Recently, as the oceanic activities are more and more frequently carried out, marine oil spill accidents bring to enormous harm to the economy and society in China, especially in the Offshore China. Marine oil spill i...Recently, as the oceanic activities are more and more frequently carried out, marine oil spill accidents bring to enormous harm to the economy and society in China, especially in the Offshore China. Marine oil spill is one kind of serious disasters which severely damages the marine environment. Aiming at the improvement of the emergency response system and response ability for the oil spill, the relative technologies on oil spill response are developed. This paper briefly introduces the developments and achievements of the oil spill numerical models, including the oil spill spreading model, the oil spill transport model, the oil particle model as well as the oil spill weathering model, which provide the theoretic criterions for the future work on the oil spill predicting and response.展开更多
Background: The Siberian moth (Dendrolimus sibiricus) (SM) defoliates several tree species from the genera Larix, Piceo and Abies in northern Asia, east of the Urals. The SM is a potential invasive forest pest in...Background: The Siberian moth (Dendrolimus sibiricus) (SM) defoliates several tree species from the genera Larix, Piceo and Abies in northern Asia, east of the Urals. The SM is a potential invasive forest pest in Europe because Europe has several suitable host species and climatic conditions of central and northern Europe are favourable for the SM. Methods: This study developed a grid-based spatio-temporal model for simulating the spread of the SM in case it enters Europe from Russia via border stations. The spread rate was modeled as a function of the spatial distribution of host species, climatic suitability of different locations for the SM, human population density, transportation of moth-carrying material, and flying of moths from tree to tree. Results and conclusions: The simulations showed that the SM is most likely to spread in the forests of northeast Belarus, the Baltic countries, and southern and central Finland. Climatic conditions affected the occurrence of the SM more than human population density and the coverage of suitable host species.展开更多
The growing number of COVID-19 cases puts pressure on healthcare services and public institutions worldwide.The pandemic has brought much uncertainty to the global economy and the situation in general.Forecasting meth...The growing number of COVID-19 cases puts pressure on healthcare services and public institutions worldwide.The pandemic has brought much uncertainty to the global economy and the situation in general.Forecasting methods and modeling techniques are important tools for governments to manage critical situations caused by pandemics,which have negative impact on public health.The main purpose of this study is to obtain short-term forecasts of disease epidemiology that could be useful for policymakers and public institutions to make necessary short-term decisions.To evaluate the effectiveness of the proposed attention-based method combining certain data mining algorithms and the classical ARIMA model for short-term forecasts,data on the spread of the COVID-19 virus in Lithuania is used,the forecasts of epidemic dynamics were examined,and the results were presented in the study.Nevertheless,the approach presented might be applied to any country and other pandemic situations.The COVID-19 outbreak started at different times in different countries,hence some countries have a longer history of the disease with more historical data than others.The paper proposes a novel approach to data registration and machine learning-based analysis using data from attention-based countries for forecast validation to predict trends of the spread of COVID-19 and assess risks.展开更多
The width spread of Ni-based alloy plates in the rolling process is studied. An equation for describing therolling spread of Ni-based alloy plate is proposed based on production data and the Bachtinow equation, which ...The width spread of Ni-based alloy plates in the rolling process is studied. An equation for describing therolling spread of Ni-based alloy plate is proposed based on production data and the Bachtinow equation, which cannot fully account for the compositional variability of Ni-based alloys. To address this, a new coefficient for alloying is added to the equation based on production data. By adding alloying coefficients, it is possible to improve the prediction accuracy for the rolling spread of Ni-based alloy plates and thus better control the width of the rolling spread of different steel grades.展开更多
In this paper, we establish a mathematical model of the forest fire spread process based on a partial differential equation. We describe the distribution of time field and velocity field in the whole two-dimensional s...In this paper, we establish a mathematical model of the forest fire spread process based on a partial differential equation. We describe the distribution of time field and velocity field in the whole two-dimensional space by vector field theory. And we obtain a continuous algorithm to predict the dynamic behavior of forest fire spread in a short time. We use the algorithm to interpolate the fire boundary by cubic non-uniform rational B-spline closed curve. The fire boundary curve at any time can be simulated by solving the Eikonal equation. The model is tested in theory and in practice. The results show that the model has good accuracy and stability, and it’s compatible with most of the existing models, such as the elliptic model and the cellular automata model.展开更多
