are presented according to the shapes and attributes of geographic entities, and the transition rules of vector-based CA model are improved by taking spatial variables of the study area into consideration. The vector-based CA model is applied to simulate land use changes in downtown of Qidong City, Jiangsu Province, China and its validation is confirmed by the methods of visual assessment and spatial accuracy. The simulation result of vector-based CA model reveals that nearly 75% of newly increased urban cells are located in the northwest and southwest parts of the study area from 2002 to 2007, which is in consistent with real land use map. In addition, the simulation results of the vector-based and raster-based CA models are compared to real land use data and their spatial accuracies are found to be 84.0% and 81.9%, respectively. In conclusion, results from this study indicate that the vector-based CA model is a practical and applicable method for the simulation of urbanization processes. 展开更多
关键词 vector-based Cellular Automata(CA) land use change transition rule spatial accuracy Qidong City
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Numerical simulation of solidification morphologies of Cu-0.6Cr casting alloy using modified cellular automaton model 被引量:9
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作者 TSAI De-chang HWANG Weng-sing 《Transactions of Nonferrous Metals Society of China》 SCIE EI CAS CSCD 2010年第6期1072-1077,共6页
The purpose of this study is to predict the morphologies in the solidification process for Cu-0.6Cr(mass fraction,%)alloy by vacuum continuous casting(VCC)and verify its accuracy by the observed experimental results.I... The purpose of this study is to predict the morphologies in the solidification process for Cu-0.6Cr(mass fraction,%)alloy by vacuum continuous casting(VCC)and verify its accuracy by the observed experimental results.In numerical simulation aspect, finite difference(FD)method and modified cellular automaton(MCA)model were used to simulate the macro-temperature field, micro-concentration field,nucleation and grain growth of Cu-0.6Cr alloy using real data from actual casting operations.From the observed casting experiment,the preliminary grain morphologies are the directional columnar grains by the VCC process.The solidification morphologies by MCAFD model are in agreement with the result of actual casting experiment well. 展开更多
关键词 Cu-Cr alloy vacuum continuous casting solidification morphology simulation modified cellular automaton model finite difference method
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Research on a Multi-grid Model for Passenger Evacuation in Ships 被引量:4
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作者 Miao Chen Duanfeng Han Haipeng Zhang 《Journal of Marine Science and Application》 2011年第3期340-346,共7页
In order to enhance the authenticity and accuracy of passenger evacuation simulation in ships, a new multi-grid model was proposed on the basis of a traditional cellular automata model. In the new model finer lattices... In order to enhance the authenticity and accuracy of passenger evacuation simulation in ships, a new multi-grid model was proposed on the basis of a traditional cellular automata model. In the new model finer lattices were used, interaction of force among pedestrians or between pedestrians and constructions was considered, and static floor fields in a multi-level exit environment were simplified into cabin and exit static floor fields. Compared with the traditional cellular automata model, the multi-grid model enhanced the continuity of the passengers'track and the precision of the boundary qualifications. The functions of the dislocation distribution of passengers as well as partial overlap of tracks due to congestion were realized. Furthermore, taking the typical cabin environment as an example, the two models were used to analyze passenger evacuation under the same conditions. It was found that the laws of passenger evacuation simulated by the two models are similar, while the simulation's authenticity and accuracy are enhanced by the multi-grid model. 展开更多
关键词 passengers' evacuation in ships multi-grid model simulation evacuation floor field interaction of force
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Improved Water Network Macroscopic Model Utilising Auto-Control Adjusting Valve by PLS
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作者 李霞 赵新华 王晓东 《Transactions of Tianjin University》 EI CAS 2005年第6期452-457,共6页
In order to overcome the low precision and weak applicability problems of the current municipal water network state simulation model, the water network structure is studied. Since the telemetry system has been applied... In order to overcome the low precision and weak applicability problems of the current municipal water network state simulation model, the water network structure is studied. Since the telemetry system has been applied increasingly in the water network, and in order to reflect the network operational condition more accurately, a new water network macroscopic model is developed by taking the auto-control adjusting valve opening state into consideration. Then for highly correlated or collinear independent variables in the model, the partial least squares (PLS) regression method provides a model solution which can distinguish between the system information and the noisy data. Finally, a hypothetical water network is introduced for validating the model. The simulation results show that the relative error is less than 5.2%, indicating that the model is efficient and feasible, and has better generalization performance. 展开更多
