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Global Strong Solutions to the Nonhomogeneous Boussinesq Equations for Magnetohydrodynamics Convection with Zero Heat Diffusion and Large Initial Data
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作者 YANG Wanji 《数学进展》 北大核心 2025年第5期992-1014,共23页
We study the two-dimensional(2D)Cauchy problem of nonhomogeneous Boussinesq system for magnetohydrodynamics convection without heat diffusion in the whole plane.Based on delicate weighted estimates,we derive the globa... We study the two-dimensional(2D)Cauchy problem of nonhomogeneous Boussinesq system for magnetohydrodynamics convection without heat diffusion in the whole plane.Based on delicate weighted estimates,we derive the global existence and uniqueness of strong solutions.In particular,the initial data can be arbitrarily large and the initial density may contain vacuum states and even have compact support. 展开更多
关键词 nonhomogeneous Boussinesq-MHD system global well-posedness Cauchy problem zero heat diffusion large initial data
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On the Riemann-Hilbert problem for the reverse space-time nonlocal Hirota equation with step-like initial data
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作者 Bei-Bei Hu Ling Zhang +1 位作者 Zu-Yi Shen Ji Lin 《Communications in Theoretical Physics》 2025年第2期30-38,共9页
In this paper,we use the Riemann-Hilbert(RH)method to investigate the Cauchy problem of the reverse space-time nonlocal Hirota equation with step-like initial data:q(z,0)=o(1)as z→-∞and q(z,0)=δ+o(1)as z→∞,where... In this paper,we use the Riemann-Hilbert(RH)method to investigate the Cauchy problem of the reverse space-time nonlocal Hirota equation with step-like initial data:q(z,0)=o(1)as z→-∞and q(z,0)=δ+o(1)as z→∞,whereδis an arbitrary positive constant.We show that the solution of the Cauchy problem can be determined by the solution of the corresponding matrix RH problem established on the plane of complex spectral parameterλ.As an example,we construct an exact solution of the reverse space-time nonlocal Hirota equation in a special case via this RH problem. 展开更多
关键词 nonlocal Hirota equation Cauchy problem Riemann-Hilbert problem step-like initial data
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An Initial Residual Stress Inference Method by Incorporating Monitoring Data and Mechanism Model 被引量:2
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作者 Shuguo Wang Yingguang Li +1 位作者 Changqing Liu Zhiwei Zhao 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2022年第5期47-65,共19页
Initial residual stress is the main reason causing machining deformation of the workpiece,which has been deemed as one of the most important aspects of machining quality issues.The inference of the distribution of ini... Initial residual stress is the main reason causing machining deformation of the workpiece,which has been deemed as one of the most important aspects of machining quality issues.The inference of the distribution of initial residual stress inside the blank has significant meaning for machining deformation control.Due to the principle error of existing residual stress detection methods,there are still challenges in practical applications.Aiming at the detection problem of the initial residual stress field,an initial residual stress inference method by incorporating monitoring data and mechanism model is proposed in this paper.Monitoring data during machining process is used to represent the macroscopic characterization of the unbalanced residual stress,and the finite element numerical model is used as the mechanism model so as to solve the problem that the analytic mechanism model is difficult to establish;the policy gradient approach is introduced to solve the gradient descent problem of the combination of learning model and mechanism model.Finally,the initial residual stress field is obtained through iterative calculation based on the fusing method of monitoring data and mechanism model.Verification results show that the proposed inference method of initial residual stress field can accurately and effectively reflect the machining deformation in the actual machining process. 展开更多
关键词 initial residual stress INFERENCE Monitoring data Mechanism model Policy gradient
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ON THE CAUCHY PROBLEM OF THEKURAMOTO-SIVASHINSKY EQUATION WITH SINGULAR INITIAL DATA
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作者 赵会江 柳再华 陈世平 《Acta Mathematica Scientia》 SCIE CSCD 1998年第1期25-34,共10页
