Search results for "Saddle"
showing 10 items of 74 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 .
Degradation and rehabilitation of Gerber saddles of concrete bridges
2022
In recent decades, many concrete bridges, built in the 60s and 70s of the 20th Century with a Gerber-girder scheme, show severe damage of the saddles due to concrete degradation and reinforcement corrosion. On the basis of the recent Ministerial Guidelines for the assessment of existing bridges, it is necessary to evaluate the state of the Gerber saddles in a large number of bridges on both main and secondary roads. To do this, it is necessary to apply flexible assessment procedures that can be adapted to several situations and that allow a speedy assessment of the intervention priorities. The methodologies of intervention represent the crucial point for a rapid rehabilitation of these infr…
Control of a Non-isothermal CSTR by Type-2 Fuzzy Logic Controllers
2009
The paper describes the application of a type-2 fuzzy logic controller (FLC) to a non-isothermal continuous stirred tank reactor (CSTR) characterized by the presence of saddle node and Hopf bifurcations. Its performance is compared with a type-1 fuzzy logic controller performance. A full analysis of the uncontrolled CSTR dynamic was carried out and used for the feedback-feedforward fuzzy controllers development. Simulation results confirm the effectiveness and the robustness of the type-2 FLCs which outperform their type-1 counterparts, particularly when uncertainties are present in the system.
Asymptotics of correlation functions of the Heisenberg-Ising chain in the easy-axis regime
2016
We analyze the long-time large-distance asymptotics of the longitudinal correlation functions of the Heisenberg-Ising chain in the easy-axis regime. We show that in this regime the leading asymptotics of the dynamical two-point functions is entirely determined by the two-spinon contribution to their form factor expansion. Its explicit form is obtained from a saddle-point analysis of the corresponding double integral. It describes the propagation of a wave front with velocity $v_{c_1}$ which is found to be the maximal possible group velocity. Like in wave propagation in dispersive media the wave front is preceded by a precursor running ahead with velocity $v_{c_2}$. As a special case we obta…
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…
Unfolding of saddle-nodes and their Dulac time
2016
Altres ajuts: UNAB10-4E-378, co-funded by ERDF "A way to build Europe" and by the French ANR-11-BS01-0009 STAAVF. In this paper we study unfoldings of saddle-nodes and their Dulac time. By unfolding a saddle-node, saddles and nodes appear. In the first result (Theorem A) we give a uniform asymptotic expansion of the trajectories arriving at the node. Uniformity is with respect to all parameters including the unfolding parameter bringing the node to a saddle-node and a parameter belonging to a space of functions. In the second part, we apply this first result for proving a regularity result (Theorem B) on the Dulac time (time of Dulac map) of an unfolding of a saddle-node. This result is a b…
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…
Assessment and strengthening of reinforced concrete bridges with half-joint deterioration
2022
Existing Niagara-type concrete cantilever bridges, which in Italy are called Gerber bridges, suffer from degradation due to reinforcement corrosion and a consequent reduced load-bearing capacity. The assessment of these structures is therefore an important part of the procedures for analyzing the state of existing bridges and any interventions required for their retrofitting. In particular, safety against failure of the half-joint must be evaluated with respect to the behavior of the entire bridge and its state of conservation, determining what the conditions are that lead to failure, in terms of loads, state of stress, and possibly cracking state. This evaluation has to be carried out cons…