关键词 water supply network state simulation macroscopic model auto-control adjusting valve partial least squares PLS) regression
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Simulation of Decoherence by Averaged Semiquantum Method for Spin-Boson Model
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作者 WANG Zhuo 《Communications in Theoretical Physics》 SCIE CAS CSCD 2009年第11期881-887,共7页
We investigate the dynamics of a system coupled to an environment by averaged semiquantum method. The theory origins from the time-dependent variational principle (TDVP) formulation and contains nondiagonal matrix e... We investigate the dynamics of a system coupled to an environment by averaged semiquantum method. The theory origins from the time-dependent variational principle (TDVP) formulation and contains nondiagonal matrix elements. So it can be applied to study dissipation, measurement, and decoherence problems in the model (H= hs+hE+ht ). In the calculation, the influence of the environment govern by differential dynamical equation is incorporated through a mean field. We have performed averaged semiquantum method for a spin-boson model, which reproduce the results from stochastic Schrodinger equation method and Hierarchical approach quite accurately. The problems, dynamics in nonequilibrium environments, have also been studied by our method. 展开更多
关键词 ENVIRONMENT semiquantum method DECOHERENCE spin-boson
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Computer Based Modeling of Vegetation Propagation across a Disturbed Space Linked to GIS
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作者 Lubos Matejicek Pavel Kovar 《Journal of Earth Science and Engineering》 2015年第7期410-416,共7页
The paper is focused on computer simulation of natural vegetation propagation across two selected disturbed sites. Two sites located in the different environments, the abandoned sedimentation basin of a former pyrite ... The paper is focused on computer simulation of natural vegetation propagation across two selected disturbed sites. Two sites located in the different environments, the abandoned sedimentation basin of a former pyrite ore mine and the ash deposits of a power station, were selected to illustrate the proposed spatio-temporal model. Aerial images assisted in identifying and monitoring the progress in the propagation of vegetation. Analysis of the aerial images was based on varying vegetation coverage explored by classification algorithms. A new approach is proposed entailing coupling of a local dynamic model and a spatial model for vegetation propagation. The local dynamic model describes vegetation growth using a logistic growth approach based on delayed variables. Vegetation propagation is described by rules related to seed and its dispersal phenomena on a local scale and on the scale of outlying spreading. The disturbed sites are divided into a grid of microsites. Each microsite is represented by a 5 m x 5 m square. A state variable in each microsite indicates the relative vegetation density on a scale from 0 (no vegetation) to 1 (long-term maximum of vegetation density). Growth, local vegetation propagation and the effects of outlying vegetation propagation in each cell are described by an ordinary differential equation with delayed state variables. The grid of cells forms a set of ordinary differential equations. The abandoned sedimentation basin and the ash deposits are represented by grids of 185 x 345 and 212 x 266 cells, respectively. A few case-oriented studies are provided to show various predictions of vegetation propagation across two selected disturbed sites. The first case study simulates vegetation growing without spatial propagations and delayed variables in the spatio-temporal model. The second and the third case studies extend the previous study by including local and outlying vegetation propagation, respectively. The fourth case study explores delayed impacts in the logistic growth term and the delayed outcome by vegetation propagation across the disturbed space. The performed case-oriented studies confirm the applicability of the proposed spatio-temporal model to predict vegetation propagation in short-term successions and to estimate approximate vegetation changes in long-term development. As a result, it can be concluded that remotely sensed data are a valuable source of information for estimates of model parameters and provide an effective method for monitoring the progress of vegetation propagation across the selected sites, spaces disturbed by human activities. 展开更多
关键词 Spatio-temporal modelling vegetation propagation disturbed space remote sensing GIS.
