Search results for "Saddle"
showing 10 items of 74 documents
The period function of reversible quadratic centers
2006
Abstract In this paper we investigate the bifurcation diagram of the period function associated to a family of reversible quadratic centers, namely the dehomogenized Loud's systems. The local bifurcation diagram of the period function at the center is fully understood using the results of Chicone and Jacobs [C. Chicone, M. Jacobs, Bifurcation of critical periods for plane vector fields, Trans. Amer. Math. Soc. 312 (1989) 433–486]. Most of the present paper deals with the local bifurcation diagram at the polycycle that bounds the period annulus of the center. The techniques that we use here are different from the ones in [C. Chicone, M. Jacobs, Bifurcation of critical periods for plane vecto…
Vibrational Analysis of Paraelectric–Ferroelectric Transition of LiNbO3: An Ab-Initio Quantum Mechanical Treatment
2021
FSG acknowledges the CINECA award under the ISCRA initiative (HP10BJO47B) for the availability of high-performance computing resources and support.
Transitions between metastable states in silica clusters
1999
Relaxation phenomena in glasses can be related to jump processes between different minima of the potential energy in the configuration space. These transitions play a key role in the low temperature regime, giving rise to tunneling systems responsible for the anomalous specific heat and thermal conductivity in disordered solids with respect to crystals. By using a recently developed numerical algorithm, we study the potential energy landscape of silica clusters, taking as a starting point the location of first order saddle points. This allows us to find a great number of adjacent minima. We analyze the degree of cooperativity of these transitions and the connection of physical properties wi…
The response field and the saddle points of quantum mechanical path integrals
2021
In quantum statistical mechanics, Moyal's equation governs the time evolution of Wigner functions and of more general Weyl symbols that represent the density matrix of arbitrary mixed states. A formal solution to Moyal's equation is given by Marinov's path integral. In this paper we demonstrate that this path integral can be regarded as the natural link between several conceptual, geometric, and dynamical issues in quantum mechanics. A unifying perspective is achieved by highlighting the pivotal role which the response field, one of the integration variables in Marinov's integral, plays for pure states even. The discussion focuses on how the integral's semiclassical approximation relates to…
Towards a quantitative comparison between global and local stability analysis
2017
A methodology is proposed here to estimate the stability characteristics of bluff-body wakes using local analysis under the assumption of weakly non-parallel flows. In this connection, a generalisation of the classic spatio-temporal stability analysis for fully three-dimensional flows is first described. Secondly, an additional higher-order correction term with respect to the common saddle-point global frequency estimation is included in the analysis. The proposed method is first validated for the case of the flow past a circular cylinder and then applied to two fully three-dimensional flows: the boundary layer flow over a wall-mounted hemispherical body and the wake flow past a fixed spher…
Observation of mass-asymmetric fission of mercury nuclei in heavy ion fusion
2015
Background: Mass-asymmetric fission has been observed in low energy fission of $^{180}\mathrm{Hg}$. Calculations predicted the persistence of asymmetric fission in this region even at excitation energies of 30--40 MeV.Purpose: To investigate fission mass distributions by populating different isotopes of Hg using heavy ion fusion reactions.Methods: Fission fragment mass-angle distributions have been measured for two reactions, $^{40}\mathrm{Ca}+^{142}\mathrm{Nd}$ and $^{13}\mathrm{C}+^{182}\mathrm{W}$, populating $^{182}\mathrm{Hg}$ and $^{195}\mathrm{Hg}$, respectively, using the Heavy Ion Accelerator Facility and CUBE spectrometer at the Australian National University. Measurements were ma…
On the application of canonical perturbation theory to floppy molecules
2000
International audience; Canonical perturbation theory (CPT) is a powerful tool in the field of molecular physics. It consists of a series of coordinate transformations aimed at rewriting the Hamiltonian in a simpler form without modifying the geometry of the phase space. The major achievement of CPT is the straightforward derivation of relations between the physically meaningful parameters of potential energy surfaces and the coefficients of the so-called effective Hamiltonians. While most of the studies performed up to date deal with surfaces expanded in polynomial series around a single minimum, CPT has also been applied to mixed polynomial/trigonometric expansions in the treatment of tor…
On the saddle loop bifurcation
1990
It is shown that the set of C∞ (generic) saddle loop bifurcations has a unique modulus of stability γ ≥]0, 1[∪]1, ∞[ for (C0, Cr)-equivalence, with 1≤r≤∞. We mean for an equivalence (x,μ) ↦ (h(x,μ), ϕ(μ)) with h continuous and ϕ of class Cr. The modulus γ is the ratio of hyperbolicity at the saddle point of the connection. Already asking ϕ to be a lipeomorphism forces two saddle loop bifurcations to have the same modulus, while two such bifurcations with the same modulus are (C0,±Identity)-equivalent.
Desingularization Theory and Bifurcation of Non-elementary Limit Periodic Sets
1998
In the study of the Bogdanov-Takens unfolding, we introduced in 4.3.5.2 the following formulas of rescaling in the phase-space and in the parameter space: $$ x = {r^2}\bar x,y = {r^3}\bar y,\mu = - {r^4},\nu = {r^2}\bar \nu . $$
Fission fragment angular distributions in the capture reactions 50Ti, 56Fe + 208Pb
2008
The analysis of %-ray mult ip l ic i t ies measured I in coincidence with capture fission events in reactions of 26Mg through 54Cr, 58Fe, and 64Ni with 208pb in terms of Ko and~eff revealed1 that the resulting values of ~ /~e f f were rather independent of for a given system and, in a compound nucleus picture, were more in agreement with the 'shape of the non-rotating saddle than with the actually expected rotating saddle I f non-compound systenmhave to be considered these values of ~/J~ff__ shapes. suggested at least that the captured systems near the turning point from the inward radial motion to symmetric fragmentation had reached a remarkable compactness.