The Neo-Tethys Ocean was an eastward-gaping triangular oceanic embayment between Laurasia to the north and Gondwana to the south.The Neo-Tethys Ocean was initiated from the Early Permian with mircoblocks rifted from t...The Neo-Tethys Ocean was an eastward-gaping triangular oceanic embayment between Laurasia to the north and Gondwana to the south.The Neo-Tethys Ocean was initiated from the Early Permian with mircoblocks rifted from the northern margin of Gondwana.As the microblocks drifted northwards,the Neo-Tethys Ocean was expanded.Most of these microblocks collided with the Eurasia continent in the Late Triassic,leading to the final closure of the Paleo-Tethys Ocean,followed by oceanic subduction of the Neo-Tethys oceanic slab beneath the newly formed southern margin of the Eurasia continent.As the splitting of Gondwana continued,African-Arabian,Indian and Australian continents were separated from Gondwana and moved northwards at different rates.Collision of these blocks with the Eurasia continent occurred at different time during the Cenozoic,resulting in the closure of the Neo-Tethys Ocean and building of the most significant Alps-Zagros-Himalaya orogenic belt on Earth.The tectonic evolution of the Neo-Tethys Ocean shows different characteristics from west to east:Multi-oceanic basins expansion,bidirectional subduction and microblocks collision dominate in the Mediterranean region;northward oceanic subduction and diachronous continental collision along the Zagros suture occur in the Middle East;the Tibet and Southeast Asia are characterized by multi-block riftings from Gondwana and multi-stage collisions with the Eurasia continent.The negative buoyancy of subducting oceanic slabs can be considered as the main engine for northward drifting of Gondwana-derived blocks and subduction of the Neo-Tethys Ocean.Meanwhile,mantle convection and counterclockwise rotation of Gondwana-derived blocks and the Gondwana continent around an Euler pole in West Africa in non-free boundary conditions also controlled the evolution of the Neo-Tethys Ocean.展开更多
The regular solutions of the isentropic Euler equations with degenerate linear damping for a perfect gas are studied in this paper. And a critical degenerate linear damping coefficient is found, such that if the degen...The regular solutions of the isentropic Euler equations with degenerate linear damping for a perfect gas are studied in this paper. And a critical degenerate linear damping coefficient is found, such that if the degenerate linear damping coefficient is larger than it and the gas lies in a compact domain initially, then the regular solution will blow up in finite time; if the degenerate linear damping coefficient is less than it, then under some hvpotheses on the initial data. the regular solution exists globally.展开更多
The article explores the issue of designing a new design of a loading cylinder with a casing filled with vulcanized rubber for pneumomechanical spinning machines. The theoretical calculation of the deformed state of a...The article explores the issue of designing a new design of a loading cylinder with a casing filled with vulcanized rubber for pneumomechanical spinning machines. The theoretical calculation of the deformed state of a cylindrical shell filled with vulcanized rubber is given. Deflections and stresses in the rubber layer are determined, which we use approximately for the Ritz methods. The theory of the radial and axial moving rubber layer was analyzed. The specific energy of deformation of a cylindrical layer of a compound cylinder is determined. The statics of the case and the loading cylinder of spinning machines are thoroughly studied.展开更多
The analytic and discretized dissipativity of nonlinear infinite-delay systems of the form x＇（t） = g（x（t）,x（qt））（q∈ （0, 1）, t 〉 0） is investigated. A sufficient condition is presented to ensure that the...The analytic and discretized dissipativity of nonlinear infinite-delay systems of the form x＇（t） = g（x（t）,x（qt））（q∈ （0, 1）, t 〉 0） is investigated. A sufficient condition is presented to ensure that the above nonlinear system is dissipative. It is proved the backward Euler method inherits the dissipativity of the underlying system. Numerical examples are given to confirm the theoretical results.展开更多