In this paper, it is considered that the global existence, uniqueness and regularity results for the Cauchy problem of the well-known Kuramoto-Sivashinsky equation [GRAPHICS] only under the condition u(0)(x) is an ele... In this paper, it is considered that the global existence, uniqueness and regularity results for the Cauchy problem of the well-known Kuramoto-Sivashinsky equation [GRAPHICS] only under the condition u(0)(x) is an element of L-2(R-N, R-n). Where u(t, x) = (u(1)(t, x), ..., u(n)(t, x))(T) is the unknown vector-valued function. Results show that for N < 6,.u(0)(x) is an element of L-2(R-N, R-n), the above Cauchy problem admits a unique global solution u(t, x) which belongs to C-infinity,C-infinity(R-N x (0, infinity)). 展开更多
关键词 Kuramoto-Sivashinsky equation singular initial data Sobolev imbedding theorem
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ASYMPTOTIC HOMOGENIZATION IN A PARABOLIC SEMILINEAR PROBLEM WITH PERIODIC COEFFICIENTS AND INTEGRABLE INITIAL DATA
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作者 Rogerio Luiz Quintino de OLIVEIRA JUNIOR 《Acta Mathematica Scientia》 SCIE CSCD 2013年第5期1275-1292,共18页
In this paper, we study the large time behavior of solutions of the parabolic semilinear equation δtu-div(a(x)△↓u) = -|u|^αu in (0,∞) × R^N, where α 〉 0 is constant and a∈ Cb^1(R^N) is a symmetr... In this paper, we study the large time behavior of solutions of the parabolic semilinear equation δtu-div(a(x)△↓u) = -|u|^αu in (0,∞) × R^N, where α 〉 0 is constant and a∈ Cb^1(R^N) is a symmetric periodic matrix satisfying some ellipticity assumptions.Considering an integrable initial data u0 and α ∈ (2/N, 3/N), we prove that the large time behavior of solutions is given by the solution U(t, x) of the homogenized linear problem δtU-div(a^h△↓U)=0,U(0) = C, where a^h is the homogenized matrix of a(x), C is a positive constant and δ is the Dirac measure at 0. 展开更多
关键词 HOMOGENIZATION similinear parabolic equation integrable initial data matrix with periodic coefficient large time behavior
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FIRST ORDER QUASILINEAR EQUATIONS IN SEVERAL INDEPENDENT VARIABLES WITH SINGULAR INITIAL DATA L^p(P<∞)
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作者 赵会江 《Acta Mathematica Scientia》 SCIE CSCD 1996年第3期308-320,共13页
We study the existence problem for the equations of first order quasilinearequations in several inpendent variables with singular initial data Lp(P<∞). We the convergence of the Lp(P<∞) bounded approximating s... We study the existence problem for the equations of first order quasilinearequations in several inpendent variables with singular initial data Lp(P<∞). We the convergence of the Lp(P<∞) bounded approximating sequences generatedby the method of vanishing viscosity. The uniqueness of the generalized solutions whichcan be obtained by the method of vanishing viscosity is also obtained. 展开更多
关键词 Singular initial data quasilinear equations global weak solutions
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Large-time Behavior of Solutions for Parabolic Conservation Laws with Large Initial Data
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作者 WANG Li-juan 《Chinese Quarterly Journal of Mathematics》 CSCD 2012年第2期232-237,共6页
In this paper,we study the large-time behavior of periodic solutions for parabolic conservation laws.There is no smallness assumption on the initial data.We firstly get the local existence of the solution by the itera... In this paper,we study the large-time behavior of periodic solutions for parabolic conservation laws.There is no smallness assumption on the initial data.We firstly get the local existence of the solution by the iterative scheme,then we get the exponential decay estimates for the solution by energy method and maximum principle,and obtain the global solution in the same time. 展开更多
关键词 parabolic conservation law periodic solution large initial data exponential decay
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THE REGULARITY AND UNIQUENESS OF A GLOBAL SOLUTION TO THE ISENTROPIC NAVIER-STOKES EQUATION WITH ROUGH INITIAL DATA
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作者 王海涛 张雄韬 《Acta Mathematica Scientia》 SCIE CSCD 2023年第4期1675-1716,共42页
