摘要:

AbstractIf a plane shock hits a wedge, a self‐similar pattern of reflected shocks travels outward as the shock moves forward in time. The nature of the pattern is explored for weak incident shocks (strengthb) and small wedge angles 2θwthrough potential theory, a number of different scalings, some study of mixed equations and matching asymptotics for the different scalings. The self‐similar equations are of mixed type. A linearization gives a linear mixed flow valid away from a sonic curve. Near the sonic curve a shock solution is constructed in another scaling except near the zone of interaction between the incident shock and the wall where a special scaling is used. The parameter β = c1θ2w(γ + 1)branges from 0 to ∞. Here γ is the polytropic constant andC1is the sound speed behind the incident shock.For β>2 regular reflection (weak or strong) can occur and the whole pattern is reconstructed to lowest order in shock strength. For β<1/2 Mach reflection occurs and the flow behind the reflection is subsonic and can be constructed in principle (with an open elliptic problem) and matched. The case β = 0 can be solved. For 1/2<β<2 or even larger β the flow behind a Mach reflection may be transonic and further investigation must be made to determine what happens.The basic pattern of reflection is an almost semi‐circular shock issuing, for regular reflection, from the reflection point on the wedge and for Mach reflection, matched with a local interaction flow. Assuming their nature, choosing the least entropy generation, the weak regular reflection will occur for β sufficiently large (von Neumann paradox). An accumulation point of vorticity occurs on the wedge above the leading point. © 1994 J

ISSN:0010-3640    

DOI:10.1002/cpa.3160470502

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1994

数据来源: WILEY

摘要:

AbstractIn the theory of monotone twist mappings of a cylinder one constructs for every rotation number α invariant minimal setsMα. In this paper an approximation of these Mather sets by smooth invariant curvesMvαis devised, which forv→ 0 converge toMαalmost everywhere. The main point of the construction is that the approximating curvesMvαform forv>0 a smooth foliation. The approximation is achieved with the help of a regularized version of the Percival variational problem. © 1994 John Wiley&So

ISSN:0010-3640    

DOI:10.1002/cpa.3160470503

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1994

数据来源: WILEY

摘要:

AbstractNecessary and sufficient conditions are found for the convergence at a pre‐assigned point of the spherical partial sums (resp. integrals) of the Fourier series (resp. integral) in the class of piecewise smooth functions on Euclidean space. These results carry over unchanged to spherical harmonic expansions, Fourier transforms on hyperbolic space, and Dirichlet eigenfunction expansions with respect to the Laplace operator on a class of Riemannian manifolds. © 1994 John Wiley&Sons, I

ISSN:0010-3640    

DOI:10.1002/cpa.3160470504

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1994

数据来源: WILEY

摘要:

AbstractMany of the basic equations of conservative continuum mechanics (Euler, Vlasov‐Poisson, Vlasov‐Maxwell, MHD, etc.) are Hamiltonian systems with respect to Lie‐Poisson brackets on dual spaces of infinite dimensional Lie algebras. The development of Lie‐Poisson integrators for finite dimensional Lie‐Poisson systems has shown that they are superior in the numerical simulations of these systems, especially with regard to long term phenomena.This paper shows how to truncate one of these systems, the Vlasov‐Poisson equation of plasma physics, to a finite dimensional Lie‐Poisson system. This requires replacing the functions on single‐particle phase space, with their Poisson bracket Lie algebra structure, by a finite dimensional Lie algebra. Replacing the densities by their moments of order up tokabout a fixed reference point corresponds to replacing the functions by their Taylor expansions up to orderk.Unfortunately, these truncated Taylor expansions do not form a Lie algebra, since the functions which vanish through orderkdo not form an ideal under Poisson bracket. Geometrically, this corresponds to the fact that canonical transformations which fix the reference point do not form a normal subgroup.Introducing the location of a reference point in phase space as an extra variable and truncating with respect to this moving point turns out to decouple the “location” from “shape” coordinates of a lump of density in phase space, as far as the Poisson bracket is concerned. One can then replace the shape coordinates by a finite number of moments.The central result of the paper is a construction of the decoupling map described above in the general context of the decomposition of a Lie group as a product of subgroups. The main theorem is first proved by the general theory of Poisson reduction, then by explicit calculation, and lastly by showing that the Poisson isomorphism follows from the lift of a natural groupoid isomorphism. The groupoid aspect of the theory also provides natural Poisson maps, useful in the application of Ruth‐type integration techniques, which do not seem easily derivable from the general theory of Poisson reduction. ©

ISSN:0010-3640    

DOI:10.1002/cpa.3160470505

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1994

数据来源: WILEY

ISSN:0010-3640    

DOI:10.1002/cpa.3160470506

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1994

数据来源: WILEY

ISSN:0010-3640    

DOI:10.1002/cpa.3160470507

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1994

数据来源: WILEY

ISSN:0010-3640    

DOI:10.1002/cpa.3160470508

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1994

数据来源: WILEY

摘要:

AbstractAn analogy of Levi sums is considered for a class of stochastic partial differential equations to construct theirstochastic fundamental solutions.These notions are shown to coincide withDonsker's delta functions, typical generalized Wiener functionals, which have been studied in the frame of the Malliavin calculus. © 1994 John Wiley&Sons, Inc

ISSN:0010-3640    

DOI:10.1002/cpa.3160470509

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1994

数据来源: WILEY

ISSN:0010-3640    

DOI:10.1002/cpa.3160470501

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1994

数据来源: WILEY