Based on the method deriving dissipative compact linear schemes ( DCS), novel high-order dissipative weighted compact nonlinear schemes (DWCNS) are developed. By Fourier analysis, the dissipative and dispersive featur...Based on the method deriving dissipative compact linear schemes ( DCS), novel high-order dissipative weighted compact nonlinear schemes (DWCNS) are developed. By Fourier analysis, the dissipative and dispersive features of DWCNS are discussed. In view of the modified wave number, the DWCNS are equivalent to the fifth-order upwind biased explicit schemes in smooth regions and the interpolations at cell-edges dominate the accuracy of DWCNS. Boundary and near boundary schemes are developed and the asymptotic stabilities of DWCNS on both uniform and stretching grids are analyzed. The multi-dimensional implementations for Euler and Navier-Stokes equations are discussed. Several numerical inviscid and viscous results are given which show the good performances of the DWCNS for discontinuities capturing, high accuracy for boundary layer resolutions, good convergent rates (the root-mean-square of residuals approaching machine zero for solutions with strong shocks) and especially the damping effect on the spurious oscillations which were found in the solutions obtained by TVD and ENO schemes.展开更多
Let p 〉 3 be a prime. A p-adic congruence is called a super congruence if it happens to hold modulo some higher power of p. The topic of super congruences is related to many fields including Gauss and Jacobi sums and...Let p 〉 3 be a prime. A p-adic congruence is called a super congruence if it happens to hold modulo some higher power of p. The topic of super congruences is related to many fields including Gauss and Jacobi sums and hypergeometric series. We prove that ∑k=0^p-1（k^2k/2k）≡（-1）^（p-1）/2-p^2Ep-3（modp^3） ∑k=1^（p-1）/2（k^2k）/k≡（-1）^（p＋1）/2 8/3pEp-3（mod p^2）,∑k=0^（p-1）/2（k^2k）^2/16k≡（-1）^（p-1）/2＋p^2Ep-3（mod p^3）,where E0, E1, E2,... are Euler numbers. Our new approach is of combinatorial nature. We also formulate many conjectures concerning super congruences and relate most of them to Euler numbers or Bernoulli numbers. Motivated by our investigation of super congruences, we also raise a conjecture on 7 new series for π2, π-2 and the constant K ：= ∑k=1^∞（k/3）/k^2 （with （-） the Jacobi symbol）, two of which are ∑k=1^∞（10k-3）8k/k2（k^2k）^2（k^3k）=π^2/2and ∑k=1^∞（15k-4）（-27）^k-1/k^3（k^2k）^2（k^3k）=K.展开更多
A hybrid Euler/full potential/Lagrangian wake method,based on single-blade simulation,for predicting unsteady aerodynamic flow around helicopter rotors in hover and forward flight has been developed.In this method,an ...A hybrid Euler/full potential/Lagrangian wake method,based on single-blade simulation,for predicting unsteady aerodynamic flow around helicopter rotors in hover and forward flight has been developed.In this method,an Euler solver is used to model the near wake evolution and transonic flow phenomena in the vicinity of the blade,and a full potential equation（FPE） is used to model the isentropic potential flow region far away from the rotor,while the wake effects of other blades and the far wake are incorporated into the flow solution as an induced inflow distribution using a Lagrangian based wake analysis.To further reduce the execution time,the computational fluid dynamics（CFD） solution and rotor wake analysis（including induced velocity up-date） are conducted parallelly,and a load balancing strategy is employed to account for the information exchange between two solvers.By the developed method,several hover and forward-flight cases on Caradonna-Tung and Helishape 7A rotors are per-formed.Good agreements of the loadings on blade surface with available measured data demonstrate the validation of the method.Also,the CPU time required for different computation runs is compared in the paper,and the results show that the pre-sent hybrid method is superior to conventional CFD method in time cost,and will be more efficient with the number of blades increasing.展开更多
The measurement of spherical rotor orientation is crucial to the close-loop control of spherical motors. This paper presents a novel method for the measuring of three-degree-of-freedom (DOF) rotor orientation of spher...The measurement of spherical rotor orientation is crucial to the close-loop control of spherical motors. This paper presents a novel method for the measuring of three-degree-of-freedom (DOF) rotor orientation of spherical motors using optical sensors. The spatial orientation of spherical rotor is output in the form of ZXZ Euler angles. Firstly, the structure of the measuring system composed of optical sensors and the patterns on the rotor surface are presented, and the operational principle of recognizing intersection points between the optical ring detectors and the latitude/longitude on the rotor surface is illustrated. The analytical model of input-output characteristic is established for the measuring system of three-DOF rotor orientation. Afterwards, the effect of parameters of the optical ring detectors on the linearity, sensitivity, resolving power and measuring range of the measuring system is analyzed using the analytical model. Finally, the feasibility of the measurement is validated through experiments of prototype measuring system. The analysis is expected to be a basis for the design parameter optimization of the orientation measuring system of a PM spherical motor.展开更多
