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A non-affine constitutive model for the extremely large deformation of hydrogel polymer network based on network modeling method
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作者 Jincheng Lei Yuan Gao +1 位作者 Danyang Wang Zishun Liu 《Acta Mechanica Sinica》 2025年第7期69-80,共12页
Current hyperelastic constitutive models of hydrogels face difficulties in capturing the stress-strain behaviors of hydrogels under extremely large deformation because the effect of non-affine deformation of the polym... Current hyperelastic constitutive models of hydrogels face difficulties in capturing the stress-strain behaviors of hydrogels under extremely large deformation because the effect of non-affine deformation of the polymer network inside is ambiguous.In this work,we construct periodic random network(PRN)models for the effective polymer network in hydrogels and investigate the non-affine deformation of polymer chains intrinsically originates from the structural randomness from bottom up.The non-affine deformation in PRN models is manifested as the actual stretch of polymer chains randomly deviated from the chain stretch predicted by affine assumption,and quantified by a non-affine ratio of each polymer chain.It is found that the non-affine ratios of polymer chains are closely related to bulk deformation state,chain orientation,and initial chain elongation.By fitting the non-affine ratio of polymer chains in all PRN models,we propose a non-affine constitutive model for the hydrogel polymer network based on micro-sphere model.The stress-strain curves of the proposed constitutive models under uniaxial tension condition agree with the simulation results of different PRN models of hydrogels very well. 展开更多
关键词 Non-affine deformation periodic random network model Large deformation Constitutive model
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Numerical modeling of cracking pattern's influence on the dynamic response of thickened tailings disposals: a periodic approach 被引量:1
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作者 Gabriel Ferrer Esteban Sáez Christian Ledezma 《Earthquake Engineering and Engineering Vibration》 SCIE EI CSCD 2018年第1期179-190,共12页
Copper production is an essential component of the Chilean economy. During the extraction process of copper, large quantities of waste materials(tailings) are produced, which are typically stored in large tailing po... Copper production is an essential component of the Chilean economy. During the extraction process of copper, large quantities of waste materials(tailings) are produced, which are typically stored in large tailing ponds. Thickened Tailings Disposal(TTD) is an alternative to conventional tailings ponds. In TTD, a considerable amount of water is extracted from the tailings before their deposition. Once a thickened tailings layer is deposited, it loses water and it shrinks, forming a relatively regular structure of tailings blocks with vertical cracks in between, which are then filled up with "fresh" tailings once the new upper layer is deposited. The dynamic response of a representative column of this complex structure made out of tailings blocks with softer material in between was analyzed using a periodic half-space finite element model. The tailings' behavior was modeled using an elasto-plastic multi-yielding constitutive model, and Chilean earthquake records were used for the seismic analyses. Special attention was given to the liquefaction potential evaluation of TTD. 展开更多
关键词 Thickened tailings Liquefaction periodic modeling
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THREE- DIMENSIONAL PERIODICITY ANDTENFOLD ROTATIONAL SYMMETRY
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作者 闵乐泉 吴玉珍 《International Journal of Minerals,Metallurgy and Materials》 SCIE EI CAS CSCD 1995年第1期70+63-70,共9页
Electron-diffraction pattern with 'tenfold rotational symmetry' of Al-Fe alloyphase is assumed to be produced by periodic structure. One 3D periodic structure is presentedbased on so-called C polyhedra. The st... Electron-diffraction pattern with 'tenfold rotational symmetry' of Al-Fe alloyphase is assumed to be produced by periodic structure. One 3D periodic structure is presentedbased on so-called C polyhedra. The structure can be used as atomic model to describethe Al-Fe alloy phase. The Fourier transform patterns of the model are in good agreementwith the corresponding electron-diffraction patterns. Several other models with' tenfold symmetry' Fourier transform patterns have briefly been mentioned. 展开更多
关键词 DIFFRACTION QUASICRYSTAL Al-Fe decagonal phase periodic model
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Bifurcation and dynamics in double-delayed Chua circuits with periodic perturbation 被引量:1
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作者 Wenjie 《Chinese Physics B》 SCIE EI CAS CSCD 2022年第2期164-172,共9页
