A Complex Variable Circle Theorem for Plane Stokes Flows
نویسندگان
چکیده
منابع مشابه
Complex Descartes Circle Theorem
We present a short proof of Descartes Circle Theorem on the “curvaturecenters” of four mutually tangent circles. Key to the proof is associating an octahedral configuration of spheres to four mutually tangent circles. We also prove an analogue for spheres. It can be traced back to at least Descartes that four mutually tangent circles have curvatures (reciprocals of radii) satisfying the relatio...
متن کاملStokes’ Theorem
I. Introduction. Stokes' theorem on a manifold is a central theorem of mathematics. Special cases include the integral theorems of vector analysis and the Cauchy-Goursat theorem. My purpose here is to prove this version of Stokes' Theorem. Let ω be a continuous differential (n − 1)-form on a compact oriented n-manifold M with boundary ∂M. Suppose that ω is differen-tiable on M − ∂M and dω is Le...
متن کاملStokes' Theorem for Nonsmooth Chains
Much of the vast literature on the integral during the last two centuries concerns extending the class of integrable functions. In contrast, our viewpoint is akin to that taken by Hassler Whitney [Geometric integration theory, Princeton Univ. Press, Princeton, NJ, 1957] and by geometric measure theorists because we extend the class of integrable domains. Let oi be an «-form defined on Rm . We s...
متن کاملArtificial boundary conditions for stationary Navier-Stokes flows past bodies in the half-plane
We discuss artificial boundary conditions for stationary Navier-Stokes flows past bodies in the half-plane, for a range of low Reynolds numbers. When truncating the half-plane to a finite domain for numerical purposes, artificial boundaries appear. We present an explicit Dirichlet condition for the velocity at these boundaries in terms of an asymptotic expansion for the solution to the problem....
متن کاملA generalized “surfaceless” Stokes’ theorem
We derive a generalized Stokes' theorem, valid in any dimension and for arbitrary loops, even if self intersecting or knotted. The generalized theorem does not involve an auxiliary surface, but inherits a higher rank gauge symmetry from the invariance under deformations of the surface used in the conventional formulation.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Journal of Applied Mathematics and Theoretical Physics
سال: 2017
ISSN: 2575-5919
DOI: 10.11648/j.ijamtp.20170301.12