The crustal movements of the Chinese mainland include an average regional movement trend of the mainland and complex local deformations. Thus, both trends in the crustal movement of the mainland and local distortions ...The crustal movements of the Chinese mainland include an average regional movement trend of the mainland and complex local deformations. Thus, both trends in the crustal movement of the mainland and local distortions should be simultaneously taken into consideration in crustal movement estimations. A combined collocation model based on Euler vector (taken as trend parameters) and local distortions (taken as signals) is proposed in this paper. We assume that prior covariance matrices between signals and observations should be consistent with their uncertainties. Otherwise, the station movement estimates provided by the collocation will be distorted. Thus, an adaptive collocation estimator based on simplified Helmert variance components is applied. This means that the contributions of signals and observations to estimates of crustal movements are balanced and reasonable, and consistent covariance matrices of the signals and observations are achieved through the adjustment of the adaptive factor. The calculation of actual horizontal movements of the Chinese crust shows that the estimates of horizontal crustal movement velocities are made more accurate by the adaptive collocation model.展开更多
The purpose of this paper is to define the generalized Euler numbers and the generalized Euler numbers of higher order, their recursion formula and some properties were established, accordingly Euler numbers and Euler...The purpose of this paper is to define the generalized Euler numbers and the generalized Euler numbers of higher order, their recursion formula and some properties were established, accordingly Euler numbers and Euler numbers of higher order were extended.展开更多
In general, the orientation interpolation of industrial robots has been done based on Euler angle system which can result in singular point （so-called Gimbal Lock）. However, quaternion interpolation has the advantag...In general, the orientation interpolation of industrial robots has been done based on Euler angle system which can result in singular point （so-called Gimbal Lock）. However, quaternion interpolation has the advantage of natural （specifically smooth） orientation interpolation without Gimbal Lock. This work presents the application of quatemion interpolation, specifically Spherical Linear IntERPolation （SLERP）, to the orientation control of the 6-axis articulated robot （RS2） using LabVIEW and RecurDyn. For the comparison of SLERP with linear Euler interpolation in the view of smooth movement （profile） of joint angles （torques）, the two methods are dynamically simulated on RS2 by using both LabVIEW and RecurDyn. Finally, our original work, specifically the implementation of SLERP and linear Euler interpolation on the actual robot, i.e. RS2, is done using LabVIEW motion control tool kit. The SLERP orientation control is shown to be effective in terms of smooth joint motion and torque when compared to a conventional （linear） Euler interpolation.展开更多
In this paper,we consider the cascadic multigrid method for a parabolic type equation.Backward Euler approximation in time and linear finite element approximation in space are employed.A stability result is establishe...In this paper,we consider the cascadic multigrid method for a parabolic type equation.Backward Euler approximation in time and linear finite element approximation in space are employed.A stability result is established under some conditions on the smoother.Using new and sharper estimates for the smoothers that reflect the precise dependence on the time step and the spatial mesh parameter,these conditions are verified for a number of popular smoothers.Optimal error bound sare derived for both smooth and non-smooth data.Iteration strategies guaranteeing both the optimal accuracy and the optimal complexity are presented.展开更多