A global weak solution to the isentropic Navier-Stokes equation with initial data around a constant state in the L^(1)∩BV class was constructed in[1].In the current paper,we will continue to study the uniqueness and ... A global weak solution to the isentropic Navier-Stokes equation with initial data around a constant state in the L^(1)∩BV class was constructed in[1].In the current paper,we will continue to study the uniqueness and regularity of the constructed solution.The key ingredients are the Holder continuity estimates of the heat kernel in both spatial and time variables.With these finer estimates,we obtain higher order regularity of the constructed solution to Navier-Stokes equation,so that all of the derivatives in the equation of conservative form are in the strong sense.Moreover,this regularity also allows us to identify a function space such that the stability of the solutions can be established there,which eventually implies the uniqueness. 展开更多
关键词 compressible Navier-Stokes equation BV initial data REGULARITY UNIQUENESS
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CAUCHY PROBLEM FOR LINEARIZED SYSTEM OF TWO-DIMENSIONAL ISENTROPIC FLOW WITH AXISYMMETRICAL INITIAL DATA IN GAS DYNAMICS
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作者 Zhang Hua Sheng Wancheng 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2006年第1期30-40,共11页
The explicit solution to Cauchy problem for linearized system of two-dimensional isentropic flow with axisymmetrical initial data in gas dynamics is given.
关键词 Cauchy prohlem with axisymmetrical initial data linearized system 2-D isentropic flow explicit solution.
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ALMOST SURE GLOBAL WELL-POSEDNESS FOR THE FOURTH-ORDER NONLINEAR SCHR?DINGER EQUATION WITH LARGE INITIAL DATA
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作者 陈明娟 张帅 《Acta Mathematica Scientia》 SCIE CSCD 2023年第5期2215-2233,共19页
We consider the fourth-order nonlinear Schr?dinger equation(4NLS)(i?t+εΔ+Δ2)u=c1um+c2(?u)um-1+c3(?u)2um-2,and establish the conditional almost sure global well-posedness for random initial data in Hs(Rd)for s∈(sc-... We consider the fourth-order nonlinear Schr?dinger equation(4NLS)(i?t+εΔ+Δ2)u=c1um+c2(?u)um-1+c3(?u)2um-2,and establish the conditional almost sure global well-posedness for random initial data in Hs(Rd)for s∈(sc-1/2,sc],when d≥3 and m≥5,where sc:=d/2-2/(m-1)is the scaling critical regularity of 4NLS with the second order derivative nonlinearities.Our proof relies on the nonlinear estimates in a new M-norm and the stability theory in the probabilistic setting.Similar supercritical global well-posedness results also hold for d=2,m≥4 and d≥3,3≤m<5. 展开更多
关键词 fourth-order Schrodinger equation random initial data almost sure global well-posedness M-norm stability theory
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Roles of initial ocean states on predicting the 2002/03 central Pacific El Nino 被引量:2
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作者 ZHENG Fei WANG Hui WAN Liying 《Acta Oceanologica Sinica》 SCIE CAS CSCD 2015年第12期72-79,共8页
The 2002/03 El Ni?o event, a new type of El Ni?o with maximum warm anomaly occurring in the central equatorial Pacific, is known as central-Pacific(CP) El Ni?o. In this study, on the basis of an El Ni?o predicti... The 2002/03 El Ni?o event, a new type of El Ni?o with maximum warm anomaly occurring in the central equatorial Pacific, is known as central-Pacific(CP) El Ni?o. In this study, on the basis of an El Ni?o prediction system, roles of the initial ocean surface and subsurface states on predicting the 2002/03 CP El Ni?o event are investigated to determine conditions favorable for predicting El Ni?o growth and are isolated in three sets of hindcast experiments. The hindcast is initialized through assimilation of only the sea surface temperature(SST)observations to optimize the initial surface condition(Assim_SST), only the sea level(SL) data to update the initial subsurface state(Assim_SL), or both the SST and SL data(Assim_SST+SL). Results highlight that the hindcasts with three different initial states all can successfully predict the 2002/03 El Ni?o event one year in advance and that the Assim_SST+SL hindcast performs best. A comparison between the various sets of hindcast results further demonstrates that successful prediction is significantly affected by both of the initial surface and subsurface conditions, but in different developing phases of the 2002/03 El Ni?o event. The accurate initial surface state can easier trigger the prediction of the 2002/03 El Ni?o, whereas a more reasonable initial subsurface state can contribute to improving the prediction in the growth of the warm event. 展开更多
关键词 initial oceanic states CP El Ni?o Seasonal prediction data assimilation
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Using Satellite Data to Analyze the Initiation and Evolution of Deep Convective Clouds 被引量:1