Based on the infectious disease model with disease latency, this paper proposes a new model for the rumor spreading process in online social network. In this paper what we establish an SEIR rumor spreading model to de...Based on the infectious disease model with disease latency, this paper proposes a new model for the rumor spreading process in online social network. In this paper what we establish an SEIR rumor spreading model to describe the online social network with varying total number of users and user deactivation rate. We calculate the exact equilibrium points and reproduction number for this model. Furthermore, we perform the rumor spreading process in the online social network with increasing population size based on the original real world Facebook network. The simulation results indicate that the SEIR model of rumor spreading in online social network with changing total number of users can accurately reveal the inherent characteristics of rumor spreading process in online social network.展开更多
After decades of researches and discussions on occurrence regularity and control technology of citrus psyl id (Diaphorina citri Kuwayana) and Liberobacter asi-aticum, the occurrence regularity and sampling technique...After decades of researches and discussions on occurrence regularity and control technology of citrus psyl id (Diaphorina citri Kuwayana) and Liberobacter asi-aticum, the occurrence regularity and sampling technique of citrus psyl id in orange forests in Taizhou was defined and the connections between the infection rate and carrying rate of citrus psyl id and Liberobacter asiaticum as wel as the correlations between the Liberobacter asiaticum and citrus yield loss were discussed. This paper discussed the warnings of Liberobacter asiaticum and citrus psylid control index, the economic life span of orange forests was then predicted by building the diseases spreading models with different management styles. At last, the paper put forward the comprehensive prevention and control technology and the concept that Liber-obacter asiaticum was preventable and control able.展开更多
Non-line-of-sight(NLOS)imaging has emerged as a prominent technique for reconstructing obscured objects from images that undergo multiple diffuse reflections.This imaging method has garnered significant attention in d...Non-line-of-sight(NLOS)imaging has emerged as a prominent technique for reconstructing obscured objects from images that undergo multiple diffuse reflections.This imaging method has garnered significant attention in diverse domains,including remote sensing,rescue operations,and intelligent driving,due to its wide-ranging potential applications.Nevertheless,accurately modeling the incident light direction,which carries energy and is captured by the detector amidst random diffuse reflection directions,poses a considerable challenge.This challenge hinders the acquisition of precise forward and inverse physical models for NLOS imaging,which are crucial for achieving high-quality reconstructions.In this study,we propose a point spread function(PSF)model for the NLOS imaging system utilizing ray tracing with random angles.Furthermore,we introduce a reconstruction method,termed the physics-constrained inverse network(PCIN),which establishes an accurate PSF model and inverse physical model by leveraging the interplay between PSF constraints and the optimization of a convolutional neural network.The PCIN approach initializes the parameters randomly,guided by the constraints of the forward PSF model,thereby obviating the need for extensive training data sets,as required by traditional deep-learning methods.Through alternating iteration and gradient descent algorithms,we iteratively optimize the diffuse reflection angles in the PSF model and the neural network parameters.The results demonstrate that PCIN achieves efficient data utilization by not necessitating a large number of actual ground data groups.Moreover,the experimental findings confirm that the proposed method effectively restores the hidden object features with high accuracy.展开更多
Research works on width compensation and correction were carried out in order to eliminate the effects of the PVPC ( plan view pattern control) on width accuracy of plate mill. The thickness correction calculation f...Research works on width compensation and correction were carried out in order to eliminate the effects of the PVPC ( plan view pattern control) on width accuracy of plate mill. The thickness correction calculation formula was derived for compensation the width deviation caused by PVPC function, and the formula is unified under the thinning and thickening conditions. In order to improve the width calculation accuracy, width spread calculation process was modified with dividing one large reduction pass to several small reduction calculation steps. The thickness wedge was simplified to rectangle based on the volume constant principle, and the width spread model for PVPC was constructed. The width compensation and correction for the PVPC functions are used for the online control process, and the Product dimension accuracy is improved. With the decrease of Crop losses, the Droduct yield was increased with 0. 2%.展开更多
In wireless communication environment, the time-varying channel and angular spreads caused by multipath fading and the mobility of Mobile Stations (MS) degrade the performance of the conventional Direction-Of-Arrival ...In wireless communication environment, the time-varying channel and angular spreads caused by multipath fading and the mobility of Mobile Stations (MS) degrade the performance of the conventional Direction-Of-Arrival (DOA) tracking algorithms. On the other hand, although the DOA estimation methods based on the Maximum Likelihood (ML) principle have higher resolution than the beamforming and the subspace based methods, prohibitively heavy computation limits their practical applications. This letter first proposes a new suboptimal DOA estimation algorithm that combines the advantages of the lower complexity of subspace algorithm and the high accuracy of ML based algo- rithms, and then proposes a Kalman filtering based tracking algorithm to model the dynamic property of directional changes for mobile terminals in such a way that the association between the estimates made at different time points is maintained. At each stage during tracking process, the current suboptimal estimates of DOA are treated as measurements, predicted and updated via a Kalman state equation, hence adaptive tracking of moving MS can be carried out without the need to perform unduly heavy computations. Computer simulation results show that this proposed algorithm has better per- formance of DOA estimation and tracking of MS than the conventional ML or subspace based algo- rithms in terms of accuracy and robustness.展开更多