Level Set interface treatment method is introduced into Euler method,which is employed for interface treatment method for multi-materials. Combined with the ghost fluid method,the moving interface is tracked. Fifth-or...Level Set interface treatment method is introduced into Euler method,which is employed for interface treatment method for multi-materials. Combined with the ghost fluid method,the moving interface is tracked. Fifth-order WENO spatial discretization and third-order TVD Runge-Kutta time discretization methods are used. Shock-wave action on bubble,implosion and velocity field Shock effect bubbles; implosion and velocity field are simulated by means of LS-MMIC3D programmed by C++. Nu-merical results show that the Level Set interface treatment method is effective and feasible for multi-material interface treatment in comparison with the WENO method.展开更多
This writing is an attempt to explain a reliable numerical treatment for stochastic computer virus model.We are comparing the solutions of stochastic and deterministic computer virus models.This paper reveals that a s...This writing is an attempt to explain a reliable numerical treatment for stochastic computer virus model.We are comparing the solutions of stochastic and deterministic computer virus models.This paper reveals that a stochastic computer virus paradigm is pragmatic in contrast to the deterministic computer virus model.Outcomes of threshold number C^?hold in stochastic computer virus model.If C^?<1 then in such a condition virus controlled in the computer population while C^?>1 shows virus persists in the computer population.Unfortunately,stochastic numerical methods fail to cope with large step sizes of time.The suggested structure of the stochastic non-standard finite difference scheme(SNSFD)maintains all diverse characteristics such as dynamical consistency,boundedness and positivity as defined by Mickens.The numerical treatment for the stochastic computer virus model manifested that increasing the antivirus ability ultimates small virus dominance in a computer community.展开更多
Provides information on a study which presented a numerical method for solving Euler system of equations in reproducing kernel space. Definition and properties of reproducing kernel space; Construction of reproducing ...Provides information on a study which presented a numerical method for solving Euler system of equations in reproducing kernel space. Definition and properties of reproducing kernel space; Construction of reproducing kernel finite difference method; Numerical results of the study.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.41688103)the International Cooperation Program of the Chinese Academy of Sciences(Grant No.GJHZ1776)。
文摘The Neo-Tethys Ocean was an eastward-gaping triangular oceanic embayment between Laurasia to the north and Gondwana to the south.The Neo-Tethys Ocean was initiated from the Early Permian with mircoblocks rifted from the northern margin of Gondwana.As the microblocks drifted northwards,the Neo-Tethys Ocean was expanded.Most of these microblocks collided with the Eurasia continent in the Late Triassic,leading to the final closure of the Paleo-Tethys Ocean,followed by oceanic subduction of the Neo-Tethys oceanic slab beneath the newly formed southern margin of the Eurasia continent.As the splitting of Gondwana continued,African-Arabian,Indian and Australian continents were separated from Gondwana and moved northwards at different rates.Collision of these blocks with the Eurasia continent occurred at different time during the Cenozoic,resulting in the closure of the Neo-Tethys Ocean and building of the most significant Alps-Zagros-Himalaya orogenic belt on Earth.The tectonic evolution of the Neo-Tethys Ocean shows different characteristics from west to east:Multi-oceanic basins expansion,bidirectional subduction and microblocks collision dominate in the Mediterranean region;northward oceanic subduction and diachronous continental collision along the Zagros suture occur in the Middle East;the Tibet and Southeast Asia are characterized by multi-block riftings from Gondwana and multi-stage collisions with the Eurasia continent.The negative buoyancy of subducting oceanic slabs can be considered as the main engine for northward drifting of Gondwana-derived blocks and subduction of the Neo-Tethys Ocean.Meanwhile,mantle convection and counterclockwise rotation of Gondwana-derived blocks and the Gondwana continent around an Euler pole in West Africa in non-free boundary conditions also controlled the evolution of the Neo-Tethys Ocean.
