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On mathematical modelling of gust response using the finite element method

Sváček, Petr, Horáček, Jaromír (2013)

Applications of Mathematics 2013

In this paper the numerical approximation of aeroelastic response to sudden gust is presented. The fully coupled formulation of two dimensional incompressible viscous fluid flow over a flexibly supported structure is used. The flow is modelled with the system of Navier-Stokes equations written in Arbitrary Lagrangian-Eulerian form and coupled with system of ordinary differential equations describing the airfoil vibrations with two degrees of freedom. The Navier-Stokes equations are spatially discretized...

On quasijet bundles

Tomáš, Jiří (2000)

Proceedings of the 19th Winter School "Geometry and Physics"

In this paper a Weil approach to quasijets is discussed. For given manifolds M and N , a quasijet with source x M and target y N is a mapping T x r M T y r N which is a vector homomorphism for each one of the r vector bundle structures of the iterated tangent bundle T r [A. Dekrét, Casopis Pest. Mat. 111, No. 4, 345-352 (1986; Zbl 0611.58004)]. Let us denote by Q J r ( M , N ) the bundle of quasijets from M to N ; the space J ˜ r ( M , N ) of non-holonomic r -jets from M to N is embeded into Q J r ( M , N ) . On the other hand, the bundle Q T m r N of ( m , r ) -quasivelocities...

On sectioning multiples of the nontrivial line bundle over Grassmannians

Horanská, Ľubomíra (1998)

Proceedings of the 17th Winter School "Geometry and Physics"

Let G n , k ( G ˜ n , k ) denote the Grassmann manifold of linear k -spaces (resp. oriented k -spaces) in n , d n , k = k ( n - k ) = dim G n , k and suppose n 2 k . As an easy consequence of the Steenrod obstruction theory, one sees that ( d n , k + 1 ) -fold Whitney sum ( d n , k + 1 ) ξ n , k of the nontrivial line bundle ξ n , k over G n , k always has a nowhere vanishing section. The author deals with the following question: What is the least s ( = s n , k ) such that the vector bundle s ξ n , k admits a nowhere vanishing section ? Obviously, s n , k d n , k + 1 , and for the special case in which k = 1 , it is known that s n , 1 = d n , 1 + 1 . Using results...

On sectioning tangent bundles and other vector bundles

Korbaš, Július, Zvengrowski, Peter (1996)

Proceedings of the Winter School "Geometry and Physics"

This paper has two parts. Part one is mainly intended as a general introduction to the problem of sectioning vector bundles (in particular tangent bundles of smooth manifolds) by everywhere linearly independent sections, giving a survey of some ideas, methods and results.Part two then records some recent progress in sectioning tangent bundles of several families of specific manifolds.

On sets of small measure

Kulcsárová, Ol'ga, Riečan, Beloslav (1987)

Proceedings of the 14th Winter School on Abstract Analysis

On simplicial red refinement in three and higher dimensions

Korotov, Sergey, Křížek, Michal (2013)

Applications of Mathematics 2013

We show that in dimensions higher than two, the popular "red refinement" technique, commonly used for simplicial mesh refinements and adaptivity in the finite element analysis and practice, never yields subsimplices which are all acute even for an acute father element as opposed to the two-dimensional case. In the three-dimensional case we prove that there exists only one tetrahedron that can be partitioned by red refinement into eight congruent subtetrahedra that are all similar to the original...

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