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Cellular Automaton Simulations for Target Waves in Excitable Media 被引量:1
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作者 张立升 邓敏艺 +2 位作者 孔令江 刘慕仁 唐国宁 《Communications in Theoretical Physics》 SCIE CAS CSCD 2010年第1期171-174,共4页
Using the Greenberg-Hasting cellular automata model, we study the properties of target waves in excitable media under the no-flux boundary conditions. For the system has only one excited state, the computer simulation... Using the Greenberg-Hasting cellular automata model, we study the properties of target waves in excitable media under the no-flux boundary conditions. For the system has only one excited state, the computer simulation and analysis lead to the conclusions that, the number of refractory states does not influence the wave-front speed; the wave- front speed decreases as the excitation threshold increases and increases as the neighbor radius increases; the period of target waves is equal to the number of cell states; the excitation condition for target waves is that the wave-front speed must be bigger than half of the neighbor radius. 展开更多
关键词 cellular automata excitable media target wave
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Preliminary Study on Simulation of Global Seismic Activities with Global Strain Rate
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作者 Wang Wuxing Shi Yaolin 《Earthquake Research in China》 2014年第2期164-176,共13页
The relationship between the strain rate field observed by GPS and global distribution of strong earthquakes is analyzed in this work. How do we recognize the characteristics of global seismic activities with space ob... The relationship between the strain rate field observed by GPS and global distribution of strong earthquakes is analyzed in this work. How do we recognize the characteristics of global seismic activities with space observation technology? A preliminary model of Cellular Automata that could simulate the global seismic activities both in time and space has been established based on the results of global strain rate field provided by the GSRM Program. The grid of the model is evenly divided,which is consistent with that of GSRM.The status of each cell is its strain state,and is adjusted according to the evolution rules.Maximum shear strain criterion is adopted in the evolution of the Cellular Automata. The threshold for cells in surface expansion is 80% of that for those in compression. The preliminary model could in general simulate the main characteristics of the distribution of the global seismic activities. It could exhibit in general the global distribution of weak and active tectonic activities. Although the preliminary Cellular Automata model needs to be improved in many aspects,the result suggests the possibility of modeling the general features of rather complicated global seismic activities based on the strain rates obtained by GPS and other observations. 展开更多
关键词 Global strain rate Cellular Automata SIMULATION Seismic activity
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A Study on Heterogeneous Cellular Automaton Simulation of the Influencing Factors on Seismicity 被引量:1
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作者 Li Meng Yang Feng 《Earthquake Research in China》 2013年第2期250-260,共11页
For the purpose of investigating conditions of earthquake pregnancies,a heterogeneous 2-D single fault model with 81 × 81 cells is set up. By using cellular automata models and changing the model heterogeneity an... For the purpose of investigating conditions of earthquake pregnancies,a heterogeneous 2-D single fault model with 81 × 81 cells is set up. By using cellular automata models and changing the model heterogeneity and correlation parameters, we compute and get different synthetic event catalogues for analyzing general seismic activity and intensity distribution properties. The results show that different heterogeneous structures produce different seismic sequence types and G-R relationship,so the heterogeneity is an important influencing factor on seismicity. Nevertheless,both the coefficients of stress redistribution and local friction loss can also influence seismicity to some extent. This is possibly useful for further understanding of the complexity of earthquake processes. 展开更多
关键词 Cellular automata model Heterogeneity Seismicity G-R relationship
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Phase Transitions Induced by Top-Priority of Randomization
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作者 WEI Yah-Fang GUO Si-Ling XUE Yu 《Communications in Theoretical Physics》 SCIE CAS CSCD 2007年第3期499-502,共4页
We study the characteristics of phase transition to take the top-priority of randomization in the rules of NaSch model (i.e. noise-first model) into account via computing the relaxation time and the order parameter... We study the characteristics of phase transition to take the top-priority of randomization in the rules of NaSch model (i.e. noise-first model) into account via computing the relaxation time and the order parameter. The scaling exponents of the relaxation time and the scaling relation of order parameter, respectively, are obtained. 展开更多
关键词 traffic flow cellular automaton phase transition relaxation time order parameter
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Simulation of solidification microstructure of Fe-6.5%Si alloy using cellular automaton-finite element method
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作者 SONG Wei ZHANG Jiong-ming +2 位作者 WANG Shtm-xi WANG Bo HAN Li-lei 《Journal of Central South University》 SCIE EI CAS CSCD 2016年第9期2156-2164,共9页