基金Project supported by the National Natural Science Foundation of China (No,10131050)the Science and Technology Committee Foundation of Shanghai (No.03JC14013).
文摘The regular solutions of the isentropic Euler equations with degenerate linear damping for a perfect gas are studied in this paper. And a critical degenerate linear damping coefficient is found, such that if the degenerate linear damping coefficient is larger than it and the gas lies in a compact domain initially, then the regular solution will blow up in finite time; if the degenerate linear damping coefficient is less than it, then under some hvpotheses on the initial data. the regular solution exists globally.
文摘The article explores the issue of designing a new design of a loading cylinder with a casing filled with vulcanized rubber for pneumomechanical spinning machines. The theoretical calculation of the deformed state of a cylindrical shell filled with vulcanized rubber is given. Deflections and stresses in the rubber layer are determined, which we use approximately for the Ritz methods. The theory of the radial and axial moving rubber layer was analyzed. The specific energy of deformation of a cylindrical layer of a compound cylinder is determined. The statics of the case and the loading cylinder of spinning machines are thoroughly studied.
基金This work is supported by the National Natural Science Foundation of China(Grant No.10571147).
文摘The analytic and discretized dissipativity of nonlinear infinite-delay systems of the form x＇（t） = g（x（t）,x（qt））（q∈ （0, 1）, t 〉 0） is investigated. A sufficient condition is presented to ensure that the above nonlinear system is dissipative. It is proved the backward Euler method inherits the dissipativity of the underlying system. Numerical examples are given to confirm the theoretical results.
基金This work was supported by the project of Basic Research on Frontier Problems in Fluid and Aerodynamics China and the National Natural Science Foundation of China (Grant No.19772072) .
文摘Based on the method deriving dissipative compact linear schemes ( DCS), novel high-order dissipative weighted compact nonlinear schemes (DWCNS) are developed. By Fourier analysis, the dissipative and dispersive features of DWCNS are discussed. In view of the modified wave number, the DWCNS are equivalent to the fifth-order upwind biased explicit schemes in smooth regions and the interpolations at cell-edges dominate the accuracy of DWCNS. Boundary and near boundary schemes are developed and the asymptotic stabilities of DWCNS on both uniform and stretching grids are analyzed. The multi-dimensional implementations for Euler and Navier-Stokes equations are discussed. Several numerical inviscid and viscous results are given which show the good performances of the DWCNS for discontinuities capturing, high accuracy for boundary layer resolutions, good convergent rates (the root-mean-square of residuals approaching machine zero for solutions with strong shocks) and especially the damping effect on the spurious oscillations which were found in the solutions obtained by TVD and ENO schemes.
基金supported by the National Natural Science Foundation of China(GrantNo.10871087)the Overseas Cooperation Fund of China(Grant No.10928101)
文摘Let p 〉 3 be a prime. A p-adic congruence is called a super congruence if it happens to hold modulo some higher power of p. The topic of super congruences is related to many fields including Gauss and Jacobi sums and hypergeometric series. We prove that ∑k=0^p-1（k^2k/2k）≡（-1）^（p-1）/2-p^2Ep-3（modp^3） ∑k=1^（p-1）/2（k^2k）/k≡（-1）^（p＋1）/2 8/3pEp-3（mod p^2）,∑k=0^（p-1）/2（k^2k）^2/16k≡（-1）^（p-1）/2＋p^2Ep-3（mod p^3）,where E0, E1, E2,... are Euler numbers. Our new approach is of combinatorial nature. We also formulate many conjectures concerning super congruences and relate most of them to Euler numbers or Bernoulli numbers. Motivated by our investigation of super congruences, we also raise a conjecture on 7 new series for π2, π-2 and the constant K ：= ∑k=1^∞（k/3）/k^2 （with （-） the Jacobi symbol）, two of which are ∑k=1^∞（10k-3）8k/k2（k^2k）^2（k^3k）=π^2/2and ∑k=1^∞（15k-4）（-27）^k-1/k^3（k^2k）^2（k^3k）=K.