Rank-1 attractors play a vital role in biological systems and the circuit systems.In this paper,we consider a periodically kicked Chua model with two delays in a circuit system.We first analyze the local stability of ... Rank-1 attractors play a vital role in biological systems and the circuit systems.In this paper,we consider a periodically kicked Chua model with two delays in a circuit system.We first analyze the local stability of the equilibria of the Chua system and obtain the existence conditions of supercritical Hopf bifurcations.Then,we derive some explicit formulas about Hopf bifurcation,which could help us find the form of Hopf bifurcation and the stability of bifurcating period solutions through the Hassards method.Also,we show that rank-1 chaos occurs when the Chua model with two delays undergoes a supercritical Hopf bifurcation and encounters a periodic kick,which shows the effect of two delays on the circuit system.Finally,we illustrate the theoretical analysis by simulations and try to explain the mechanism of delay in our system. 展开更多
关键词 rank one chaos periodically kicked Chua model time delay
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Phase diagram,correlations,and quantum critical point in the periodic Anderson model
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作者 Jian-Wei Yang Qiao-Ni Chen 《Chinese Physics B》 SCIE EI CAS CSCD 2018年第3期362-367,共6页
Periodic Anderson model is one of the most important models in the field of strongly correlated electrons. With the recent developed numerical method density matriX embedding theory, we study the ground state properti... Periodic Anderson model is one of the most important models in the field of strongly correlated electrons. With the recent developed numerical method density matriX embedding theory, we study the ground state properties of the periodic Anderson model on a two-dimensional square lattice. We systematically investigate the phase diagram away from half filling. We find three different phases in this region, which are distinguished by the local moment and the spin-spin correlation functions. The phase transition between the two antiferromagnetic phases is of first order. It is the so-called Lifshitz transition accompanied by a reconstruction of the Fermi surface. As the filling is close to half filling, there is no difference between the two antiferromagnetic phases. From the results of the spin-spin correlation, we find that the Kondo singlet is formed even in the antiferromagnetic phase. 展开更多
关键词 periodic Anderson model Kondo singlet states density matrix embedding theory
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STOCHASTIC MODEL OF PERIODIC OPERATION PERFORMANCE FOR THE CONTINUOUS COUNTER-CURRENT ADSORPTION PROCESS
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作者 Sun Shuyu Niu Wengtai Jiang Zhixin 《Chinese Journal of Reactive Polymers》 1995年第1期8-19,共12页
A stochastic model is developed to predict the peniodic operation performance ofthe continuous counter-current adsorption process. The model takes into account theeffects of random backmixing of particles, axial dispe... A stochastic model is developed to predict the peniodic operation performance ofthe continuous counter-current adsorption process. The model takes into account theeffects of random backmixing of particles, axial dispersion of liquid phase, liquid- film mass transfer, intraparticle diffusion and panticle shape, and can revealclearly the behavior of solid and liquid phase in adsorption process. The simulation results agree with the experimental data rather well. 展开更多
关键词 periodic operation Adsorption process Stochastic model Simulation
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Cellular and Circuitry Bases of Autism:Lessons Learned from the Temporospatial Manipulation of Autism Genes in the Brain 被引量:3
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作者 Samuel W.Hulbert Yong-hui Jiang 《Neuroscience Bulletin》 SCIE CAS CSCD 2017年第2期205-218,共14页
Transgenic mice carrying mutations that cause Autism Spectrum Disorders(ASDs) continue to be valuable for determining the molecular underpinnings of the disorders. Recently, researchers have taken advantage of such ... Transgenic mice carrying mutations that cause Autism Spectrum Disorders(ASDs) continue to be valuable for determining the molecular underpinnings of the disorders. Recently, researchers have taken advantage of such models combined with Cre-lox P and similar systems to manipulate gene expression over space and time. Thus, a clearer picture is starting to emerge of the cell types, circuits, brain regions, and developmental time periods underlying ASDs. ASD-causing mutations have been restricted to or rescued speci?cally in excitatory or inhibitory neurons, different neurotransmitter systems, and cells speci?c to the forebrain or cerebellum. In addition,mutations have been induced or corrected in adult mice,providing some evidence for the plasticity and reversibility of core ASD symptoms. The limited availability of Cre lines that are highly speci?c to certain cell types or time periods provides a challenge to determining the cellular and circuitry bases of autism, but other technological advances may eventually overcome this obstacle. 展开更多
关键词 Autism Mouse models Behavior CreloxP Cerebellum Critical period