Commwarrior worm is capable of spreading through both Bluetooth and multimedia messaging service (MMS) in smart phone networks. According to the propagation characteristics of Bluetooth and MMS, we built the suscept...Commwarrior worm is capable of spreading through both Bluetooth and multimedia messaging service (MMS) in smart phone networks. According to the propagation characteristics of Bluetooth and MMS, we built the susceptibleexposed-infected-recovered-dormancy (SEIRD) model for the Bluetooth and MMS hybrid spread mode and performed the stability analysis. The simulation results show good correlation with our theoretical analysis and demonstrate the effectiveness of this dynamic propagation model. On the basis of the SEIRD model, we further discuss at length the influence of the propagation parameters such as user gather density in groups, moving velocity of smart phone, the time for worm to replicate itself, and other interrelated parameters on the propagation of the virus. On the basis of these analytical and simulation results, some feasible control strategies will be proposed to restrain the spread of mobile worm such as commwarrior on smart phone network.展开更多
The emergence of novel infectious diseases has become a serious global problem.Convenient transportation networks lead to rapid mobilization in the context of globalization,which is an important factor underlying the ...The emergence of novel infectious diseases has become a serious global problem.Convenient transportation networks lead to rapid mobilization in the context of globalization,which is an important factor underlying the rapid spread of infectious diseases.Transportation systems can cause the transmission of viruses during the epidemic period,but they also support the reopening of economies after the epidemic.Understanding the mechanism of the impact of mobility on the spread of infectious diseases is thus important,as is establishing the risk model of the spread of infectious diseases in transportation networks.In this study,the basic structure and application of various epidemic spread models are reviewed,including mathematical models,statistical models,network-based models,and simulation models.The advantages and limitations of model applications within transportation systems are analyzed,including dynamic characteristics of epidemic transmission and decision supports for management and control.Lastly,research trends and prospects are discussed.It is suggested that there is a need for more in-depth research to examine the mutual feedback mechanism of epidemics and individual behavior,as well as the proposal and evaluation of intervention measures.The findings in this study can help evaluate disease intervention strategies,provide decision supports for transport policy during the epidemic period,and ameliorate the deficiencies of the existing system.展开更多
Array processing is to process the signals carried by the propagating waves received at an array of sensors. When the signals propagate through the practical random time-variant medium, their wavefronts can show the p...Array processing is to process the signals carried by the propagating waves received at an array of sensors. When the signals propagate through the practical random time-variant medium, their wavefronts can show the progressive losses of coherence with increasing spatial separation. These decorrelations of wavefronts result in an angular spread in the wavenumber spectrum centered about the true signal dircction-of-arrival. This paper puts the emphasis upon the array processing of the angular-spread signal which is called the Generalized Directional (GD) signal and aims to match array processing to this signal model in the energy sense. In this paper, we also present a method of the computer simulation of the generalized directional signal model. Some results of computer simulation experiments and lake-tests in Xinanjiang River are given.展开更多
In the Phase Ⅱ Project at the Hefei Light Source, a fourth-harmonic "Landau" cavity will be operated in order to suppress the coupled-bunch instabilities and increase the beam lifetime of the Hefei storage ring. In...In the Phase Ⅱ Project at the Hefei Light Source, a fourth-harmonic "Landau" cavity will be operated in order to suppress the coupled-bunch instabilities and increase the beam lifetime of the Hefei storage ring. Instabilities limit the utility of the higher-harmonic cavity when the storage ring is operated with a small momentum compaction. Analytical modeling and simulations show that the instabilities result from Robinson mode coupling. In the analytic modeling, we operate an algorithm to consider the Robinson instabilities. To study the evolution of unstable behavior, simulations have been performed in which macroparticles are distributed among the buckets. Both the analytic modeling and simulations agree for passive operation of the harmonic cavity.展开更多
文摘Recently, as the oceanic activities are more and more frequently carried out, marine oil spill accidents bring to enormous harm to the economy and society in China, especially in the Offshore China. Marine oil spill is one kind of serious disasters which severely damages the marine environment. Aiming at the improvement of the emergency response system and response ability for the oil spill, the relative technologies on oil spill response are developed. This paper briefly introduces the developments and achievements of the oil spill numerical models, including the oil spill spreading model, the oil spill transport model, the oil particle model as well as the oil spill weathering model, which provide the theoretic criterions for the future work on the oil spill predicting and response.