基金National Natural Science Foundation of China (10872094)
文摘A hybrid Euler/full potential/Lagrangian wake method,based on single-blade simulation,for predicting unsteady aerodynamic flow around helicopter rotors in hover and forward flight has been developed.In this method,an Euler solver is used to model the near wake evolution and transonic flow phenomena in the vicinity of the blade,and a full potential equation（FPE） is used to model the isentropic potential flow region far away from the rotor,while the wake effects of other blades and the far wake are incorporated into the flow solution as an induced inflow distribution using a Lagrangian based wake analysis.To further reduce the execution time,the computational fluid dynamics（CFD） solution and rotor wake analysis（including induced velocity up-date） are conducted parallelly,and a load balancing strategy is employed to account for the information exchange between two solvers.By the developed method,several hover and forward-flight cases on Caradonna-Tung and Helishape 7A rotors are per-formed.Good agreements of the loadings on blade surface with available measured data demonstrate the validation of the method.Also,the CPU time required for different computation runs is compared in the paper,and the results show that the pre-sent hybrid method is superior to conventional CFD method in time cost,and will be more efficient with the number of blades increasing.
基金supported in part by the National Key Basic Research Program of China ("973" Project) (Grant No. 2013CB035602)the Key Program of National Natural Science Foundation of China (Grant No.51037004)the National Natural Science Foundation of China (Grant No. 51007061)
文摘The measurement of spherical rotor orientation is crucial to the close-loop control of spherical motors. This paper presents a novel method for the measuring of three-degree-of-freedom (DOF) rotor orientation of spherical motors using optical sensors. The spatial orientation of spherical rotor is output in the form of ZXZ Euler angles. Firstly, the structure of the measuring system composed of optical sensors and the patterns on the rotor surface are presented, and the operational principle of recognizing intersection points between the optical ring detectors and the latitude/longitude on the rotor surface is illustrated. The analytical model of input-output characteristic is established for the measuring system of three-DOF rotor orientation. Afterwards, the effect of parameters of the optical ring detectors on the linearity, sensitivity, resolving power and measuring range of the measuring system is analyzed using the analytical model. Finally, the feasibility of the measurement is validated through experiments of prototype measuring system. The analysis is expected to be a basis for the design parameter optimization of the orientation measuring system of a PM spherical motor.
基金supported by National Natural Science Foundation of China (Grant Nos. 41020144004 and 41004013)
文摘The crustal movements of the Chinese mainland include an average regional movement trend of the mainland and complex local deformations. Thus, both trends in the crustal movement of the mainland and local distortions should be simultaneously taken into consideration in crustal movement estimations. A combined collocation model based on Euler vector (taken as trend parameters) and local distortions (taken as signals) is proposed in this paper. We assume that prior covariance matrices between signals and observations should be consistent with their uncertainties. Otherwise, the station movement estimates provided by the collocation will be distorted. Thus, an adaptive collocation estimator based on simplified Helmert variance components is applied. This means that the contributions of signals and observations to estimates of crustal movements are balanced and reasonable, and consistent covariance matrices of the signals and observations are achieved through the adjustment of the adaptive factor. The calculation of actual horizontal movements of the Chinese crust shows that the estimates of horizontal crustal movement velocities are made more accurate by the adaptive collocation model.
基金Supported by the NNSF of China(10001016) SF for the Prominent Youth of Henan Province
文摘The purpose of this paper is to define the generalized Euler numbers and the generalized Euler numbers of higher order, their recursion formula and some properties were established, accordingly Euler numbers and Euler numbers of higher order were extended.