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Antiferromagnetism and Kondo screening on a honeycomb lattice
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作者 林恒福 陶红帅 +1 位作者 郭文祥 刘伍明 《Chinese Physics B》 SCIE EI CAS CSCD 2015年第5期489-497,共9页
Magnetic adatoms in the honeycomb lattice have received tremendous attention due to the interplay between Ruderman-Kittel-Kasuya-Yosida interaction and Kondo coupling leading to very rich physics. Here we study the co... Magnetic adatoms in the honeycomb lattice have received tremendous attention due to the interplay between Ruderman-Kittel-Kasuya-Yosida interaction and Kondo coupling leading to very rich physics. Here we study the competition between the antiferromagnetism and Kondo screening of local moments by the conduction electrons on the honeycomb lattice using the determinant quantum Monte Carlo method. While changing the interband hybridization V, we systemat- ically investigate the antiferromagnetic-order state and the Kondo singlet state transition, which is characterized by the behavior of the local moment, antiferromagnetic structure factor, and the short range spin-spin correlation. The evolution of the single particle spectrum are also calculated as a function of hybridization V, we find that the system presents a small gap in the antiferromagnetic-order region and a large gap in the Kondo singlet region in the Fermi level. We also find that the localized and itinerant electrons coupling leads to the midgap states in the conduction band in the Fermi level at very small V. Moreover, the formation of antiferromagnetic order and Kondo singlet are studied as on-site interaction U or temperature T increasing, we have derived the phase diagrams at on-site interaction U (or temperature T) and hybridization V plane. 展开更多
关键词 periodic Anderson model ANTIFERROMAGNETISM Kondo screening
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Interactional models for adults of two populations with maturation delays
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作者 HE Ze-rong LI Jian-quan 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2008年第2期127-135,共9页
This paper is concerned with interactional models for adults of two species delayed by their mature periods. The existence and local stability of equilibria are discussed thoroughly for competitive systems, cooperativ... This paper is concerned with interactional models for adults of two species delayed by their mature periods. The existence and local stability of equilibria are discussed thoroughly for competitive systems, cooperative systems and predator-prey systems, respectively. For systems with interaction of competition and cooperation, it is found that the two populations are uniformly persistent if the positive equilibrium is stable. For predator-prey interaction, however, some further conditions are needed to guarantee the persistence of the systems. 展开更多
关键词 interactional models mature period equilibrium stability uniform persistence.
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Laboratory Models for the Study of the Peri-implantation Period
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作者 STANLEY R.GLASSER 《Biomedical and Environmental Sciences》 SCIE CAS CSCD 1991年第1期48-55,共8页
The greatest risks to mammalian pregnancy occur during the peri-implantation period (passage through the uterotubal junction, blastulation, zona shedding, embryonic signaling and recognition, blastocyst attachment, po... The greatest risks to mammalian pregnancy occur during the peri-implantation period (passage through the uterotubal junction, blastulation, zona shedding, embryonic signaling and recognition, blastocyst attachment, postattachment events initiating placentation). Conventional markers and screening methods do not provide the means to clarify the relationship between exposure of a reproductively competent woman to a xenobiotic compound and the specific error in the functional expression of an embryogenetic process identified by impairment or deletion of that process. Laboratory models which provide the flexibility of in vitro culture methods and allow integration of cellular and molecular techniques have identified cell-specific, stage-specific markers that could focus on the mechanism of xenobiotic action. In vitro models have been used to define postattachment trophoblast cell differentiation. Trophoblast specific peptide hormones prove to be valid markers of established pregnancy. They provide no assessment of the risk to the embryo during the peri-implantation period. The relationship between developmental time of exposure and risk is discussed in terms of trophoblast differentiation. 展开更多
关键词 Laboratory Models for the Study of the Peri-implantation Period
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Invasion reproductive numbers for periodic epidemic models 被引量:1
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作者 Christopher Mitchell Christopher Kribs 《Infectious Disease Modelling》 2019年第1期124-141,共18页
