15,240 research outputs found
Convergence of the Ginzburg-Landau approximation for the Ericksen-Leslie system
We establish the local well-posedness of the general Ericksen-Leslie system
in liquid crystals with the initial velocity and director field in . In particular, we prove that the solutions of the Ginzburg-Landau
approximation system converge smoothly to the solution of the Ericksen-Leslie
system for any with a maximal existence time of the
Ericksen- Leslie system
Properties of Catlin's reduced graphs and supereulerian graphs
A graph is called collapsible if for every even subset ,
there is a spanning connected subgraph of such that is the set of
vertices of odd degree in . A graph is the reduction of if it is
obtained from by contracting all the nontrivial collapsible subgraphs. A
graph is reduced if it has no nontrivial collapsible subgraphs. In this paper,
we first prove a few results on the properties of reduced graphs. As an
application, for 3-edge-connected graphs of order with for any where are given, we show how such graphs
change if they have no spanning Eulerian subgraphs when is increased from
to 10 then to
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