基金Project supported by the Second Stage of Brain Korea 21 Projectssupported by Basic Science Research Program through the National Research Foundation of Korea (NRF)funded by the Ministry of Education,Science and Technology (2011-0013902)
文摘In general, the orientation interpolation of industrial robots has been done based on Euler angle system which can result in singular point （so-called Gimbal Lock）. However, quaternion interpolation has the advantage of natural （specifically smooth） orientation interpolation without Gimbal Lock. This work presents the application of quatemion interpolation, specifically Spherical Linear IntERPolation （SLERP）, to the orientation control of the 6-axis articulated robot （RS2） using LabVIEW and RecurDyn. For the comparison of SLERP with linear Euler interpolation in the view of smooth movement （profile） of joint angles （torques）, the two methods are dynamically simulated on RS2 by using both LabVIEW and RecurDyn. Finally, our original work, specifically the implementation of SLERP and linear Euler interpolation on the actual robot, i.e. RS2, is done using LabVIEW motion control tool kit. The SLERP orientation control is shown to be effective in terms of smooth joint motion and torque when compared to a conventional （linear） Euler interpolation.
基金the National Science Foundation(Grant Nos.DMS0409297,DMR0205232,CCF-0430349)US National Institute of Health-National Cancer Institute(Grant No.1R01CA125707-01A1)+2 种基金the National Natural Science Foundation of China(Grant No.10571172)the National Basic Research Program(Grant No.2005CB321704)the Youth's Innovative Program of Chinese Academy of Sciences(Grant Nos.K7290312G9,K7502712F9)
文摘In this paper,we consider the cascadic multigrid method for a parabolic type equation.Backward Euler approximation in time and linear finite element approximation in space are employed.A stability result is established under some conditions on the smoother.Using new and sharper estimates for the smoothers that reflect the precise dependence on the time step and the spatial mesh parameter,these conditions are verified for a number of popular smoothers.Optimal error bound sare derived for both smooth and non-smooth data.Iteration strategies guaranteeing both the optimal accuracy and the optimal complexity are presented.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10872085 and 10472042)Program for New Century Excellent Talents of Ministry of Education (Grant No. NCET-08-0043)+1 种基金National Basic Research Program of China (Grant No. 2010CB832700 6)Key Program of Numerical Simulation Key Laboratory of Sichuan Higher School (Grant No. 07NJZZ001)
文摘Level Set interface treatment method is introduced into Euler method,which is employed for interface treatment method for multi-materials. Combined with the ghost fluid method,the moving interface is tracked. Fifth-order WENO spatial discretization and third-order TVD Runge-Kutta time discretization methods are used. Shock-wave action on bubble,implosion and velocity field Shock effect bubbles; implosion and velocity field are simulated by means of LS-MMIC3D programmed by C++. Nu-merical results show that the Level Set interface treatment method is effective and feasible for multi-material interface treatment in comparison with the WENO method.
文摘This writing is an attempt to explain a reliable numerical treatment for stochastic computer virus model.We are comparing the solutions of stochastic and deterministic computer virus models.This paper reveals that a stochastic computer virus paradigm is pragmatic in contrast to the deterministic computer virus model.Outcomes of threshold number C^?hold in stochastic computer virus model.If C^?<1 then in such a condition virus controlled in the computer population while C^?>1 shows virus persists in the computer population.Unfortunately,stochastic numerical methods fail to cope with large step sizes of time.The suggested structure of the stochastic non-standard finite difference scheme(SNSFD)maintains all diverse characteristics such as dynamical consistency,boundedness and positivity as defined by Mickens.The numerical treatment for the stochastic computer virus model manifested that increasing the antivirus ability ultimates small virus dominance in a computer community.
基金NSFC and Project (HIT 2000.01) supported by the Scientific ResearchFoundation of Harbin institute of Technology.
文摘Provides information on a study which presented a numerical method for solving Euler system of equations in reproducing kernel space. Definition and properties of reproducing kernel space; Construction of reproducing kernel finite difference method; Numerical results of the study.