3D microstructures of Fe–6.5%Si(mass fraction) alloys prepared under different cooling conditions were simulated via finite element-cellular automaton(CAFE) method. The simulated results were compared to experimental... 3D microstructures of Fe–6.5%Si(mass fraction) alloys prepared under different cooling conditions were simulated via finite element-cellular automaton(CAFE) method. The simulated results were compared to experimental results and found to be in accordance. Variations in the temperature field and solid-liquid region, which plays important roles in determining solidification structures, were also examined under various cooling conditions. The proposed model was utilized to determine the effects of Gaussian distribution parameters to find that the lower the mean undercooling, the higher the equiaxed crystal zone ratio; also, the larger the maximum nucleation density, the smaller the grain size. The influence of superheat on solidification structure and columnar to equiaxed transition(CET) in the cast ingot was also investigated to find that decrease in superheat from 52 K to 20 K causes the equiaxed crystal zone ratio to increase from 58.13% to 65.6%, the mean gain radius to decrease from 2.102 mm to 1.871 mm, and the CET to occur ahead of schedule. To this effect, low superheat casting is beneficial to obtain finer equiaxed gains and higher equiaxed dendrite zone ratio in Fe–6.5%Si alloy cast ingots. 展开更多
关键词 finite element-cellular automaton Fe-6.5%Si alloy MICROSTRUCTURE temperature field Gaussian distribution parameters
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Sequential Estimate for Generalized Linear Models with Uncertain Number of Effective Variables 被引量:1
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作者 LU Haibo WANG Zhanfeng WU Yaohua 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2015年第2期424-438,共15页
For the generalized linear model,the authors propose a sequential sampling procedure based on an adaptive shrinkage estimate of parameter.This method can determine a minimum sample size under which effective variables... For the generalized linear model,the authors propose a sequential sampling procedure based on an adaptive shrinkage estimate of parameter.This method can determine a minimum sample size under which effective variables contributing to the model are identified and estimates of regression parameters achieve the required accuracy.The authors prove that the proposed sequential procedure is asymptotically optimal.Numerical simulation studies show that the proposed method can save a large number of samples compared to the traditional sequential approach. 展开更多
关键词 Confidence set generalized linear regression sequential sampling stopping rule
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Forecasting Gas Consumption Based on a Residual Auto-Regression Model and Kalman Filtering Algorithm 被引量:9
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作者 ZHU Meifeng WU Qinglong WANG Yongqin 《Journal of Resources and Ecology》 CSCD 2019年第5期546-552,共7页
Consumption of clean energy has been increasing in China.Forecasting gas consumption is important to adjusting the energy consumption structure in the future.Based on historical data of gas consumption from 1980 to 20... Consumption of clean energy has been increasing in China.Forecasting gas consumption is important to adjusting the energy consumption structure in the future.Based on historical data of gas consumption from 1980 to 2017,this paper presents a weight method of the inverse deviation of fitted value,and a combined forecast based on a residual auto-regression model and Kalman filtering algorithm is used to forecast gas consumption.Our results show that:(1)The combination forecast is of higher precision:the relative errors of the residual auto-regressive model,the Kalman filtering algorithm and the combination model are within the range(–0.08,0.09),(–0.09,0.32)and(–0.03,0.11),respectively.(2)The combination forecast is of greater stability:the variance of relative error of the residual auto-regressive model,the Kalman filtering algorithm and the combination model are 0.002,0.007 and 0.001,respectively.(3)Provided that other conditions are invariant,the predicted value of gas consumption in 2018 is 241.81×10~9 m^3.Compared to other time-series forecasting methods,this combined model is less restrictive,performs well and the result is more credible. 展开更多
关键词 residual auto-regressive model Kalman filtering algorithm inverse fitting value deviation method combined forecast
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PATTERN FORMATION IN CHEMOTAXIC REACTION-DIFFUSION SYSTEMS
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作者 HIROTO SHOJI KEITARO SAITOH 《International Journal of Biomathematics》 2012年第3期205-213,共9页
In this study, we investigate two-dimensional patterns generated by chemotaxis reaction-diffusion systems. We numerically examine the Keller-Segel models with the volume-filling aggregation term and the receptor aggre... In this study, we investigate two-dimensional patterns generated by chemotaxis reaction-diffusion systems. We numerically examine the Keller-Segel models with the volume-filling aggregation term and the receptor aggregation term in two dimensions. Spotted, striped and reversed spotted patterns are obtained as stable motionless equi- librium patterns. The relative stability of these patterns is studied numerically on the basis of the derived free energy. The intuitive understanding of these generated patterns and the relation with three-dimensional patterns are also discussed. 展开更多
关键词 CHEMOTAXIS Keller Segel model stability analysis.
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