There are many cases within epidemiology where infections compete to persist within a population.In studying models for such cases,one of the goals is to determine which infections can invade a population and persist ... There are many cases within epidemiology where infections compete to persist within a population.In studying models for such cases,one of the goals is to determine which infections can invade a population and persist when other infections are already resident within the population.Invasion reproductive numbers(IRN),which are tied to the stability of boundary endemic equilibria,can address this question.By reinterpreting resident infections epidemiologically,this study extends methods for finding IRNs to periodic systems,and presents some examples which illustrate the often complex computations required.Results identify conditions under which a simple time-average can be used to derive IRNs,and apply the methods to examine how seasonal fluctuations in influenza incidence facilitate the year-round persistence of bacterial respiratory infections. 展开更多
关键词 Mathematical epidemiology periodic models Basic reproductive number
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Dynamics of a stochastic periodic SIRS model with time delay
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作者 Xiangyun Shi Yimeng Cao 《International Journal of Biomathematics》 SCIE 2020年第8期25-42,共18页
Dynamical behaviors of a siocluustic periodic SIRS epidemic model with time delay are investigated.By constructing suitable Lyapunov functions and applying Ito's formula,the existence of the global positive soluti... Dynamical behaviors of a siocluustic periodic SIRS epidemic model with time delay are investigated.By constructing suitable Lyapunov functions and applying Ito's formula,the existence of the global positive solution and the property of stochastically ultimate boundedness of model(1.1)are proved.Moreover,the extinction and the persistence of the disease are established.The results are verified by numerical simulations. 展开更多
关键词 Stochastic periodic model DELAY EXTINCTION stochcistically ultimate boundedness PERSISTENCE
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Optimal Investment with Multiple Risky Assets for an Insurer with Modified Periodic Risk Process
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作者 ZHAO Hui RONG Ximin 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2015年第4期997-1014,共18页
This paper considers the optimal investment problem for an insurer in the sense of maximizing the adjustment coefficient of the risk process.The authors propose a modified periodic risk model in which the periodic ris... This paper considers the optimal investment problem for an insurer in the sense of maximizing the adjustment coefficient of the risk process.The authors propose a modified periodic risk model in which the periodic risk process is perturbed by a standard Brownian motion.The insurer can invest in multiple risky assets and one risk-free asset and the correlations between the risky assets and the risk process are considered.Optimal strategy is obtained explicitly,which is a function of time and related to the risk process.The effects of market parameters on the optimal strategy are discussed and a numerical example is also given. 展开更多
关键词 Adjustment coefficient modified periodic risk model multiple risky assets optimalinvestment ruin probability.
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MODELLING AND NUMERICAL SOLUTIONS OF A GAUGE PERIODIC TIME DEPENDENT GINZBURG-LANDAU MODEL FOR TYPE-Ⅱ SUPERCONDUCTORS
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作者 Zhi-ming Chen (Institute of Mathematics, Chinese Academy of Sciences, Beijing, China) 《Journal of Computational Mathematics》 SCIE CSCD 1997年第4期365-384,共20页
In this paper we seek the solutions of the time dependent Ginzburg-Landau model for type-Ⅱ superconductors such that the associated physical observables are spatially periodic with respect to some lattice whose basic... In this paper we seek the solutions of the time dependent Ginzburg-Landau model for type-Ⅱ superconductors such that the associated physical observables are spatially periodic with respect to some lattice whose basic lattice cell is not necessarily rectangular. After appropriately foring the gange, the model can be formulated as a system of nonlinear parabolic partial differential equations with quasi-periodic boundary conditions. We first give some results concerning the existence, uniqueness and regularity of solutions and then we propose a semiimplicit finite element scheme solving the system of nonlinear partial dmerential equations and show the optimal error estimates both in the L2 and energy norm.We also report on some numerical results at the end of the paper. 展开更多
关键词 Math QT MODELLING AND NUMERICAL SOLUTIONS OF A GAUGE periodic TIME DEPENDENT GINZBURG-LANDAU MODEL FOR TYPE SUPERCONDUCTORS
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Discussion on the paper “Analyzing short time series data from periodically fluctuating rodent populations by threshold models: A nearestblock bootstrap approach”