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作者 CAO Zhi-Qiang HUANG Qing-Ni ZHAO Su-Rong 《Atmospheric and Oceanic Science Letters》 CSCD 2013年第6期445-450,共6页
In this study, two deep convective cloud cases were analyzed in detail to study their initiation and evolution. In both cases, all deep convective clouds were positioned at the rear of the cold front cloud bands and p... In this study, two deep convective cloud cases were analyzed in detail to study their initiation and evolution. In both cases, all deep convective clouds were positioned at the rear of the cold front cloud bands and propagated backward. Satellite data showed that prior to initiation of the deep convective clouds, thermodynamic and moist conditions were favorable for their formation. In the morning, a deep convective cloud at the rear of cold front cloud band propagated backward, the outflow boundary of which created favorable conditions for initiation. An additional deep convective cloud cluster moved in from the west and interacted with the outflow boundary to develop a mesoscale convective system(MCS) with large, ellipse-shaped deep convective clouds that brought strong rainfall. The initiation and evolution of these clouds are shown clearly in satellite data and provide significant information for nowcasting and short-term forecasting. 展开更多
关键词 deep convective clouds satellite data initiATION EVOLUTION
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Initial Stable State of Ocean Floor Deposits
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作者 洪振舜 石名磊 《海洋工程:英文版》 EI 2004年第3期469-476,共8页
Extensive oedometer tests and physical tests have been conducted on remolded and reconstituted marine soils with different initial water contents and liquid limits. The oedometer test data can be well fitted with a st... Extensive oedometer tests and physical tests have been conducted on remolded and reconstituted marine soils with different initial water contents and liquid limits. The oedometer test data can be well fitted with a straight line in the bilogarithmic ln(1+ e ) ~ lg p plot. The initial effective stress corresponding to the initial void ratio is determined by extrapolation of the bilogarithmic compression line. This new way of extrapolating oedometer test data to the initial void ratio overcomes the difficulty of measuring the residual effective stress of soils in the remolded state. The initial stable compression line of ocean floor deposits under different deposition environments corresponds to the compression line at the sensitivity equal to one. This initial stable compression line obtained in this study is consistent with the available compression line at the sensitivity equal to one which is proposed based on the experimental data of remolded undrained strength and the theoretical concept of Cam clay critical state line. 展开更多
关键词 initial effective stress initial stable state initial void ratio interpretation of oedometer test data normalized initial void ratio ocean floor deposits sensitivity equal to one
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Open Source Initiatives for Big Data Governance and Security:A Survey
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作者 hu baiqing wang wenjie chi harold liu 《ZTE Communications》 2018年第2期55-66,共12页
With the rapid development of lnternet technology, the volume of data has increased exponentially. As the large amounts of data are no longer easy to be managed and secured by the owners, big data security and privacy... With the rapid development of lnternet technology, the volume of data has increased exponentially. As the large amounts of data are no longer easy to be managed and secured by the owners, big data security and privacy has become a hot issue. One of the most popular research fields for solving the data security and data privacy is within the scope of big data governance and security, In this paper, we introduce the basic concepts of data governance and security. Then, all the state-of-the-art open source frameworks for data governance and security, including Apache Falcon, Apache Atlas, Apache Ranger, Apache Sentry and Kerberos, are detailed and discussed with descriptions of their implementation principles and possible applications. 展开更多
关键词 big data SECURITY GOVERNANCE open source initiatives
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Incompressible Limit of Nonisentropic Ideal Magnetohydrodynamic Flows with General Initial Data
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作者 MENG Fanrui WANG Jiawei 《Journal of Partial Differential Equations》 2025年第1期101-114,共14页
