Search results for "asymptotic expansion"
showing 10 items of 38 documents
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…
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).
Techniques in the Theory of Local Bifurcations: Cyclicity and Desingularization
1993
A fundamental open question of the bifurcation theory of vector fields in dimension 2 is whether the number of locally bifurcating limit cycles in an analytic unfolding is bounded, or more precisely, whether any limit periodic set has finite cyclicity. In these notes we introduce several techniques for attacking this question: asymptotic expansion of return maps, ideal of coefficients, desingularization of parametrized families. Moreover, because of their practical interest, we present some partial results obtained by these techniques.
The Fatou coordinate for parabolic Dulac germs
2017
We study the class of parabolic Dulac germs of hyperbolic polycycles. For such germs we give a constructive proof of the existence of a unique Fatou coordinate, admitting an asymptotic expansion in the power-iterated log scale.
The 0-Parameter Case
1998
As an introduction to the theory of bifurcations, in this chapter we want to consider individual vector fields, i.e., families of vector fields with a 0-dimensional parameter space. We will present two fundamentals tools: the desingularization and the asymptotic expansion of the return map along a limit periodic set. In the particular case of an individual vector field these techniques give the desired final result: the desingularization theorem says that any algebraically isolated singular point may be reduced to a finite number of elementary singularities by a finite sequence of blow-ups. If X is an analytic vector field on S 2, then the return map of any elementary graphic has an isolate…
Riemann-Hilbert approach to the time-dependent generalized sine kernel
2011
We derive the leading asymptotic behavior and build a new series representation for the Fredholm determinant of integrable integral operators appearing in the representation of the time and distance dependent correlation functions of integrable models described by a six-vertex R-matrix. This series representation opens a systematic way for the computation of the long-time, long-distance asymptotic expansion for the correlation functions of the aforementioned integrable models away from their free fermion point. Our method builds on a Riemann–Hilbert based analysis.
Analytic Bergman operators in the semiclassical limit
2018
Transposing the Berezin quantization into the setting of analytic microlocal analysis, we construct approximate semiclassical Bergman projections on weighted $L^2$ spaces with analytic weights, and show that their kernel functions admit an asymptotic expansion in the class of analytic symbols. As a corollary, we obtain new estimates for asymptotic expansions of the Bergman kernel on $\mathbb{C}^n$ and for high powers of ample holomorphic line bundles over compact complex manifolds.
Method of analytic continuation by duality in QCD: Beyond QCD sum rules
1986
We present the method of analytic continuation by duality which allows the approximate continuation of QCD amplitudes to small values of the momentum variables where direct perturbative calculations are not possible. This allows a substantial extension of the domain of applications of hadronic QCD phenomenology. The method is illustrated by a simple example which shows its essential features.
Zero viscosity limit of the Oseen equations in a channel
2001
Oseen equations in the channel are considered. We give an explicit solution formula in terms of the inverse heat operators and of projection operators. This solution formula is used for the analysis of the behavior of the Oseen equations in the zero viscosity limit. We prove that the solution of Oseen equations converges in W1,2 to the solution of the linearized Euler equations outside the boundary layer and to the solution of the linearized Prandtl equations inside the boundary layer. © 2001 Society for Industrial and Applied Mathematics.
Probabilistic analysis of truss structures with uncertain parameters (virtual distortion method approach)
2004
A new approach for probabilistic characterization of linear elastic redundant trusses with uncertainty on the various members subjected to deterministic loads acting on the nodes of the structure is presented. The method is based on the simple observation that variations of structural parameters are equivalent to superimposed strains on a reference structure depending on the axial forces on the elastic modulus of the original structure as well as on the uncertainty (virtual distortion method approach). Superposition principle may be applied to separate contribution to mechanical response due to external loads and parameter variations. Statically determinate trusses dealt with the proposed m…