基金the EU-funded project ISEFOR (Increasing Sustainability of European Forests:modelling for security against invasive pests and pathogens under climate change)
文摘Background: The Siberian moth (Dendrolimus sibiricus) (SM) defoliates several tree species from the genera Larix, Piceo and Abies in northern Asia, east of the Urals. The SM is a potential invasive forest pest in Europe because Europe has several suitable host species and climatic conditions of central and northern Europe are favourable for the SM. Methods: This study developed a grid-based spatio-temporal model for simulating the spread of the SM in case it enters Europe from Russia via border stations. The spread rate was modeled as a function of the spatial distribution of host species, climatic suitability of different locations for the SM, human population density, transportation of moth-carrying material, and flying of moths from tree to tree. Results and conclusions: The simulations showed that the SM is most likely to spread in the forests of northeast Belarus, the Baltic countries, and southern and central Finland. Climatic conditions affected the occurrence of the SM more than human population density and the coverage of suitable host species.
基金This project has received funding from the Research Council of Lithuania(LMTLT),agreement No S-COV-20-4.
文摘The growing number of COVID-19 cases puts pressure on healthcare services and public institutions worldwide.The pandemic has brought much uncertainty to the global economy and the situation in general.Forecasting methods and modeling techniques are important tools for governments to manage critical situations caused by pandemics,which have negative impact on public health.The main purpose of this study is to obtain short-term forecasts of disease epidemiology that could be useful for policymakers and public institutions to make necessary short-term decisions.To evaluate the effectiveness of the proposed attention-based method combining certain data mining algorithms and the classical ARIMA model for short-term forecasts,data on the spread of the COVID-19 virus in Lithuania is used,the forecasts of epidemic dynamics were examined,and the results were presented in the study.Nevertheless,the approach presented might be applied to any country and other pandemic situations.The COVID-19 outbreak started at different times in different countries,hence some countries have a longer history of the disease with more historical data than others.The paper proposes a novel approach to data registration and machine learning-based analysis using data from attention-based countries for forecast validation to predict trends of the spread of COVID-19 and assess risks.
文摘The width spread of Ni-based alloy plates in the rolling process is studied. An equation for describing therolling spread of Ni-based alloy plate is proposed based on production data and the Bachtinow equation, which cannot fully account for the compositional variability of Ni-based alloys. To address this, a new coefficient for alloying is added to the equation based on production data. By adding alloying coefficients, it is possible to improve the prediction accuracy for the rolling spread of Ni-based alloy plates and thus better control the width of the rolling spread of different steel grades.
文摘In this paper, we establish a mathematical model of the forest fire spread process based on a partial differential equation. We describe the distribution of time field and velocity field in the whole two-dimensional space by vector field theory. And we obtain a continuous algorithm to predict the dynamic behavior of forest fire spread in a short time. We use the algorithm to interpolate the fire boundary by cubic non-uniform rational B-spline closed curve. The fire boundary curve at any time can be simulated by solving the Eikonal equation. The model is tested in theory and in practice. The results show that the model has good accuracy and stability, and it’s compatible with most of the existing models, such as the elliptic model and the cellular automata model.