The incompressible limit of nonisentropic ideal magnetohydrodynamic equations with general initial data in the whole space R^(3) is proved in this paper.The uniform estimates of solutions with respect to the Mach numb... The incompressible limit of nonisentropic ideal magnetohydrodynamic equations with general initial data in the whole space R^(3) is proved in this paper.The uniform estimates of solutions with respect to the Mach number are obtained by using energy estimate.Strong convergence results of the smooth solutions are established by using Strichartz's estimates in the whole space. 展开更多
关键词 Incompressible limit general initial data nonisentropic MHD equations
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The materials data ecosystem: Materials data science and its role in data-driven materials discovery 被引量:2
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作者 Hai-Qing Yin Xue Jiang +4 位作者 Guo-Quan Liu Sharon Elder Bin Xu Qing-Jun Zheng Xuan-Hui Qu 《Chinese Physics B》 SCIE EI CAS CSCD 2018年第11期120-125,共6页
Since its launch in 2011, the Materials Genome Initiative(MGI) has drawn the attention of researchers from academia,government, and industry worldwide. As one of the three tools of the MGI, the use of materials data... Since its launch in 2011, the Materials Genome Initiative(MGI) has drawn the attention of researchers from academia,government, and industry worldwide. As one of the three tools of the MGI, the use of materials data, for the first time, has emerged as an extremely significant approach in materials discovery. Data science has been applied in different disciplines as an interdisciplinary field to extract knowledge from data. The concept of materials data science has been utilized to demonstrate its application in materials science. To explore its potential as an active research branch in the big data era, a three-tier system has been put forward to define the infrastructure for the classification, curation and knowledge extraction of materials data. 展开更多
关键词 Materials Genome initiative materials data science data classification life-cycle curation
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Radar Data Assimilation for the Simulation of Mesoscale Convective Systems 被引量:2
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作者 Jo-Han LEE Hyun-Ha LEE +2 位作者 Yonghan CHOI Hyung-Woo KIM Dong-Kyou LEE 《Advances in Atmospheric Sciences》 SCIE CAS CSCD 2010年第5期1025-1042,共18页
A heavy rainfall case related to Mesoscale Convective Systems (MCSs) over the Korean Peninsula was selected to investigate the impact of radar data assimilation on a heavy rainfall forecast. The Weather Research and... A heavy rainfall case related to Mesoscale Convective Systems (MCSs) over the Korean Peninsula was selected to investigate the impact of radar data assimilation on a heavy rainfall forecast. The Weather Research and Forecasting (WRF) three-dimensional variational (3DVAR) data assimilation system with tuning of the length scale of the background error covariance and observation error parameters was used to assimilate radar radial velocity and reffectivity data. The radar data used in the assimilation experiments were preprocessed using quality-control procedures and interpolated/thinned into Cartesian coordinates by the SPRINT/CEDRIC packages. Sensitivity experiments were carried out in order to determine the optimal values of the assimilation window length and the update frequency used for the rapid update cycle and incremental analysis update experiments. The assimilation of radar data has a positive influence on the heavy rainfall forecast. Quantitative features of the heavy rainfall case, such as the maximum rainfall amount and Root Mean Squared Differences (RMSDs) of zonal/meridional wind components, were improved by tuning of the length scale and observation error parameters. Qualitative features of the case, such as the maximum rainfall position and time series of hourly rainfall, were enhanced by an incremental analysis update technique. The positive effects of the radar data assimilation and the tuning of the length scale and observation error parameters were clearly shown by the 3DVAR increment. 展开更多
关键词 WRF 3DVAR 3DVAR cycling initialIZATION tuning heavy rainfall radar data
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Coupling effects of influence factors on probability of corrosion initiation time of reinforced concrete 被引量:6
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作者 张小刚 赵衍刚 +1 位作者 邢锋 卢朝辉 《Journal of Central South University》 SCIE EI CAS 2011年第1期223-229,共7页
