Search results for "Asymptotic"
showing 10 items of 230 documents
Focus on quantum Einstein gravity
2012
The gravitational asymptotic safety program summarizes the attempts to construct a consistent and predictive quantum theory of gravity within Wilson's generalized framework of renormalization. Its key ingredient is a non-Gaussian fixed point of the renormalization group flow which controls the behavior of the theory at trans-Planckian energies and renders gravity safe from unphysical divergences. Provided that the fixed point comes with a finite number of ultraviolet-attractive (relevant) directions, this construction gives rise to a consistent quantum field theory which is as predictive as an ordinary, perturbatively renormalizable one. This opens up the exciting possibility of establishin…
About the link between the detailed description of transitions in an ion and the average-ion models
2009
We study the link which exists between microscopic (detailed) models for the evolution of the electronic configurations in a population of ions and the macroscopic (average ion) models. Rigorous asymptotics are presented in situations where they exist (large temperature; almost empty or almost full shells), and numerical simulations are presented.
Self-Enrichment in Globular Clusters: Is There a Role for the Super-Asymptotic Giant Branch Stars?
2008
In four globular clusters (GCs) a non negligible fraction of stars can be interpreted only as a very helium rich population. The evidence comes from the presence of a "blue" main sequence in $\omega$ Cen and NGC 2808, and from the the very peculiar horizontal branch morphology in NGC 6441 and NGC 6388. Although a general consensus is emerging on the fact that self--enrichment is a common feature among GCs, the helium content required for these stars is Y$\simgt$0.35, and it is difficult to understand how it can be produced without any --or, for $\omega$ Cen, without a considerable--associated metal enhancement. We examine the possible role of super--AGB stars, and show that they may provide…
Lithium in the intermediate age cluster NGC 3680: Following Li evolution along the C-M diagram
2001
We present an analysis of high resolution spectroscopic observations (R 30 000, S=N =6 0 150) of 24 members of the intermediate age (1.5 Gyr) open cluster NGC 3680, covering all regions of the cluster colour-magnitude (C{M) diagram where cluster members are known to exist. These observations represent in many aspects challenges to our understanding of stellar interior and mixing. Four main sequence G stars have, within the errors, the same Li abundance, 0.3 dex lower than similar stars in the1 Gyr younger Hyades but comparable with those observed in the coeval cluster IC 4651. The cluster shows a clear Li-dip located around the turn-o; two stars on the upper part of the turn-o are out of th…
Time-dependent density-functional theory for strongly interacting electrons
2017
We consider an analytically solvable model of two interacting electrons that allows for the calculation of the exact exchange-correlation kernel of time-dependent density functional theory. This kernel, as well as the corresponding density response function, is studied in the limit of large repulsive interactions between the electrons and we give analytical results for these quantities as an asymptotic expansion in powers of the square root of the interaction strength. We find that in the strong interaction limit the three leading terms in the expansion of the kernel act instantaneously while memory terms only appear in the next orders. We further derive an alternative expansion for the ker…
Gauss-Type Quadrature Formulae for Parabolic Splines with Equidistant Knots
2010
We construct Gauss, Lobatto, and Radau quadrature formulae associated with the spaces of parabolic splines with equidistant knots. These quadrature formulae are known to be asymptotically optimal in Sobolev spaces W p 3. Sharp estimates for the error constant in W ∞ 3 are given.
Use of a running coupling in the NLO calculation of forward hadron production
2018
We address and solve a puzzle raised by a recent calculation [1] of the cross-section for particle production in proton-nucleus collisions to next-to-leading order: the numerical results show an un- reasonably large dependence upon the choice of a prescription for the QCD running coupling, which spoils the predictive power of the calculation. Specifically, the results obtained with a prescription formulated in the transverse coordinate space differ by one to two orders of magnitude from those obtained with a prescription in momentum space. We show that this discrepancy is an artefact of the interplay between the asymptotic freedom of QCD and the Fourier transform from coordinate space to mo…
Generalised power series solutions of sub-analytic differential equations
2006
Abstract We show that if a solution y ( x ) of a sub-analytic differential equation admits an asymptotic expansion ∑ i = 1 ∞ c i x μ i , μ i ∈ R + , then the exponents μ i belong to a finitely generated semi-group of R + . We deduce a similar result for the components of non-oscillating trajectories of real analytic vector fields in dimension n. To cite this article: M. Matusinski, J.-P. Rolin, C. R. Acad. Sci. Paris, Ser. I 342 (2006).
The linear saturated decentralized strategy for constrained flow control is asymptotically optimal
2013
We present an algorithm for constrained network flow control in the presence of an unknown demand. Our algorithm is decentralized in the sense that it is implemented by a team of agents, each controlling just the flow on a single arc of the network based only on the buffer levels at the nodes at the extremes of the arc, while ignoring the actions of other agents and the network topology. We prove that our algorithm is also stabilizing and steady-state optimal. Specifically, we show that it asymptotically produces the minimum-norm flow. We finally generalize our algorithm to networks with a linear dynamics and we prove that certain least-square optimality properties still hold.
Fixed points for asymptotic contractions of integral Meir-Keeler type
2012
In this paper we introduce the notion of asymptotic contraction of integral Meir-Keeler type on a metric space and we prove a theorem which ensures existence and uniqueness of fixed points for such contractions. This result generalizes some recent results in the literature.