基金Supported by National Natural Science Foundation of China under Grant Nos.11275017 and 11173028
文摘Based on the infectious disease model with disease latency, this paper proposes a new model for the rumor spreading process in online social network. In this paper what we establish an SEIR rumor spreading model to describe the online social network with varying total number of users and user deactivation rate. We calculate the exact equilibrium points and reproduction number for this model. Furthermore, we perform the rumor spreading process in the online social network with increasing population size based on the original real world Facebook network. The simulation results indicate that the SEIR model of rumor spreading in online social network with changing total number of users can accurately reveal the inherent characteristics of rumor spreading process in online social network.
基金Supported by the Ministry of Agriculture and public service sectors(agriculture)Research and Special Project Funds ‘Comprehensive Prevention and Control Technology Research and Demonstration of Liberibacter americanus and Canker’(201003067)Science and Technology Planning Project of Zhejiang Province ‘Research of Surveillance and Control Strategy of Liberibacter americanus’(2004C32087)~~
文摘After decades of researches and discussions on occurrence regularity and control technology of citrus psyl id (Diaphorina citri Kuwayana) and Liberobacter asi-aticum, the occurrence regularity and sampling technique of citrus psyl id in orange forests in Taizhou was defined and the connections between the infection rate and carrying rate of citrus psyl id and Liberobacter asiaticum as wel as the correlations between the Liberobacter asiaticum and citrus yield loss were discussed. This paper discussed the warnings of Liberobacter asiaticum and citrus psylid control index, the economic life span of orange forests was then predicted by building the diseases spreading models with different management styles. At last, the paper put forward the comprehensive prevention and control technology and the concept that Liber-obacter asiaticum was preventable and control able.
基金supported by the Instrument Developing Project of the Chinese Academy of Sciences (Grant No.YJKYYQ20190044)the National Key Research and Development Program of China (Grant No.2022YFB3903100)+1 种基金the High-level introduction of talent research start-up fund of Hefei Normal University in 2020 (Grant No.2020rcjj34)the HFIPS Director’s Fund (Grant No.YZJJ2022QN12).
文摘Non-line-of-sight(NLOS)imaging has emerged as a prominent technique for reconstructing obscured objects from images that undergo multiple diffuse reflections.This imaging method has garnered significant attention in diverse domains,including remote sensing,rescue operations,and intelligent driving,due to its wide-ranging potential applications.Nevertheless,accurately modeling the incident light direction,which carries energy and is captured by the detector amidst random diffuse reflection directions,poses a considerable challenge.This challenge hinders the acquisition of precise forward and inverse physical models for NLOS imaging,which are crucial for achieving high-quality reconstructions.In this study,we propose a point spread function(PSF)model for the NLOS imaging system utilizing ray tracing with random angles.Furthermore,we introduce a reconstruction method,termed the physics-constrained inverse network(PCIN),which establishes an accurate PSF model and inverse physical model by leveraging the interplay between PSF constraints and the optimization of a convolutional neural network.The PCIN approach initializes the parameters randomly,guided by the constraints of the forward PSF model,thereby obviating the need for extensive training data sets,as required by traditional deep-learning methods.Through alternating iteration and gradient descent algorithms,we iteratively optimize the diffuse reflection angles in the PSF model and the neural network parameters.The results demonstrate that PCIN achieves efficient data utilization by not necessitating a large number of actual ground data groups.Moreover,the experimental findings confirm that the proposed method effectively restores the hidden object features with high accuracy.
基金Sponsored by the Fundamental Research Funds for the Central Universities(Grant No.N120407007)
文摘Research works on width compensation and correction were carried out in order to eliminate the effects of the PVPC ( plan view pattern control) on width accuracy of plate mill. The thickness correction calculation formula was derived for compensation the width deviation caused by PVPC function, and the formula is unified under the thinning and thickening conditions. In order to improve the width calculation accuracy, width spread calculation process was modified with dividing one large reduction pass to several small reduction calculation steps. The thickness wedge was simplified to rectangle based on the volume constant principle, and the width spread model for PVPC was constructed. The width compensation and correction for the PVPC functions are used for the online control process, and the Product dimension accuracy is improved. With the decrease of Crop losses, the Droduct yield was increased with 0. 2%.
