Search results for "Saddle"

The transition state and cognate concepts

2019

Abstract This review aims firstly to clarify the meanings of key terms and concepts associated with the idea of the transition state, as developed by theoreticians and applied by experimentalist, and secondly to provide an update to the meaning and significance of the transition state in an era when computational simulation, in which complexity is being increasingly incorporated, is commonly employed as a means by which to bridge the realms of theory and experiment. The relationship between the transition state and the potential-energy surface for an elementary reaction is explored, with discussion of the following terms: saddle point, minimum-energy reaction path, reaction coordinate, acti…

High excitations in coupled-cluster series: vibrational energy levels of ammonia

2004

The ammonia molecule containing large amplitude inversion motion is a revealing system in examining high-order correlation effects on potential energy surfaces. Correlation contributions to the equilibrium and saddle point geometries, inversion barrier height and vibrational energy levels, including inversion splittings, have been investigated. A six-dimensional Taylor-type series expansion of the Born–Oppenheimer potential energy surface, which is scaled to different levels of theory, is used to determine vibrational energy levels and inversion splittings variationally. The electronic energies are calculated by coupled-cluster methods, combining explicitly correlated R12 theory (which incl…

Propagule dispersal and larval patch cohesiveness in a Mediterranean coastal fish

2016

The assessment of fish dispersal is fundamental for both conservation and management of fishery resources as it provides crucial information for the establishment of more effective marine protected areas (MPAs) and networks of MPAs. In this study, we investigated the elemental composition of otoliths in early life stages of the saddled sea bream Oblada melanura (Linnaeus, 1758) (Perciformes: Sparidae) in order to obtain information on its propagule (egg and larva) dispersal in the south-western Mediterranean Sea. Specifically, using pre-settlement individuals we investigated (1) larval patch cohesiveness during the last phase of larval life; and with early post-settlement individuals we inv…

Abelian integrals and limit cycles

2006

Abstract The paper deals with generic perturbations from a Hamiltonian planar vector field and more precisely with the number and bifurcation pattern of the limit cycles. In this paper we show that near a 2-saddle cycle, the number of limit cycles produced in unfoldings with one unbroken connection, can exceed the number of zeros of the related Abelian integral, even if the latter represents a stable elementary catastrophe. We however also show that in general, finite codimension of the Abelian integral leads to a finite upper bound on the local cyclicity. In the treatment, we introduce the notion of simple asymptotic scale deformation.

Alien limit cycles near a Hamiltonian 2-saddle cycle

2005

Abstract It is known that perturbations from a Hamiltonian 2-saddle cycle Γ can produce limit cycles that are not covered by the Abelian integral, even when it is generic. These limit cycles are called alien limit cycles. This phenomenon cannot appear in the case that Γ is a periodic orbit, a non-degenerate singularity, or a saddle loop. In this Note, we present a way to study this phenomenon in a particular unfolding of a Hamiltonian 2-saddle cycle, keeping one connection unbroken at the bifurcation. To cite this article: M. Caubergh et al., C. R. Acad. Sci. Paris, Ser. I 340 (2005).

An evaluation of clinical, radiological and three-dimensional dental tomography findings in ectodermal dysplasia cases

2015

Background:This study aimed to review the results related to head and jaw disorders in cases of ectodermal dysplasia. The evaluation of ectodermal dysplasia cases was made by clincal examination and examination of the jaw and facial areas radiologically and on cone-beam 3-dimensional dental tomography (CBCT) images. Material and Methods: In the 36 cases evaluated in the study, typical clinical findings of pure hypohidrotic ectodermal displasia (HED) were seen, such as missing teeth, dry skin, hair and nail disorders. CBCT images were obtained from 12 of the 36 cases, aged 1.5- 45 years, and orthodontic analyses were made on these images. Results: The clinical and radiological evaluations de…

Computation of Unstable Binodals Not Requiring Concentration Derivatives of the Gibbs Energy

1998

The equilibrium of three liquid phases in a binary mixture implies the existence of tie lines and binodals that are different from the normal experimentally observable ones. First of all, there are the metastable extensions of the binodal built up by S/S tie lines. These S/S tie lines fulfill the equilibrium condition of the minimum of the Gibbs energy of the entire two-phase system. Both coexisting phases are located within the meta(stable) region. There are two additional types of tie lines:  U/U (maximum of the Gibbs energy; both end points within the unstable area) and U/S tie lines (saddle point; one end point within the (meta)stable, the other within the unstable region). All types of…

Quantum chemical calculations of the electron center diffusion in MgO crystals

1996

Large-scale quantum chemical simulations of the diffusion hops of empty cation and anion vacancies, as well as F + and F centers in MgO crystals have been done. The atomic configurations for 224-site cluster and charge density distribution are analyzed for the equilibrium and saddle-point configurations during the defect hops. The relevant activation energy for diffusion increases monotonically in the series V a → F + → F center.

Stationary Point Processes

2008

Adatom Island Diffusion on Metal Fcc(100) Surfaces

2001

We study the energetics and atomic mechanisms of diffusion of adatom islands on fcc(100) metal surfaces. For small islands, we perform detailed microscopic calculations using semi-empirical embedded-atom model and glue potentials in the case of Cu and Al, respectively. Combining systematic saddle-point search methods and molecular statics simulations allows us to find all the relevant transition paths for island motion. In particular, we demonstrate that there are novel many-body mechanisms such as internal row shearing which can, in some cases, control the island dynamics. Next, we show how using the master equation formalism, diffusion coefficients for small islands up to about five atoms…