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作者 HALL Peter 《Science China Mathematics》 SCIE 2009年第6期1107-1108,共2页
This is a very attractive article. It combines fascinating new methodology with a most interesting dataset, and a highly motivating presentation. However, despite the many
关键词 time A nearestblock bootstrap approach Analyzing short time series data from periodically fluctuating rodent populations by threshold models Discussion on the paper data
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Discussion on the paper “Analyzing short time series data from periodically fluctuating rodent populations by threshold models: A nearestblock bootstrap approach”
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作者 LI W.K.& LI GuoDong Department of statistics and Actuarial Science,University of Hong Kong,Pokfulam Road,Hong Kong,China 《Science China Mathematics》 SCIE 2009年第6期1109-1110,共2页
The authors are to be congratulated for an innovative paper in terms of both modelling methodology and subject matter significance. The analysis of short time series is known to be
关键词 time Discussion on the paper A nearestblock bootstrap approach Analyzing short time series data from periodically fluctuating rodent populations by threshold models GARCH data
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Secular trends of asthma mortality in China and the United States from 1990 to 2019 被引量:3
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作者 Xiaochen Li Mingzhou Guo +2 位作者 Yang Niu Min Xie Xiansheng Liu 《Chinese Medical Journal》 SCIE CAS CSCD 2024年第3期273-282,共10页
Background:Asthma imposes a large healthcare burden in China and the United States(US).However,the trends of asthma mortality and the relative risk factors have not been comparatively analyzed between the countries.Th... Background:Asthma imposes a large healthcare burden in China and the United States(US).However,the trends of asthma mortality and the relative risk factors have not been comparatively analyzed between the countries.The aim of this study was to compare the mortality and risk factors between China and the US.Methods:The deaths,and mortality rates of asthma in China and the US during 1990–2019 were obtained from the Global Burden of Disease Study 2019.The age–period–cohort model was used to estimate these mortality rates based on a log-linear scale with additive age,period,and cohort effects.The population attributable fractions of risk factors for asthma were estimated.Results:In 1990–2019,the asthma mortality rate was higher in China than in the US.The crude and age-standardized asthma mortality rates trended downward in both China and the US from 1990 to 2019.The decline in mortality was more obvious in China.Mortality gap between the two countries was narrowing.A sex difference in asthma mortality was observed with higher mortality in males in China and females in the US.The age effects showed that mortality increased with age in adults older than 20 years,particularly in the elderly.Downward trends were generally observed in the period and cohort rate ratios in both countries,with China experiencing a more obvious decrease.Smoking and high body mass index(BMI)were the leading risk factors for asthma mortality in China and the US,respectively.Mortality attributable to occupational asthmagens and smoking decreased the most in China and the US,respectively.Conclusions:In 1990–2019,the asthma mortality rate was higher in China than in the US;however,the mortality gap has narrowed.Mortality increased with age in adults.The improvements in asthma death risk with period and birth cohort were more obvious in China than in the US.Smoking,high BMI,and aging are major health problems associated with asthma control.The role of occupational asthmagens in asthma mortality underscores the importance of management and prevention of occupational asthma. 展开更多
关键词 ASTHMA MORTALITY Global disease burden China the United States Age–period–cohort model
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Global,regional and national disease burden of food-borne trematodiases:projections to 2030 based on the Global Burden of Disease Study 2021 被引量:1
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作者 Lu Liu Li‑Dan Lu +4 位作者 Guo‑Jing Yang Men‑Bao Qian Kun Yang Feng Tan Xiao‑Nong Zhou 《Infectious Diseases of Poverty》 CSCD 2024年第6期108-108,共1页
