For solving water entry problems, a numerical method is presented, which is a CFD method based on free surface capturing method and Cartesian cut cell mesh.In this approach, incompressible Euler equations for a variab...For solving water entry problems, a numerical method is presented, which is a CFD method based on free surface capturing method and Cartesian cut cell mesh.In this approach, incompressible Euler equations for a variable density fluid are numerically calculated by the finite volume method.Then artificial compressibility method, dual time-stepping technique and Roe's approximate Riemann solver are adopted in the numerical scheme.Finally, some application cases are designed to show the ability of the current method to cope with water entry problems in ocean engineering.展开更多
This paper shows detailed steps for modeling a quadcopter with Euler-Lagrange equations, followed by controlling it with intelligent control that includes states decoupling. In addition, this control shows non-convent...This paper shows detailed steps for modeling a quadcopter with Euler-Lagrange equations, followed by controlling it with intelligent control that includes states decoupling. In addition, this control shows non-conventional membership functions for the most instable states, in order to get a fast and effective response.展开更多
The global stability of Lipschitz continuous solutions with discontinuous initial data for the relativistic Euler equations is established in a broad class of entropy solutions in L∞ containing vacuum states. As a co...The global stability of Lipschitz continuous solutions with discontinuous initial data for the relativistic Euler equations is established in a broad class of entropy solutions in L∞ containing vacuum states. As a corollary, the uniqueness of Lipschitz solutions with discontinuous initial data is obtained in the broad class of entropy solutions in L∞.展开更多
In this paper,solutions with nonvanishing vorticity are established for the three dimensional stationary incompressible Euler equations on simply connected bounded three dimensional domains with smooth boundary.A clas...In this paper,solutions with nonvanishing vorticity are established for the three dimensional stationary incompressible Euler equations on simply connected bounded three dimensional domains with smooth boundary.A class of additional boundary conditions for the vorticities are identified so that the solution is unique and stable.展开更多
The authors consider the local smooth solutions to the isentropic relativistic Euler equations in(3+1)-dimensional space-time for both non-vacuum and vacuum cases.The local existence is proved by symmetrizing the syst...The authors consider the local smooth solutions to the isentropic relativistic Euler equations in(3+1)-dimensional space-time for both non-vacuum and vacuum cases.The local existence is proved by symmetrizing the system and applying the FriedrichsLax-Kato theory of symmetric hyperbolic systems.For the non-vacuum case,according to Godunov,firstly a strictly convex entropy function is solved out,then a suitable symmetrizer to symmetrize the system is constructed.For the vacuum case,since the coefficient matrix blows-up near the vacuum,the authors use another symmetrization which is based on the generalized Riemann invariants and the normalized velocity.展开更多
The authors consider the Euler equations for a compressible fluid in one space dimensionwhen the equation of state of the fluid does not fulfill standard convexity assumptions andviscosity and capillarity effects are ...The authors consider the Euler equations for a compressible fluid in one space dimensionwhen the equation of state of the fluid does not fulfill standard convexity assumptions andviscosity and capillarity effects are taken into account. A typical example of nonconvex con-stitutive equation for fluids is Van der Waals' equation. The first order terms of these partialdifferential equations form a nonlinear system of mixed (hyperbolic-elliptic) type. For a class ofnonconvex equations of state, an existence theorem of traveling waves solutions with arbitrarylarge amplitude is established here. The authors distinguish between classical (compressive) andnonclassical (undercompressive) traveling waves. The latter do not fulfill Lax shock inequali-ties, and are characterized by the so-called kinetic relation, whose properties are investigatedin this paper.展开更多
The authors investigate the stability of a steady ideal plane flow in an arbitrary domain in terms of the L^2 norm of the vorticity. Linear stability implies nonlinear instability provided the growth rate of the line...The authors investigate the stability of a steady ideal plane flow in an arbitrary domain in terms of the L^2 norm of the vorticity. Linear stability implies nonlinear instability provided the growth rate of the linearized system exceeds the Liapunov exponent of the flow. In contrast,a maximizer of the entropy subject to constant energy and mass is stable. This implies the stability of certain solutions of the mean field equation.展开更多
The partial regularity of the weak heat flow of harmonic maps from a Riemannian manifold Al with boundary into general compact Riemannian manifold N without boundary is consid-ered. It is shown that the singular set S...The partial regularity of the weak heat flow of harmonic maps from a Riemannian manifold Al with boundary into general compact Riemannian manifold N without boundary is consid-ered. It is shown that the singular set Sing(u) of the weak heat flow satisfies H(Sing(u)) 0, with is = dimensionM. Here is Hausdorff measure with respect to parabolic metric ρ(x,t),(y,s)=max{|x-y|, }.展开更多
基金Supported by the National 863 Plan Foundation under Grant No.2006AA09A104
文摘For solving water entry problems, a numerical method is presented, which is a CFD method based on free surface capturing method and Cartesian cut cell mesh.In this approach, incompressible Euler equations for a variable density fluid are numerically calculated by the finite volume method.Then artificial compressibility method, dual time-stepping technique and Roe's approximate Riemann solver are adopted in the numerical scheme.Finally, some application cases are designed to show the ability of the current method to cope with water entry problems in ocean engineering.
