In this paper, a one-dimensional bipolar Euler-Poisson system （a hydrodynamic model） from semiconductors or plasmas with boundary effects is considered. This system takes the form of Euler-Poisson with an electric f...In this paper, a one-dimensional bipolar Euler-Poisson system （a hydrodynamic model） from semiconductors or plasmas with boundary effects is considered. This system takes the form of Euler-Poisson with an electric field and frictional damping added to the momentum equations. The large-time behavior of uniformly bounded weak solutions to the initial-boundary value problem for the one-dimensional bipolar Euler-Poisson system is firstly presented. Next, two particle densities and the corresponding current momenta are verified to satisfy the porous medium equation and the classical Darcy＇s law time asymp- totically. Finally, as a by-product, the quasineutral limit of the weak solutions to the initial-boundary value problem is investigated in the sense that the bounded L∞ entropy solution to the one-dimensional bipolar Euler-Poisson system converges to that of the cor- responding one-dimensional compressible Euler equations with damping exponentially fast as t → ＋∞. As far as we know, this is the first result about the asymptotic behavior and the quasineutral limit for the one-dimensional bipolar Euler-Poisson system with boundary effects and a vacuum.展开更多
The authors are concerned with a zero-flux type initial boundary value problem for scalar conservation laws.Firstly,a kinetic formulation of entropy solutions is established.Secondly,by using the kinetic formulation a...The authors are concerned with a zero-flux type initial boundary value problem for scalar conservation laws.Firstly,a kinetic formulation of entropy solutions is established.Secondly,by using the kinetic formulation and kinetic techniques,the uniqueness of entropy solutions is obtained.Finally,the parabolic approximation is studied and an error estimate of order η 1/3 between the entropy solution and the viscous approximate solutions is established by using kinetic techniques,where η is the size of artificial viscosity.展开更多
This paper is concerned with an initial boundary value problem for strictly convex conservation laws whose weak entropy solution is in the piecewise smooth solution class consisting of finitely many discontinuities. B...This paper is concerned with an initial boundary value problem for strictly convex conservation laws whose weak entropy solution is in the piecewise smooth solution class consisting of finitely many discontinuities. By the structure of the weak entropy solution of the corresponding initial value problem and the boundary entropy condition developed by Bardos-Leroux Nedelec, we give a construction method to the weak entropy solution of the initial boundary value problem. Compared with the initial value problem, the weak entropy solution of the initial boundary value problem includes the following new interaction type： an expansion wave collides with the boundary and the boundary reflects a new shock wave which is tangent to the boundary. According to the structure and some global estimates of the weak entropy solution, we derive the global L^1-error estimate for viscous methods to this initial boundary value problem by using the matching travelling wave solutions method. If the inviscid solution includes the interaction that an expansion wave collides with the boundary and the boundary reflects a new shock wave which is tangent to the boundary, or the inviscid solution includes some shock wave which is tangent to the boundary, then the error of the viscosity solution to the inviscid solution is bounded by O（ε^1/2） in L^1-norm; otherwise, as in the initial value problem, the L^1-error bound is O（ε｜ In ε｜）.展开更多
Following Ben-Artzi and LeFloch, we consider nonlinear hyperbolic conservation laws posed on a Riemannian manifold, and we establish an L1-error estimate for a class of finite volume schemes allowing for the approxima...Following Ben-Artzi and LeFloch, we consider nonlinear hyperbolic conservation laws posed on a Riemannian manifold, and we establish an L1-error estimate for a class of finite volume schemes allowing for the approximation of entropy solutions to the initial value problem. The error in the L1 norm is of order h1/4 at most, where h represents the maximal diameter of elements in the family of geodesic triangulations. The proof relies on a suitable generalization of Cockburn, Coquel, and LeFloch＇s theory which was originally developed in the Euclidian setting. We extend the arguments to curved manifolds, by taking into account the effects to the geometry and overcoming several new technical difficulties.展开更多
