Search results for "Saddle point"
showing 10 items of 35 documents
Smooth and non-smooth traveling wave solutions of some generalized Camassa–Holm equations
2014
In this paper we employ two recent analytical approaches to investigate the possible classes of traveling wave solutions of some members of a recently-derived integrable family of generalized Camassa-Holm (GCH) equations. A recent, novel application of phase-plane analysis is employed to analyze the singular traveling wave equations of three of the GCH NLPDEs, i.e. the possible non-smooth peakon, cuspon and compacton solutions. Two of the GCH equations do not support singular traveling waves. The third equation supports four-segmented, non-smooth $M$-wave solutions, while the fourth supports both solitary (peakon) and periodic (cuspon) cusp waves in different parameter regimes. Moreover, sm…
Regular and singular pulse and front solutions and possible isochronous behavior in the short-pulse equation: Phase-plane, multi-infinite series and …
2014
In this paper we employ three recent analytical approaches to investigate the possible classes of traveling wave solutions of some members of a family of so-called short-pulse equations (SPE). A recent, novel application of phase-plane analysis is first employed to show the existence of breaking kink wave solutions in certain parameter regimes. Secondly, smooth traveling waves are derived using a recent technique to derive convergent multi-infinite series solutions for the homoclinic (heteroclinic) orbits of the traveling-wave equations for the SPE equation, as well as for its generalized version with arbitrary coefficients. These correspond to pulse (kink or shock) solutions respectively o…
A theoretical study of the collinear reaction F+H2→HF+H using multiconfigurational second-order perturbation theory (CASPT2)
1993
Abstract The second-order perturbation method (CASPT2) with a single state multiconfigurational reference function generated in complete active self-consistent field (CASSCF) calculations has been used to compute the collinear barrier height, saddle point geometry, and exothermicity of the reaction F+H 2 →HF+H. Comparison with full configuration (FCI) calculations with small basis sets shows that the CASPT2 method is capable of reproducing accurately the exact benchmark results correlating seven electrons. Large atomic natural orbital basis sets are used at the seven- and nine-electron level of correlation. With the largest ANO basis set used, F[7s6p5d4f2g]/H[6s5p4d2f], the computed nine-el…
Modelling the carbon Snoek peak in ferrite: Coupling molecular dynamics and kinetic Monte-Carlo simulations
2008
Abstract Molecular statics, molecular dynamics and kinetic Monte-Carlo are used to model the carbon Snoek peak in ferrite. Using an interatomic EAM potential for the Fe–C system, saddle point energies for the diffusion of carbon have been evaluated under uniaxial stress by molecular statics. These energies have been reintroduced in a kinetic Monte-Carlo scheme to predict the repartition of carbon atoms in different octahedral sites. This repartition leads to an anelastic deformation calculated by molecular dynamics, which causes internal friction (the Snoek peak) for cyclic stress. This approach leads to quantitative predictions of the internal friction, which are in good agreement with exp…
Spin Glasses on Thin Graphs
1995
In a recent paper we found strong evidence from simulations that the Isingantiferromagnet on ``thin'' random graphs - Feynman diagrams - displayed amean-field spin glass transition. The intrinsic interest of considering such random graphs is that they give mean field results without long range interactions or the drawbacks, arising from boundary problems, of the Bethe lattice. In this paper we reprise the saddle point calculations for the Ising and Potts ferromagnet, antiferromagnet and spin glass on Feynman diagrams. We use standard results from bifurcation theory that enable us to treat an arbitrary number of replicas and any quenched bond distribution. We note the agreement between the f…
Solving Two-Person Zero-Sum Stochastic Games With Incomplete Information Using Learning Automata With Artificial Barriers
2021
Learning automata (LA) with artificially absorbing barriers was a completely new horizon of research in the 1980s (Oommen, 1986). These new machines yielded properties that were previously unknown. More recently, absorbing barriers have been introduced in continuous estimator algorithms so that the proofs could follow a martingale property, as opposed to monotonicity (Zhang et al., 2014), (Zhang et al., 2015). However, the applications of LA with artificial barriers are almost nonexistent. In that regard, this article is pioneering in that it provides effective and accurate solutions to an extremely complex application domain, namely that of solving two-person zero-sum stochastic games that…
Energy and entropy barriers of two-level systems in argon clusters: An energy landscape approach
1999
Abstract Free argon clusters containing up to 160 atoms have been studied by means of a numerical algorithm for finding thousands of adjacent minima connected through a first-order saddle point. Many minimum-saddle-minimum systems have been found to be good candidates for forming two-level systems. The ground state splitting has been evaluated by taking into account both energy and entropy barriers. The role of the latter in auenching or enhancing the ground state splitting is discussed with the aid of a simple model potential.
Evidence for quasi-fission in40Ar+208Pb collisions near the coulomb-barrier
1987
Fission-fragment angular distributions were measured in the reaction of40Ar with208Pb near the fusion barrier. For nearly symmetric mass-/charge splits we find angular distributions symmetric around θ=90 degrees, however, with unusually large anisotropies. These develop gradually into forward-backward asymmetric distributions as one moves away from mass-/charge symmetry. This indicates that non-compound fission (‘quasi-fission’) competes with true fusion-fission. The relative contribution of quasi-fission to the total fission cross section is somewhere between 51 and 85%. In the framework of the extra-push model this is equivalent to an extra-extra push energy for compound-nucleus formation…
Quantized ATDHF: theory and realistic applications to heavy ion fusion
1982
The quantized ATDHF theory is reviewed and discussed in the context of the generator coordinate method. This allows for a derivation which does not require an a posteriori quantization process. The ATDHF equations are then solved numerically on a coordinate and momentum grid in fully three dimensional geometry. The theory is applied to various heavy ion systems, where potentials, mass parameters and quantum corrections are evaluated and compared to conventional results from constrained Hartree-Fock. Subbarrier fusion cross sections are calculated and compared with experiment.
Guaranteed lower bounds for cost functionals of time-periodic parabolic optimization problems
2019
In this paper, a new technique is shown for deriving computable, guaranteed lower bounds of functional type (minorants) for two different cost functionals subject to a parabolic time-periodic boundary value problem. Together with previous results on upper bounds (majorants) for one of the cost functionals, both minorants and majorants lead to two-sided estimates of functional type for the optimal control problem. Both upper and lower bounds are derived for the second new cost functional subject to the same parabolic PDE-constraints, but where the target is a desired gradient. The time-periodic optimal control problems are discretized by the multiharmonic finite element method leading to lar…