文摘This paper shows detailed steps for modeling a quadcopter with Euler-Lagrange equations, followed by controlling it with intelligent control that includes states decoupling. In addition, this control shows non-conventional membership functions for the most instable states, in order to get a fast and effective response.
基金Project supported by the National Natural Science Foundation of China (No.10101011) the Natural Science Foundation of Shanghai (No.04ZR14090).
文摘The global stability of Lipschitz continuous solutions with discontinuous initial data for the relativistic Euler equations is established in a broad class of entropy solutions in L∞ containing vacuum states. As a corollary, the uniqueness of Lipschitz solutions with discontinuous initial data is obtained in the broad class of entropy solutions in L∞.
基金supported by the National Natural Science Foundation of China (No.10771173)the Zheng Ge Ru Foundation,the Hong Kong RGC Earmarked Research (Nos.CUHK4028/04P,CUHK4040/06P,CUHK4042/08P)the RGC Central Allocation (No.CA05/06.SC01)
文摘In this paper,solutions with nonvanishing vorticity are established for the three dimensional stationary incompressible Euler equations on simply connected bounded three dimensional domains with smooth boundary.A class of additional boundary conditions for the vorticities are identified so that the solution is unique and stable.
基金supported by the National Natural Science Foundation of China(Nos.11201308,10971135)the Science Foundation for the Excellent Youth Scholars of Shanghai Municipal Education Commission(No.ZZyyy12025)+1 种基金the Innovation Program of Shanghai Municipal Education Commission(No.13zz136)the Science Foundation of Yin Jin Ren Cai of Shanghai Institute of Technology(No.YJ2011-03)
文摘The authors consider the local smooth solutions to the isentropic relativistic Euler equations in(3+1)-dimensional space-time for both non-vacuum and vacuum cases.The local existence is proved by symmetrizing the system and applying the FriedrichsLax-Kato theory of symmetric hyperbolic systems.For the non-vacuum case,according to Godunov,firstly a strictly convex entropy function is solved out,then a suitable symmetrizer to symmetrize the system is constructed.For the vacuum case,since the coefficient matrix blows-up near the vacuum,the authors use another symmetrization which is based on the generalized Riemann invariants and the normalized velocity.
文摘The authors consider the Euler equations for a compressible fluid in one space dimensionwhen the equation of state of the fluid does not fulfill standard convexity assumptions andviscosity and capillarity effects are taken into account. A typical example of nonconvex con-stitutive equation for fluids is Van der Waals' equation. The first order terms of these partialdifferential equations form a nonlinear system of mixed (hyperbolic-elliptic) type. For a class ofnonconvex equations of state, an existence theorem of traveling waves solutions with arbitrarylarge amplitude is established here. The authors distinguish between classical (compressive) andnonclassical (undercompressive) traveling waves. The latter do not fulfill Lax shock inequali-ties, and are characterized by the so-called kinetic relation, whose properties are investigatedin this paper.
文摘The authors investigate the stability of a steady ideal plane flow in an arbitrary domain in terms of the L^2 norm of the vorticity. Linear stability implies nonlinear instability provided the growth rate of the linearized system exceeds the Liapunov exponent of the flow. In contrast,a maximizer of the entropy subject to constant energy and mass is stable. This implies the stability of certain solutions of the mean field equation.
基金the National Natural Science Foundation of China (No.10071013).
文摘The partial regularity of the weak heat flow of harmonic maps from a Riemannian manifold Al with boundary into general compact Riemannian manifold N without boundary is consid-ered. It is shown that the singular set Sing(u) of the weak heat flow satisfies H(Sing(u)) 0, with is = dimensionM. Here is Hausdorff measure with respect to parabolic metric ρ(x,t),(y,s)=max{|x-y|, }.