A method which is especially suitable for microcomputer calculation of the true orientation distribution function (ODF) according to the maximum-entropy estimate is proposed for hexagonal system polycrystalline materi...A method which is especially suitable for microcomputer calculation of the true orientation distribution function (ODF) according to the maximum-entropy estimate is proposed for hexagonal system polycrystalline materials with physical symmetry.The resultant computational software system has been also designed and first carried out in a microcomputer PANAFACOM-U1200 being on line with the X-ray diffractometer D/max-3A.The simu- lated calculation shows that the method is concisely pragmatic and easily popularized,while the results obtained are trust worthy.展开更多
The problem of seismic danger estimate in Japan after Tohoku mega-earthquake 11 March of 2011 is considered. The estimates are based on processing low-frequency seismic noise wave-forms from broadband network F-net. A...The problem of seismic danger estimate in Japan after Tohoku mega-earthquake 11 March of 2011 is considered. The estimates are based on processing low-frequency seismic noise wave-forms from broadband network F-net. A new method of dynamic estimate of seismic danger is used for this problem. The method is based on calculating multi-fractal properties and minimum entropy of squared orthogonal wavelet coefficients for seismic noise. The analysis of the data using notion of “spots of seismic danger” shows that the seismic danger in Japan remains at high level after 2011. 03. 11 within north-east part of Philippine plate—at the region of Nankai Though which traditionally is regarded as the place of strongest earthquakes. It is well known that estimate of time moment of future shock is the most difficult problem in earthquake prediction. In this paper we try to find some peculiarities of the seismic noise data which could extract future danger time interval by analogy with the behavior before Tohoku earthquake. Two possible precursors of this type were found. They are the results of estimates within 1-year moving time window: based on correlation between 2 mean multi-fractal parameters of the noise and based on cluster analysis of annual clouds of 4 mean noise parameters. Both peculiarities of the noise data extract time interval 2013-2014 as the danger.展开更多
基金supported by the National Natural Science Foundation of China(No.11171223)the Innovation Program of Shanghai Municipal Education Commission(No.13ZZ109)
文摘In this paper, a one-dimensional bipolar Euler-Poisson system （a hydrodynamic model） from semiconductors or plasmas with boundary effects is considered. This system takes the form of Euler-Poisson with an electric field and frictional damping added to the momentum equations. The large-time behavior of uniformly bounded weak solutions to the initial-boundary value problem for the one-dimensional bipolar Euler-Poisson system is firstly presented. Next, two particle densities and the corresponding current momenta are verified to satisfy the porous medium equation and the classical Darcy＇s law time asymp- totically. Finally, as a by-product, the quasineutral limit of the weak solutions to the initial-boundary value problem is investigated in the sense that the bounded L∞ entropy solution to the one-dimensional bipolar Euler-Poisson system converges to that of the cor- responding one-dimensional compressible Euler equations with damping exponentially fast as t → ＋∞. As far as we know, this is the first result about the asymptotic behavior and the quasineutral limit for the one-dimensional bipolar Euler-Poisson system with boundary effects and a vacuum.
基金supported by the National Natural Science Foundation of China (No. 10971135)the Program for New Century Excellent Talents of the Ministry of Education of China (No. NCET-07-0546)+2 种基金the University Young Teacher Sciences Foundation of Anhui Province (No. 2010SQRL145)Shanghai Jiao Tong University Innovation Fund for Postgraduates (No. AE071202)the Quality Project Fund of Fuyang Teachers College (No. 2010JPKC07)
文摘The authors are concerned with a zero-flux type initial boundary value problem for scalar conservation laws.Firstly,a kinetic formulation of entropy solutions is established.Secondly,by using the kinetic formulation and kinetic techniques,the uniqueness of entropy solutions is obtained.Finally,the parabolic approximation is studied and an error estimate of order η 1/3 between the entropy solution and the viscous approximate solutions is established by using kinetic techniques,where η is the size of artificial viscosity.
