# The two-state linear curve crossing problems revisited. I. Analysis of Stokes phenomenon and expressions for scattering matrices

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Based on the exact solution of the linear curve crossing problems reported in the first paper of this series, approximate analytical solution is discussed here for the opposite sign of slopes of the two diabatic potentials (nonadiabatic tunneling case). Two new compact analytical formulas for...

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We construct semi-integral curves which bound the projections of the global attractors of the 3D NS-Î± and 3D Leray-Î± sub-grid scale turbulence models in the plane spanned by their energy and enstrophy. We note the dependence of these bounds on the filter width parameter Î±, and determine...

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Local estimates are derived for solutions to a perturbed Stokes system, which arises as a reduction of the Stokes system near a curved part of the boundary of the domain if a diffeomorphism flattening the boundary is applied. The estimates obtained in the paper play the crucial role in the...

- Nonresonant case of intersection of bifurcation curves in the Couette-Taylor problem. Morshneva, I.; Ovchinnikova, S. // Journal of Applied Mechanics & Technical Physics;Dec2010, Vol. 51 Issue 6, p819
The nonresonant case (Res 0) of the motion of a viscous incompressible fluid between rotating coaxial cylinders in a small neighborhood of a bifurcation point of codimension 2 is considered, where the amplitude system has only essential resonant terms. Existence and stability conditions are...