Search results for "Saddle point"
showing 5 items of 35 documents
Diagonalization of indefinite saddle point forms
2020
We obtain sufficient conditions that ensure block diagonalization (by a direct rotation) of sign-indefinite symmetric sesquilinear forms as well as the associated operators that are semi-bounded neither from below nor from above. In the semi-bounded case, we refine the obtained results and, as an example, revisit the block Stokes operator from fluid dynamics.
Stable products of spheres in the non-linear coupling of oscillators or quasi-periodic motions
2004
Abstract For generic families of vector fields or transformations, normally hyperbolic invariant products of spheres appear near partially elliptic rest points. To cite this article: M. Kammerer-Colin de Verdiere, C. R. Acad. Sci. Paris, Ser. I 339 (2004).
On the number of limit cycles which appear by perturbation of separatrix loop of planar vector fields
1986
Consider a fami ly of vector fCelds x~ on the plane. This fami ly depends on a parameter ~ ~ /R A, for some A ~ /~, and is supposed to be 0 ~ in (m,~) 6 /i~ 2X /~A. Suppose that for ~ = O, the vector f i e l d X o has a separatrix loop. This means that X o has an hyperbol ic saddle point s o and that one of the stable separatr ix of 8 o coincides with one of the unstable one. The union of th is curve and s o is the loop ?. A return map is defined on one side of r .
Self-Consistent Tilted-Axis-Cranking Study of Triaxial Strongly Deformed Bands inEr158at Ultrahigh Spin
2012
Stimulated by recent experimental discoveries, triaxial strongly deformed (TSD) states in $^{158}\mathrm{Er}$ at ultrahigh spins have been studied by means of the Skyrme-Hartree-Fock model and the tilted-axis-cranking method. Restricting the rotational axis to one of the principal axes---as done in previous cranking calculations---two well-defined TSD minima in the total Routhian surface are found for a given configuration: one with positive and another with negative triaxial deformation $\ensuremath{\gamma}$. By allowing the rotational axis to change direction, the higher-energy minimum is shown to be a saddle point. This resolves the long-standing question of the physical interpretation o…
On Transition Structures for Hydride Transfer Step: A Theoretical Study of the Reaction Catalyzed by Dihydrofolate Reductase Enzyme
1996
Abstract A theoretical study is presented of the catalytic mechanism of dihydrofolate reductase (DHFR) enzyme based upon the characterization of the transition structure (TS) for the hydride transfer step. Analytical gradients at AM1 and PM3 semiempirical levels have been used to characterize the saddle point of index one (SPi-1) on global energy hypersurface for the hydride transfer in the active site of DHFR enzyme. The geometry, stereochemistry, electronic structure, and transition vector (TV) components associated to SPi-1 are qualitatively computational level independent. The TV amplitudes show primary and secondary isotope effects to be strongly coupled. The geometrical arrangement of…