The coupling model of major influence factors such state affecting the chloride diffusion process in concrete is as environmental relative humidity, load-induced crack and stress discussed. The probability distributio... The coupling model of major influence factors such state affecting the chloride diffusion process in concrete is as environmental relative humidity, load-induced crack and stress discussed. The probability distributions of the critical chloride concentration Cc, the chloride diffusion coefficient D, and the surface chloride concentration Cs were determined based on the collected natural exposure data. And the estimation of probability of corrosion initiation considering the coupling effects of influence factors is presented. It is found that the relative humidity and curing time are the most effective factors affecting the probability of corrosion initiation before and after 10 years of exposure time. At the same exposure time, the influence of load-induced crack and stress state on the probability of corrosion initiation is obvious, in which the effect of crack is the most one 展开更多
关键词 reinforced concrete corrosion initiation time coupling influence model influence factors natural exposure data probability distribution
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Role of the interaction between a gust front and a mesoscale air mass boundary in convection initiation:a case study 被引量:3
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作者 CUI Xinyan QIN Rui +1 位作者 CHEN Mingxuan HAN Lei 《Atmospheric and Oceanic Science Letters》 CSCD 2019年第5期337-342,共6页
The local convection initiation(CI)mechanisms of a convective case that occurred on5 August 2017 in Cangzhou,northern China,were studied using Doppler radar and automatic weather station observational analysis,along w... The local convection initiation(CI)mechanisms of a convective case that occurred on5 August 2017 in Cangzhou,northern China,were studied using Doppler radar and automatic weather station observational analysis,along with Variational Doppler Radar Analysis System assimilation analysis.During the convective process,a gust front appeared ahead of two existing convective systems,respectively.In the warm and moist environment ahead of the gust fronts in the south,there was a mesoscale air mass boundary.With the process of a gust front moving southward,approaching the mesoscale air mass boundary,the convergence intensified in the area between the gust front and the mesoscale air mass boundary.Finally,the strong convergent updraft exceeded the level of free convection and triggered the new convection. 展开更多
关键词 Convection initiation gust front mesoscale air mass boundary 4D variational data assimilation
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Shock initiation performance of NTO-based polymer bonded explosive 被引量:2
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作者 Peng-song Nie Shao-hua Jin +4 位作者 Li-xiao-song Du Li-jie Li Kun Chen Yu Chen Rui Yu 《Defence Technology(防务技术)》 SCIE EI CAS CSCD 2022年第9期1538-1545,共8页
3-nitro-1,2,4-tri-azol-5-one(NTO) is a high energy insensitive explosive. To study the shock initiation process of NTO-based polymer bonded explosive JEOL-1(32%octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine(HMX), 32... 3-nitro-1,2,4-tri-azol-5-one(NTO) is a high energy insensitive explosive. To study the shock initiation process of NTO-based polymer bonded explosive JEOL-1(32%octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine(HMX), 32% NTO, 28% Al and 8% binder system), the cylinder test, the gap experiments and numerical simulation were carried out. Firstly, we got the detonation velocity(7746 m/s) and the parameters of Jones-Wilkins-Lee(JWL) equation of state(EOS) for detonation product by cylinder test and numerical simulation. Secondly, the Hugoniot curve of unreacted explosive for JEOL-1 was obtained calculating the data of pressure and time at different Lagrangian positions. Then the JWL EOS of unreacted explosive was obtained by utilizing the Hugoniot curve as the reference curve. Finally, we got the pressure growth history of JEOL-1 under shock wave stimulation and the parameters of the ignition and growth reaction rate equation were obtained by the pressure-time curves measured by the shockinitiation gap experiment and numerical simulation. The determined trinomial ignition and growth model(IG model) parameters can be applied to subsequently simulation analysis and design of insensitive ammunition with NTO-based polymer bonded explosive. 展开更多
关键词 NTO Shock initiation Hugoniot data JWL Ignition and growth reactive model
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