Background Food-borne trematodiases(FBTs),mainly encompassing clonorchiasis,fascioliasis,fasciolopsiasis,opisthorchiasis,and paragonimiasis,is a neglected public health problem,particularly in the WHO South-East Asia ... Background Food-borne trematodiases(FBTs),mainly encompassing clonorchiasis,fascioliasis,fasciolopsiasis,opisthorchiasis,and paragonimiasis,is a neglected public health problem,particularly in the WHO South-East Asia and the Western Pacific regions.This study evaluates the global,regional,and national disease burden of FBTs from 1990 to 2021 and projects trends to 2030,underscore the need for targeted prevention and control.Methods Using the Global Burden of Disease 2021 database,the crude and the age-standardized prevalence rate(ASPR)and age-standardized prevalence disability-adjusted life years rate(ASDR)of FBTs at the global,regional and national level from 1990 to 2021 were described.The pivotal years of trend changes were identified using joinpoint regression analysis.The effects of age,period,cohort on FBTs prevalence and correlation with the sociode-mographic index(SDI)was analyzed.Finally,the worldwide disability-adjusted life years(DALYs)for FBTs,projected up to 2030 using the Bayesian age-period-cohort model,were analyzed.Results In 2021,44,466,329 FBTs cases[95%uncertainty interval(UI):40,017,217,50,034,921],and 998,028 DALYs[95%UI:569,766,1,638,112]were estimated across 17 countries.The Western Pacific region exhibited the highest ASPR and ASDR,with the values of 1649.26(95%UI:1461.95,1881.64)and 36.54(95%UI:19.77,64.16),respectively.From 1990 to 2021,Lao PDR,Thailand,and the Philippines showed the most substantial declines in FBTs,while Kazakhstan had the largest average annual percentage change in DALYs(-6.60,95%UI:-7.10,-6.10).High-middle and middle SDI countries exhibited higher burden,with ASDR values of 28.03(95%UI:15.41,48.73)and 16.63(95%UI:9.32,27.68),respectively.The disease burden was greater among males,peaking in the 50-59 age group.The projected ASDR in 2030 is 13.10 for males and 8.40 for females.Conclusions FBTs remain a public health threat,with the global ASDR projected to remain stable,showing only a slight decrease by 2030.Low-income countries face ambiguous mortality rates and underestimated disease burdens,highlighting the need for improved surveillance.To achieve the 2030 NTD goal,comprehensive surveillance and integrated strategies derived using a One Health approach should be prioritized to control FBTs effectively. 展开更多
关键词 Disease burden Food‑borne trematodiases Bayesian age‑period‑cohort analysis model
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THE INFLUENCE OF ARCTIC AND ANTARCTIC ICE ON SOUTHERN OSCILLATION 被引量:4
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作者 黄嘉佑 《Acta meteorologica Sinica》 SCIE 1999年第4期439-449,共11页
The analysis of the relationship between sea ice in Arctic and Antarctic, and the Southern Oscillation Index (SOI) variation on the temporal scale of month, season and year is made in this paper. The negative correlat... The analysis of the relationship between sea ice in Arctic and Antarctic, and the Southern Oscillation Index (SOI) variation on the temporal scale of month, season and year is made in this paper. The negative correlation between sea ice in Arctic and the SOI. and the positive correlation between sea ice in Antarctic and the SOI are found. The variation of sea ice in Antarctic Pacific seems to play an important role in the influence to atmosphere. Their nonlinear relationships present more strongly than the linear relationship between them. The relationship between sea ice in Arctic and Antarctic and the SOI in the early stage is investigated. Their variation shows periodic phenomena. The maximum correlation is used to build the model for forecasting the variation of the SOI on the condition of the sea ice in Arctic and Antarctic. The explained variance of the simulated series is greater than 0.90. There exists a 17-month period in the relationship between sea ice in Arctic and Antarctic and SOI. The existing of the common factor with larger scale is discussed in this paper. 展开更多
关键词 analysis of time scale nonlinear relationship simulation on statistic-dynamic model periodic model
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COMBINING SINGULAR SPECTRUM ANALYSIS AND PAR(p) STRUCTURES TO MODEL WIND SPEED TIME SERIES 被引量:1
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作者 MENEZES Moises Lima de SOUZA Reinaldo Castro PESSANHA Jos Francisco Moreira 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2014年第1期29-46,共18页
Singular spectrum analysis (SSA) is a technique that decomposes a time series into a set of components, such as, trend, harmonics, and residuals. Leaving out the residual components and adding up the others, the tim... Singular spectrum analysis (SSA) is a technique that decomposes a time series into a set of components, such as, trend, harmonics, and residuals. Leaving out the residual components and adding up the others, the time series can be smoothed. This procedure has been used to model Brazilian electricity consumption and flow series. The PAR(p), periodic autoregressive models, has been broadly used in modelling energy series in Brazil. This paper presents an approach of this decomposition method, by fitting the PAR(p), considering its multivariate version known as multivariate SSA (MSSA). The method was applied to a vector of two wind speed series recorded at two locations in the Brazilian Northeast region. The obtained results, when compared to the univariate decomposition of each series, were far superior, showing that the spatial correlation between the two series were considered by MSSA decomposition stage. 展开更多
关键词 MSSA periodic autoregressive model SSA wind speed series.
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