文摘In wireless communication environment, the time-varying channel and angular spreads caused by multipath fading and the mobility of Mobile Stations (MS) degrade the performance of the conventional Direction-Of-Arrival (DOA) tracking algorithms. On the other hand, although the DOA estimation methods based on the Maximum Likelihood (ML) principle have higher resolution than the beamforming and the subspace based methods, prohibitively heavy computation limits their practical applications. This letter first proposes a new suboptimal DOA estimation algorithm that combines the advantages of the lower complexity of subspace algorithm and the high accuracy of ML based algo- rithms, and then proposes a Kalman filtering based tracking algorithm to model the dynamic property of directional changes for mobile terminals in such a way that the association between the estimates made at different time points is maintained. At each stage during tracking process, the current suboptimal estimates of DOA are treated as measurements, predicted and updated via a Kalman state equation, hence adaptive tracking of moving MS can be carried out without the need to perform unduly heavy computations. Computer simulation results show that this proposed algorithm has better per- formance of DOA estimation and tracking of MS than the conventional ML or subspace based algo- rithms in terms of accuracy and robustness.
基金the National Natural Science Foundation of China (60574036)the Natural Science Foundation of Tianjin (08JCYBJC12800)+1 种基金the Program for New Century Excellent Talents in University (NCET2005-290)the Science and Technology Innovation Fund of Nankai University (Z1A2006012)
文摘Commwarrior worm is capable of spreading through both Bluetooth and multimedia messaging service (MMS) in smart phone networks. According to the propagation characteristics of Bluetooth and MMS, we built the susceptibleexposed-infected-recovered-dormancy (SEIRD) model for the Bluetooth and MMS hybrid spread mode and performed the stability analysis. The simulation results show good correlation with our theoretical analysis and demonstrate the effectiveness of this dynamic propagation model. On the basis of the SEIRD model, we further discuss at length the influence of the propagation parameters such as user gather density in groups, moving velocity of smart phone, the time for worm to replicate itself, and other interrelated parameters on the propagation of the virus. On the basis of these analytical and simulation results, some feasible control strategies will be proposed to restrain the spread of mobile worm such as commwarrior on smart phone network.
基金supported by the National Key R&D Program of China under Grant No.2018YFB1601100National Natural Science Foundation of China under Grant No.71601145。
文摘The emergence of novel infectious diseases has become a serious global problem.Convenient transportation networks lead to rapid mobilization in the context of globalization,which is an important factor underlying the rapid spread of infectious diseases.Transportation systems can cause the transmission of viruses during the epidemic period,but they also support the reopening of economies after the epidemic.Understanding the mechanism of the impact of mobility on the spread of infectious diseases is thus important,as is establishing the risk model of the spread of infectious diseases in transportation networks.In this study,the basic structure and application of various epidemic spread models are reviewed,including mathematical models,statistical models,network-based models,and simulation models.The advantages and limitations of model applications within transportation systems are analyzed,including dynamic characteristics of epidemic transmission and decision supports for management and control.Lastly,research trends and prospects are discussed.It is suggested that there is a need for more in-depth research to examine the mutual feedback mechanism of epidemics and individual behavior,as well as the proposal and evaluation of intervention measures.The findings in this study can help evaluate disease intervention strategies,provide decision supports for transport policy during the epidemic period,and ameliorate the deficiencies of the existing system.
文摘Array processing is to process the signals carried by the propagating waves received at an array of sensors. When the signals propagate through the practical random time-variant medium, their wavefronts can show the progressive losses of coherence with increasing spatial separation. These decorrelations of wavefronts result in an angular spread in the wavenumber spectrum centered about the true signal dircction-of-arrival. This paper puts the emphasis upon the array processing of the angular-spread signal which is called the Generalized Directional (GD) signal and aims to match array processing to this signal model in the energy sense. In this paper, we also present a method of the computer simulation of the generalized directional signal model. Some results of computer simulation experiments and lake-tests in Xinanjiang River are given.
基金Supported by National Natural Science Foundation of China(10979045,11175180,11175182)
文摘In the Phase Ⅱ Project at the Hefei Light Source, a fourth-harmonic "Landau" cavity will be operated in order to suppress the coupled-bunch instabilities and increase the beam lifetime of the Hefei storage ring. Instabilities limit the utility of the higher-harmonic cavity when the storage ring is operated with a small momentum compaction. Analytical modeling and simulations show that the instabilities result from Robinson mode coupling. In the analytic modeling, we operate an algorithm to consider the Robinson instabilities. To study the evolution of unstable behavior, simulations have been performed in which macroparticles are distributed among the buckets. Both the analytic modeling and simulations agree for passive operation of the harmonic cavity.