基金the NSF-Guangdong China(04010473)Jinan University Foundation(51204033)the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry(No.2005-383)
文摘This paper is concerned with an initial boundary value problem for strictly convex conservation laws whose weak entropy solution is in the piecewise smooth solution class consisting of finitely many discontinuities. By the structure of the weak entropy solution of the corresponding initial value problem and the boundary entropy condition developed by Bardos-Leroux Nedelec, we give a construction method to the weak entropy solution of the initial boundary value problem. Compared with the initial value problem, the weak entropy solution of the initial boundary value problem includes the following new interaction type： an expansion wave collides with the boundary and the boundary reflects a new shock wave which is tangent to the boundary. According to the structure and some global estimates of the weak entropy solution, we derive the global L^1-error estimate for viscous methods to this initial boundary value problem by using the matching travelling wave solutions method. If the inviscid solution includes the interaction that an expansion wave collides with the boundary and the boundary reflects a new shock wave which is tangent to the boundary, or the inviscid solution includes some shock wave which is tangent to the boundary, then the error of the viscosity solution to the inviscid solution is bounded by O（ε^1/2） in L^1-norm; otherwise, as in the initial value problem, the L^1-error bound is O（ε｜ In ε｜）.
基金supported by the A. N. R. (Agence Nationale de la Recherche) through the grant 06-2-134423 entitled "Mathematical Methods in General Relativity" (MATH-GR)by the Centre National de la Recherche Scientifique (CNRS)+1 种基金supported by the grant 311759/2006-8 from the National Counsel of Technological Scientific Development (CNPq)by an internation project between Brazil and France
文摘Following Ben-Artzi and LeFloch, we consider nonlinear hyperbolic conservation laws posed on a Riemannian manifold, and we establish an L1-error estimate for a class of finite volume schemes allowing for the approximation of entropy solutions to the initial value problem. The error in the L1 norm is of order h1/4 at most, where h represents the maximal diameter of elements in the family of geodesic triangulations. The proof relies on a suitable generalization of Cockburn, Coquel, and LeFloch＇s theory which was originally developed in the Euclidian setting. We extend the arguments to curved manifolds, by taking into account the effects to the geometry and overcoming several new technical difficulties.
文摘A method which is especially suitable for microcomputer calculation of the true orientation distribution function (ODF) according to the maximum-entropy estimate is proposed for hexagonal system polycrystalline materials with physical symmetry.The resultant computational software system has been also designed and first carried out in a microcomputer PANAFACOM-U1200 being on line with the X-ray diffractometer D/max-3A.The simu- lated calculation shows that the method is concisely pragmatic and easily popularized,while the results obtained are trust worthy.
文摘The problem of seismic danger estimate in Japan after Tohoku mega-earthquake 11 March of 2011 is considered. The estimates are based on processing low-frequency seismic noise wave-forms from broadband network F-net. A new method of dynamic estimate of seismic danger is used for this problem. The method is based on calculating multi-fractal properties and minimum entropy of squared orthogonal wavelet coefficients for seismic noise. The analysis of the data using notion of “spots of seismic danger” shows that the seismic danger in Japan remains at high level after 2011. 03. 11 within north-east part of Philippine plate—at the region of Nankai Though which traditionally is regarded as the place of strongest earthquakes. It is well known that estimate of time moment of future shock is the most difficult problem in earthquake prediction. In this paper we try to find some peculiarities of the seismic noise data which could extract future danger time interval by analogy with the behavior before Tohoku earthquake. Two possible precursors of this type were found. They are the results of estimates within 1-year moving time window: based on correlation between 2 mean multi-fractal parameters of the noise and based on cluster analysis of annual clouds of 4 mean noise parameters. Both peculiarities of the noise data extract time interval 2013-2014 as the danger.
